students' attitude towards problem solving

• Open supplemental data
• Reference Manager
• Simple TEXT file

People also looked at

Brief research report article, the influence of attitudes and beliefs on the problem-solving performance.

• 1 Department of Mathematics and Computer Science, University of Education of Ludwigsburg, Ludwigsburg, Germany
• 2 Hamburg Center for University Teaching and Learning, University of Hamburg, Hamburg, Germany

The problem-solving performance of primary school students depend on their attitudes and beliefs. As it is not easy to change attitudes, we aimed to change the relationship between problem-solving performance and attitudes with a training program. The training was based on the assumption that self-generated external representations support the problem-solving process. Furthermore, we assumed that students who are encouraged to generate representations will be successful, especially when they analyze and reflect on their products. A paper-pencil test of attitudes and beliefs was used to measure the constructs of willingness, perseverance, and self-confidence. We predicted that participation in the training program would attenuate the relationship between attitudes and problem-solving performance and that non-participation would not affect the relationship. The results indicate that students’ attitudes had a positive effect on their problem-solving performance only for students who did not participate in the training.

Introduction

Mathematical problem solving is considered to be one of the most difficult tasks primary students have to deal with ( Verschaffel et al., 1999 ) since it requires them to apply multiple skills ( De Corte et al., 2000 ). It is decisive in this respect that “difficulty should be an intellectual impasse rather than a computational one” ( Schoenfeld, 1985 , p. 74). When solving problems, it is not enough to retrieve procedural knowledge and reproduce a known solution approach. Rather, problem-solving tasks require students to come up with new ways of thinking ( Bransford and Stein, 1993 ). Problem-solvers must activate their existing knowledge network and adapt it to the respective problem situation ( van Dijk and Kintsch, 1983 ). They have to succeed in generating an adequate representation of the problem situation (e.g., Mayer and Hegarty, 1996 ). This requires conceptual knowledge, which novice problem-solvers have to acquire ( Bransford et al., 2000 ). As problem solving is the foundation for learning mathematics, an important goal of primary school mathematics teaching is to strengthen students’ problem-solving performance. One central problem is that problem-solving performance is highly influenced by students’ attitudes towards problem solving ( Reiss et al., 2002 ; Schoenfeld, 1985 ; Verschaffel et al., 2000 ).

Attitudes and beliefs are considered quite stable once they are developed ( Hannula, 2002 ; Goldin, 2003 ). However, students who are novices in a particular content area are still in the process of development, as are their attitudes and beliefs. It can therefore be assumed that their attitudes change over time ( Hannula, 2002 ). However, such a change does not take place quickly ( Higgins, 1997 ; Mason and Scrivani, 2004 ). Nevertheless, in a shorter period of time, it might be possible to reduce the influence of attitudes on problem-solving performance ( Hannula et al., 2019 ). In this paper, we present a training program for primary school students, which aims to do exactly that.

Problem-Solving Performance

Successful problem solving can be observed on two levels: problem-solving success and problem-solving skills. Many studies measure the problem-solving performance of students on the basis of correctly or incorrectly solved problem-solving tasks, that is, the product (e.g., Boonen et al., 2013 ; de Corte et al., 1992 ; Hegarty et al., 1992 ; Verschaffel et al., 1999 ). In this case, only problem-solving success, that is, specifically whether the numerically obtained result is correct or incorrect, is evaluated. This is a strict assessment measure, since the problem-solving process is not taken into account. As a result, the problem-solving performance is only considered from a single, product-oriented perspective. For instance students’ performance is assessed as unsuccessful when they apply an essentially correct procedure or strategy but achieve the wrong result, or it is considered successful when students achieve the right result even though they have misunderstood the problem ( Lester and Kroll, 1990 ). An advantage of this operationalization, however, is that student performance tends to be underestimated rather than overestimated.

A more differentiated view of successful problem solving includes the solver’s problem-solving process ( Lester and Kroll, 1990 ; cf. Adibnia and Putt, 1998 ). In this way, sub-skills such as understanding the problem, adequately representing the situation, applying strategies, or achieving partial solutions are taken into account. These are then incorporated into the evaluation of performance and, thus, of problem-solving skills ( Charles et al., 1987 ; cf. Sturm, 2019 ). The advantage of this operationalization option is that it also takes into account smaller advances by the solver, although they may not yet lead to the correct result. It is therefore less likely to underestimate students’ performance. In order to assess and evaluate the problem-solving skills of students in the best way and, thus, avoid over- and under-estimating their skills, direct observation and questioning should be implemented (e.g., Lester and Kroll, 1990 ). An analysis of written work should not be the only means of assessment ( Lester and Kroll, 1990 ).

Attitudes and Beliefs

Attitudes are dispositions to like or dislike objects, persons, institutions, or events ( Ajzen, 2005 ). They influence behavior (Ajzen, 1991). Therefore, it is not surprising that attitudes–which are sometimes also synonymously referred to as beliefs–are a central construct in psychology ( Ajzen, 2005 ).

Individual attitudes to word problems influence, albeit rather unconsciously, approaches to such problems and willingness to learn mathematics and solve problems ( Grigutsch et al., 1998 ; Awofala, 2014 ). Research on attitudes of primary students to word problems is scarce. Most research focuses on students with well-established attitudes. However, the importance of the attitudes of younger children is undisputed ( Di Martino, 2019 ). Di Martino (2019) conducted a study on kindergarten children as well as on first-, third-, and fifth-graders and found that, with increasing age, students’ perceived competence in problem solving decreases, and negative emotions towards mathematical problems increase. Whether a solver can overcome problem barriers when dealing with word problems depends not only on his or her previous knowledge, abilities, and skills, but also on his or her attitudes and beliefs ( Schoenfeld, 1985 ; Verschaffel et al., 2000 ; Reiss et al., 2002 ). It has been shown many times that attitudes towards problem solving are influencing factors on performance and learning success which should not be underestimated ( Charles et al., 1987 ; Lester et al., 1989 ; Lester & Kroll, 1990 ; De Corte et al., 2002 ; Goldin et al., 2009 ; Awofala, 2014 ). Learners associate a specific feeling with an object, in this case with a word problem, triggering a specific emotional state ( Grigutsch et al., 1998 ). The feelings and states generated are subjective and can therefore vary between individuals ( Goldin et al., 2009 ).

Attitudes towards problem solving can be divided into willingness, perseverance, and self-confidence ( Charles et al., 1987 ; Lester et al., 1989 ). This distinction comes from the Mathematical Problem-Solving Project, in which Webb, Moses, and Kerr (1977) found that willingness to solve problems, perseverance in attempting to find a solution, and self-confidence in the ability to solve problems are the most important influences on problem-solving performance. When students are willing to work on a variety of mathematics tasks and persevere with tasks until they find a solution, they are more task oriented and easier to motivate ( Reyes, 1984 ). Perseverance is defined as the willing pursuit of a goal-oriented behavior even if this involves overcoming obstacles, difficulties, and disappointments ( Peterson and Seligman, 2004 ). Confidence is an individual’s belief in his or her ability to succeed in solving even challenging problems as well as an individual’s belief in his or her own competence with respect to his or her peers ( Lester et al., 1989 ). Students’ lack of confidence in themselves as problem-solvers or their beliefs about mathematics can considerably undermine their ability to solve or even approach problems in a productive way ( Shaughnessy, 1985 ). The division of attitudes into these three sub-categories can also be found in current studies ( Zakaria and Yusoff, 2009 ; Zakaria and Ngah, 2011 ).

Reducing the Influence of Attitudes and Beliefs

As it seems impossible to change attitudes within a short time frame, we developed a training program to reduce the influence of attitudes on problem solving, on the one hand, and to foster the problem-solving performance of primary-school students, on the other hand.

The training program was an integral part of regular math classes and focused on teaching students to generate and use external representations ( Sturm, 2019 ; Sturm et al., 2016 ; Sturm and Rasch, 2015 ; see also Supplementary Appendix A ). Such a program that concentrates on the strengths and weaknesses of novices and on their individually generated external representations can be a benefit for primary-school students in two ways. The class discusses how the structure described in the problem can be adequately represented so that the solution can be found, working out multiple approaches based on different student representations. The students are thus exposed to ideas about how a problem can be solved in different ways. Such a training program fulfils, albeit rather implicitly, another essential component. By respectfully considering their individual thoughts and difficulties, the students are made aware of their strengths and their creativity and of the fact that there is not a single correct approach or solution that everyone has to find ( Lester and Cai, 2016 ; Di Martino, 2019 ). This can counteract fears of failure and lack of self-confidence, and generate positive attitudes ( Lester and Cai, 2016 ; Di Martino, 2019 ). The teacher pays attention to the solution process rather than to the numerical result in order to reduce the influence of attitudes on performance ( Di Martino, 2019 ). In the same way, experiencing success and perceiving increasing flexibility and agility can reduce the influence of attitudes. As a result, we expected attitudes and beliefs to have a smaller effect on problem-solving performance.

Based on previous research, our goal was to reduce the influence of attitudes on the problem-solving performance of students (see Figure 1 ). To this end, the hypothesis was derived that participation in the training program would minimize the effect of attitudes and beliefs on problem-solving success, so that students would succeed at the end of the training despite initial negative attitudes and beliefs.

FIGURE 1 . The moderation model with the single moderator variable training influencing the effect of attitudes and beliefs on problem-solving success.

Participants

In total 335 students from 20 Grade 3 classes from eight different primary schools in the German state of Rhineland-Palatinate took part in the intervention study (172 boys and 163 girls). Nineteen students dropped out because of illness during the intervention. The age of the participants ranged between seven and ten years ( M = 8.10, SD = 0.47).

This investigation was part of a large interdisciplinary project 1 . A central focus of the project was to investigate whether representation training has a demonstrable effect on the performance of third-graders (cf. Sturm, 2019 ). For this reason, we implemented a pretest-posttest control group design. The intervention took place between Measurement Points 1 and 2. We measured the problem-solving performance of the students with a word-problem-solving test (WPST) at Measurement Points 1 and 2. All other variables were measured at Measurement Point 1 only (factors to establish comparable experimental conditions: intelligence, text comprehension, and mathematical abilities; co-variates for the mediation model: metacognitive skills, mathematical abilities).

In the intervention, third-grade students worked on challenging word problems for one regular mathematics lesson a week. The intervention was based on six task types with different structures ( Sturm and Rasch, 2015 ): 1) comparison tasks, 2) motion tasks, 3) tasks involving comparisons and balancing items or money, 4) tasks involving combinatorics, 5) tasks in which structure reflects the proportion of spaces and limitations, and 6) tasks with complex information. Two word problems were included for each task type and were presented to all classes in the same random sequence. Each task had to be completed in a maximum of one lesson.

The training was implemented for half of the classes and was conducted by the first author; the other half worked on the tasks with their regular mathematics teacher. They were not informed on the purpose of the intervention and not given any instructions on how to process the tasks. In the lessons for students doing the training, the students were explicitly cognitively stimulated to generate external representations and to use them to develop solutions. They were repeatedly encouraged to persevere and not to give up. The diverse external representations generated by the students were analyzed, discussed, and compared by the class during the training. They jointly identified the characteristics of representations that enabled them to specifically solve the tasks and identified different approaches (for more details about the study, see Sturm and Rasch, 2015 ). With the goal of reducing the influence of attitudes on performance, the class worked directly on the students’ own representations instead of on prefabricated representations. The aim was that students realized that it was worthwhile investing effort into creating representations and that they were able to solve problem tasks independently.

Thus, the study was composed of two experimental conditions: training program ( n = 176; 47% boys) (hereinafter abbreviated to T+) and no training program ( n = 159; 58% boys) (hereinafter abbreviated to T-). In order to control potential interindividual differences, the 20 classes were assigned to the experimental conditions by applying parallelization at class level ( Breaugh and Arnold, 2007 ; Myers and Hansen, 2012 ). The classes were grouped into homogeneous blocks using the R package blockTools Version 0.6-3 and then randomly assigned to the experimental conditions ( Greevy et al., 2004 ; Moore, 2012 ; see also Supplementary Appendix B for more information).

Word-Problem-Solving Test

Before the intervention and immediately after it, the students worked on a WPST, which we created. It consisted in each case of three challenging word problems with an open answer format. Each of the three tasks represented a different type of problem. The word problems from the WPST at Measurement Point 1 and the word problems from the WPST at Measurement Point 2 had the same structure. We implemented two parallel versions; only the context was changed by exchanging single words (see Supplementary Appendix C ). An example of an item from the test is a task with complex information ( Sturm, 2018 ): Classes 3a and 3b go to the computer room. Some students have to work at a computer in pairs. In total there are 25 computers, but 40 students. How many students work alone at a computer? How many students work at a computer in pairs? Direct observation and questioning could not be conducted due to the large number of participants in the project; only the students’ written work was available for analysis. The problem-solving process of the students could therefore only be assessed indirectly. For this reason, the performance of students in the two tests was evaluated based on problem-solving success, ruling out overestimation of performance.

Problem-Solving Success

The success of the solution was measured dichotomously in two forms: 1) correct solution and (0) incorrect solution. Only the correctness of the result achieved was evaluated. This dependent variable acted as a strict criterion that could be quantified with high observer agreement (κ = 0.97; κ min = 0.93, κ max = 1.00). A confirmatory factor analysis using the R package lavaan version 0.6-7 confirmed that the WPST measured the one-dimensional construct problem-solving success. The one-dimensional model exhibited a good model fit ( Nussbeck et al., 2006 ; Hair et al., 2009 ): χ 2 (27) = 36.613, p = 0.103; χ 2 /df = 1.356, CFI = 0.985, TLI = 0.981, SRMR = 0.032, RMSEA = 0.033 ( p = 0.854). The reliability coefficients at Measurement Point 1 were classified as low (Cronbach’s α = 0.39) because the test consisted of only three items ( Eid et al., 2011 ) and a homogeneous sample was required at this measurement point ( Lienert and Raatz, 1998 ). The Cronbach’s alpha for the second measurement point (α = 0.60) was considered to be sufficient ( Hair et al., 2009 ). The test score represented the mean value of all three task scores.

Attitudes and Beliefs About Problem Solving

The attitudes and beliefs of the learners were recorded with the Attitudes Inventory Items ( Webb et al., 1977 ; Charles et al., 1987 ). The original questionnaire comprises 20 items, which are measured dichotomously (“I agree” and “I disagree”). The Attitudes Inventory measures the three categories of attitudes and beliefs related to problem solving: a) willingness (six items), b) perseverance (six items), and c) self-confidence (eight items). An example of an item for willingness is: “I will try to solve almost any problem.” An example of an item for perseverance is: “When I do not get the right answer right away, I give up.” An example of an item for self-confidence is: “I am sure I can solve most problems.”

