we have had homework in mathematics recently

Grammar Exercise: Quantifiers

Grammar exercise - quantifiers, do the exercises below on quantifiers and click on the button to check your answers..

(Before doing the exercises you may want to read the lesson on quantifiers )

Choose the correct quantifier.

• They have had much any many lots of a lot little a little few most homework in mathematics recently.
• How much any many lots of a lot little a little few most time do you need to finish the work?
• There are too much any many lots of a lot little a little few most students in the library.
• Have you visited much any many lots of a lot little a little few most foreign countries?
• Although he's very ill, he didn't take much any many lots of a lot little a little few most medicine.
• Much any Many Lots of A lot Little A little Few Most people know as much about linguistics as John does.
• They say any many a lot little few most knowledge is a dangerous thing.
• He's having  much any many lots of a lot little a little few most of trouble passing his driving test.
• I spend any many lots of few most of my time reading novels.
• He knows much any many lots of a lot little a little few most English. He knows enough English to manage.

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They have had ________homework in mathematics recently.

How ___________time do you need to finish the work?

There are too ____________students in the library.

Have you visited ___________ foreign countries?

Although he's very ill, he didn't take ___________ medicine.

________people know as much about linguistics as John does.

They say ___________ knowledge is a dangerous thing.

He's having ___________ of trouble passing his driving test.

I spend _____________ of my time reading novels.

He knows ________ English. He knows enough English to manage.

We are going to be late. There is too ______ (much / many) traffic.

Yeah, the ______________ (amount / number) of people driving is incredible.

I've never seen this ________________ cars.

Can you bring soda to the picnic? I don't have __________

Yeah, I think I've got _____________ left over from the

How do you feel about your new job? Do you have as ______ responsibilities as you used to?

The job is great. I have about the same __________ of

work to do as before, but I have _______ stress and problems.

many , amount, less, fewer

much, number, little , fewer

many , number , few, a little

much , amount , little, fewer.

This president had _________ power.

She spoke __________ English. It was nearly impossible to understand her.

They got __________ complaints.

I'm sorry, but I have __________ time to waste.

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Has Completed, Had Completed, & Have Completed: Grammar Rules Explained

Last Updated: September 17, 2023

This article was co-authored by Tristen Bonacci and by wikiHow staff writer, Jessica Gibson . Tristen Bonacci is a Licensed English Teacher with more than 20 years of experience. Tristen has taught in both the United States and overseas. She specializes in teaching in a secondary education environment and sharing wisdom with others, no matter the environment. Tristen holds a BA in English Literature from The University of Colorado and an MEd from The University of Phoenix. This article has been viewed 49,945 times.

The English language is full of grammar rules that can take a little practice to learn. Take “has completed” or “had completed”—they’re very similar, but used in specific cases. We’ll guide you through when to use “has completed,” or “had completed.” We’ll also explain when “have completed” is the best choice.

When to Use "Has Completed"

• She has completed the marathon.
• The computer has completed running its diagnostics.
• He has completed filling out the forms.

When to Use "Had Completed"

• I had completed my work when my friends showed up.
• They had completed their task before starting their next challenge.
• We had completed our homework, but we forgot it at home.

When to Use "Have Completed"

• I have completed outlining my essay.
• You have completed listening to the podcast.
• I have completed my training.

• They have completed their project.
• We have completed our assignment.
• The kids have completed their homework.

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You might also like.

• ↑ https://youtu.be/DkbjCY2kCuc
• ↑ https://www.dailywritingtips.com/has-vs-had/
• ↑ https://www.grammarly.com/blog/present-perfect-tense/

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by isabel olmedo

Choose the correct quantifier. 1. They have had _________ homework in mathematics recently. 2. How _________ time do you need to finish the work? 3. There are too __________ students in the library. 4. Have you visited _______ foreign country? 5.... More

Choose the correct quantifier. 1. They have had _________ homework in mathematics recently. 2. How _________ time do you need to finish the work? 3. There are too __________ students in the library. 4. Have you visited _______ foreign country? 5. Although he s very ill, he didn t take ________ medicine. 6. ________ people know as much about linguistics as John does. 7. They say ________ knowledge is a dangerous thing. 8. He s having ________ of trouble passing his driving test. 9. I spend ____________ of my time reading novels. 10. He knows ____________ English. He knows enough English to manage. In the following sentences, fill in the gaps with one of the following quantifiers: much, many, a lot of, most, a little, little, a few, few 1. It seems to me that we haven t had assignments in English this term. 2. How material can we be expected to read in one week? 3. I ve unfortunately had headaches already because of stress. 4. Our yard looks awful this summer. T Less

Choose the correct quantifier. 1. They have had _________ homework in mathematics recently. 2. How _________ time do you need to finish the work? 3. There are too __________ students in the library. 4. Have you visited _______ foreign country? 5. Although he s very ill, he didn t take ________ medicine. 6. ________ people know as much about linguistics as John does. 7. They say ________ knowledge is a dangerous thing. 8. He s having ________ of trouble passing his driving test. 9. I spend ____________ of my time reading novels. 10. He knows ____________ English. He knows enough English to manage. In the following sentences, fill in the gaps with one of the following quantifiers: much, many, a lot of, most, a little, little, a few, few 1. It seems to me that we haven t had assignments in English this term. 2. How material can we be expected to read in one week? 3. I ve unfortunately had headaches already because of stress. 4. Our yard looks awful this summer. There are too weeds. 5. I didn t use fertilizer last spring, and that has made a difference. 6. Also, I ve paid very attention to how rain we ve had. 7. I m afraid it s rained times this summer, and that is why the grass is turning brown and dying. Farmers are very upset. 8. How good would it do if we watered the plants ourselves? . 9. of the advice I have ever received from so-called "experts" has been useless. 10. They said that just help could make a big difference. 11. people know as much about computers as Tomas does. 12. It does us good when the banking system collapses. Choose the correct quantifier. 13. They have had lots of homework in mathematics recently. 14. How much time do you need to finish the work?

15. There are too many students in the library. 16. Have you visited any foreign country? 17. Although he s very ill, he didn t take any medicine. 18. Few people know as much about linguistics as John does. 19. They say little knowledge is a dangerous thing. 20. He s having a lot of trouble passing his driving test. 21. I spend most of my time reading novels. 22. He knows a little English. He knows enough English to manage.

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Rethinking Homework for This Year—and Beyond

A schoolwide effort to reduce homework has led to a renewed focus on ensuring that all work assigned really aids students’ learning.

I used to pride myself on my high expectations, including my firm commitment to accountability for regular homework completion among my students. But the trauma of Covid-19 has prompted me to both reflect and adapt. Now when I think about the purpose and practice of homework, two key concepts guide me: depth over breadth, and student well-being.

Homework has long been the subject of intense debate, and there’s no easy answer with respect to its value. Teachers assign homework for any number of reasons: It’s traditional to do so, it makes students practice their skills and solidify learning, it offers the opportunity for formative assessment, and it creates good study habits and discipline. Then there’s the issue of pace. Throughout my career, I’ve assigned homework largely because there just isn’t enough time to get everything done in class.

A Different Approach

Since classes have gone online, the school where I teach has made a conscious effort as a teaching community to reduce, refine, and distill our curriculum. We have applied guiding questions like: What is most important? What is most transferable? What is most relevant? Refocusing on what matters most has inevitably made us rethink homework.

We have approached both asking and answering these questions through a science of learning lens. In Make It Stick: The Science of Successful Learning , the authors maintain that deep learning is slow learning. Deep learning requires time for retrieval, practice, feedback, reflection, and revisiting content; ultimately it requires struggle, and there is no struggle without time.

As someone who has mastered the curriculum mapping style of “get it done to move on to get that next thing done,” using an approach of “slow down and reduce” has been quite a shift for me. However, the shift has been necessary: What matters most is what’s best for my students, as opposed to my own plans or mandates imposed by others.

Listening to Students

To implement this shift, my high school English department has reduced content and texts both in terms of the amount of units and the content within each unit. We’re more flexible with dates and deadlines. We spend our energy planning the current unit instead of the year’s units. In true partnership with my students, I’m constantly checking in with them via Google forms, Zoom chats, conferences, and Padlet activities. In these check-ins, I specifically ask students how they’re managing the workload for my class and their other classes. I ask them how much homework they’re doing. And I adjust what I do and expect based on what they tell me. For example, when I find out a week is heavy with work in other classes, I make sure to allot more time during class for my tasks. At times I have even delayed or altered one of my assignments.

To be completely transparent, the “old” me is sheepish in admitting that I’ve so dramatically changed my thinking with respect to homework. However, both my students and I have reaped numerous benefits. I’m now laser-focused when designing every minute of my lessons to maximize teaching and learning. Every decision I make is now scrutinized through the lens of absolute worth for my students’ growth: If it doesn’t make the cut, it’s cut. I also take into account what is most relevant to my students.

For example, our 10th-grade English team has redesigned a unit that explores current manifestations of systemic oppression. This unit is new in approach and longer in duration than it was pre-Covid, and it has resulted in some of the deepest and hardest learning, as well as the richest conversations, that I have seen among students in my career. Part of this improved quality comes from the frequent and intentional pauses that I instruct students to take in order to reflect on the content and on the arc of their own learning. The reduction in content that we need to get through in online learning has given me more time to assign reflective prompts, and to let students process their thoughts, whether that’s at the end of a lesson as an exit slip or as an assignment.

Joining Forces to Be Consistent

There’s no doubt this reduction in homework has been a team effort. Within the English department, we have all agreed to allot reading time during class; across each grade level, we’re monitoring the amount of homework our students have collectively; and across the whole high school, we have adopted a framework to help us think through assigning homework.

Within that framework, teachers at the school agree that the best option is for students to complete all work during class. The next best option is for students to finish uncompleted class work at home as a homework assignment of less than 30 minutes. The last option—the one we try to avoid as much as possible—is for students to be assigned and complete new work at home (still less than 30 minutes). I set a maximum time limit for students’ homework tasks (e.g., 30 minutes) and make that clear at the top of every assignment.

This schoolwide approach has increased my humility as a teacher. In the past, I tended to think my subject was more important than everyone else’s, which gave me license to assign more homework. But now I view my students’ experience more holistically: All of their classes and the associated work must be considered, and respected.