Because the reported reliabilities were only satisfactory to some extent (α = 0.79, mean = 0.64) ( Webb et al., 1977 ), the Attitudes Inventory was initially tested on a smaller sample ( n = 74; M = 8.6 years old; 59% girls). A satisfactory Cronbach’s α = 0.86 was achieved (mean α = 0.73). The number of items was reduced to 13 (four items for willingness, four items for perseverance, five items for self-confidence), which had only a minor influence on reliability (α = 0.83). For economic reasons, the shortened questionnaire was used in the study. The three-factor structure of the questionnaire was confirmed with a confirmatory factor analysis using the R package lavaan version 0.6–7. As the fit indices show, the three-factor model had a good model fit: χ 2 (62) = 134.856, p < 0.001; χ 2 / df = 2.175, CFI = 0.948, TLI = 0.935, RMSEA = 0.062 ( p = 0.086) ( Hair et al., 2009 ; Brown, 2015 ). The three-factor model had a better fit than the single-factor model ( p = 0.0014): χ 2 (65) = 152.121, p < 0.001; χ 2 / df = 2.340, CFI = 0.938, TLI = 0.926, SRMR = 0.061, RMSEA = 0.066 ( p = 0.028). The students were grouped into three groups ( M –1 SD ; M ; M +1 SD ). The responses were coded in such a way that high scores ( M +1 SD ) indicated positive attitudes and beliefs, and low scores ( M –1 SD ) indicated negative attitudes and beliefs.

Additional Influencing Factors

In order to ensure the internal validity of the investigation, we collected student-related factors that influence the solution of word problems from a theoretical and empirical point of view. It has been shown that the mathematical abilities and metacognitive skills of students significantly influence their performance ( Sturm et al., 2015 ).

Mathematical Abilities

The basic mathematical abilities were determined using a standardized German-language test as a group test (Heidelberger Rechentest HRT 1–4, Haffner et al., 2005 ). The test consists of eleven subtests, from which three scale values were determined: calculation operations, numerical-logical and spatial-visual skills as well as the overall performance for all eleven subtests. The reliability was only satisfactory (Cronbach’s α = 0.74). Total performance was included in the study.

Metacognitive Skills

The metacognitive skills of the students were measured using a paper-pencil version of EPA2000, a test to measure metacognitive skills before and/or after the solving of tasks ( Clercq et al., 2000 ). The prediction skills and evaluation skills of the students were collected for all three word problems of the WPST using a 4-point rating scale: 1) “absolutely sure, it’s wrong,” 2) “sure, it’s wrong,” 3) “sure, it’s right,” and 4) “absolutely sure, it’s right” ( Clercq et al., 2000 ). If the students’ assessments of “absolutely sure” matched their solution, they were awarded 2 points. If they agreed with “sure,” they received 1 point. No match was scored with 0 points ( Desoete et al., 2003 ). The reliabilities were only satisfactory (Cronbach’s α total =0.74, α prediction =0.56, α evaluation = 0.73). A confirmatory factor analysis revealed that prediction skills and evaluation skills represent a single factor (χ 2 (9) = 16.652, p < 0.001; χ 2 / df = 1.850, CFI = 0.952, TLI = 0.919, RMSEA = 0.053 ( p = 0.396)). The aggregated factor was used as a control variable in the moderator analysis.

In addition to the variables considered in this paper, text comprehension and intelligence were also surveyed in the project. However, they are not the focus of this paper; additional information can be found in Sturm et al. (2015) .

Descriptive Statistics and Correlations Between the Measures

The descriptive statistics and correlations of all scales are presented in Table 1 (see Supplementary Appendix D for a separate overview for each of the experimental conditions). The signs for all correlations were as expected. The variable training program is not listed because it is the dichotomous moderator variable (T+ and T−).

TABLE 1 . Descriptive statistics and correlations of all variables for both experimental conditions.

Moderated Regression Analyses

The hypothesis was tested with a moderated regression analysis using product terms from mean-centered predictor variables ( Hayes, 2018 ). This model imposed the constraint that any effect of attitudes and beliefs was independent of all other variables in the model. This was achieved by controlling for mathematical abilities, metacognitive skills, and problem-solving performance at Measurement Point 1. The estimated main effects and interaction terms are presented in Table 2 .

TABLE 2 . Results from the regression analysis examining the moderation of the effect of attitudes and beliefs on problem-solving success (t 2 ) by participation in the training program, controlling for mathematical abilities, metacognitive skills, and problem-solving success from the pretest.

When testing the hypothesis, we found a significant main effect of attitudes and beliefs, a significant main effect of the training program, and a significant moderator effect of the training on attitudes and beliefs as a predictor of problem-solving success. The main effect of the training program indicated that students who participated in the training performed better in the second WPST. The main effect of attitudes and beliefs showed that students with more positive attitudes and beliefs were more successful than students with negative attitudes and beliefs.

To further explore the interaction between attitudes and beliefs and the training program, we analyzed simple slopes at values of 1 SD above and 1SD below the means of attitudes and beliefs ( Hayes, 2018 ). As can be seen from the conditional expectations in Figure 2 , attitudes and beliefs did not affect the problem-solving success of students who participated in the training program. Attitudes and beliefs only had a positive effect on the problem-solving success of students who did not participate in the training.

FIGURE 2 . Moderator effect of the training program on problem-solving success at Measurement Point 2.

Our results confirm previous findings that the attitudes and beliefs of students correlate with their problem-solving performance. They indicate that this correlation can be moderated by student participation in a training program. Negative attitudes and beliefs did not affect the performance of students who participated in a problem-solving training program over several weeks. Whether the training program also causes a change in the attitudes and beliefs of the students over time has to be investigated in a follow-up study, which is planned with a longer intervention period with at least two measurements of attitudes and beliefs. A longer intervention period would have the advantage that attitudes develop depending on the individual experiences of a person ( Hannula, 2002 ; Lim and Chapman, 2015 ), for instance, when new experience is gathered or new knowledge is acquired (e.g., Ajzen, 2005 ).

Some limitations need to be considered when interpreting the results of the study. For example, the mitigating processes need to be investigated further. It is also unclear as to which components of the training are ultimately responsible for counteracting the effect of attitudes and beliefs. Although the study did not provide results in this regard, we assume that the following factors might have an effect: generating external representations, reflecting on the representations together as a group, and fostering an appreciative and constructive approach to mistakes. Further studies are needed to show whether and to what extent these factors actually attenuate the effect of attitudes and beliefs.

Furthermore, the measurement instruments for the control variables mathematical abilities and metacognitive skills were rather limited. If researchers are interested in understanding further effects of metacognitive skills, more aspects should be included. Furthermore, according to Lester et al. (1987), investigating attitudes and beliefs using a questionnaire is associated with disadvantages. How accurately students answer the questions depends on how objectively and accurately they can reflect on and assess their own attitudes. Misinterpretations and errors cannot be ruled out. The most serious disadvantage, however, is that data collection using an inventory can easily be assumed to have unjustified validity and reliability. For a deeper insight into the attitudes and beliefs of primary school students, qualitative interviews have to be implemented.

However, for the purpose of this study, it seems sufficient to consider the two control variables mathematical abilities and metacognitive abilities. We were able to ensure that the correlation between attitudes and beliefs and the mathematical performance of students was not influenced by these factors.

Regardless of the limitations, our study has some practical implications. Participation in the training program, independently of the mathematical abilities and text comprehension of students, reduced the influence of attitudes and beliefs on their performance. Thus, for teaching practice, it can be concluded that it is important not only to implement regular problem-solving activities in mathematics lessons, but also to encourage students to externalize and find their own solutions. The aim is to establish a teaching culture that promotes a variety of approaches and procedures, allows mistakes to be made, and makes mistakes a subject for learning. Reflecting on different possible solutions and also on mistakes helps students to progress. Thus, students develop a repertoire of external representations from which they can profit in the long term when solving problems.

Data Availability Statement

The original contributions presented in the study are included in the article/ Supplementary Material , further inquiries can be directed to the corresponding author.

Ethics Statement

The studies involving human participants were reviewed and approved by the Ethics Committee of the Department of Psychology, University of Koblenz and Landau, Germany. Written informed consent to participate in this study was provided by the participants' legal guardian. This study was also carried out in accordance with the guidelines for scientific studies in schools in the German state Rhineland-Palatinate (Wissenschaftliche Untersuchungen an Schulen in Rheinland-Pfalz), Aufsichts- und Dienstleistungsdirektion Trier. The protocol was approved by the Aufsichts- und Dienstleistungsdirektion Trier.

Author Contributions

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

The project was funded by grants from the Deutsche Forschungsgemeinschaft (DFG, grant number GK1561/1).

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feduc.2021.525923/full#supplementary-material

1 This project was part of the first author’s PhD thesis

Adibnia, A., and Putt, I. J. (1998). Teaching problem solving to year 6 students: A new approach. Math. Educ. Res. J. 10 (3), 42–58. doi:10.1007/BF03217057

Ajzen, I. (2005). Attitudes, personality and behavior . Maidenhead, United Kingdom: Open University Press .

Google Scholar

Ajzen, I. (1998). The theory of planned behavior. Organizational Behavior and Human Decision Proc. 50 (2), 179–211. doi:10.1016/0749-5978(91)90020-T

Amarel, S. (1966). On the mechanization of creative processes. IEEE Spectr. 3 (4), 112–114. doi:10.1109/MSPEC.1966.5216589

CrossRef Full Text | Google Scholar

Awofala, A. O. A. (2014). Examining personalisation of instruction, attitudes toward and achievement in mathematics word problems among nigerian senior secondary school students. Ijemst 2 (4), 273–288. doi:10.18404/ijemst.91464

Boonen, A. J. H., van der Schoot, M., van Wesel, F., de Vries, M. H., and Jolles, J. (2013). What underlies successful word problem solving? A path analysis in sixth grade students. Contemporary Educ. psychol. 38 (3), 271–279. doi:10.1016/j.cedpsych.2013.05.001

Bransford, J. D., Brown, A. L., and Cocking, R. R. (2000). How people learn: brain, mind, experience, and school . Washington, DC: National Academy Press .

Bransford, J. D., and Stein, B. S. (1993). The ideal problem solver: a guide for improving thinking, learning, and creativity . 2nd Edn. New York, NY: W. H. Freeman .

Breaugh, J. A., and Arnold, J. (2007). Controlling nuisance variables by using a matched-groups design. Organ. Res. Methods 10 (3), 523–541. doi:10.1177/1094428106292895

Brown, T. A. (2015). Confirmatory factor analysis for applied research . 2nd Edn. New York, NY: Guilford Press .

Charles, R. I., Lester, F. K., and O’Daffer, P. G. (1987). How to evaluate progress in problem solving . Reston, VA: National Council of Teachers of Mathematics .

Clercq, A. D., Desoete, A., and Roeyers, H. (2000). Epa2000: a multilingual, programmable computer assessment of off-line metacognition in children with mathematical-learning disabilities. Behav. Res. Methods Instrum. Comput. 32 (2), 304–311. doi:10.3758/BF03207799

PubMed Abstract | CrossRef Full Text | Google Scholar

Cox, R., and Brna, P. (1995). Supporting the use of external representation in problem solving: the need for flexible learning environments. J. Artif. Intell. Educ. 6 (2–3), 239–302. .

Cox, R. (1999). Representation construction, externalised cognition and individual differences. Learn. InStruct. 9 (4), 343–363. doi:10.1016/S0959-4752(98)00051-6

De Corte, E., Op t Eynde, P., and Verschaffel, L. (2002). ““Knowing what to believe”: the relevance of students’ mathematical beliefs for mathematics education,” in Personal epistemology: the psychology of beliefs about knowledge and knowing . Editors B. K. Hofer, and P. R. Pintrich (New Jersey, United States: Lawrence Erlbaum Associates Publishers ), 297–320. doi:10.4324/9780203424964

De Corte, E., Verschaffel, L., and Op’t Eynde, P. (2000). “Self-regulation: a characteristic and a goal of mathematics education,” in Handbook of self-regulation . Editors P. R. Pintrich, M. Boekaerts, and M. Zeidner (Cambridge, MA: Academic Press ), 687–726.

de Corte, E., Verschaffel, L., and Pauwels, A. (1992). Solving compare problems: An eye movement test of Lewis and Mayer’s consistency hypothesis. J. Educ. Psychol. 84 (1), 85–94. doi:10.1037/0022-0663.84.1.85

Desoete, A., Roeyers, H., and De Clercq, A. (2003). Can offline metacognition enhance mathematical problem solving?. J. Educ. Psychol. 95 (1), 188–200. doi:10.1037/0022-0663.95.1.188

Di Martino, P. (2019). Pupils’ view of problems: the evolution from kindergarten to the end of primary school. Educ. Stud. Math. 100 (3), 291–307. doi:10.1007/s10649-018-9850-3

Duval, R. (1999). “Representation, vision, and visualization: cognitive functions in mathematical thinking. Basic issues for learning (ED466379),” in Proceedings of the twenty-first annual meeting of the north American chapter of the international group for the psychology of mathematics education XXI , Cuernavaca, Mexico , October 23–26, 1999 . Editors F. Hitt, and M. Santos ( ERIC ), 1, 3–26.

Eid, M., Gollwitzer, M., and Schmitt, M. (2011). Statistik und Forschungsmethoden: lehrbuch . [Statistics and research methods] . 2nd Edn. Weinheim, Germany: Beltz .

Goldin, G. A. (2003). “Affect, meta-affect, and mathematical belief structures,” in Beliefs: a hidden variable in mathematics education? . Editors G. C. Leder, E. Pehkonen, and G. Törner (Amsterdam, Netherlands: Kluwer Academic Publishers ), 31, 59–72. doi:10.1007/0-306-47958-3_4

Goldin, G. A., Rösken, B., and Törner, G. (2009). “Beliefs—No longer a hidden variable in mathematical teaching and learning processes,” in Beliefs and attitudes in mathematics education . Editors J. Maasz, and W. Schloeglmann (Rotterdam, Netherlands; Sense Publishers ), 1–18.

Greevy, R., Lu, B., Silber, J. H., and Rosenbaum, P. (2004). Optimal multivariate matching before randomization. Biostatistics 5 (2), 263–275. doi:10.1093/biostatistics/5.2.263

Grigutsch, S., Raatz, U., and Törner, G. (1998). Einstellungen gegenüber Mathematik bei Mathematiklehrern. Jmd 19 (1), 3–45. doi:10.1007/BF03338859

Haffner, J., Baro, K., Parzer, P., and Resch, F. (2005). Heidelberger Rechentest (HRT 1-4): erfassung mathematischer Basiskompetenzen im Grundschulalter [Heidelberger Rechentest (HRT 1-4): assessment of basic mathematical skills at primary school age] . Göttingen, Germany: Hogrefe .

Hair, J. F., Black, W. C., Babin, B. J., and Anderson, R. E. (2009). Multivariate data analysis . 7th Edn. London, United Kingdom: Pearson .

Hannula, M. S. (2002). Attitude towards mathematics: emotions, expectations and values. Educ. Stud. Math. 49 (1), 25–46. doi:10.1023/A:1016048823497

Hayes, A. F. (2018). Introduction to mediation, moderation, and conditional process analysis: a regression-based approach . 2nd Edn. New York, NY: Guilford Press .

Hegarty, M., Mayer, R. E., and Green, C. E. (1992). Comprehension of arithmetic word problems: Evidence from students' eye fixations. J. Educ. Psychol. 84 (1), 76–84. doi:10.1037/0022-0663.84.1.76

Higgins, K. M. (1997). The effect of year-long instruction in mathematical problem solving on middle-school students’ attitudes, beliefs, and abilities. J. Exp. Educ. 66 (1), 5–28. doi:10.1080/00220979709601392

Kirsh, D. (2010). Thinking with external representations. AI Soc. 25 (4), 441–454. doi:10.1007/s00146-010-0272-8

Lester, F. K., and Cai, J. (2016). “Can mathematical problem solving be taught? Preliminary answers from 30 years of research,” in Posing and solving mathematical problems . Editors P. Felmer, E. Pehkonen, and J. Kilpatrick (Washington, DC: Springer ), 117–135. doi:10.1007/978-3-319-28023-3_8

Lester, F. K., Garofalo, J., and Kroll, D. L. (1989). “Self-confidence, interest, beliefs, and metacognition: key influences on problem-solving behavior,” in Affect and mathematical problem solving . Editors D. B. McLeod, and V. M. Adams (Berlin, Germany: Springer-Verlag ), 75–88. doi:10.1007/978-1-4612-3614-6_6

Lester, F. K., and Kroll, D. L. (1990). “Assessing student growth in mathematical problem solving,” in Assessing higher order thinking in mathematics . Editor G. Kulm (Washington, DC: AAAS Publication ), 53–70.

Lester, F. K. (1985). “Methodological considerations in research on mathematical problem-solving instruction,” in Teaching and learning mathematical problem solving: multiple research perspectives . Editor E. A. Silver (Mahwah NJ: Erlbaum ), 41–69.

Lienert, G. A., and Raatz, U. (1998). Testaufbau und Testanalyse [Test construction and test analysis] . 6th Edn. Weinheim, Germany: Beltz .

Lim, S. Y., and Chapman, E. (2015). Effects of using history as a tool to teach mathematics on students' attitudes, anxiety, motivation and achievement in grade 11 classrooms. Educ. Stud. Math. 90 (2), 189–212. doi:10.1007/s10649-015-9620-4

Mason, L., and Scrivani, L. (2004). Enhancing students' mathematical beliefs: an intervention study. Learn. InStruct. 14 (2), 153–176. doi:10.1016/j.learninstruc.2004.01.002

Mayer, R. E., and Hegarty, M. (1996). “The process of understanding mathematical problems,” in The nature of mathematical thinking . Editors R. J. Sternberg, and T. Ben-Zeev (Mahwah NJ: Lawrence Erlbaum ), 29–54.

Moore, R. T. (2012). Multivariate continuous blocking to improve political science experiments. Polit. Anal. 20 (4), 460–479. doi:10.1093/pan/mps025

M. S. Hannula, G. C. Leder, F. Morselli, M. Vollstedt, and Q. Zhang (Editors) (2019). Affect and mathematics education: fresh perspectives on motivation, engagement, and identity . New York, NY: Springer International Publishing . doi:10.1007/978-3-030-13761-8

Myers, A., and Hansen, C. H. (2012). Experimental psychology . 7th Edn. Belmont, CA: Wadsworth .

Newell, A., and Simon, H. A. (1972). Human problem solving . Upper Saddle River, NJ: Prentice-Hall .

Norman, D. A. (1993). Things that make us smart: defending human attributes in the age of the machine . New York, NY: Perseus Books .

Nussbeck, F. W., Eid, M., and Lischetzke, T. (2006). Analysing multitrait-multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: what sample size is needed for valid results?. Br. J. Math. Stat. Psychol. 59 (1), 195–213. doi:10.1348/000711005X67490

Peterson, C., and Seligman, M. E. P. (2004). Character strengths and virtues: a handbook and classification . Oxford, United Kingdom: Oxford University Press .

Rasch, R. (2008). 42 Denk- und Sachaufgaben. Wie Kinder mathematische Aufgaben lösen und diskutieren [42 thinking and problem solving tasks. How children solve and discuss mathematical tasks] . 3rd Edn. Seelze-Velber, Germany: Kallmeyer .

Reisberg, D. (1987). “External representations and the advantages of externalizing one’s thought,” in The ninth annual conference of the cognitive science society , Seattle, WA , July 1, 1987 (Hove, United Kingdom: Psychology Press ), 281–293.

Reiss, K., Hellmich, F., and Thomas, J. (2002). “Individuelle und schulische Bedingungsfaktoren für Argumentationen und Beweise im Mathematikunterricht [Individual and educational conditioning factors for argumentation and evidence in mathematics teaching],” in Bildungsqualität von Schule: schulische und außerschulische Bedingungen mathematischer, naturwissenschaftlicher und überfachlicher Kompetenzen . Editors M. Prenzel, and J. Doll ( Weinheim, Germany: Beltz ), 51–64.

Reyes, L. H. (1984). Affective variables and mathematics education. Elem. Sch. J. 84 (5), 558–581. doi:10.1086/461384

Schnotz, W., Baadte, C., Müller, A., and Rasch, R. (2010). “Creative thinking and problem solving with depictive and descriptive representations,” in Use of representations in reasoning and problem solving: analysis and improvement . Editors L. Verschaffel, E. de Corte, T. de Jong, and J. Elen (Abingdon, United Kingdom: Routledge ), 11–35.

Schoenfeld, A. H. (1985). Mathematical problem solving . Cambridge, MA: Academic Press .

Shaughnessy, J. M. (1985). Problem-solving derailers: The influence of misconceptions on problem-solving performance. In E. A. Silver (Hrsg.), Teaching and learning mathematical problem solving: Multiple research perspectives (S. 399 -415). Lawrence Erlbaum.

Stuart, E. A., and Rubin, D. B. (2008). “Best practices in quasi-experimental designs: matching methods for causal inference,” in Best practices in quantitative methods . Editor J. W. Osborne (Thousand Oaks, CA: SAGE ), 155–176.

Sturm, N. (2018). Problemhaltige Textaufgaben lösen: einfluss eines Repräsentationstrainings auf den Lösungsprozess von Drittklässlern [Solving word problems: influence of representation training on the problem-solving process of third-graders . Berlin, Germany: Springer . | Google Scholar

Sturm, N., and Rasch, R. (2015). “Forms of representation for solving mathematical word problems – development of an intervention study,” in Multidisciplinary research on teaching and learning . Editors W. Schnotz, A. Kauertz, H. Ludwig, A. Müller, and J. Pretsch (London, United Kingdom: Palgrave Macmillan ), 201–223.

Sturm, N., Rasch, R., and Schnotz, W. (2016). Cracking word problems with sketches, tables, calculations and reasoning: do all primary students benefit equally from using them? Pers. Indiv. Differ. 101, 519. doi:10.1016/j.paid.2016.05.317

Sturm, N. (2019). “Self-generated representations as heuristic tools for solving word problems,” in Implementation research on problem solving in school settings. Proceedings of the 2018 joint conference of ProMath and the GDM working group on problem solving . Editors A. Kuzle, I. Gebel, and B. Rott (Münster, Germany: WTM-Verlag ), 173–192.

Sturm, N., Wahle, C. V., Rasch, R., and Schnotz, W. (2015). “Self-generated representations are the key: the importance of external representations in predicting problem-solving success,” in Proceedings of the 39th conference of the international group for the psychology of mathematics education . Editors K. Beswick, T. Muir, and J. Wells ( Basingstoke, United Kingdom: PME ), 4, 209–216.

Sweller, J. (1994). Cognitive load theory, learning difficulty, and instructional design. Learn. InStruct. 4 (4), 295–312. doi:10.1016/0959-4752(94)90003-5

van Dijk, T. A., and Kintsch, W. (1983). Strategies of discourse comprehension . Cambridge, MA: Acadamic Press .

Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., and Ratinckx, E. (1999). Learning to solve mathematical application problems: a design experiment with fifth graders. Math. Think. Learn. 1 (3), 195–229. doi:10.1207/s15327833mtl0103_2

Verschaffel, L., Greer, B., and de Corte, E. (2000). Making sense of word problems . Netherlands: Swets and Zeitlinger .

Webb, N. L., Moses, B. E., and Kerr, D. R. (1977). Mathematical problem solving project technical report IV: developmental acctivities related to summative evaluation (1975–1976) : Mathematics Education Development Center. Bloomington, IN: Indiana University .

Zakaria, E., and Ngah, N. (2011). A preliminary analysis of students’ problem-posing ability and its relationship to attitudes towards problem solving. Res. J. Appl. Sci. Eng. Technol. 3 (9), 866–870.

Zakaria, E., and Yusoff, N. (2009). Attitudes and problem-solving skills in algebra among malaysian matriculation college students. Eur. J. Soc. Sci. 8 (2), 232–245.

Keywords: attitudes and beliefs, word problem, training program design, problem-solving, problem-solving success, primary school, moderation effect analysis

Citation: Sturm N and Bohndick C (2021) The Influence of Attitudes and Beliefs on the Problem-Solving Performance. Front. Educ. 6:525923. doi: 10.3389/feduc.2021.525923

Received: 21 May 2020; Accepted: 18 January 2021; Published: 17 February 2021.

Reviewed by:

Copyright © 2021 Sturm and Bohndick. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Nina Sturm, [email protected]

This article is part of the Research Topic

Psychology and Mathematics Education

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• My Account Login
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Open access
• Published: 10 December 2022

Secondary school students’ attitude towards mathematics word problems

• Robert Wakhata   ORCID: orcid.org/0000-0001-9144-0420 1 ,
• Védaste Mutarutinya 2 &
• Sudi Balimuttajjo 3  

Humanities and Social Sciences Communications volume  9 , Article number:  444 ( 2022 ) Cite this article

15k Accesses

2 Citations

2 Altmetric

Metrics details

• Operational research

Students’ positive attitude towards mathematics leads to better performance and may influence their overall achievement and application of mathematics in real-life. In this article, we present the findings of an investigation on students’ attitude towards linear programming (LP) mathematics word problems (LPMWPs). An explanatory sequential quasi-experimental design involving a pre-intervention-intervention-post-intervention non-equivalent control group was adopted. A sample of 851 grade 11 Ugandan students (359 male and 492 female) from eight secondary schools (public and private) participated. Cluster random sampling was applied to select respondents from eight schools; four from central Uganda and four from eastern Uganda. The attitude towards mathematics inventory-short form (ATMI-SF) was adapted (with α  = 0.75) as a multidimensional measurement tool for measuring students’ attitude towards LPMWPs. The results revealed that students’ attitude towards LPMWPs was generally negative. Enjoyment, motivation, and confidence were weekly negatively correlated while usefulness was positively correlated. Additionally, the results found no significant statistical relationship between students’ attitudes towards LPMWPs and their age, gender, school location, school status, and school ownership. The discrepancy is perhaps explained by both theoretical and/or psychometric limitations, and related factors, for instance, students’ academic background, school characteristics, and transitional beliefs from primary to secondary education. This study acknowledges the influence of and supplements other empirical findings on students’ attitude towards learning mathematics word problems. The present study provides insight to different educational stakeholders in assessing students’ attitude towards LPMWPs and may provide remediation and interventional strategies aimed at creating students’ conceptual change. The study recommends that teachers should cultivate students’ interests in mathematics as early as possible. Varying classroom instructional practices could be a remedy to enhance students’ understanding, achievement, and, motivation in learning mathematics word problems. The teachers’ continuous professional development courses should be enacted to improve instruction, assessment, and students’ attitude. Overall, the study findings support the theoretical framework for enhancing the learning of mathematics word problems in general and LP in particular.

Similar content being viewed by others

The selections and differences in mathematical problem-posing strategies of junior high school students

Students’ performance, attitude, and classroom observation data to assess the effect of problem-based learning approach supplemented by YouTube videos in Ugandan classroom

Math items about real-world content lower test-scores of students from families with low socioeconomic status

Introduction.

The term attitude is not a new concept in mathematics education. It has been defined by different authors in different settings and contexts. For instance, Aiken ( 1970 ) defined attitude as “a learned disposition or tendency on the part of an individual to respond positively or negatively to some object, situation, concept or another person” (p. 551). According to Lin and Huang ( 2014 ), attitude towards mathematics can be referred to as positive, negative, or neutral feelings and dispositions. Attitude can be categorized as bi-dimensional (person’s emotions and beliefs) or multidimensional (affect, behavior, and cognition). Over the last decades, an extensive body of research from different settings and contexts have investigated variables that influence students’ attitude towards Science, Technology Engineering and, Mathematics (STEM) (e.g., Aiken, 1970 ; Gardner, 1975 ; Kempa and McGough, 1977 ). In this study, we are particularly concerned with students’ attitude towards mathematics word problems, and linear programming (LP) in particular due to the significant roles LP plays in constructing models for understanding the three (STE).