As always, I ground this new pedagogical approach not just in what’s best for students’ academic learning, but also what’s best for them socially and emotionally. 2020 has been traumatic for educators, parents, and students. There is no doubt the level of trauma varies greatly ; however, one can’t argue with the fact that homework typically means more screen time when students are already spending most of the day on their devices. They need to rest their eyes. They need to not be sitting at their desks. They need physical activity. They need time to do nothing at all.

Eliminating or reducing homework is a social and emotional intervention, which brings me to the greatest benefit of reducing the homework load: Students are more invested in their relationship with me now that they have less homework. When students trust me to take their time seriously, when they trust me to listen to them and adjust accordingly, when they trust me to care for them... they trust more in general.

And what a beautiful world of learning can be built on trust.

Homework and Mathematics Learning: What Can We Learn from the TIMSS Series Studies in the Last Two Decades?

Cite this chapter.

• Yan Zhu 6  

Part of the book series: Research in Mathematics Education ((RME))

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3 Citations

As a way to extend learning beyond schools, homework is generally recommended or a common practice in many education systems around the world. However, there is no conclusive evidence about its importance and the mechanism by which it might improve students’ mathematics learning. The ongoing debate about homework inside and outside academia over the years suggests its complex nature. Some researchers attribute the inclusiveness to the deficiency in using inappropriate methodology in many earlier studies. Given these considerations, this study analyzed mathematics homework-related data from TIMSS series surveys of various parties, including students, mathematics teachers, school principals, and curriculum experts, in eight selected education systems. Analyses were carried out from both between-system and within-system perspectives to identify the commonalities and differences across systems as well as the changes in individual systems across years. Both implications and suggestions are made accordingly.

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See The Homework Debate , retrieved on September 6, 2013, from http://northshoremums.com.au/the-homework-debate/

See France ’ s Hollande Promises Pupils “ No More Homework ”, retrieved on October 11, 2012, from http://www.france24.com/en/20121010-hollande-promises-school-children-no-more-homework-education-reform-france/

See Parents in Australia Call for Ban on Homework , retrieved on April 10, 2007, from http://www.foxnews.com/story/2007/04/10/parents-in-australia-call-for-ban-on-homework/

T stands for teacher questionnaires, whereas S stands for student questionnaires.

Effect size for a Chi-square test (on nominal data) is expressed by Cramer’s φ (small: φ  = 0.10, medium: φ  = 0.30, large: φ  = 0.50), when a significant χ 2 is detected.

A 5-point Likert scale was used in TIMSS 1995/1999/2011 (1: never, 2: less than once a week, 3: once or twice a week, 4: 3 or 4 times a week, 5: every day); the first option in TIMSS 2011 was stated as “I do not assign mathematics homework”.

A 3-point Likert scale was used in TIMSS 2003/2007 (1: every or almost every lesson, 2: about half the lessons, 3: some lessons).

Though TIMSS 1995/1999 student questionnaires also had one item on homework assigning frequency, they used a different 4-point Likert scale for the measurement (1: almost always, 2: pretty often, 3: once a while, 4: never). Due to the incomparability, no analysis was done on TIMSS 1995/1999 student data on this item.

Effect size for a Wilcoxon signed rank test (on matched ordinal data between two groups) is expressed by r (small: r  = 0.10, medium: r  = 0.30, large: r  = 0.50), when a significant Z is detected.

The item stem in the teacher questionnaire is “when you assign mathematics homework to the TIMSS class, about how many minutes do you usually assign?” and that in the student questionnaire is “when your teacher gives you mathematics homework, about how many minutes do you usually spend on your homework?”

A 5-point Likert scale was used on the items about time spent (1: fewer than 15 min (or “15 min or less” in TIMSS 2011), 2: 15–30 min (or “16–30 min” in TIMSS 2011), 3: 31–60 min, 4: 61–90 min, 5: more than 90 min). One additional option “I do not assign homework” in TIMSS 1995 questionnaire was merged with “less than 15 min” in the later analysis.

In the two most recent TIMSS years, student questionnaires added one more option on the time spent item (TIMSS 2007: zero minutes; TIMSS 2011: my teacher never gives me homework in mathematics), which was combined with “1–15 min” to be recoded as “15 min or less” for the later analysis.

The measurement is based on a 4-point Likert scale (1: never; 2: rarely; 3: sometimes; 4: always). A fifth option “I don’t assign homework” was used in TIMSS 1995, which was recoded as missing data in the later analysis.

TIMSS 2003/2007 used a 3-point Likert scale (1: always or almost always, 2: sometimes, 3: never or almost never), which was reversed into an ascending order in the later analysis so as to ease the interpretation.

Effect size for a Mann-Whitney U test (on independent ordinal data between two groups) is expressed by r (small: r  = 0.10, medium: r  = 0.30, large: r  = 0.50), when a significant U is detected.

Effect size for a Friedman test (on matched ordinal data across more than two groups) is expressed by Kendall’s W (small: W  = 0.60, medium: W  = 0.40, large: W  = 0.20), when a significant χ 2 is detected.

TIMSS 2003/2007/2011 teacher surveys used a descending 3-point Likert scale (1: always or almost always, 2: sometimes, 3: never or almost never).

Effect size for a Kruskal Wallis test (on independent ordinal data across more than two groups) is expressed by ƞ 2 (small: ƞ 2  = 0.01, medium: ƞ 2  = 0.06, large: ƞ 2  = 0.14), when a significant χ 2 is detected.

A 4-point Likert scale was used on the two parent-related items in TIMSS 2011 (1: every day or almost every day, 2: once or twice a week, 3: once or twice a month, 4: never or almost never), which was reversed before the analysis to ease the interpretation.

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Walker, R. (2011). Should children do traditional homework? The Sydney Morning Herald . Retrieved January 13, 2012, from http://www.smh.com.au/federal-politics/the-question/should-children-do-traditional-homework-20110923-1kpaj.html

Warton, P. M. (1997). Homework: Learning from practice . London: The Stationery Office.

Warton, P. M. (2001). The forgotten voices in homework: Views of students. Educational Psychologist, 36 (3), 155–165.

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Zhu, Y., & Leung, F. K. S. (2012). Homework and mathematics achievement in Hong Kong: Evidence from the TIMSS 2003. International Journal of Science and Mathematics Education, 10 (4), 907–925.

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Zhu, Y. (2015). Homework and Mathematics Learning: What Can We Learn from the TIMSS Series Studies in the Last Two Decades?. In: Middleton, J., Cai, J., Hwang, S. (eds) Large-Scale Studies in Mathematics Education. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-07716-1_10

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Student Opinion

Should We Get Rid of Homework?

Some educators are pushing to get rid of homework. Would that be a good thing?

By Jeremy Engle and Michael Gonchar

Do you like doing homework? Do you think it has benefited you educationally?

Has homework ever helped you practice a difficult skill — in math, for example — until you mastered it? Has it helped you learn new concepts in history or science? Has it helped to teach you life skills, such as independence and responsibility? Or, have you had a more negative experience with homework? Does it stress you out, numb your brain from busywork or actually make you fall behind in your classes?

Should we get rid of homework?

In “ The Movement to End Homework Is Wrong, ” published in July, the Times Opinion writer Jay Caspian Kang argues that homework may be imperfect, but it still serves an important purpose in school. The essay begins:

Do students really need to do their homework? As a parent and a former teacher, I have been pondering this question for quite a long time. The teacher side of me can acknowledge that there were assignments I gave out to my students that probably had little to no academic value. But I also imagine that some of my students never would have done their basic reading if they hadn’t been trained to complete expected assignments, which would have made the task of teaching an English class nearly impossible. As a parent, I would rather my daughter not get stuck doing the sort of pointless homework I would occasionally assign, but I also think there’s a lot of value in saying, “Hey, a lot of work you’re going to end up doing in your life is pointless, so why not just get used to it?” I certainly am not the only person wondering about the value of homework. Recently, the sociologist Jessica McCrory Calarco and the mathematics education scholars Ilana Horn and Grace Chen published a paper, “ You Need to Be More Responsible: The Myth of Meritocracy and Teachers’ Accounts of Homework Inequalities .” They argued that while there’s some evidence that homework might help students learn, it also exacerbates inequalities and reinforces what they call the “meritocratic” narrative that says kids who do well in school do so because of “individual competence, effort and responsibility.” The authors believe this meritocratic narrative is a myth and that homework — math homework in particular — further entrenches the myth in the minds of teachers and their students. Calarco, Horn and Chen write, “Research has highlighted inequalities in students’ homework production and linked those inequalities to differences in students’ home lives and in the support students’ families can provide.”

Mr. Kang argues:

But there’s a defense of homework that doesn’t really have much to do with class mobility, equality or any sense of reinforcing the notion of meritocracy. It’s one that became quite clear to me when I was a teacher: Kids need to learn how to practice things. Homework, in many cases, is the only ritualized thing they have to do every day. Even if we could perfectly equalize opportunity in school and empower all students not to be encumbered by the weight of their socioeconomic status or ethnicity, I’m not sure what good it would do if the kids didn’t know how to do something relentlessly, over and over again, until they perfected it. Most teachers know that type of progress is very difficult to achieve inside the classroom, regardless of a student’s background, which is why, I imagine, Calarco, Horn and Chen found that most teachers weren’t thinking in a structural inequalities frame. Holistic ideas of education, in which learning is emphasized and students can explore concepts and ideas, are largely for the types of kids who don’t need to worry about class mobility. A defense of rote practice through homework might seem revanchist at this moment, but if we truly believe that schools should teach children lessons that fall outside the meritocracy, I can’t think of one that matters more than the simple satisfaction of mastering something that you were once bad at. That takes homework and the acknowledgment that sometimes a student can get a question wrong and, with proper instruction, eventually get it right.

Students, read the entire article, then tell us:

Should we get rid of homework? Why, or why not?

Is homework an outdated, ineffective or counterproductive tool for learning? Do you agree with the authors of the paper that homework is harmful and worsens inequalities that exist between students’ home circumstances?

Or do you agree with Mr. Kang that homework still has real educational value?

When you get home after school, how much homework will you do? Do you think the amount is appropriate, too much or too little? Is homework, including the projects and writing assignments you do at home, an important part of your learning experience? Or, in your opinion, is it not a good use of time? Explain.