Numerous studies have been published on students’ attitude towards mathematics, which is always translated as liking and disliking of the subject (Arslan et al., 2014 ; Davadas and Lay, 2020 ; Pepin, 2011 ; Utsumi and Mendes, 2000 ). To some secondary school students, mathematics appears to be abstract, difficult to comprehend, sometimes boring, and viewed with limited relationship or relevance to everyday life experiences. At primary and secondary school levels, students start well but gradually start disliking mathematics feeling uncomfortable and nervous. Consequently, they may lack self-confidence and motivation during problem-solving. To some students, persevering and studying advanced mathematics has become a nightmare. Indeed, some students do not seem to know the significance of learning mathematics beyond the compulsory level. Students may (or may not) relate mathematical concepts beyond the classroom environment if they have a negative attitude towards the subject. This may lead to their failure to positively transfer mathematical knowledge and skills in solving societal problems.

Mathematicians have attempted to research and understand affective variables that significantly influence students’ attitude towards mathematics (e.g., Barmby et al., 2008 ; Davadas and Lay, 2020 ; Di Martino and Zan, 2011 ; Evans and Field, 2020 ; Grootenboer and Hemmings, 2007 ; Hannula, 2002 ; Maamin et al., 2022 ; Marchis, 2011 ; Pongsakdi et al., 2019 ; Yasar, 2016 ; Zan et al., 2006 ). Some researchers have gone ahead to ask fundamental questions on whether or not students’ attitude towards mathematics is a general phenomenon or dependent on some specific variables. To this effect, some empirical findings report students’ attitude towards specific units or topics in mathematics aimed at enhancing the learning of specific mathematical content and mathematics generally (e.g., Arslan et al., 2014 ; Estrada and Batanero, 2019 ; Gagatsis and Kyriakides, 2000 ; Julius et al., 2018 ; Mumcu and Aktaş, 2015 ; Selkirk, 1975 ; Townsend and Wilton, 2003 ).

Rather than investigating students’ general attitudes toward mathematics, recent research has also attempted to identify background factors that may provide a basis for understanding students’ attitude towards mathematics. Thus, students at different academic levels may have a negative or positive attitude towards mathematics due to fundamentally different reasons. Yet, other studies show the existence of a positive relationship between attitude and achievement in mathematics (e.g., Berger et al., 2020 ; Chen et al., 2018 ; Davadas and Lay, 2020 ; Grootenboer and Hemmings, 2007 ; Hwang and Son, 2021 ; Lipnevich et al., 2011 ; Ma, 1997 ; Maamin et al., 2022 ; Mazana et al., 2018 ; Mulhern and Rae, 1998 ; Opolot-okurut, 2010 ; Sandman, 1980 ; Tapia, 1996 ). From the above studies, it appears that multiple factors ranging from students’ to teachers’ classroom instructional practices may influence students’ attitudes towards, and achievement in mathematics.

Ugandan context

In Uganda, studies on predictors of students’ attitude towards science and mathematics are scanty. There are no recent empirical findings on secondary school students’ attitude towards Mathematics and mathematics word problems in particular. Solving LP tasks (by graphical method) is one of the topics taught to 11th-grade Ugandan lower secondary school students (NCDC, 2008 , 2018 ). Despite students’ general and specific learning challenges in mathematics and LP, the objectives of learning LP are embedded within the aims of the Ugandan lower secondary school mathematics curriculum (Supplementary Appendix 3 ). Some of the specific aims of learning mathematics in Ugandan secondary schools include …enabling individuals to apply acquired skills and knowledge in solving community problems, instilling a positive attitude towards productive work…” (NCDC, 2018 ). Generally, the learning of LP word problems aims to develop students’ problem-solving abilities, application of prior algebraic concepts, knowledge, and understanding of linear equations and inequalities in writing models from word problems, and real-life-world problems. Despite the learning challenges, the topic of LP is also aimed at equipping learners with adequate knowledge and skills for doing advanced mathematics courses beyond the 11th-grade (locally called senior four) minimum mathematical proficiency at Uganda Certificate of Education (UCE).

However, every academic year, the Uganda National Examinations Board (UNEB) highlights students’ strengths and weaknesses in previous examinations at UCE. The consistent reports (e.g., UNEB, 2016 , 2018 , 2019 , 2020 ) on previous examinations on the work of candidates show that students’ performance in mathematics is not satisfactory, especially at the distinction level. In particular, the above previous examiners’ reports show students’ poor performance in mathematics word problems. The examination reports have consistently revealed numerous students’ specific deficiencies in the topic of LP (please see Supplementary Appendix 1 ). Students’ challenges in LP mainly stem from comprehension of word problems to the formation of wrong linear equations and inequalities (in two dimensions) from the given word problems in real-life situations. Thus, wrong models derived from questions may result in incorrect graphical representations, and consequently wrong solutions and interpretations of optimal solutions. These challenges (and others) may consequently hinder and/or interfere with students’ construction of relevant models in science, mathematics, and technology. Moreover, learners have consistently demonstrated cognitive obstacles in answering questions on LP, while the majority elude these questions during national examinations by answering questions from presumably “simpler” topics. Noticeably absent in all the UNEB reports are factors that account for students’ weaknesses in learning LP and the specific interventions to overcome students’ challenges. Some students have, however, developed a negative attitude towards the topic. Yet, students’ attitudes may directly impact their learning outcomes (Code et al., 2016 ).

Although some empirical findings (e.g., Opolot-okurut, 2010 ) have reported on students’ attitude towards mathematics in the secondary school context, this paper presents results from a more specific investigation into students’ attitudes towards mathematics word problems. Specifically, the present study investigated secondary school students’ attitude towards solving linear programming mathematics word problems (LPMWPs). This is because studies concerning attitudes towards and achievement in mathematics have begun to drift from examining general attitudes to a more differentiated conceptualization of specific students’ attitude formations, and in different units (topics). Although different attitudinal scales (e.g., Code et al., 2016 ; Fennema and Sherman, 1976 ; Tapia, 1996 ) were developed to measure different variables influencing students’ attitudes towards mathematics, this study specifically investigated the influence of some of these constructs on students’ attitude towards learning LP. According to the above-stated authors (and other empirical findings), students’ attitude is a consequence of both general and specific latent factors.

Mathematics word problems

Verschaffel et al. ( 2010 ) define word problems as “verbal descriptions of problem situations wherein one or more questions have raised the answer to which can be obtained by the application of mathematical operations to numerical data available in the problem statement.” The authors categorized word problems based on their inclusion in real-life world scenarios. Thus, mathematics word problems play significant roles in equipping learners with the basic knowledge, skills, and, understanding of problem-solving and mathematical modeling. Some empirical findings (e.g., Boonen et al., 2016 ) show that mathematics word problems link school mathematics to real-life world applications. However, the learning of mathematics word problems and related algebraic concepts is greatly affected by students’ cognitive and affective factors (Awofala, 2014 ; Jupri & Drijvers, 2016 ; Pongsakdi et al., 2019 ). Mathematics word problems are an area where the majority of students experience learning obstacles in secondary schools and beyond (Abdullah et al., 2014 ; Awofala, 2014 ; Dooren et al., 2018 ; Goulet-Lyle et al., 2020 ; Julius et al., 2018 ; Pearce et al., 2011 ; Sa’ad et al., 2014 ; Verschaffel et al., 2010 , 2020a , 2020b ). By contrast, comprehension of mathematics word problems explains relational difficulties. Consequently, this has undermined students’ competence, confidence, and achievement in word problems and mathematics in general.

Yet, mathematics word problems are intended to help learners to apply mathematics beyond the classroom in solving real-life-world problems. Verschaffel et al. ( 2020a , 2020b ) and Boonen et al. ( 2016 ) have argued that mathematics word problems are difficult, complex, and pause comprehension challenges to most learners. This is because word problems require learners to understand and apply previously learned basic algebraic mathematical principles, rules, and techniques. Indeed, most learners find it difficult to understand text in word problems before transformation into models. This is partly due to variations in their comprehension abilities and language (Strohmaier et al., 2020 ). Consequently, learners fail to write required mathematical algebraic symbolic operations and models. Yet, incorrect models lead to wrong algebraic manipulations and consequently wrong graphical representations and solutions.

Notably, research findings by Meara et al. ( 2019 ), and Evans and Field ( 2020 ) indicate that students’ mathematical inefficiency is due to their transitional epistemological and ontological challenges from primary to secondary education. Other studies (e.g., Georgiou et al., 2007 ; Grootenboer and Hemmings, 2007 ; Li et al., 2018 ; Norton, 1998 ; Sherman, 1979 ; Sherman, 1980 ) attribute students’ poor performance and achievement in mathematics to gender differences. Thus, students may start learning mathematics well from primary but gradually lose interest in some specific units and finally in mathematics generally. For the case of LP, and as indicated above, it is likely that students’ attitude towards mathematics and equations, inequalities, and LP in particular gradually drop in favor of other presumably simpler topics. However, to boost performance in mathematics word problems, Goulet-Lyle et al. ( 2020 ) proposed a step-by-step problem-solving strategy to enhance mastery and develop a positive attitude towards learning.

Students’ attitudes should, therefore, be investigated as well as their influence on their conceptual changes. Several empirical studies have also investigated the relationship between attitude towards, and achievement in mathematics across all levels, and in different contexts (e.g., Bayaga and Wadesango, 2014 ; Camacho et al., 1998 ; Chun and Eric, 2011 ; Davadas and Lay, 2020 ; Karjanto, 2017 ; Khavenson et al., 2012 ; Ozdemir and Ovez, 2012 ; Quaye, 2015 ; Selkirk, 1975 ; Tahar et al., 2010 ; Utsumi and Mendes, 2000 ; Yáñez-Marquina and Villardón-Gallego, 2016 ). In particular, these studies generally focused on students’ attitude towards mathematics, and many of them were conducted from the western context (Kasimu and Imoro, 2017 ). Yet, students may have different perceptions and attitudes towards specific content (topics) in mathematics irrespective of their setting, context, and learning environment.

To enhance mathematical conceptual proficiency, educators should target and/or boost students’ cognitive and affective domains in specific mathematics content. In a related genre, students’ proficiency in LP word tasks may largely depend on their prior algebraic knowledge, skills, and experiences. Julius et al. ( 2018 ) noted that prior conceptual understanding coupled with students’ attitudes towards solving algebraic concepts impacted students’ inherent procedures in writing relational symbolic mathematical models (inequalities) from word problems, and provision of correct numerical solutions. Despite numerous difficulties encountered by students in algebraic inequalities as reported in Fernández and Molina ( 2017 ), Molina et al. ( 2017 ), Bazzini and Tsamir ( 2004 ), Tsamir and Almog ( 2001 ), Tsamir and Bazzini ( 2004 , 2006 ), and Tsamir and Tirosh ( 2006 ) have suggested a combination of approaches, methodologies, and strategies than applying one specific method. Adopting this instructional and assessment approach may help to overcome students’ learning and related algebraic challenges, which are all aimed at enhancing the learning of mathematics.

The theoretical framework

This study is situated on the theoretical framework according to constructivism, and Eccles, Wigfield, and colleagues’ expectancy-value model of achievement motivation (Wigfield, 1994 ; Wigfield and Eccles, 2000 ). The expectancy-value model is based on the expectancy-value theories of achievement. Thus, the theory is based on the premise that success on specific tasks and the values inherent in those tasks is positively correlated with achievement, and consequently students’ attitude towards specific mathematical tasks. In the context of the attitude towards mathematics inventory-short form (ATMI-SF), the theory combines motivation, enjoyment, confidence, value (usefulness), and related latent variables to explain students’ success in learning mathematics. Constructivism is a form of discovery learning that is based on the premise that teachers facilitate learning by actively involving learners so that they construct their world knowledge and understanding based on individual prior experiences and schema (Olusegun, 2015 ; Ültanır, 2012 ). Thus, previous knowledge, understanding, and reflection with new knowledge are inevitable for supporting subsequent learning and acquisition of both conceptual and procedural knowledge. These knowledge components may later arouse learners’ attitude towards specific mathematics content and mathematics achievement generally.

We are particularly concerned about students’ efforts, and persistence, their perceived difficulties and related challenges in learning LPMWPs and the experiences learners may encounter when solving LP word tasks. Empirical findings and our own experiences as mathematics educators show that students’ challenges in LP largely depend on their insufficient previous algebraic knowledge and experiences in applying the knowledge of equations and inequalities. In this article, we discuss students’ attitude towards LPMWPs using the expectancy-value model theory within the constructivism paradigm. Using this paradigm helped to explain the ATMI-SF constructs and their significance in enhancing the learning of mathematics in secondary schools. The expectancy-value theory and constructivism have been widely applied to enhance the learning of mathematics and science (Awofala, 2014 ; Fielding-Wells et al., 2017 ; Meyer et al., 2019 ; Wigfield and Eccles, 2000 ; Yurt, 2015 ). To foster a positive attitude, teachers (educators) should assign different tasks to students based on their academic level so that they apply previously acquired knowledge, understanding, and experiences in subsequent learning. Stein et al. ( 2000 ) reasoned that students’ proficiency and competency are determined by the mathematical tasks they are given. Tasks at the lower cognitive stage (memorization level), for example, must be different from those at the highest cognitive level (doing mathematics). In the context of learning LP, students should first understand and appropriately apply the basic knowledge of equations and inequalities to adequately and proficiently solve non-routine LPMWPs.

Attitude towards mathematics and the learning of linear programming word problems

Linear programming is one of the algebraic topics that require students’ understanding of basic mathematical principles and rules before the application of computer software for solving and optimizing more advanced and complex LP problems. Linear programming is a classical unit, “the cousin” of mathematics word problems, which has gained significant applications in mathematics, science, and technology (Aboelmagd, 2018 ; Colussi et al., 2013 ; Parlesak et al., 2016 ; Romeijn et al., 2006 ) because the topic is used for formulating models that link theoretical to practical mathematical applications. Thus, LP provides basic elementary modeling skills (Vanderbei, 2014 ).

Previous empirical studies have revealed that LP and/or related concepts are not only difficult for learners but also challenging to teach (Awofala, 2014 ; Goulet-Lyle et al., 2020 ; Kenney et al., 2020 ; Verschaffel et al., 2020a , 2020b ). Different factors account for learners’ challenges in mathematics word problems (e.g., Ahmad et al., 2010 ; Haghverdi et al., 2012 ; Heydari et al., 2015 ). The challenges range from students’ comprehension of word problem statements, and their attitude towards the topic, to their transformation from conceptual to procedural knowledge and understanding. Learners’ attitude towards solving algebraic word problems should, therefore, be investigated and integrated during classroom instruction to help educational stakeholders provide appropriate and/or specific instructional strategies and remedies.

Several attitudinal scales (with both cognitive and behavioral components) have been developed (Lim and Chapman, 2013 ; Yáñez-Marquina and Villardón-Gallego, 2016 ) adopted or adapted (Lin and Huang, 2014 ) to assess students’ attitude towards mathematics and in specific mathematics content. For instance, Geometry Attitude Scales (Avcu and Avcu, 2015 ), Statistics Attitude Scales (Ayebo et al., 2019 ; Khavenson et al., 2012 ), Attitudes toward Mathematics Word Problem Inventory (Awofala, 2014 ), the Attitude towards Geometry Inventory (ATGI) instrument (Utley, 2007 ), and others. In this study, we adapted the ATMI-SF instrument (Lin and Huang, 2014 ) to investigate the 11th-grade students’ attitude towards learning LP word problems (see Supplementary Appendix 1 ). Taken together, research shows that a high percentage of educational stakeholders around the world are concerned about attitude towards mathematics and word tasks in particular. However, to fully understand students’ attitude towards mathematics, it is necessary to investigate beyond general mathematics attitudes and examine specific underlying aspects of these attitudes. Thus, the present study examines students’ attitude towards solving LP mathematics word problems.

Methodology

This study investigated students’ attitude towards linear programming mathematics word problems (LPMWPs). To achieve this purpose, a quantitative survey research design was used (Creswell and Plano Clark, 2018 ). The authors contend that the quantitative approach provides a more general understanding of the views of participants in an entire population. Thus, this approach was applied to collect, analyze, and describe the secondary school students’ ATLPWPs, their experiences, and latent behavior.

Research design

The present study was part of a large study that investigated the effect of active learning heuristic problem-solving approach on students’ achievement and attitude towards learning LP word problems. The present study adopted a quantitative approach to gain a deeper and broader understanding of students’ ATLPWPs (Creswell, 2014 ; Creswell and Plano Clark, 2018 ; Djamba and Neuman, 2002 ). A quasi-experimental pre-test, post-test, and non-equivalent control group study design was adopted. By using the stated approach and design, researchers ably compared and contrasted students’ ALPMWPs. Learners from the experimental group, and in their intact classes participated. The main reason for adopting intact classes was to avoid interference with the internal school-set timetables and already set operational schedules.

The analysis reported in this study comprised a research study of 851 grade 11 students from eight randomly selected private or public secondary schools (both rural and urban), four from Mbale district, eastern Uganda, and the remaining four from Mukono district, central Uganda. Cluster random sampling was used to select regions and schools. The sampled schools were allocated to the experimental and comparison groups by a toss of a coin. Four hundred thirty-two (50.8%) students were assigned to the comparison group while four hundred nineteen (49.2%), were assigned to the treatment group. Two schools from both regions were assigned to the experimental group. The selection of students from the two distant schools within/outside the regions and assigning them to treatment groups was to avoid spurious results. In a situation where a particular school had more than one class (“stream”), at the time of data collection, at least one hundred students were randomly picked from different classes in that specific school to respond to the attitudinal questionnaires. The main reason for selecting the 11th-grade students as research participants are based on curriculum materials in which LP is taught to the 11th-grade students (see NCDC, 2018 ). Indeed, at the time of data collection, students were preparing for UCE national examinations for the 2019/2020 academic year. The school heads revealed that the mathematics syllabus containing LP word problems (Supplementary Appendix 1 ) had been completed. The students were selected to provide their experiences and attitudes toward learning LP word problems. Of the 851 students who participated, 359 (42.2%) were males and 492 (57.8%) were females with a mean age of 18.32 (S.D. = 0.94) years. We predicted that the participants had adequate knowledge and understanding of solving LP word problems by graphical method. Identification numbers were allotted to participants before they anonymously and voluntarily completed adapted ATMI-SF questionnaire items.

Research instruments and procedure for administration

In addition to demographic questions, the ATMI-SF (Lin and Huang, 2014 ), a 14-item instrument questionnaire consisting of four subscales (enjoyment, motivation, value/usefulness, and self-confidence) was adapted to measure students’ attitude towards learning LP mathematics word problems. The ATMI-SF is a 5-point Likert-type scale with response options ranging from “Strongly Disagree (1)” to “Strongly Agree (5).” The ATMI-SF items were developed by Lim and Chapman ( 2013 ), which were also developed and validated from several mathematics attitudinal questionnaire items (Fennema and Sherman, 1976 ; Kasimu and Imoro, 2017 ; Mulhern and Rae, 1998 ; Primi et al., 2020 ; Tapia, 1996 ). The ATMI-SF was adapted because it directly correlates with the learning of LP, “the cousin of mathematics word problems.” English is the language of instruction in Ugandan secondary schools’ curricula, and translation of questionnaire items was not required. The content validity of the questionnaire was assessed by three experts (one senior teacher for mathematics, one senior lecturer for mathematics education, and one tutor at a teacher training institution). The experts were selected based on their vast experience in teaching mathematics at various academic levels. The experts further evaluated the appropriateness and relevance of the adapted questionnaire items. Based on their recommendations, suggestions, and comments, some questionnaire items were adjusted to suit students’ academic level and language to adequately measure students’ ATLPMWPs.

To adequately implement active learning heuristic problem-solving strategies, teachers from the treatment group were trained. First, students’ basic prior conceptual knowledge of equations and inequalities plus the basic algebraic principles and understanding were reviewed to link previous concepts to the learning of LP. Second, several learning materials were applied to help students adequately master the concepts. The materials included the use of graphs, grid boards, excel, and GeoGebra software. These strategies were further integrated with problem-solving strategies (Polya, 2004 ) by ensuring that students understand the LP word problem, devise a plan, adequately carry out the plan and finally look back to verify solution sketches and procedures. To ensure that students minimize errors and misconceptions, the learning of LP was further integrated with Newman Error Analysis (NEA) model prompts. The teachers emphasized question reading and decoding, comprehension, transformation, process skills, and encoding to cultivate students’ positive attitude towards LPMWPs.

The procedure and data analysis

The ATLPMWP questionnaires were completed by individual students at their respective schools in their natural classroom settings. The 11th-grade students completed this study in at most 20 min on average. The survey contained a ‘filter statement’, as a Social Desirability Response (SDR) to verify and discard respondents’ questionnaires, especially those who did not read (see item 15 in Supplementary Appendix 1 ) or finish answering questionnaire items (Bäckström and Björklund, 2013 ; Latkin et al., 2017 ). Written consent was received from all participants and participation in this study was completely voluntary and confidential. Participants who felt uncomfortable completing the questionnaire were not penalized. Data were collected with the help of mathematics heads of the department who were selected from sampled schools as experts. Participants were explained, the purpose of the study before administering and/or filling in questionnaire items. In the presence of the principal researcher, research assistants, and some selected school administrators, participants completed and returned all the questionnaires. In addition to the administration of questionnaire items, 12 heads of department and 24 students (a boy and a girl from each sampled school) were interviewed to correlate the data collected in trying to adequately assess the learning of LP word problems. Descriptive and inferential statistics were used to analyze the collected data about the background characteristics. Data were analyzed using the Statistical Package for Social Sciences (SPSS) version 26. In addition, and where necessary, excerpts were used to make a judgment about students’ ATMWPs, and how this affects the learning and achievement in mathematics and LP in particular.

Preliminary results and interpretation

Psychometric properties of the atlpmwp scale.

IBM SPSS (version 26) software package was used for analysis. Preliminary statistical analysis revealed no evidence of missing data due to a few cases, which were ignored because they did not exceed 5% of sample cases (Barbara and Tabachnick, 2001 ; Kline Rex, 1998 ; Lim and Chapman, 2013 ). However, out of 885 questionnaires distributed, 31 questionnaires were removed because the participants did not either conform to SDR (Bäckström and Björklund, 2013 ; Latkin et al., 2017 ) or had incomplete data. Univariate analysis was run to examine the degree of normality (Hair et al., 2010 ; Pallant, 2011 ). The indices for skewness and kurtosis were within the acceptable ranges (±2 and ±7 respectively) (Byrne, 2010 ; Curran et al., 1996 ; Hair et al., 2010 ). Thus, data were fairly normally distributed (Table 1 ). Exploratory factor analysis was run using initial pilot data collected from 215 students outside the study sample to check the correlation between the items. Most of the ATMI-SF scale inter-item means were below 3.0; suggesting that students generally had negative attitude ALPMWPs. However, browsing through the data, psychometric average scores for items still confirmed and indicated that most students (both male and female) irrespective of the school type and location had a negative attitude towards learning LP word problems (albeit their agreement and consideration that LP is useful).

Factor analysis was performed to confirm the factor structure. Principal component (with varimax) analysis to was used to show interrelationships (Tabachnick, 2001 ; Pallant, 2011 ; Pituch, 2016 ). Four constructs with eigenvalues greater than 1 accounted for 55.89% of the total variance. All items loaded significantly on four factors (enjoyment: 0.91, motivation: 0.89, value/usefulness: 0.94, and self-confidence: 0.95 with p  < 0.05, respectively). The values obtained were consistent with previous empirical findings (see Lin and Huang, 2014 , Awofala, 2014 ). The Kaiser-Meyer-Olkin measure of sampling adequacy test (KMO) and Bartlett’s test of sphericity were conducted. The value of KMO in our analysis was 0.71 > 0.60, and that of Bartlett’s Test was significant ( X 2 (760) = 13792.55, p  < 0.005) indicating a substantial correlation in the data and an acceptable fit (Nunnally and Berstain, 1994 , Pallant, 2011 ). Following the above recommendations, all items were found to be acceptable with adequate construct validity, internal consistency, and homogeneity. Overall, these items were deemed fit to measure students’ ATLPWPs in secondary schools.

Tables 1 and 2 show descriptive statistics (mean, standard deviation, skewness, and kurtosis). Important to note are students’ scores on ATMI-SF questionnaires during the pre-test and post-test. The results show no significant differences between the two groups in the pre-test and for the four scales (enjoyment, motivation, usefulness, and self-confidence). Indeed, both experimental and comparison groups were similar during the pre-test. There was however a slight change in students’ ATLPWPs due to the intervention administered to students from the experimental group (Table 3 ). The findings, however, show that students generally had a negative attitude towards learning LP word problems. These findings are consistent with other research studies (e.g., see Awofala, 2014 ). Thus, the learning of LP word problems and related mathematics concepts should be structured using multiple problem-solving techniques to boost students’ understanding and attitude.

From the correlation matrix in Table 4 above, it is evident that most of the inter-item correlations are low. This suggests that the data collected shows students’ negative attitude towards LP word problems. Students’ responses may have revealed intrinsic traits as far as the learning of LP is concerned. These findings are not in any way different from UNEB annual reports on previous students’ performance in the topic of LP. The additional qualitative data collected from senior teachers on why students elude questions on LP during internal and national examinations confirmed our investigations.

The results found no significant statistical difference between students’ ATLPMWPs, and their age (Table 5 ), gender (Table 6 ), school location (Table 7 ), school status (Table 8 ), and school ownership (Table 9 ).

Discussions, conclusions, and recommendations

This study sought to investigate the 11th-grade Ugandan students’ attitude towards LPMWPs. The psychometric properties of the adapted ATMI-SF instrument were found acceptable. We were fundamentally interested in students’ motivation, confidence, usefulness, and enjoyment in learning LP, and related mathematics word problems. These were the four main reliable latent dimensions identified through principal component factor analysis to explain the underlying students’ attitude towards LPMWPs. At first, students’ attitude towards LPMWPs for both groups (comparison and experimental groups) were not significantly different irrespective of the student’s age, gender, school status, or school location. These findings show that students generally had negative attitude towards LPMWPs. Yet, Arslan et al. ( 2014 ) show that there exists a positive significant relationship between attitude and problem-solving.

Although students’ ratings were below the neutral attitude (please see Table 2 ), they indicated the usefulness of LP in daily life. The experimental group showed a slightly favorable attitude towards LP word problems (Table 3 ) after an intervention because the active learning heuristic problem-solving instruction was applied compared to students in the comparison group who learned LP conventionally. Face-to-face interviews with some students and teachers have not been provided in this quantitative study. However, a section of students whom we interacted with revealed that LP concepts are more stimulating, require prior conceptual knowledge and understanding of equations and inequalities and that these questions are not interesting to learn in comparison to other topics in mathematics. Our findings concord with Chen et al. ( 2018 ) who postulated that positive attitude influences early career performance.

The explanation provided indicated that some teachers either teach this topic hurriedly towards national examinations or some of them avoid teaching it completely. This means teachers have not adequately applied instructional techniques and suitable learning materials to fully explain the concepts of LP to the students. However, it was observed that teachers encouraged students to constantly practice model formation from word problem statements to demystify the negative belief that LP word problems are hard for students to conceptualize. Negative beliefs limit students’ understanding, thereby making them fear the topic and consequently develop a negative attitude towards learning LP. However, students’ attitudes towards LPMWPs from the experimental group slightly improved compared to their counterparts from the comparison group who almost had a similar attitude towards LP before and after an intervention.

Participants from the experimental group and the comparison groups acknowledged the fact that LP is a challenging topic, although they highly recognized its significance in constructing models, and in developing models for optimization in real-life scenarios. The importance of LP rests in its application and thus teachers were tasked to help learners to develop a positive attitude towards, and their conceptual understanding so that they can reason insightfully, think logically, critically and, coherently. The teachers’ competence in applying instructional strategies helped learners from the experimental group to gain deeper and broader insight, conceptual and procedural understanding, reasoning, and positive attitude towards LPMWPs. As Mazana et al. ( 2018 ) noted, aspects of attitude (motivation, confidence, value, increased anxiety and enjoyment) enhance students’ learning and hence performance. The control group, however, in their conventional instruction still perceived LP as one of the hardest topics. A negative attitude was observed in this particular group of students as indicated in the results of most learners’ ATMI-SF questionnaires.

Thus, teachers recognized that hard work and application of prior conceptual knowledge and understanding may favorably help students to develop a positive attitude and perform better. Generally, students seemed not to have adequately developed the knowledge of logical thinking and reasoning of basic and prior LP concepts to aid in learning LP. They did not view the learning of LP from a broader perspective beyond passing national examinations at UCE. The results of this study are likely to inform educational stakeholders in assessing students’ ATLPWPs and provide remediation and interventional strategies aimed at creating a conceptual change in students’ attitudes towards learning LP and related topics. This will further act as a lens in examining the relationships between students’ achievement and their attitude toward learning specific mathematics concepts, as indicators of students’ confidence, motivation, usefulness, and enjoyment in learning LP word problems and mathematics generally.