In these letters to the editor , one reader makes a distinction between elementary school and high school:

Homework’s value is unclear for younger students. But by high school and college, homework is absolutely essential for any student who wishes to excel. There simply isn’t time to digest Dostoyevsky if you only ever read him in class.

What do you think? How much does grade level matter when discussing the value of homework?

Is there a way to make homework more effective?

If you were a teacher, would you assign homework? What kind of assignments would you give and why?

Want more writing prompts? You can find all of our questions in our Student Opinion column . Teachers, check out this guide to learn how you can incorporate them into your classroom.

Students 13 and older in the United States and Britain, and 16 and older elsewhere, are invited to comment. All comments are moderated by the Learning Network staff, but please keep in mind that once your comment is accepted, it will be made public.

Jeremy Engle joined The Learning Network as a staff editor in 2018 after spending more than 20 years as a classroom humanities and documentary-making teacher, professional developer and curriculum designer working with students and teachers across the country. More about Jeremy Engle

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How Can We Make Homework Worthwhile?

Please try again

Do American students have too much homework, or too little? We often hear passionate arguments for either side, but I believe that we ought to be asking a different question altogether. What should matter to parents and educators is this: How effectively do children’s after-school assignments advance learning?

The quantity of students’ homework is a lot less important than its quality. And evidence suggests that as of now, homework isn’t making the grade. Although surveys show that the amount of time our children spend on homework has risen over the last three decades, American students are mired in the middle of international academic rankings: 17th in reading, 23rd in science and 31st in math, according to the most recent results from the Program for International Student Assessment (PISA).

In a 2008 survey , one-third of parents polled rated the quality of their children’s homework assignments as fair or poor, and 4 in 10 said they believed that some or a great deal of homework was busywork. A recent study , published in the Economics of Education Review, reports that homework in science, English and history has “little to no impact” on student test scores. (The authors did note a positive effect for math homework.) Enriching children’s classroom learning requires making homework not shorter or longer, but smarter.

Fortunately, research is available to help parents, teachers and school administrators do just that. In recent years, neuroscientists, cognitive scientists and educational psychologists have made a series of remarkable discoveries about how the human brain learns. They have founded a new discipline, known as Mind, Brain and Education , that is devoted to understanding and improving the ways in which children absorb, retain and apply knowledge.

Educators have begun to implement these methods in classrooms around the country and have enjoyed measurable success. A collaboration between psychologists at Washington University in St. Louis and teachers at nearby Columbia Middle School, for example, lifted seventh- and eighth-grade students’ science and social studies test scores by 13 to 25 percent.

But the innovations have not yet been applied to homework. Mind, Brain and Education methods may seem unfamiliar and even counterintuitive, but they are simple to understand and easy to carry out. And after-school assignments are ripe for the kind of improvements the new science offers.

“Spaced repetition” is one example of the kind of evidence-based techniques that researchers have found have a positive impact on learning. Here’s how it works: instead of concentrating the study of information in single blocks, as many homework assignments currently do—reading about, say, the Civil War one evening and Reconstruction the next—learners encounter the same material in briefer sessions spread over a longer period of time. With this approach, students are re-exposed to information about the Civil War and Reconstruction throughout the semester.

[RELATED READING: Parents Wonder: Why So Much Homework? ]

It sounds unassuming, but spaced repetition produces impressive results. Eighth-grade history students who relied on a spaced approach to learning had nearly double the retention rate of students who studied the same material in a consolidated unit, reported researchers from the University of California-San Diego in 2007. The reason the method works so well goes back to the brain: when we first acquire memories, they are volatile, subject to change or likely to disappear. Exposing ourselves to information repeatedly over time fixes it more permanently in our minds, by strengthening the representation of the information that is embedded in our neural networks.

A second learning technique, known as “retrieval practice,” employs a familiar tool—the test—in a new way: not to assess what students know, but to reinforce it. We often conceive of memory as something like a storage tank and a test as a kind of dipstick that measures how much information we’ve put in there. But that’s not actually how the brain works. Every time we pull up a memory, we make it stronger and more lasting, so that testing doesn’t just measure, it changes learning. Simply reading over material to be learned, or even taking notes and making outlines, as many homework assignments require, doesn’t have this effect .

According to one experiment , language learners who employed the retrieval practice strategy to study vocabulary words remembered 80 percent of the words they studied, while learners who used conventional study methods remembered only about a third of them. Students who used retrieval practice to learn science retained about 50 percent more of the material than students who studied in traditional ways, reported researchers from Purdue University in 2011. Students—and parents—may groan at the prospect of more tests, but the self-quizzing involved in retrieval practice need not provoke any anxiety. It’s simply an effective way to focus less on the input of knowledge (passively reading over textbooks and notes) and more on its output (calling up that same information from one’s own brain).

[RELATED READING: Redefining 'Cheating' With Homework ]

Another common misconception about how we learn holds that if information feels easy to absorb, we’ve learned it well. In fact, the opposite is true. When we work hard to understand information, we recall it better; the extra effort signals the brain that this knowledge is worth keeping. This phenomenon, known as cognitive disfluency , promotes learning so effectively that psychologists have devised all manner of “ desirable difficulties ” to introduce into the learning process: for example, sprinkling a passage with punctuation mistakes, deliberately leaving out letters, shrinking font size until it’s tiny or wiggling a document while it’s being copied so that words come out blurry.

Teachers are unlikely to start sending students home with smudged or error-filled worksheets, but there is another kind of desirable difficulty — called interleaving — that can readily be applied to homework. An interleaved assignment mixes up different kinds of situations or problems to be practiced, instead of grouping them by type. When students can’t tell in advance what kind of knowledge or problem-solving strategy will be required to answer a question, their brains have to work harder to come up with the solution, and the result is that students learn the material more thoroughly.

Researchers at California Polytechnic State University conducted a study of interleaving in sports that illustrates why the tactic is so effective. When baseball players practiced hitting, interleaving different kinds of pitches improved their performance on a later test in which the batters did not know the type of pitch in advance (as would be the case, of course, in a real game).

Interleaving produces the same sort of improvement in academic learning. A study published in 2010 in the journal Applied Cognitive Psychology asked fourth-graders to work on solving four types of math problems and then to take a test evaluating how well they had learned. The scores of those whose practice problems were mixed up were more than double the scores of those students who had practiced one kind of problem at a time.

The application of such research-based strategies to homework is a yet-untapped opportunity to raise student achievement. Science has shown us how to turn homework into a potent catalyst for learning. Our assignment now is to make it happen.

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Credit: August de Richelieu

Does homework still have value? A Johns Hopkins education expert weighs in

Joyce epstein, co-director of the center on school, family, and community partnerships, discusses why homework is essential, how to maximize its benefit to learners, and what the 'no-homework' approach gets wrong.

By Vicky Hallett

The necessity of homework has been a subject of debate since at least as far back as the 1890s, according to Joyce L. Epstein , co-director of the Center on School, Family, and Community Partnerships at Johns Hopkins University. "It's always been the case that parents, kids—and sometimes teachers, too—wonder if this is just busy work," Epstein says.

But after decades of researching how to improve schools, the professor in the Johns Hopkins School of Education remains certain that homework is essential—as long as the teachers have done their homework, too. The National Network of Partnership Schools , which she founded in 1995 to advise schools and districts on ways to improve comprehensive programs of family engagement, has developed hundreds of improved homework ideas through its Teachers Involve Parents in Schoolwork program. For an English class, a student might interview a parent on popular hairstyles from their youth and write about the differences between then and now. Or for science class, a family could identify forms of matter over the dinner table, labeling foods as liquids or solids. These innovative and interactive assignments not only reinforce concepts from the classroom but also foster creativity, spark discussions, and boost student motivation.

"We're not trying to eliminate homework procedures, but expand and enrich them," says Epstein, who is packing this research into a forthcoming book on the purposes and designs of homework. In the meantime, the Hub couldn't wait to ask her some questions:

What kind of homework training do teachers typically get?

Future teachers and administrators really have little formal training on how to design homework before they assign it. This means that most just repeat what their teachers did, or they follow textbook suggestions at the end of units. For example, future teachers are well prepared to teach reading and literacy skills at each grade level, and they continue to learn to improve their teaching of reading in ongoing in-service education. By contrast, most receive little or no training on the purposes and designs of homework in reading or other subjects. It is really important for future teachers to receive systematic training to understand that they have the power, opportunity, and obligation to design homework with a purpose.

Why do students need more interactive homework?

If homework assignments are always the same—10 math problems, six sentences with spelling words—homework can get boring and some kids just stop doing their assignments, especially in the middle and high school years. When we've asked teachers what's the best homework you've ever had or designed, invariably we hear examples of talking with a parent or grandparent or peer to share ideas. To be clear, parents should never be asked to "teach" seventh grade science or any other subject. Rather, teachers set up the homework assignments so that the student is in charge. It's always the student's homework. But a good activity can engage parents in a fun, collaborative way. Our data show that with "good" assignments, more kids finish their work, more kids interact with a family partner, and more parents say, "I learned what's happening in the curriculum." It all works around what the youngsters are learning.

Is family engagement really that important?

At Hopkins, I am part of the Center for Social Organization of Schools , a research center that studies how to improve many aspects of education to help all students do their best in school. One thing my colleagues and I realized was that we needed to look deeply into family and community engagement. There were so few references to this topic when we started that we had to build the field of study. When children go to school, their families "attend" with them whether a teacher can "see" the parents or not. So, family engagement is ever-present in the life of a school.

My daughter's elementary school doesn't assign homework until third grade. What's your take on "no homework" policies?

There are some parents, writers, and commentators who have argued against homework, especially for very young children. They suggest that children should have time to play after school. This, of course is true, but many kindergarten kids are excited to have homework like their older siblings. If they give homework, most teachers of young children make assignments very short—often following an informal rule of 10 minutes per grade level. "No homework" does not guarantee that all students will spend their free time in productive and imaginative play.

Some researchers and critics have consistently misinterpreted research findings. They have argued that homework should be assigned only at the high school level where data point to a strong connection of doing assignments with higher student achievement . However, as we discussed, some students stop doing homework. This leads, statistically, to results showing that doing homework or spending more minutes on homework is linked to higher student achievement. If slow or struggling students are not doing their assignments, they contribute to—or cause—this "result."

Teachers need to design homework that even struggling students want to do because it is interesting. Just about all students at any age level react positively to good assignments and will tell you so.

Did COVID change how schools and parents view homework?

Within 24 hours of the day school doors closed in March 2020, just about every school and district in the country figured out that teachers had to talk to and work with students' parents. This was not the same as homeschooling—teachers were still working hard to provide daily lessons. But if a child was learning at home in the living room, parents were more aware of what they were doing in school. One of the silver linings of COVID was that teachers reported that they gained a better understanding of their students' families. We collected wonderfully creative examples of activities from members of the National Network of Partnership Schools. I'm thinking of one art activity where every child talked with a parent about something that made their family unique. Then they drew their finding on a snowflake and returned it to share in class. In math, students talked with a parent about something the family liked so much that they could represent it 100 times. Conversations about schoolwork at home was the point.

How did you create so many homework activities via the Teachers Involve Parents in Schoolwork program?

We had several projects with educators to help them design interactive assignments, not just "do the next three examples on page 38." Teachers worked in teams to create TIPS activities, and then we turned their work into a standard TIPS format in math, reading/language arts, and science for grades K-8. Any teacher can use or adapt our prototypes to match their curricula.

Overall, we know that if future teachers and practicing educators were prepared to design homework assignments to meet specific purposes—including but not limited to interactive activities—more students would benefit from the important experience of doing their homework. And more parents would, indeed, be partners in education.

Posted in Voices+Opinion

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“Homework Should Be…but We Do Not Live in an Ideal World”: Mathematics Teachers’ Perspectives on Quality Homework and on Homework Assigned in Elementary and Middle Schools

Pedro rosário.

1 Departamento de Psicologia Aplicada, Escola de Psicologia, Universidade do Minho, Braga, Portugal

Jennifer Cunha

Tânia nunes, ana rita nunes, tânia moreira, josé carlos núñez.

2 Departamento de Psicología, Universidad de Oviedo, Oviedo, Spain

Associated Data

Existing literature has analyzed homework characteristics associated with academic results. Researchers and educators defend the need to provide quality homework, but there is still much to be learned about the characteristics of quality homework (e.g., purposes, type). Acknowledging that teachers play an important role in designing and assigning homework, this study explored teachers’ perspectives regarding: (i) the characteristics of quality homework and (ii) the characteristics of the homework tasks assigned. In the current study, mathematics teachers from elementary and middle schools ( N = 78) participated in focus group discussions. To enhance the trustworthiness of the findings, homework tasks assigned by 25% of the participants were analyzed for triangulation of data purposes. Data were analyzed using thematic analysis for elementary and middle school separately. Teachers discussed the various characteristics of quality homework (e.g., short assignments, adjusted to the availability of students) and shared the characteristics of the homework tasks typically assigned, highlighting a few differences (e.g., degree of individualization of homework, purposes) between these two topics. Globally, data on the homework tasks assigned were consistent with teachers’ reports about the characteristics of the homework tasks they usually assigned. Findings provide valuable insights for research and practice aimed to promote the quality of homework and consequently students’ learning and progress.

Introduction

The extensive literature on homework suggests the importance of completing homework tasks to foster students’ academic achievement (e.g., Trautwein and Lüdtke, 2009 ; Hagger et al., 2015 ; Núñez et al., 2015a ; Valle et al., 2016 ; Fernández-Alonso et al., 2017 ). However, existing research also indicate that the amount of homework assigned is not always related to high academic achievement ( Epstein and Van Voorhis, 2001 ; Epstein and Van Voorhis, 2012 ). In the words of Dettmers et al. (2010) “homework works if quality is high” (p. 467). However, further research is needed to answer the question “What is quality homework?”.

Teachers are responsible for designing and assigning homework, thus our knowledge on their perspectives about this topic and the characteristics of the homework typically assigned is expected to be a relevant contribution to the literature on the quality of homework. Moreover, data on the characteristics of homework could provide valuable information to unveil the complex network of relationships between homework and academic achievement (e.g., Cooper, 2001 ; Trautwein and Köller, 2003 ; Trautwein et al., 2009a ; Xu, 2010 ).

Thus, focusing on the perspective of mathematics teachers from elementary and middle school, the aims of the present study are twofold: to explore the characteristics of quality homework, and to identify the characteristics of the homework tasks typically assigned at these school levels. Findings may help deepen our understanding of why homework may impact differently the mathematics achievement of elementary and middle school students (see Fan et al., 2017 ).

Research Background on Homework Characteristics

Homework is a complex educational process involving a diverse set of variables that each may influence students’ academic outcomes (e.g., Corno, 2000 ; Trautwein and Köller, 2003 ; Cooper et al., 2006 ; Epstein and Van Voorhis, 2012 ). Cooper (1989 , 2001 ) presented a model outlining the factors that may potentially influence the effect of homework at the three stages of the homework process (i.e., design of the homework assignment, completion of homework and homework follow-up practices). At the first stage teachers are expected to consider class characteristics (e.g., students’ prior knowledge, grade level, number of students per class), and also variables that may influence the impact of homework on students’ outcomes, such as homework assignment characteristics. In 1989, Cooper (see also Cooper et al., 2006 ) presented a list of the characteristics of homework assignments as follows: amount (comprising homework frequency and length), purpose, skill area targeted, degree of individualization, student degree of choice, completion deadlines, and social context. Based on existing literature, Trautwein et al. (2006b) proposed a distinct organization for the assignment characteristics. The proposal included: homework frequency (i.e., how often homework assignments are prescribed to students), quality, control, and adaptivity. “Homework frequency” and “adaptivity” are similar to “amount” and “degree of individualization” in Cooper’s model, respectively. Both homework models provide a relevant theoretical framework for the present study.

Prior research has analyzed the relationship between homework variables, students’ behaviors and academic achievement, and found different results depending on the variables examined (see Trautwein et al., 2009b ; Fan et al., 2017 ). For example, while homework frequency consistently and positively predicted students’ academic achievement (e.g., Trautwein et al., 2002 ; Trautwein, 2007 ; Fernández-Alonso et al., 2015 ), findings regarding the amount of homework assigned (usually assessed by the time spent on homework) have shown mixed results (e.g., Trautwein, 2007 ; Dettmers et al., 2009 ; Núñez et al., 2015a ). Data indicated a positive association between the amount of homework and students’ academic achievement in high school (e.g., OECD, 2014a ); however, this relationship is almost null in elementary school (e.g., Cooper et al., 2006 ; Rosário et al., 2009 ). Finally, other studies reported a negative association between time spent on homework and students’ academic achievement at different school levels (e.g., Trautwein et al., 2009b ; Rosário et al., 2011 ; Núñez et al., 2015a ).

Homework purposes are among the factors that may influence the effect of homework on students’ homework behaviors and academic achievement ( Cooper, 2001 ; Trautwein et al., 2009a ; Epstein and Van Voorhis, 2012 ; Rosário et al., 2015 ). In his model Cooper (1989 , 2001 ) reported instructional purposes (i.e., practicing or reviewing, preparation, integration and extension) and non-instructional purposes (i.e., parent-child communication, fulfilling directives, punishment, and community relations). Depending on their nature, homework instructional purposes may vary throughout schooling ( Muhlenbruck et al., 2000 ; Epstein and Van Voorhis, 2001 ). For example, in elementary school, teachers are likely to use homework as an opportunity to review the content taught in class, while in secondary school (6th–12th grade), teachers are prone to use homework to prepare students for the content to be learned in subsequent classes ( Muhlenbruck et al., 2000 ). Still, studies have recently shown that practicing the content learned is the homework purpose most frequently used throughout schooling (e.g., Xu and Yuan, 2003 ; Danielson et al., 2011 ; Kaur, 2011 ; Bang, 2012 ; Kukliansky et al., 2014 ). Studies using quantitative methodologies have analyzed the role played by homework purposes in students’ effort and achievement ( Trautwein et al., 2009a ; Rosário et al., 2015 , 2018 ), and reported distinct results depending on the subject analyzed. For example, Foyle et al. (1990) found that homework assignments with the purposes of practice and preparation improved the performance of 5th-grade students’ social studies when compared with the no-homework group. However, no statistical difference was found between the two types of homework purposes analyzed (i.e., practice and preparation). When examining the homework purposes reported by 8th-grade teachers of French as a Second Language (e.g., drilling and practicing, motivating, linking school and home), Trautwein et al. (2009a) found that students in classes assigned tasks with high emphasis on motivation displayed more effort and achieved higher outcomes than their peers. On the contrary, students in classes assigned tasks with high drill and practice reported less homework effort and achievement ( Trautwein et al., 2009a ). A recent study by Rosário et al. (2015) analyzed the relationship between homework assignments with various types of purposes (i.e., practice, preparation and extension) and 6th-grade mathematics achievement. These authors reported that homework with the purpose of “extension” impacted positively on students’ academic achievement while the other two homework purposes did not.

Cooper (1989 , 2001 ) identified the “degree of individualization” as a characteristic of homework focused on the need to design homework addressing different levels of performance. For example, some students need to be assigned practice exercises with a low level of difficulty to help them reach school goals, while others need to be assigned exercises with high levels of complexity to foster their motivation for homework ( Trautwein et al., 2002 ). When there is a disparity between the level of difficulty of homework assignments and students’ skills level, students may have to spend long hours doing homework, and they may experience negative emotions or even avoid doing homework ( Corno, 2000 ). On the contrary, when homework assignments meet students’ learning needs (e.g., Bang, 2012 ; Kukliansky et al., 2014 ), both students’ homework effort and academic achievement increase (e.g., Trautwein et al., 2006a ; Zakharov et al., 2014 ). Teachers may also decide on the time given to students to complete their homework ( Cooper, 1989 ; Cooper et al., 2006 ). For example, homework may be assigned to be delivered in the following class (e.g., Kaur et al., 2004 ) or within a week (e.g., Kaur, 2011 ). However, research on the beneficial effects of each practice is still limited.