The study findings also point to important issues and may provide insight to the educational stakeholders in cultivating an early positive attitude in mathematics, aimed at investigating students’ challenges in specific topics from primary to secondary school mathematics. This may be a potential strategy for applying different active learning heuristic problem-solving approaches and methods to significantly improve students’ attitude and performance. The active learning heuristic problem-solving approach is likely to support collaboration and discussions between teachers and amongst students themselves during the learning process. The findings show that most students from the experimental group worked collaboratively in their small groups and individually hence the conceptual and attitudinal change. The students helped and guided each other during peer teaching, hence boosting their attitude. As noted by Asempapa ( 2022 ), suitable teachers’ instructional strategies that emphasize individual students’ academic differences may change students’ attitude towards LPMWPs, thereby providing both academic and social support.

Consequently, the low performers gained conceptual understanding, morale, and problem-solving strategies, hence positive attitude towards learning. This further enhanced students’ learning and attitude towards mathematics and LP in particular. Besides, the active learning heuristic problem-solving approach applied to the experimental group boosted students’ confidence in answering both routine and non-routine LP problems. Students’ fear of comprehending LP word problems and attempting to answer LP questions decreased. Moreover, the heuristic problem-solving approach boosted students’ attitude towards LPMWPs. Students were actively involved in problem-solving. This gradually built their motivation, competence, and confidence in learning LP and related concepts. This generally and significantly fostered students’ positive attitude towards LPMWPs.

Limitations of the study and future research directions

The purpose of this research was to explore students’ attitude towards LPMWPs. The findings provide preliminary insights into the fundamental concepts of the introduction of LP for supporting the learning of advanced mathematics. Our key observation is that the present study involved schools from two regions (Eastern Uganda and Central Uganda), and the study was specifically conducted in two districts (Mukono and Mbale). Yet, there are at least 120 districts in Uganda. Hence, the sample may not adequately represent all the 11th grade Ugandan students. Future studies should consider the inclusion of sampled students from all districts. While the quantitative study is important and valuable for yielding robust and comprehensive data in social sciences research, its limitations must be acknowledged. Triangulation of data collection and analysis methods might have yielded additional results. We, therefore, recommend future studies in different or similar settings and contexts, and in different mathematics topics (content) with a diversity of methods to compare and contrast our findings and to gain deeper and broader insights into students’ attitude towards LPMWPs.

Students’ attitudes point to issues related to demographic variables and latent constructs for learning mathematics. Specifically, to gain more insight, this research recommends that future researchers should use qualitative methods such as interviews and observation to provide more evidence on students’ experiences in learning LP. The teachers ‘attitude towards LPMWPs is also a potential area for further investigation aimed at improving the instructional strategies, pedagogical content knowledge, and mathematical knowledge for teaching. To achieve this, the teachers’ professional development programs should be enacted to emphasize content knowledge and pedagogical content knowledge of learning LPMWPs. Teachers coming together to share learning experiences and strategies, may improve students’ attitude towards learning LP, and other related but challenging topics. Indeed, teachers need continuous routine professional development support to successfully implement the learning activities. Despite some limitations, this study supplements other empirical shreds of evidence in support of enhancing students’ attitude towards learning mathematics word problems, and LP in particular.

Data availability

All the data analyzed and reported in this study is available and may be accessed on request.

Aiken LR (1970) Attitudes toward Mathematics. Rev Educ Res 40(4):551–596

Article   ADS   Google Scholar  

Abdullah N, Halim L, Zakaria E (2014) VStops: a thinking strategy and visual representation approach in mathematical word problem solving toward enhancing STEM literacy. Eurasia J Math Sci Technol Educ 10(3):165–174. https://doi.org/10.12973/eurasia.2014.1073a

Article   Google Scholar  

Aboelmagd YMR (2018) Linear programming applications in construction sites. Alex Eng J 57(4):4177–4187. https://doi.org/10.1016/j.aej.2018.11.006

Ahmad A, Tarmizi RA, Nawawi M (2010) Visual representations in mathematical word problem solving among form four students in Malacca. Procedia Soc Behav Sci 8:356–361. https://doi.org/10.1016/j.sbspro.2010.12.050

Arslan C, Yavuz G, Deringol-Karatas Y (2014) Attitudes of elementary school students towards solving mathematics problems. Procedia Soc Behav Sci 152:557–562. https://doi.org/10.1016/j.sbspro.2014.09.243

Asempapa RS (2022) Examining practicing teachers‘ knowledge and attitudes toward mathematical modeling. Int J Educ Math Sci Technol (IJEMST) 10(2):272–292. https://doi.org/10.46328/ijemst.2136

Avcu R, Avcu S (2015) Utley geometritutumölçeğinintürkçeuyarlaması: Geçerlikvegüvenirlikçalışması. EgitimArastirmalari Eurasian J Educ Res 15(58):89–112. https://doi.org/10.14689/ejer.2015.58.1

Awofala AOA (2014) Examining personalization of instruction, attitudes toward and achievement in mathematics word problems among Nigerian Senior Secondary School Students. Int J Educ Math Sci Technol 2(4):273. https://doi.org/10.18404/ijemst.91464

Ayebo A, Bright J, Ballam C (2019) Examining the factor structure of the survey of attitudes towards statistics among undergraduate health science students. Int Electron J Math Educ 15(1):1–8. https://doi.org/10.29333/iejme/5942

Bäckström M, Björklund F (2013) Social desirability in personality inventories: Symptoms, diagnosis and prescribed cure. Scand J Psychol 54(2):152–159. https://doi.org/10.1111/sjop.12015

Barbara G, Tabachnick LSF (2001) Using multivariate statistics, 2nd edn. Pearson. p. 163

Barmby P, Kind PM, Jones K (2008) Examining changing attitudes in secondary school science. Int J Sci Educ 30(8):1075–1093. https://doi.org/10.1080/09500690701344966

Bayaga A, Wadesango N (2014) Analysis of students’ attitudes on mathematics achievement-factor structure approach. Int J Educ Sci 6(1):45–50. https://doi.org/10.1080/09751122.2014.11890116

Bazzini L, Tsamir P(2004) Algebraic equations and inequalities: issues for research and teaching. In: Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education. vol. I. pp. 137–166

Berger N, Mackenzie E, Holmes K (2020) Positive attitudes towards mathematics and science are mutually beneficial for student achievement: a latent profile analysis of TIMSS 2015. Aust Educ Res 47(3):409–444. https://doi.org/10.1007/s13384-020-00379-8

Boonen AJH, de Koning BB, Jolles J, van der Schoot M (2016) Word problem solving in contemporary math education: a plea for reading comprehension skills training. Front Psychol 7. https://doi.org/10.3389/fpsyg.2016.00191

Byrne BM (2010) Basic Concepts, Applications, and Programming Second Edition Structural Equation Modeling with AMOS

Camacho M, Socas MM, Hernandez J (1998) An analysis of future mathematics teachers’ conceptions and attitudes towards mathematics. Int J Math Educ Sci Technol 29(3):317–324. https://doi.org/10.1080/0020739980290301

Chen L, Bae SR, Battista C, Qin S, Chen T, Evans TM, Menon V (2018) Positive attitude toward math supports early academic success: behavioral evidence and neurocognitive mechanisms. Psychol Sci 29(3):390–402. https://doi.org/10.1177/0956797617735528

Chun C, Eric M (2011). Primary 6 Students’ attitudes towards mathematical problem-solving in a problem-based learning setting Chan Chun Ming Eric National Institute of Education, Nanyang Technological University , Singapore. vol. 13(1), pp. 15–31

Code W, Merchant S, Maciejewski W, Thomas M, Lo J (2016) The Mathematics Attitudes and Perceptions Survey: an instrument to assess expert-like views and dispositions among undergraduate mathematics students. Int J Math Educ Sci Technol 47(6):917–937. https://doi.org/10.1080/0020739X.2015.1133854

Colussi CF, Cristina M, Calvo M, Fernando S, de Freitas T (2013) The linear programming to evaluate the performance of oral health in primary care A Programação Linear naavaliação do desempenho da. SaúdeBucalnaAtençãoPrimária 11(55 48):95–101

Google Scholar  

Creswell JW (2014) Research design: qualitative, quantitative, and mixed methods approaches. (4th edn.). SAGE Publications India Pvt. Ltd. B

Creswell JW, Plano Clark VL (2018) Designing and conducting mixed methods research, 3rd ed. SAGE, Los Angeles, CA

Curran PJ, West SG, Finch JF (1996) Psychological methods. The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis (Vol. 1). Psychological Association, Inc

Davadas SD, Lay YF (2020) Contributing factors of secondary students’ attitude towards mathematics. Eur J Educ Res 9(2):489–498. https://doi.org/10.12973/eu-jer.9.2.489

Di Martino P, Zan R (2011) Attitude towards mathematics: a bridge between beliefs and emotions. ZDM Int J Math Educ 43(4):471–482. https://doi.org/10.1007/s11858-011-0309-6

Djamba YK, Neuman WL (2002). Social research methods: qualitative and quantitative approaches. In: Teaching Sociology. vol. 30, issue 3. Sage

van Dooren W, Lem S, de Wortelaer H, Verscha L (2018). Improving realistic word problem-solving by using humor. June. https://doi.org/10.1016/j.jmathb.2018.06.008

Estrada A, Batanero C (2019) Prospective primary school teachers’ attitudes towards probability and its teaching. Int Electron J Math Educ 15(1):1–14. https://doi.org/10.29333/iejme/5941

Evans D, Field AP (2020) Mathematics attitudes, school affect and teacher characteristics as predictors of mathematics attainment trajectories in primary and secondary education: predictors of mathematics trajectories. Royal Society Open Science, 7(10). https://doi.org/10.1098/rsos.200975

Fennema E, Sherman JA (1976) Fennema-Sherman mathematics attitudes scales: instruments designed to measure attitudes toward the learning of mathematics by females and males. J Res Math Educ 7(5):324. https://doi.org/10.2307/748467

Fernández E, Molina M (2017) Secondary students’ implicit conceptual knowledge of algebraic symbolism. An exploratory study through problem posing. Int Elecron J Math Educ 12(9):799–826

Fielding-Wells J, O’Brien M, Makar K (2017) Using expectancy-value theory to explore aspects of motivation and engagement in inquiry-based learning in primary mathematics. Math Educ Res J 29(2):237–254. https://doi.org/10.1007/s13394-017-0201-y

Gagatsis A, Kyriakides L (2000) Teachers’ attitudes towards their pupils’ mathematical errors. Educ Res Eval 3611(May). https://doi.org/10.1076/1380-3611(200003)6

Gardner PL (1975) Attitudes to science: a review. Stud Sci Educ 2(1):1–41. https://doi.org/10.1080/03057267508559818

Georgiou SN, Stavrinides P, Kalavana T (2007) Is victor better than Victoria at maths? Educ Psychol Pract 23(4):329–342. https://doi.org/10.1080/02667360701660951

Goulet-Lyle MP, Voyer D, Verschaffel L (2020) How does imposing a step-by-step solution method impact students’ approach to mathematical word problem-solving? ZDM Math Educ 52(1):139–149. https://doi.org/10.1007/s11858-019-01098-w

Grootenboer P, Hemmings B (2007) Mathematics performance and the role played by affective and background factors. Math Educ Res J19(3):3–20

Haghverdi M, Semnani AS, Seifi M (2012) The relationship between different kinds of students’ errors and the knowledge required to solve mathematics word problems. Bolema 26(42B):649–665

Hair Jr JF, Black William C, Babbin Barry J, Anderson Rolph E (2010) Multivariate data analysis (7th edn). Pearson Prentice Hall, Upper Saddle River, NJ

Hannula MS (2002) Attitude towards mathematics: emotions, expectations, and values. Educ Studi Math 49(1):25–46. https://doi.org/10.1023/A:1016048823497

Heydari M, Othman F, Qaderi K, Noori M, Parsa AS (2015) Introduction to linear programming as a popular tool in optimal reservoir operation, a review. Adv Environ Biol 9(3):906–917. https://doi.org/10.5281/zenodo.18254

Hwang S, Son T (2021) Students’ attitude towards mathematics and its relationship with mathematics achievement. J Educ E-Learn Res 8(3):272–280. https://doi.org/10.20448/JOURNAL.509.2021.83.272.280

Julius E, Abdullah AH, Suhairom N (2018) Attitude of students towards solving problems in algebra: a review of nigeria secondary schools. IOSR J Res Method Educ 8(1):26–31. https://doi.org/10.9790/7388-0801032631

Jupri A, Drijvers P (2016) Student difficulties in mathematizing word problems in Algebra. Eurasia J Math Sci Technol Educ 12(9):2481–2502. https://doi.org/10.12973/eurasia.2016.1299a

Karjanto N (2017) Attitude toward mathematics among the students at Nazarbayev University Foundation Year Programme. Int J Math Educ Sci Technol 48(6):849–863. https://doi.org/10.1080/0020739X.2017.1285060

Kasimu O, Imoro M (2017) Students’ attitudes towards mathematics: The case of private and public junior high schools in the East Mamprusi District. Ghana Osman. J Res Method Educ 7(5):38–43. https://doi.org/10.9790/7388-0705063843

Kempa RF, McGough JM (1977) A study of attitudes towards mathematics in relation to selected student characteristics. Br J Educ Psychol 47(3):296–304. https://doi.org/10.1111/j.2044-8279.1977.tb02358.x

Kenney R, An T, Kim SH, Uhan NA, Yi JS, Shamsul A (2020) Linear programming models: identifying common errors in engineering students’ work with complex word problems. Int J Sci Math Educ 18(4):635–655. https://doi.org/10.1007/s10763-019-09980-5

Khavenson T, Orel E, Tryakshina M (2012) Adaptation of Survey of Attitudes Towards Statistics (SATS 36) for Russian Sample. Procedia Soc Behav Sci 46(Sats) 36:2126–2129. https://doi.org/10.1016/j.sbspro.2012.05.440

Kline Rex B (1998) Principles and practice of structural equation modeling. 4th edn. Guilford Press, New York

Latkin CA, Edwards C, Davey-Rothwell MA, Tobin KE (2017) The relationship between social desirability bias and self-reports of health, substance use, and social network factors among urban substance users in Baltimore, Maryland. Addict Behav 73:133–136. https://doi.org/10.1016/j.addbeh.2017.05.005

Lim SY, Chapman E (2013) Development of a short form of the attitudes toward mathematics inventory. Educ Stud Math 82(1):145–164. https://doi.org/10.1007/s10649-012-9414-x