Trautwein et al. (2006b) investigated homework characteristics other than those previously reported. Their line of research analyzed students’ perception of homework quality and homework control (e.g., Trautwein et al., 2006b ; Dettmers et al., 2010 ). Findings on homework quality (e.g., level of difficulty of the mathematics exercises, Trautwein et al., 2002 ; homework “cognitively activating” and “well prepared”, Trautwein et al., 2006b , p. 448; homework selection and level of challenge, Dettmers et al., 2010 ; Rosário et al., 2018 ) varied regarding the various measures and levels of analysis considered. For example, focusing on mathematics, Trautwein et al. (2002) concluded that “demanding” exercises improved 7th-grade students’ achievement at student and class levels, while “repetitive exercises” impacted negatively on students’ achievement. Dettmers et al. (2010) found that homework assignments perceived by students as “well-prepared and interesting” (p. 471) positively predicted 9th- and 10th-grade students’ homework motivation (expectancy and value beliefs) and behavior (effort and time) at student and class level, and mathematics achievement at class level only. These authors also reported that “cognitively challenging” homework (p. 471), as perceived by students, negatively predicted students’ expectancy beliefs at both levels, and students’ homework effort at student level ( Dettmers et al., 2010 ). Moreover, this study showed that “challenging homework” significantly and positively impacted on students’ mathematics achievement at class level ( Dettmers et al., 2010 ). At elementary school, homework quality (assessed through homework selection) predicted positively 6th-grade students’ homework effort, homework performance, and mathematics achievement ( Rosário et al., 2018 ).

Finally, Trautwein and colleagues investigated the variable “homework control” perceived by middle school students and found mixed results. The works by Trautwein and Lüdtke (2007 , 2009 ) found that “homework control” predicted positively students’ homework effort in mathematics, but other studies (e.g., Trautwein et al., 2002 , 2006b ) did not predict homework effort and mathematics achievement.

The Present Study

A vast body of research indicates that homework enhances students’ academic achievement [see the meta-analysis conducted by Fan et al. (2017) ], however, maladaptive homework behaviors of students (e.g., procrastination, lack of interest in homework, failure to complete homework) may affect homework benefits ( Bembenutty, 2011a ; Hong et al., 2011 ; Rosário et al., 2019 ). These behaviors may be related to the characteristics of the homework assigned (e.g., large amount of homework, disconnect between the type and level of difficulty of homework assignments and students’ needs and abilities, see Margolis and McCabe, 2004 ; Trautwein, 2007 ).

Homework is only valuable to students’ learning when its quality is perceived by students ( Dettmers et al., 2010 ). Nevertheless, little is known about the meaning of homework quality for teachers who are responsible for assigning homework. What do teachers understand to be quality homework? To our knowledge, the previous studies exploring teachers’ perspectives on their homework practices did not relate data with quality homework (e.g., Xu and Yuan, 2003 ; Danielson et al., 2011 ; Kaur, 2011 ; Bang, 2012 ; Kukliansky et al., 2014 ). For example, Kukliansky et al. (2014) found a disconnect between middle school science teachers’ perspectives about their homework practices and their actual homework practices observed in class. However, results were not further explained.

The current study aims to explore teachers’ perspectives on the characteristics of quality homework, and on the characteristics underlying the homework tasks assigned. Findings are expected to shed some light on the role of teachers in the homework process and contribute to maximize the benefits of homework. Our results may be useful for either homework research (e.g., by informing new quantitative studies grounded on data from teachers’ perspectives) or educational practice (e.g., by identifying new avenues for teacher training and the defining of guidelines for homework practices).

This study is particularly important in mathematics for the following reasons: mathematics is among the school subjects where teachers assign the largest amount of homework (e.g., Rønning, 2011 ; Xu, 2015 ), while students continue to yield worrying school results in the subject, especially in middle and high school ( Gottfried et al., 2007 ; OECD, 2014b ). Moreover, a recent meta-analysis focused on mathematics and science homework showed that the relationship between homework and academic achievement in middle school is weaker than in elementary school ( Fan et al., 2017 ). Thus, we collected data through focus group discussions with elementary and middle school mathematics teachers in order to analyze any potential variations in their perspectives on the characteristics of quality homework, and on the characteristics of homework tasks they typically assign. Regarding the latter topic, we also collected photos of homework tasks assigned by 25% of the participating teachers in order to triangulate data and enhance the trustworthiness of our findings.

Our exploratory study was guided by the following research questions:

• simple (1) How do elementary and middle school mathematics teachers perceive quality homework?
• simple (2) How do elementary and middle school mathematics teachers describe the homework tasks they typically assign to students?

Materials and Methods

The study context.

Despite recommendations of the need for clear homework policies (e.g., Cooper et al., 2006 ; Bembenutty, 2011b ), Portugal has no formal guidelines for homework (e.g., concerning the frequency, length, type of tasks). Still, many teachers usually include homework as part of students’ overall grade and ask parents to monitor their children’s homework completion. Moreover, according to participants there is no specific training on homework practices for pre-service or in-service teachers.

The Portuguese educational system is organized as follows: the last two years of elementary school encompass 5th and 6th grade (10 and 11 years old), while middle school encompasses 7th, 8th, and 9th grade (12 to 14 years old). At the two school levels mentioned, mathematics is a compulsory subject and students attend three to five mathematics lessons per week depending on the duration of each class (270 min per week for Grades 5 and 6, and 225 min per week for Grades 7–9). All students are assessed by their mathematics teacher (through continuous assessment tests), and at the end of elementary and middle school levels (6th and 9th grade) students are assessed externally through a national exam that counts for 30% of the overall grade. In Portuguese schools assigning homework is a frequently used educational practice, mostly in mathematics, and usually counts toward the overall grade, ranging between 2% and 5% depending on school boards ( Rosário et al., 2018 ).

Participants

In the current study, all participants were involved in focus groups and 25% of them, randomly selected, were asked to submit photos of homework tasks assigned.

According to Morgan (1997) , to maximize the discussion among participants it is important that they share some characteristics and experiences related to the aims of the study in question. In the current study, teachers were eligible to participate when the following criteria were met: (i) they had been teaching mathematics at elementary or middle school levels for at least two years; and (ii) they would assign homework regularly, at least twice a week, in order to have enough experiences to share in the focus group.

All mathematics teachers ( N = 130) from 25 elementary and middle schools in Northern Portugal were contacted by email. The email informed teachers of the purposes and procedures of the study (e.g., inclusion criteria, duration of the session, session videotaping, selection of teachers to send photos of homework tasks assigned), and invited them to participate in the study. To facilitate recruitment, researchers scheduled focus group discussions considering participants’ availability. Of the volunteer teachers, all participants met the inclusion criteria. The research team did not allocate teachers with hierarchical relationships in the same group, as this might limit freedom of responses, affect the dynamics of the discussion, and, consequently, the outcomes ( Kitzinger, 1995 ).

Initially we conducted four focus groups with elementary school teachers (5th and 6th grade, 10 and 11 years old) and four focus groups with middle school teachers (7th, 8th, and 9th grade, 12, 13 and 14 years old). Subsequently, two additional focus group discussions (one for each school level) were conducted to ensure the saturation of data. Finally, seventy-eight mathematics teachers (61 females and 17 males; an acceptance rate of 60%) from 16 schools participated in our study (see Table 1 ). The teachers enrolled in 10 focus groups comprised of seven to nine teachers per group. Twenty teachers were randomly selected and asked to participate in the second data collection; all answered positively to our invitation (15 females and 5 males).

Participants’ demographic information.

According to our participants, in the school context, mathematics teachers may teach one to eight classes of different grade levels. In the current research, participants were teaching one to five classes of two or three grade levels at schools in urban or near urban contexts. The participants practiced the mandatory nationwide curriculum and a continuous assessment policy.

Data Collection

We carried out this study following the recommendations of the ethics committee of the University of Minho. All teachers gave written informed consent to participate in the research in accordance with the Declaration of Helsinki. The collaboration involved participating in one focus group discussion, and, for 25% of the participants, submitting photos by email of the homework tasks assigned.

In the current study, aiming to deepen our comprehension of the research questions, focus group interviews were conducted to capture participants’ thoughts about a particular topic ( Kitzinger, 1995 ; Morgan, 1997 ). The focus groups were conducted by two members of the research team (a moderator and a field note-taker) in the first term of the school year and followed the procedure described by Krueger and Casey (2000) . To prevent mishandling the discussions and to encourage teachers to participate in the sessions, the two facilitators attended a course on qualitative research offered at their home institution specifically targeting focus group methodology.

All focus group interviews were videotaped. The sessions were held in a meeting room at the University of Minho facilities, and lasted 90 to 105 min. Before starting the discussion, teachers filled in a questionnaire with sociodemographic information, and were invited to read and sign a written informed consent form. Researchers introduced themselves, and read out the information regarding the study purpose and the focus group ground rules. Participants were ensured of the confidentiality of their responses (e.g., names and researchers’ personal notes that might link participants to their schools were deleted). Then, the investigators initiated the discussion (see Table 2 ). At the end of each focus group discussion, participants were given the opportunity to ask questions or make further contributions.

Focus group questions.

After the focus group discussions, we randomly selected 25% of the participating teachers (i.e., 10 teachers from each school level), each asked to submit photos of the homework tasks assigned by email over the course of three weeks (period between two mathematics assessment tests). This data collection aimed to triangulate data from focus groups regarding the characteristics of homework usually assigned. To encourage participation, the research team sent teachers a friendly reminder email every evening throughout the period of data collection. In total, we received 125 photos (51% were from middle school teachers).

Data Analysis

Videotapes were used to assist the verbatim transcription of focus group data. Both focus group data and photos of the homework assignments were analyzed using thematic analysis ( Braun and Clarke, 2006 ), assisted by QSR International’s NVivo 10 software ( Richards, 2005 ). In this analysis there are no rigid guidelines on how to determine themes; to assure that the analysis is rigorous, researchers are expected to follow a consistent procedure throughout the analysis process ( Braun and Clarke, 2006 ). For the current study, to identify themes and sub-themes, we used the extensiveness of comments criterion (number of participants who express a theme, Krueger and Casey, 2000 ).

Firstly, following an inductive process one member of the research team read the first eight focus group transcriptions several times, took notes on the overall ideas of the data, and made a list of possible codes for data at a semantic level ( Braun and Clarke, 2006 ). Using a cluster analysis by word similarity procedure in Nvivo, all codes were grouped in order to identify sub-themes and themes posteriorly. All the themes and sub-themes were independently and iteratively identified and compared with the literature on homework ( Peterson and Irving, 2008 ). Then, the themes and sub-themes were compared with the homework characteristics already reported in the literature (e.g., Cooper, 1989 ; Epstein and Van Voorhis, 2001 ; Trautwein et al., 2006b ). New sub-themes emerged from participants’ discourses (i.e., “adjusted to the availability of students,” “teachers diagnose learning”), and were grouped in the themes reported in the literature. After, all themes and sub-themes were organized in a coding scheme (for an example see Table 3 ). Finally, the researcher coded the two other focus group discussions, no new information was added related to the research questions. Given that the generated patterns of data were not changed, the researcher concluded that thematic saturation was reached.

Examples of the coding scheme.

An external auditor, trained on the coding scheme, revised all transcriptions, the coding scheme and the coding process in order to minimize researchers’ biases and increase the trustworthiness of the study ( Lincoln and Guba, 1985 ). The first author and the external auditor examined the final categorization of data and reached consensus.

Two other members of the research team coded independently the photos of the homework assignments using the same coding scheme of the focus groups. To analyze data, the researchers had to define the sub-themes “short assignments” (i.e., up to three exercises) and “long assignments” (i.e., more than three exercises). In the end, the two researchers reviewed the coding process and discussed the differences found (e.g., some exercises had several sub questions, so one of the researchers coded it as “long assignments”; see the homework sample 4 of the Supplementary Material ). However, the researchers reached consensus, deciding not to count the number of sub questions of each exercise individually, because these types of questions are related and do not require a significant amount of additional time.

Inter-rater reliability (Cohen’s Kappa) was calculated. The Cohen’s Kappa was 0.86 for the data analysis of the focus groups and 0.85 for data analysis of the photos of homework assignments, which is considered very good according to Landis and Koch (1977) . To obtain a pattern of data considering the school levels, a matrix coding query was run for each data source (i.e., focus groups and photos of homework assignments). Using the various criteria options in NVivo 10, we crossed participants’ classifications (i.e., school level attribute) and nodes and displayed the frequencies of responses for each row–column combination ( Bazeley and Jackson, 2013 ).

In the end of this process of data analysis, for establishing the trustworthiness of findings, 20 teachers (i.e., ten participants of each grade level) were randomly invited, and all agreed, to provide a member check of the findings ( Lincoln and Guba, 1985 ). Member checking involved two phases. First, teachers were asked individually to read a summary of the findings and to fill in a 5-point Likert scale (1, completely disagree; 5, completely agree) with four items: “Findings reflect my perspective regarding homework quality”; “Findings reflect my perspective regarding homework practices”; “Findings reflect what was discussed in the focus group where I participated”, and “I feel that my opinion was influenced by the other teachers during the discussion” (inverted item). Secondly, teachers were gathered by school level and asked to critically analyze and discuss whether an authentic representation was made of their perspectives regarding quality homework and homework practices ( Creswell, 2007 ).

This study explored teachers’ perspectives on the characteristics of quality homework, and on the characteristics of the homework tasks typically assigned. To report results, we used the frequency of occurrence criterion of the categories defined by Hill et al. (2005) . Each theme may be classified as “General” when all participants, or all except one, mention a particular theme; “Typical” when more than half of the cases mention a theme; “Variant” when more than 3, and less than half of the cases mention a theme; and “Rare” when the frequency is between 2 and 3 cases. In the current study, only general and typical themes were reported to discuss the most salient data.

The results section was organized by each research question. Throughout the analysis of the results, quotes from participants were presented to illustrate data. For the second research question, data from the homework assignments collected as photographs were also included.

Initial Data Screening

All participating teachers defended the importance of completing homework, arguing that homework can help students to develop their learning and to engage in school life. Furthermore, participants also agreed on the importance of delivering this message to students. Nevertheless, all teachers acknowledged that assigning homework daily present a challenge to their teaching routine because of the heavy workload faced daily (e.g., large numbers of students per class, too many classes to teach, teaching classes from different grade levels which means preparing different lessons, administrative workload).

Teachers at both school levels talked spontaneously about the nature of the tasks they usually assign, and the majority reported selecting homework tasks from a textbook. However, participants also referred to creating exercises fit to particular learning goals. Data collected from the homework assigned corroborated this information. Most of participating teachers reported that they had not received any guidance from their school board regarding homework.

How do Elementary and Middle School Teachers Perceive Quality Homework?

Three main themes were identified by elementary school teachers (i.e., instructional purposes, degree of individualization/adaptivity, and length of homework) and two were identified by middle school teachers (i.e., instructional purposes, and degree of individualization/adaptivity). Figure 1 depicts the themes and sub-themes reported by teachers in the focus groups.

Characteristics of quality homework reported by mathematics teachers by school level.

In all focus group discussions, all teachers from elementary and middle school mentioned “instructional purposes” as the main characteristic of quality homework. When asked to further explain the importance of this characteristic, teachers at both school levels in all focus group talked about the need for “practicing or reviewing” the content delivered in class to strengthen students’ knowledge. A teacher illustrated this idea clearly: “it is not worth teaching new content when students do not master the material previously covered” (P1 FG3). This idea was supported by participants in all focus groups; “at home they [students] have to work on the same content as those taught in class” (P1 FG7), “students have to revisit exercises and practice” (P2 FG9), “train over and over again” (P6 FG1), “practice, practice, practice” (P4 FG2).

While discussing the benefits of designing homework with the purpose of practicing the content learned, teachers at both school levels agreed on the fact that homework may be a useful tool for students to diagnose their own learning achievements while working independently. Teachers were empathetic with their peers when discussing the instrumentality of homework as a “thermometer” for students to assess their own progress. This idea was discussed in similar ways in all focus group, as the following quotation illustrates:

P2 FG1: Homework should be a bridge between class and home… students are expected to work independently, learn about their difficulties when doing homework, and check whether they understood the content.

When asked to outline other characteristics of quality homework, several elementary school teachers in all focus group mentioned that quality homework should also promote “student development” as an instructional purpose. These participants explained that homework is an instructional tool that should be designed to “foster students’ autonomy” (P9 FG4), “develop study habits and routines” (P1 FG8), and “promote organization skills and study methods” (P6 FG7). These thoughts were unanimous among participants in all focus groups. While some teachers introduced real-life examples to illustrate the ideas posited by their colleagues, others nodded their heads in agreement.

In addition, some elementary school teachers observed that homework tasks requiring transference of knowledge could help develop students’ complex thinking, a highly valued topic in the current mathematics curriculum worldwide. Teachers discussed this topic enthusiastically in two opposite directions: while some teachers defended this purpose as a characteristic of quality homework, others disagreed, as the following conversation excerpt illustrates:

P7 FG5: For me good homework would be a real challenge, like a problem-solving scenario that stimulates learning transference and develops mathematical reasoning … mathematical insight. It’s hard because it forces them [students] to think in more complex ways; still, I believe this is the type of homework with the most potential gains for them.

P3 FG5: That’s a good point, but they [students] give up easily. They just don’t do their homework. This type of homework implies competencies that the majority of students do not master…

P1 FG5: Not to mention that this type of homework takes up a lot of teaching time… explaining, checking…, and we simply don’t have time for this.

Globally, participants agreed on the potential of assigning homework with the purpose of instigating students to transfer learning to new tasks. However, participants also discussed the limitations faced daily in their teaching (e.g., number of students per class, students’ lack of prior knowledge) and concluded that homework with this purpose hinders the successful development of their lesson plans. This perspective may help explain why many participants did not perceive this purpose as a significant characteristic of quality homework. Further commenting on the characteristics of quality homework, the majority of participants at both school levels agreed that quality homework should be tailored to meet students’ learning needs. The importance of individualized homework was intensely discussed in all focus groups, and several participants suggested the need for designing homework targeted at a particular student or groups of students with common education needs. The following statements exemplifies participants’ opinions:

P3 FG3: Ideally, homework should be targeted at each student individually. For André a simple exercise, for Ana a more challenging exercise … in an ideal world homework should be tailored to students’ needs.

P6 FG6: Given the diversity of students in our classes, we may find a rainbow of levels of prior knowledge… quality homework should be as varied as our students’ needs.

As discussed in the focus groups, to foster the engagement of high-achievers in homework completion, homework tasks should be challenging enough (as reported previously by P3 FG3). However, participants at both school levels observed that their heavy daily workload prevents them from assigning individualized homework:

P1 FG1: I know it’s important to assign differentiated homework tasks, and I believe in it… but this option faces real-life barriers, such as the number of classes we have to teach, each with thirty students, tons of bureaucratic stuff we have to deal with… All this raises real-life questions, real impediments… how can we design homework tasks for individual students?

Considering this challenge, teachers from both school levels suggested that quality homework should comprise exercises with increasing levels of difficulty. This strategy would respond to the heterogeneity of students’ learning needs without assigning individualized homework tasks to each student.

While discussing individualized homework, elementary school teachers added that assignments should be designed bearing in mind students’ availability (e.g., school timetable, extracurricular activities, and exam dates). Participants noted that teachers should learn the amount of workload their students have, and should be aware about the importance of students’ well-being.

P4 FG1: If students have large amounts of homework, this could be very uncomfortable and even frustrating… They have to do homework of other subjects and add time to extracurricular activities… responding to all demands can be very stressful.

P4 FG2: I think that we have to learn about the learning context of our students, namely their limitations to complete homework in the time they have available. We all have good intentions and want them to progress, but if students do not have enough time to do their homework, this won’t work. So, quality homework would be, for example, when students have exams and the teacher gives them little or no homework at all.

The discussion about the length of homework found consensus among the elementary school teachers in all focus group in that quality homework should be “brief”. During the discussions, elementary school teachers further explained that assigning long tasks is not beneficial because “they [students] end up demotivated” (P3 FG4). Besides, “completing long homework assignments takes hours!” (P5 FG4).

How do Elementary and Middle School Teachers Describe the Homework Tasks They Typically Assign to Students?