Li M, Zhang Y, Liu H, Hao Y (2018) Gender differences in mathematics achievement in Beijing: a meta-analysis. Br J Educ Psychol 88(4):566–583. https://doi.org/10.1111/bjep.12203

Lin S, Huang Y (2014) Development and application of a Chinese version of the short attitudes toward mathematics inventory. Int J Sci Math Educ 14(1):193–216. https://doi.org/10.1007/s10763-014-9563-8

Lipnevich AA, MacCann C, Krumm S, Burrus J, Roberts RD (2011) Mathematics attitudes and mathematics outcomes of U.S. and Belarusian middle school students. J Educ Psychol 103(1):105–118. https://doi.org/10.1037/a0021949

Ma X (1997) Assessing the Relationship Between Attitude Toward Mathematics and Achievement in Mathematics: A Meta-Analysis. J Res Math Educ 28(1)

Maamin M, Maat SM, Iksan ZH (2022) The influence of student engagement on mathematical achievement among secondary school students. Mathematics 10(1). https://doi.org/10.3390/math10010041

Marchis I (2011) Factors that influence secondary school students’ attitude to mathematics. Procedia Soc Behav Sci 29:786–793. https://doi.org/10.1016/j.sbspro.2011.11.306

Mazana MY, Montero CS, Casmir RO (2018). Investigating students’ attitude towards learning mathematics. Int Electron J Math Educ 14(1). https://doi.org/10.29333/iejme/3997

Meyer J, Fleckenstein J, Köller O (2019) Expectancy value interactions and academic achievement: differential relationships with achievement measures. Contemp Educ Psychol 58:58–74. https://doi.org/10.1016/j.cedpsych.2019.01.006

Meara NO, Prendergast M, Cantley I, Harbison L, Meara NO, Prendergast M, Cantley I, Harbison L (2019) Teachers’ self-perceptions of mathematical knowledge for teaching at the transition between primary and post-primary school. Int J Math Educ Sci Technol, 1464–5211. https://doi.org/10.1080/0020739X.2019.1589004

Molina M, Rodríguez-Domingo S, Cañadas MC, Castro E (2017) Secondary school students’ errors in the translation of algebraic statements. Int J Sci Math Educ 15(6):1137–1156. https://doi.org/10.1007/s10763-016-9739-5

Mulhern F, Rae G (1998) Development of a shortened form of the Fennema-Sherman mathematics attitudes scales. Educ Psychol Meas 58(2):295–306. https://doi.org/10.1177/0013164498058002012

Mumcu HY, Aktaş MC (2015) Multi-program high school students’ attitudes and self-efficacy perceptions toward mathematics. Eurasian J Educ Res 15(59):207–226. https://doi.org/10.14689/ejer.2015.59.12

NCDC (2008) Ministry of education and sports. Mathematics teaching syllabus for Uganda Certificate of Education. Kampala, Uganda

NCDC (2018) The lower secondary curriculum: mathematics syllabus. Kampala, Uganda

Nunnally J, Berstain I (1994). Psychometric theory (3rd ed.). In: Applied psychological measurement. vol. 19, Sage. pp. 570–572

Norton SJ (1998) Students’ Attitude towards Mathematics in Single-Sex and Coeducational Schools. Math Educ Res J, 10(1)

Olusegun S (2015) Constructivism learning theory: a paradigm for teaching and learning. J Res Method Educ 5(6):66–70. https://doi.org/10.9790/7388-05616670

Opolot-okurut C (2010) Classroom learning environment and motivation towards mathematics among secondary school students in Uganda, 267–277. https://doi.org/10.1007/s10984-010-9074-7

Ozdemir E, Ovez FTD (2012) A research on proof perceptions and attitudes towards proof and proving: some implications for elementary mathematics prospective teachers. Procedia Soc Behav Sci 46:2121–2125. https://doi.org/10.1016/j.sbspro.2012.05.439

Pallant J (2011) SPSS survival manual. J Adv Nurs 352. https://doi.org/10.1046/j.1365-2648.2001.2027c.x

Parlesak A, Tetens I, Smed S, Rayner M, Darmon N, Robertson A, Gabrijel M (2016) Use of linear programming to develop cost-minimized nutritionally adequate health-promoting food baskets. 27, 1–19. https://doi.org/10.1371/journal.pone.0163411

Pearce DL, Bruun F, Skinner K (2011) What teachers say about student difficulties solving mathematical word problems in grades 2–5. Int Electron J Math Educ 8(1):3–19

Pepin B (2011) Pupils’ attitudes towards mathematics: A comparative study of Norwegian and English secondary students. ZDM Int J Math Educ 43(4):535–546. https://doi.org/10.1007/s11858-011-0314-9

Pituch KA, Stevens JP (2016). Applied multivariate statistics for the social sciences: analyses with SAS and IBM’s SPSS. Routledge

Pongsakdi N, Laakkonen E, Laine T, Veermans K, Hannula-Sormunen MM, Lehtinen E (2019) The role of beliefs and motivational variables in enhancing word problem solving. Scand J Educ Res 63(2):179–197. https://doi.org/10.1080/00313831.2017.1336475

Polya G (2004) “How to Solve It” A new aspect of mathematical method. In PressPrinceton, NJ: Princeton University Press. https://doi.org/10.2307/j.ctvc773pk.6

Primi C, Bacherini A, Beccari C, Donati MA (2020) Assessing math attitude through the attitude toward mathematics inventory–short form in introductory statistics course students. Stud Educ Eval 64. https://doi.org/10.1016/j.stueduc.2020.100838

Quaye J (2015) Exploring students’ attitudes towards mathematics and mathematical achievement in secondary schools in England: the role of social class, gender, and ethnicity. Res Math Educ 17(1):59–60. https://doi.org/10.1080/14794802.2014.971340

Romeijn HE, Ahuja RK, Dempsey JF (2006) A new linear programming approach to radiation therapy. Treat Plan Prob 54(2):201–216. https://doi.org/10.1287/opre.1050.0261

Article   MATH   Google Scholar  

Sa’ad TU, Adamu A, Sadiq MA (2014) The causes of poor performance in mathematics among public senior secondary school students in Azare Metropolis of Bauchi State, Nigeria. J Res Method Educ 4(6):32–40. https://doi.org/10.9790/7388-04633240

Sandman RS (1980) The mathematics attitude inventory: instrument and user’s manual. J Res Math Educ 11(2):148–149. http://www.jstor.org/stable/748906

Selkirk J (1975) An inquiry into adverse attitudes towards advanced level mathematics. Int J Math Educ Sci Technol 6(2):181–186. https://doi.org/10.1080/0020739750060206

Sherman J (1979) Predicting mathematics performance in high school girls and boys. Am Psychol Assoc 71(2):242–249

Sherman JA (1980) Predicting mathematics grades of high school girls and boys: a further study. Contemp Educ Psychol 5:249–255

Strohmaier AR, Schiepe-Tiska A, Chang YP, Müller F, Lin FL, Reiss KM (2020) Comparing eye movements during mathematical word problem-solving in Chinese and German. ZDM Math Educ 52(1):45–58. https://doi.org/10.1007/s11858-019-01080-6

Stein MK, Smith MS, Henningsen M, Silver EA (2000) Implementing standards-based mathematics instruction: A casebook for professional development, 53(9)

Tahar NF, Ismail Z, Zamani ND, Adnan N (2010) Students’ attitude toward mathematics: the use of factor analysis in determining the criteria. Procedia Soc Behav Sci 8:476–481. https://doi.org/10.1016/j.sbspro.2010.12.065

Tapia M (1996) The attitudes towards mathematics instrument. Annual Meeting of the Mid-South Educational Research Association 21:ED419696

Tabachnick BG, Fidell LS (2001) Using Multivariate Statistics 2nd Edition. https://doi.org/10.1037/022267

Townsend M, Wilton K (2003) Evaluating change in attitude towards mathematics using the “then-now” procedure in a cooperative learning program. Br J Educ Psychol 73(4):473–487. https://doi.org/10.1348/000709903322591190

Tsamir P, Almog N (2001) Students’ strategies and difficulties: the case of algebraic inequalities. Int J Math Educ Sci Technol 32(4):513–524. https://doi.org/10.1080/00207390110038277

Tsamir P, Bazzini L (2004) Consistencies and inconsistencies in students’ solutions to algebraic ‘single-value’ inequalities. Int J Math Educ Sci Technol 35(6):793–812. https://doi.org/10.1080/00207390412331271357

Tsamir P, Bazzini L (2006) Consistencies and inconsistencies in students’ solutions to algebraic ‘single-value’ inequalities. Int J Math Educ Sci Technol November 2014:37–41. https://doi.org/10.1080/00207390412331271357

Tsamir P, Tirosh D (2006) Summing up and looking ahead: a personal perspective on infinite sets. Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education 1:49–63

Ültanır E (2012). An epistemological glance at the constructivist approach: constructivist learning in Dewey, Piaget, and Montessori. Int J Instruct, 5(2), www.e-iji.net

UNEB (2016) Uganda National Examinations Board, report on work of Uganda certificate of examinations candidates. Kampala, Uganda

UNEB (2018) Uganda National Examinations Board, report on work of Uganda Certificate of Examinations candidates. Kampala, Uganda

UNEB (2019) Uganda National Examinations UNEB. (2019). Uganda National Examinations Board, report on work of Uganda Certificate of Examinations candidates. Kampala, Uganda

UNEB (2020) Uganda National Examinations Board UNEB. (2020). Uganda National Examinations Board, report on work of Uganda Certificate of Examinations candidates. Kampala, Uganda

Utley J (2007) Construction and validity of geometry attitude scales. School Sci Math 107(3):89–93. https://doi.org/10.1111/j.1949-8594.2007.tb17774.x

Utsumi MC, Mendes CR (2000) Researching the attitudes towards mathematics in basic education. Educ Psychol 20(2):237–243. https://doi.org/10.1080/713663712

Vanderbei RJ (2014) Linear programming foundations and extensions (4th edn.). In: International Series in Operations Research & Management Science. Springer

Verschaffel L, Schukajlow S, Star J, van Dooren W (2020a) Word problems in mathematics education: a survey. ZDM Math Educ 52(1):1–16. https://doi.org/10.1007/s11858-020-01130-4

Verschaffel L, Schukajlow S, Star J, van Dooren W (2020b). Word problems in mathematics education: a survey. ZDM Math Educ 52(1). https://doi.org/10.1007/s11858-020-01130-4

Verschaffel L, van Dooren W, Greer B, Mukhopadhyay S (2010) Die Rekonzeptualisierung von TextaufgabenalsÜbungen in mathematischerModellierung. J Fur Mathematik-Didaktik 31(1):9–29. https://doi.org/10.1007/s13138-010-0007-x

Wigfield A (1994) Expectancy-value theory of achievement motivation: a developmental perspective. Educ Psychol Rev 6(1):49–78

Wigfield A, Eccles JS (2000) Expectancy-value theory of achievement motivation. Contemp Educ Psychol 25(1):68–81. https://doi.org/10.1006/ceps.1999.1015

Article   CAS   Google Scholar  

Yáñez-Marquina L, Villardón-Gallego L (2016) Attitudes towards mathematics at secondary level: development and structural validation of the Scale for Assessing Attitudes towards Mathematics in Secondary Education (SATMAS). Electron J Res Educ Psychol 14(3):557–581. https://doi.org/10.14204/ejrep.40.15163

Yasar M (2016) High school students’ attitudes towards mathematics. Eurasia J Math Sci Technol Educ 12(4):931–945. https://doi.org/10.12973/eurasia.2016.1571a

Yurt E (2015) Understanding middle school students’ motivation in math class: the expectancy-value model perspective. Int J Educ Math Sci Technol 3(4):288–297

Zan R, Brown L, Evans J, Hannula MS (2006) Affect in mathematics education: an introduction. Educ Stud Math 63(2):113–121. https://doi.org/10.1007/s10649-006-9028-2

Download references

Acknowledgements

This research is part of the Ph.D. Thesis that investigated the effect of active learning heuristic problem-solving approach on students’ achievement and attitude towards mathematics word problems (LP) from sampled secondary schools in Uganda. The research was funded by the African Centre of Excellence for Innovative Teaching and Learning Mathematics and Science (ACEITLMS), [ACEII (P151847)]. We appreciate the useful information provided by the students and teachers in the study sample, which helped us write this research article. The views expressed herein are those of the authors and not necessarily those of ACEITLMS. This is because the ACEITLMS was not involved in identifying the suitable study design, methods of data collection and analysis, publication decision, or manuscript preparation.

Author information

Authors and affiliations.

African Centre of Excellence for Innovative Teaching and Learning Mathematics and Science (ACEITLMS), University of Rwanda, College of Education (UR-CE), P.O Box 55, Rwamagana (Kigali), Rwanda

Robert Wakhata

College of Education (CE), University of Rwanda (UR), P.O Box 55, Rwamagana (Kigali), Rwanda

Védaste Mutarutinya

Department of Educational Foundations and Psychology, Mbarara University of Science and Technology, P.O Box 1410, Mbarara, Uganda

Sudi Balimuttajjo

You can also search for this author in PubMed   Google Scholar

Contributions

RW: Conceptualization, design of suitable methodology, investigation, software, visualization, data analysis, and/or interpretation, preparation and writing of original draft, reviewing and revising it critically for important intellectual content, and final approval of the version to be published. VM and SB: Supervision, writing, reviewing, editing and final approval of the version to be published.

Corresponding author

Correspondence to Robert Wakhata .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Ethical approval

Ethical clearance and approval were sought and granted by the Research and Ethics committee at the corresponding authors’ university. Thus, all procedures involving human participants were respected and were streamlined following the ethical standards of the University’s Directorate of research and ethics committee. Subsequent permission was sought and granted by the Ministry of Education and Sports, the district education officers, and finally the headteachers of sampled secondary schools.

Informed consent

All participants were informed and clearly explained to the purpose of the study. They were assured of confidentiality and, anonymity before they willingly signed the informed written consent form. The questionnaires were administered to the respondents during school working hours without interfering with the school-set timetable. Participants who opted not to participate in this research even after the distribution of questionnaires were allowed to withdraw. In addition, the consent form included the contact (s) of the principal researcher for further inquiries.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary materials for exploring students' attitude towards mathematics word problems, rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Cite this article.