When discussing the characteristics of the homework tasks usually assigned to their students four main themes were identified by elementary school teachers (i.e., instructional purposes, degree of individualization/adaptivity, frequency and completion deadlines), and two main themes were raised by middle school (i.e., instructional purposes, and degree of individualization/adaptivity). Figure 2 gives a general overview of the findings. Data gathered from photos added themes to findings as follows: one (i.e., length) to elementary school and two (i.e., length and completion deadlines) to middle school (see Figure 3 ).

Characteristics of the homework tasks usually assigned as reported by mathematics teachers.

Characteristics of the homework tasks assigned by mathematics teachers.

While describing the characteristics of the homework tasks usually assigned, teachers frequently felt the need to compare the quality homework characteristics previously discussed with those practices. In fact, at this stage, teachers’ discourse was often focused on the analysis of the similarities and potential discrepancies found.

The majority of teachers at both school levels in all focus group reported that they assign homework with the purpose of practicing and reviewing the materials covered earlier. Participants at both school levels highlighted the need to practice the contents covered because by the end of 6th- and 9th-grade students have to sit for a national exam for which they have to be trained. This educational context may interfere with the underlying homework purposes teachers have, as this quotation illustrates:

P3 FG3: When teaching mathematics, we set several goals, but our main focus is always the final exam they [students] have to take. I like students who think for themselves, who push themselves out of their comfort zone. However, I’m aware that they have to score high on national exams, otherwise… so, I assign homework to practice the contents covered.

Beyond assigning homework with the purpose of practicing and reviewing, middle school teachers also mentioned assigning homework with the purpose of diagnosing skills and personal development (see Figure 2 ). Many teachers reported that they use homework as a tool to diagnose students’ skills. However, several recognized that they had previously defended the importance of homework to help students to evaluate their own learning (see Figure 1 ). When discussing the latter point, participants observed the need to find out about whether students had understood the content taught in class, and to decide which changes to teaching style, homework assigned, or both may be necessary.

Participant teachers at middle school in all focus groups profusely discussed the purpose of personal development when assigning homework. In fact, not many teachers at this school level mentioned this purpose as a characteristic of quality homework (it was a variant category, so it was not reported), yet it was referred to as a cornerstone in their homework practice. Reflecting on this discrepancy, middle school teachers explained in a displeased tone that their students were expected to have developed study habits and manage their school work with autonomy and responsibility. However, this “educational scenario is rare, so I feel the need to assign homework with this aim [personal development]” (P4 FG9).

Moving further in the discussion, the majority of teachers at both school levels reported to assign whole-class homework (homework designed for the whole class with no focus on special cases). “Individualized homework requires a great amount of time to be monitored” (P1 FG6), explained several participants while recalling earlier comments. Teachers justified their position referring to the impediments already mentioned (e.g., large number of students per class, number of classes from different grade levels which means preparing different lessons). Besides, teachers discussed the challenge of coping with heterogeneous classes, as one participant noted: “the class is so diverse that it is difficult to select homework tasks to address the needs of every single student. I would like to do it…but we do not live in an ideal world” (P9 FG4).

Moreover, teachers at both school levels (see Figure 2 ) reported to assign homework according to the availability of students; still, only elementary school teachers had earlier referred to the importance of this characteristic in quality homework. When teachers were asked to elaborate on this idea, they defended the need to negotiate with students about specific homework characteristics, for example, the amount of homework and submission deadline. In some classes, matching students’ requests, teachers might assign a “weekly homework pack” (P7 FG10). This option provides students with the opportunity to complete homework according to their availability (e.g., choosing some days during the week or weekend). Teachers agreed that ‘negotiation’ fosters students’ engagement and homework compliance (e.g., “I do not agree that students do homework on weekends, but if they show their wish and actually they complete it, for me that’s okay”, P7 FG10). In addition, teachers expressed worry about their students’ often heavy workload. Many students stay in school from 8.30 am to 6.30 pm and then attend extracurricular activities (e.g., soccer training, private music lessons). These activities leave students very little free time to enjoy as they wish, as the following statement suggests:

P8 FG4: Today I talked to a group of 5th-graders which play soccer after school three times a week. They told me that sometimes they study between 10.00 and 11.00 p.m. I was astonished. How is this possible? It’s clearly too much for these kids.

Finally, elementary school teachers in all focus group referred frequency and completion deadlines as characteristics of the homework they usually assign. The majority of teachers informed that they assign homework in almost every class (i.e., teachers reported to exclude tests eves of other subjects), to be handed in the following class.

The photos of the homework assignments (see some examples in Supplementary Material ) submitted by the participating teachers served to triangulate data. The analysis showed that teachers’ discourses about the characteristics of homework assigned and the homework samples are congruent, and added information about the length of homework (elementary and middle schools) and the completion deadlines (middle school) (see Figure 3 ).

Discussion and Implications for Practice and Research

Homework research have reported teachers’ perspectives on their homework practices (e.g., Brock et al., 2007 ; Danielson et al., 2011 ; Kaur, 2011 ; Bang, 2012 ; Kukliansky et al., 2014 ), however, literature lacks research on the quality of homework. This study adds to the literature by examining the perspectives of teachers from two school levels regarding quality homework. Moreover, participants described the characteristics of the homework assignments they typically assign, which triggered the discussion about the match between the characteristics of quality homework and the tasks actually assigned. While discussing these key aspects of the homework process, the current study provides valuable information which may help deepen our understanding of the different contributions of homework to students’ learning. Furthermore, findings are expected to inform teachers and school administrators’ homework practices and, hopefully, improve the quality of students’ learning.

All teachers at both school levels valued homework as an important educational tool for their teaching practice. Consistent with the literature, participants indicated practicing or reviewing the material covered in class as the main purpose of both the homework typically assigned ( Danielson et al., 2011 ; Kaur, 2011 ) and quality homework. Despite the extended use of this homework purpose by teachers, a recent study conducted with mathematics teachers found that homework with the purpose of practicing the material covered in class did not impact significantly the academic achievement of 6th-grade students; however, homework designed with the purpose of solving problems did (extension homework) ( Rosário et al., 2015 ). Interestingly, in the current study only teachers from elementary school mentioned the homework purpose “extension” as being part of quality homework, but these teachers did not report to use it in practice (at least it was not a typical category) (see Figure 2 ). Extension homework was not referenced by middle school teachers either as quality homework or as a characteristic of homework assigned. Given that middle school students are expected to master complex math skills at this level (e.g., National Research Council and Mathematics Learning Study Committee, 2001 ), this finding may help school administrators and teachers reflect on the value and benefits of homework to students learning progress.

Moreover, teachers at both school levels stressed the use of homework as a tool to help students evaluate their own learning as a characteristic of quality homework; however, this purpose was not said to be a characteristic of the homework usually assigned. If teachers do not explicitly emphasize this homework purpose to their students, they may not perceive its importance and lose opportunities to evaluate and improve their work.

In addition, elementary school teachers identified personal development as a characteristic of quality homework. However, only middle school teachers reported assigning homework aiming to promote students’ personal development, and evaluate students’ learning (which does not imply that students evaluate their own learning). These findings are important because existing literature has highlighted the role played by homework in promoting students’ autonomy and learning throughout schooling ( Rosário et al., 2009 , 2011 ; Ramdass and Zimmerman, 2011 ; Núñez et al., 2015b ).

Globally, data show a disconnect between what teachers believe to be the characteristics of quality homework and the characteristics of the homework assigned, which should be further analyzed in depth. For example, teachers reported that middle school students lack the autonomy and responsibility expected for this school level, which translates to poor homework behaviors. In fact, contrary to what they would expect, middle school teachers reported the need to promote students’ personal development (i.e., responsibility and autonomy). This finding is consistent with the decrease of students’ engagement in academic activities found in middle school (e.g., Cleary and Chen, 2009 ; Wang and Eccles, 2012 ). This scenario may present a dilemma to middle school teachers regarding the purposes of homework. On one hand, students should have homework with more demanding purposes (e.g., extension); on another hand, students need to master work habits, responsibility and autonomy, otherwise homework may be counterproductive according to the participating teachers’ perspective.

Additionally, prior research has indicated that classes assigned challenging homework demonstrated high mathematics achievement ( Trautwein et al., 2002 ; Dettmers et al., 2010 ). Moreover, the study by Zakharov et al. (2014) found that Russian high school students from basic and advanced tracks benefited differently from two types of homework (i.e., basic short-answer questions, and open-ended questions with high level of complexity). Results showed that a high proportion of basic or complex homework exercises enhanced mathematics exam performance for students in the basic track; whereas only a high proportion of complex homework exercises enhanced mathematics exam performance for students in the advanced track. In fact, for these students, a low proportion of complex homework exercises was detrimental to their achievement. These findings, together with our own, may help explain why the relationship between homework and mathematics achievement in middle school is lower than in elementary school (see Fan et al., 2017 ). Our findings suggest the need for teachers to reflect upon the importance of assigning homework to promote students’ development in elementary school, and of assigning homework with challenging purposes as students advance in schooling to foster high academic outcomes. There is evidence that even students with poor prior knowledge need assignments with some degree of difficulty to promote their achievement (see Zakharov et al., 2014 ). It is important to note, however, the need to support the autonomy of students (e.g., providing different the types of assignments, opportunities for students to express negative feelings toward tasks, answer students’ questions) to minimize the threat that difficult homework exercises may pose to students’ sense of competence; otherwise an excessively high degree of difficulty can lead to students’ disengagement (see Patall et al., 2018 ). Moreover, teachers should consider students’ interests (e.g., which contents and types of homework tasks students like) and discuss homework purposes with their students to foster their understanding of the tasks assigned and, consequently, their engagement in homework ( Xu, 2010 , 2018 ; Epstein and Van Voorhis, 2012 ; Rosário et al., 2018 ).

We also found differences between teachers’ perspectives of quality homework and their reported homework practices concerning the degree of individualization when assigning homework. Contrary to the perspectives that quality homework stresses individual needs, teachers reported to assign homework to the whole class. In spite of the educational costs associated with assigning homework adjusted to specific students or groups of students (mentioned several times by participants), research has reported benefits for students when homework assignments match their educational needs (e.g., Cooper, 2001 ; Trautwein et al., 2006a ; Zakharov et al., 2014 ). The above-mentioned study by Zakharov et al. (2014) also shed light on this topic while supporting our participants’ suggestion to assign homework with increasing level of difficulty aiming to match the variety of students’ levels of knowledge (see also Dettmers et al., 2010 ). However, teachers did not mention this idea when discussing the characteristic of homework typically assigned. Thus, school administrators may wish to consider training teachers (e.g., using mentoring, see Núñez et al., 2013 ) to help them overcome some of the obstacles faced when designing and assigning homework targeting students’ individual characteristics and learning needs.