Wakhata, R., Mutarutinya, V. & Balimuttajjo, S. Secondary school students’ attitude towards mathematics word problems. Humanit Soc Sci Commun 9 , 444 (2022). https://doi.org/10.1057/s41599-022-01449-1

Download citation

Received : 06 April 2022

Accepted : 16 November 2022

Published : 10 December 2022

DOI : https://doi.org/10.1057/s41599-022-01449-1

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

• Help & FAQ

Student attitudes towards learning mathematics through challenging, problem solving tasks: “It’s so hard–in a good way”

Research output : Contribution to journal › Article › Research › peer-review

• mathematics education
• student attitudes
• problem solving
• self-determination theory

Access to Document

• 10.26822/iejee.2021.185 Licence: CC BY-NC-ND
• 330313090-oa Final published version, 241 KB Licence: CC BY-NC-ND

T1 - Student attitudes towards learning mathematics through challenging, problem solving tasks

T2 - “It’s so hard–in a good way”

AU - Russo, James

AU - Minas, Michael

PY - 2020/12

Y1 - 2020/12

N2 - Despite a focus on teaching mathematics through challenging, problem solving tasks, there has been limited research into student attitudes towards these learning experiences. To address this gap in the literature, we asked 52 Australian primary students who had recently experienced mathematics taught in this manner to convey their feelings about learning through problem solving. Adopting a qualitative, exploratory, research design, student participants completed a brief questionnaire, and a sub-set also contributed to follow-up focus groups. Thematic analysis of the questionnaire data revealed that three-quarters of students reported unambiguously positive attitudes towards problem solving, most others were ambivalent, and no students expressed negative attitudes. Younger students (Year 3/4) were more likely to express positive attitudes than older students (Year 5/6) and boys more likely to express positive attitudes than girls. Positive attitudes arose from students enjoying learning through problem solving, the perception that it supported their learning, and students thriving on challenge. Follow-up focus groups also reinforced the power of working collaboratively, particularly the importance of learning through discussions with peers, and opportunities to explore authentic and purposeful tasks. The findings help explain why students frequently have positive reactions to learning mathematics through problem solving.

AB - Despite a focus on teaching mathematics through challenging, problem solving tasks, there has been limited research into student attitudes towards these learning experiences. To address this gap in the literature, we asked 52 Australian primary students who had recently experienced mathematics taught in this manner to convey their feelings about learning through problem solving. Adopting a qualitative, exploratory, research design, student participants completed a brief questionnaire, and a sub-set also contributed to follow-up focus groups. Thematic analysis of the questionnaire data revealed that three-quarters of students reported unambiguously positive attitudes towards problem solving, most others were ambivalent, and no students expressed negative attitudes. Younger students (Year 3/4) were more likely to express positive attitudes than older students (Year 5/6) and boys more likely to express positive attitudes than girls. Positive attitudes arose from students enjoying learning through problem solving, the perception that it supported their learning, and students thriving on challenge. Follow-up focus groups also reinforced the power of working collaboratively, particularly the importance of learning through discussions with peers, and opportunities to explore authentic and purposeful tasks. The findings help explain why students frequently have positive reactions to learning mathematics through problem solving.

KW - mathematics education

KW - student attitudes

KW - problem solving

KW - self-determination theory

U2 - 10.26822/iejee.2021.185

DO - 10.26822/iejee.2021.185

M3 - Article

SN - 1307-9298

JO - International Electronic Journal of Elementary Education

JF - International Electronic Journal of Elementary Education

Students’ attitude towards use of ICT as tool of learning: a structural equation modelling (SEM) approach

• Original Paper
• Published: 22 May 2024
• Volume 4 , article number  103 , ( 2024 )

Cite this article

• Tasfia Zahan Ria 1 ,
• M. Zakir Saadullah Khan   ORCID: orcid.org/0000-0001-7584-4951 1 &
• Utpal Kumar De   ORCID: orcid.org/0000-0001-6444-0126 2  

22 Accesses

Explore all metrics

This paper assessed the students’ attitudes towards the use of ICT as a tool of learning by using the technology acceptance model. Primary data has been collected from six public and private universities in Bangladesh collected on perceived enjoyment, self-efficacy, ease of use, usefulness, and attitude towards ICT. The study used the technology acceptance model (TAM) and used the structural equation model (SEM) for statistical analysis. The data’s reliability and adequacy were assessed using KMO, Bartlett’s test, and Cronbach’s alpha. Confirmatory factor analysis (CFA) was used to examine the relationship between observed variables and latent variables. The reliability and validity of the model were also assessed using estimating composed reliability (CR) and average variable extraction (AVE). The study used a structural equation model to examine the relationship between constructs and covariance analysis. The results showed that the sample was adequate and the data was valid and reliable. The CFA model was a good fit, and the observed variable positively relates to the constructs. The study found that two external variables indirectly influence students’ attitudes towards ICT use, but perceived ease of use and self-efficacy had a direct and positive impact on perceived usefulness. These variables positively and significantly influence students’ attitudes towards ICT as a learning tool.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Similar content being viewed by others

Evaluating the intention to use ict collaborative tools in a social constructivist environment.

Investigating students’ intentions to use ICT: A comparison of theoretical models

Are Future Teachers Ready to Be the ICT Change Agents?

Statements and declarations.

This is to declare that this manuscript has not been published previously (in the form of an abstract, or a published lecture or academic thesis), and is not under consideration for publication elsewhere. Its publication is approved by all authors and that, if accepted, it will not be published elsewhere in the same form, in English or in any other language, including electronically without the written consent of the copyright-holders.

Data availability

Data may be available on reasonable request.

Code availability

Not Applicable.

Afshari M, Ghavifekar S, Siraj S, Jing D (2013) Students’ attitude towards computer assisted language learning. Proc Soc Behav Sci 103:852–859

Article   Google Scholar  

Agarwal D, Ahuja S (2013) Attitude of student-teachers towards the use of ICT and its impact on their academic achievement. Indian J Appl Res 3(7):186–187

Ajzen I (1991) The theory of planned behavior. Organizational Beha Human Decis Processes 50(2):179–211

Alghazo I (2006) Student attitudes toward web-enhanced instruction in an educational technology course. Coll Stud J 40(3):620–630

Google Scholar  

Alsamydai, M. J. (2014). Adaptation of the Technology Acceptance Model (TAM) to the Use of Mobile Banking Services. International Review of Management and Business Research, 3(4), 2039-2051.

Anderson JC, Gerbing DW (1988) Structural equation modeling in practice: a review and recommended two-step approach. Psychol Bull 103(3):411

Boomsma A (1982) The robustness of LISREL against small sample sizes in factor analysis models. North-Holland, Amsterdam

Boomsma A (1985) Nonconvergence, improper solutions and starting values in LISREL maximum likelihood estimation. Psychometrika 52:345–370

Browne MW, Cudeck R (1992) Alternative ways of assessing model fit. Sociol Methods Res 21(2):230–258

Byrne BM (1994) Structural equation modeling with EQS and EQS/ windows. Sage Publications, Thousand Oaks, CA

Chau PYK (1996) An empirical assessment of a modified technology acceptance model. J Manage Inf Syst 13:185-204

Cheung R, Vogel D (2013) Predicting user acceptance of collaborative technologies: an extension of the technology acceptance model for E-learning. Comput Educ 63(0):160–175

Conole G, De L, Dillon M, Darby J (2006) JISC LXP: student experiences of technologies, draft find report. https://www.yumpu.com/en/document/read/23670065/student-experiences-of-technologies-draft-final-report-jisc

Davis FD (1989) Perceived usefulness, perceived ease of use, and user acceptance of information technology. MIS Quarterly 13(3):319–340

Davis FD, Bagozzi RP, Warshaw PR (1992) Extrinsic and intrinsic motivation to use computers in the workplace. J Appl Social Psychol 22(14):1111–1132

Davis FD, Bagozzi RP, Warshaw PR (1989) User acceptance of computer technology: a comparison of two theoretical models. Manage Sci 35(8):982–1003

Edmunds R, Thorpe M, Conole G (2012) Students’ attitude towards and use of ICT in course study, work and social activity: a technology acceptance model. Br J Educ Technol 43(1):71–84

Ernst CPH, Wedel K, Rothlauf F (2014) Students’ acceptance of E-learning technologies: combining the technology acceptance model with the didactic circle. Twentieth Americas conference on information systems

Fco J, Garcia C (2001) An instrument to help teachers assess learners’ attitudes towards multimedia instruction. J Educ 122(1):94–102

Fishbein, M. (1980). Theory of reasoned action: Some applications and implications. InH.Howe&M. Page (Eds.), Nebraska SymposiumonMotivation, 1979 (pp. 65–116).Lincoln: University of Nebraska Press.

Hamid AA, Razzak FZA, Bakar AA, Abdullah WSW (2016) The effects of perceived usefulness and perceived ease of use on continuance intention to use E-government. Procedia Econ Finance 35:644–649

Hooper D, Coughlan J, Mullen MR (2008) Structural equation modeling: guidelines for determining model fit. Electron J Bus Res Methods 6(1):53–60

Kline RB (1998) Principles and practice of structural equation modeling. Guliford, New York, NY

Kline RB (2005) Principles and practice of structural equation modeling, 2nd edn. Guliford, New York, NY

Kline RB (2011) Principles and practice of structural equation modeling, 3rd edn. Guliford, New York, NY

Li Y, Wang Q, Lei J (2019) Modeling Chinese teachers’ attitudes toward using technology for teaching with a SEM approach. Comput Schools 36(2):122–141

Lidstrom H, Hemmingsson H (2014) Benefits of the use of ICT in school activities by students with motor, speech, visual and hearing impairment: a literature review. Scand J Occup Ther 21(4):251–256

Macdonald J (2004) Developing competent e-learners: the role of assessment. Assess Eval Higher Educ 29(2):215–226

Mugo DG, Njagi K, Chemwei B, Motanya JO (2017) The technology acceptance model (TAM) and its application to the utilization of mobile learning technologies. Br J Math Comput Sci 20(4):1–8

Muk A, Chung C (2015) Applying the technology acceptance model in a two-country study of SMS advertising. J Bus Res 68(1):1–6

Nair I, Das VM (2012) Using technology acceptance model to assess teachers’ attitude towards use of technology as teaching tool: a SEM approach. Int J Comput Appl 42(2):1–6. https://doi.org/10.5120/5661-7691

Ofori E (2019) Using technology acceptance model to promote students adoption and use of digital technologies in the Sunyani technical university. J Basic Appl Res Int 25(3):146–157

Park N, Rhoads M, Hou J, Lee KM (2014) Understanding the acceptance of teleconferencing systems among employees: an extension of the technology acceptance model. Comput Hum Behav 39(0):118–127

Pelgrum WJ, Plomp T (1996) Information technology and children from a global perspective. In: Collis BA et al (ed) Children and computers in school, 1st edn. Routledge, pp 23–42. https://doi.org/10.4324/9781315044996

Chapter   Google Scholar  

Renny, Guritno S, Siringoringo H (2013) Perceived usefulness, ease of use, and attitude towards online shopping usefulness towards online airlines ticket purchase. Proc Soc Behav Sci 81:212–216

Salgotra AK, Roma K (2018) Attitude of university students towards ICT in education: an empirical study. Indian J Res 7(3):478–479

Straub D, Limayem M, Karahanna E (1995) Measuring system usage: implications for is theory testing. Manage Sci 41(8):1328–1342

Teo T, Zhou M (2014) Explaining the intention to use technology among university students: a structural equation modeling approach. J Comput High Educ 26:124–142

Ullman JB (2001) Structural equation modeling. In: Tabachnick BG, Fidell LS (eds) Using multivariate statistics, 4 th edn. Allyn and Bacon, Needham Heights, MA, pp 653–771

Yang S, Kwok D (2017) A study of students’ attitudes towards using ICT in a social constructivist environment. Aust J Educat Technol 33(5):50–62

Yusuf Dauda S, Lee J (2015) Technology adoption: a conjoint analysis of consumers׳ preference on future online banking services. Inform Syst 53(0):1–15

Download references

Acknowledgements

The authors are grateful to the scholars, and academicians who have supported and encouraged directly or indirectly to prepare this manuscript. Also, the authors are grateful to the anonymous referees for their invaluable comments on the earlier draft of the paper.

There is no specific grant received from any agency or sources in the public, commercial, or profit sectors to conduct the study or for this article.

Author information

Authors and affiliations.

Department of Economics, Comilla University, Comilla, Bangladesh

Tasfia Zahan Ria & M. Zakir Saadullah Khan

Department of Economics, North-Eastern Hill University, Shillong, India

Utpal Kumar De

You can also search for this author in PubMed   Google Scholar

Contributions

Conceptualization, methodology, data collection, formal analysis, original draft preparation, critical review and editing etc. all the works have been done by the authors jointly for preparing this manuscript.

Corresponding author

Correspondence to Utpal Kumar De .

Ethics declarations

Ethics approval and consent to participate.

Not applicable for this article. However, a consent form of the following was filled by the respondents to permit the publication on the information collected from them.

Questionnaire Consent Form

I (respondent) hereby give my permission to Tasfia Zahan Ria, Dr. M. Zakir Saadullah Khan and Dr Utpal Kumar De [researchers] to allow me to respond the questionnaire and use my responses exclusively for research purposes.I understand that the research title is Students’ Attitude towards Use of ICT as Tool of Learning: A Structural Equation Modeling (SEM) Approach. I believe that hereby named Tasfia Zahan Ria, Dr. M. Zakir Saadullah Khan and Dr Utpal Kumar De will maintain my anonymity with regard to my responses to the questionnaire items.I hereby give my permission in the form with my signature below:Signature ________________________ Date_______________________Contact of Researchers:Tasfia Zahan Ria [[email protected]] Dr. M. Zakir Saadullah Khan [[email protected]]Dr Utpal Kumar De [[email protected]]

Conflicts of interest

The authors declare that there is no conflict of interest at all. Additionally, the authors declare that this research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary Material 1

Rights and permissions.

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Ria, T., Khan, M. & De, U. Students’ attitude towards use of ICT as tool of learning: a structural equation modelling (SEM) approach. SN Soc Sci 4 , 103 (2024). https://doi.org/10.1007/s43545-024-00907-8

Download citation

Received : 08 November 2023

Accepted : 05 May 2024

Published : 22 May 2024

DOI : https://doi.org/10.1007/s43545-024-00907-8

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Perceived enjoyment
• Perceived ease of use
• Perceived usefulness
• Attitude towards use
• Find a journal
• Publish with us
• Track your research