Another interesting finding is related to the sub-theme of homework adjusted to the availability of students. This was reported while discussing homework quality (elementary school) and characteristics of homework typically assigned (elementary and middle school). Moreover, some elementary and middle school teachers explained by email the reasons why they did not assign homework in some circumstances [e.g., eves of assessment tests of other subjects, extracurricular activities, short time between classes (last class of the day and next class in the following morning)]. These teachers’ behaviors show concern for students’ well-being, which may positively influence the relationship between students and teachers. As some participants mentioned, “students value this attitude” (P1 FG5). Thus, future research may explore how homework adjusted to the availability of students may contribute to encouraging positive behaviors, emotions and outcomes of students toward their homework.

Data gathered from the photos of the assigned homework tasks allowed a detailed analysis of the length and completion deadlines of homework. Long assignments did not match elementary school teachers’ perspectives of quality homework. However, a long homework was assigned once and aimed to help students practice the material covered for the mathematics assessment test. Here, practices diverged. Some teachers assigned this homework some weeks before and others assign it in last class before the test. For this reason, the “long term” completion deadline was not a typical category, hence not reported. Future research could consider studying the impact of this homework characteristic on students’ behaviors and academic performance.

Finally, our findings show that quality homework, according to teachers’ perspectives, requires attention to a combination of several characteristics of homework. Future studies may include measures to assess characteristics of homework other than “challenge” and “selection” already investigated ( Trautwein et al., 2006b ; Dettmers et al., 2010 ; Rosário et al., 2018 ); for example, homework adjusted to the availability of students.

Strengths and Limitations of the Study

The current study analyzed the teachers’ perspectives on the characteristics of quality homework and of the homework they typically assigned. Despite the incapability to generalize data, we believe that these findings provide important insights into the characteristics that may impact a homework assignment’s effectiveness, especially at middle school level. For example, our results showed a disconnect between teachers’ perspectives about the characteristics of quality homework and the characteristics of the homework they assign. This finding is relevant and emphasizes the need to reflect on the consistency between educational discourses and educational practices. Teachers and school administrators could consider finding opportunities to reflect on this disconnect, which may also occur in other educational practices (e.g., teacher feedback, types of questions asked in class). Present data indicate that middle school teachers reported to assign homework with the major purpose of practicing and reviewing the material, but they also aim to develop students’ responsibility and autonomy; still they neglect homework with the purpose of extension which is focused on encouraging students to display an autonomous role, solve problems and transfer the contents learned (see discussion section). Current findings also highlight the challenges and dilemmas teachers face when they assign homework, which is important to address in teachers’ training. In fact, assigning quality homework, that is, homework that works, is not an easy task for teachers and our findings provide empirical data to discuss and reflect upon its implications for research and educational practice. Although our findings cannot be generalized, still they are expected to provide important clues to enhance teachers’ homework practices in different contexts and educational settings, given that homework is among the most universal educational practices in the classroom, is a topic of public debate (e.g., some arguments against homework are related to the characteristics of the assignments, and to the malpractices in using this educational tool) and an active area of research in many countries ( Fan et al., 2017 ).

Moreover, these findings have identified some of the most common obstacles teachers struggle with; such data may be useful to school administrators when designing policies and to teacher training. The administrative obstacles (e.g., large number of students per class) reported by teachers may help understand some of the discrepancies found between teachers’ definition of quality homework and their actual homework practices (e.g., degree of individualization), and also identify which problems related to homework may require intervention. Furthermore, future research could further investigate this topic by interviewing teachers, videotaping classroom activities and discussing data in order to design new avenues of homework practices.

We share the perspective of Trautwein et al. (2006b) on the importance of mapping the characteristics of homework positively associated with students’ homework behaviors. Data from this study may inform future studies analyzing these relationships, promote adaptive homework behaviors and enhance learning.

Methodologically, this research followed rigorous procedures to increase the trustworthiness of findings, improving the validity of the study (e.g., Lincoln and Guba, 1985 ) that should be accounted for. Data from two data sources (i.e., focus groups and the homework assignments photographed) were consistent, and the member checking conducted in both phases allowed the opportunity to learn that the findings of the focus group seem to accurately reflect the overall teachers’ perspectives regarding quality homework and their homework practices.

Despite the promising contributions of this study to the body of research regarding homework practices, this specific research provides an incomplete perspective of the homework process as it has only addressed the perspectives of one of the agents involved. Future research may consider analyzing students’ perspectives about the same topic and contrast data with those of teachers. Findings are expected to help us identify the homework characteristics most highly valued by students and learn about whether they match those of teachers.

Furthermore, data from homework assignments (photos) were provided by 25% of the participating teachers and for a short period of time (i.e., three weeks in one school term). Future research may consider conducting small-scale studies by collecting data from various sources of information aiming at triangulating data (e.g., analyzing homework assignments given in class, interviewing students, conducting in-class observations) at different times of the school year. Researchers should also consider conducting similar studies in different subjects to compare data and inform teachers’ training.

Finally, our participants’ description does not include data regarding the teaching methodology followed by teachers in class. However, due to the potential interference of this variable in results, future research may consider collect and report data regarding school modality and the teaching methodology followed in class.

Homework is an instructional tool that has proved to enhance students’ learning ( Cooper et al., 2006 ; Fernández-Alonso et al., 2015 ; Valle et al., 2016 ; Fan et al., 2017 ; Rosário et al., 2018 ). Still, homework is a complex process and needs to be analyzed thoroughly. For instance, when planning and designing homework, teachers need to choose a set of homework characteristics (e.g., frequency, purposes, degree of individualization, see Cooper, 2001 ; Trautwein et al., 2006b ) considering students’ attributes (e.g., Cooper, 2001 ), which may pose a daily challenge even for experienced teachers as those of the current study. Regardless of grade level, quality homework results from the balance of a set of homework characteristics, several of which were addressed by our participants. As our data suggest, teachers need time and space to reflect on their practices and design homework tasks suited for their students. To improve the quality of homework design, school administrators may consider organizing teacher training addressing theoretical models of homework assignment and related research, discussing homework characteristics and their influence on students’ homework behaviors (e.g., amount of homework completed, homework effort), and academic achievement. We believe that this training would increase teachers’ knowledge and self-efficacy beliefs to develop homework practices best suited to their students’ needs, manage work obstacles and, hopefully, assign quality homework.

Ethics Statement

This study was reviewed and approved by the ethics committee of the University of Minho. All research participants provided written informed consent in accordance with the Declaration of Helsinki.

Author Contributions

PR and TN substantially contributed to the conception and the design of the work. TN and JC were responsible for the literature search. JC, TN, AN, and TM were responsible for the acquisition, analysis, and interpretation of data for the work. PR was also in charge of technical guidance. JN made important intellectual contribution in manuscript revision. PR, JC, and TN wrote the manuscript with valuable inputs from the remaining authors. All authors agreed for all aspects of the work and approved the version to be published.

Conflict of Interest Statement

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.

Acknowledgments

The authors would like to thank Fuensanta Monroy and Connor Holmes for the English editing of the manuscript.

Funding. This study was conducted at Psychology Research Centre, University of Minho, and supported by the Portuguese Foundation for Science and Technology and the Portuguese Ministry of Education and Science through national funds and when applicable co-financed by FEDER under the PT2020 Partnership Agreement (UID/PSI/01662/2013). PR was supported by the research projects EDU2013-44062-P (MINECO) and EDU2017-82984-P (MEIC). TN was supported by a Ph.D. fellowship (SFRH/BD/80405/2011) from the Portuguese Foundation for Science and Technology (FCT).

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fpsyg.2019.00224/full#supplementary-material

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Determiners Exercises for Class 11 CBSE With Answers

Looking for an easy way to learn English Grammar? then you are in right place. Here we providing basic  English Grammar  topics like Tenses Verbs, Nouns, etc…

Determiners Exercises With Answers for Class 11 CBSE Pdf

Determiners are the words that modify nouns. In other words, determiners are the words that can be used before nouns to determine or to modify their meaning. Determiners function like adjectives. They are also called fixing words. Characteristics of Determiners are as follows

• A determiner may determine or fix a place, person or thing.
• A determiner may identify two or more persons or things.
• A determiner may precede numerals or objects.
• A determiner may indicate a quantity or amount.

Classification of Determiners In English Grammar

Determiners can be classified into

• Articles A, an, the.
• Demonstrative Adjectives This, that, these, those.
• Definite : One, two, hundred,…, first, second, both etc.
• Indefinite : Some, many, much, enough, few, a few, all, little, a little, several, most etc.
• Distributive : Each, every, all, either, neither.
• Difference : Another, other.
• Comparative : More, less, fewer.
• Possessives My, your, his, her, its, our, their, mine, hers, yours, ours, theirs etc.

1. Articles— A, An, The Articles are used before nouns. ‘A’ is used before a noun starting with a consonant sound and ‘An’ is used before a noun starting with a vowel sound. ‘The’ is used before singular countable nouns, plural countable nouns and uncountable nouns.

Use of Indefinite Articles : A/An ‘A’ is used before a noun beginning with a consonant sound, e.g. a woman, a horse, a university (Here woman, horse and university are words beginning with a consonant sound.) ‘An’ is used before a noun beginning with a vowel sound, e.g. an orange, an egg, an elephant, an hour (Here orange, egg, elephant and hour are words beginning with a vowel sound.)

How to Use A and ‘An’ The use of ‘a’ and ‘an’ is determined by sound. The following words begin with a vowel, but not with a vowel sound. A unique thing, a one rupee coin, a European, a unicorn, a university, a useful thing, a union.

So here ‘a’ is used.

On the other hand, with the following words, ‘an’ is used although they begin with a consonant.

An hour, an honest man, an heir to the throne, an MCA. Here, the sound is the criterion to decide whether a/an will be used.

Use of Definite Article : The ‘The’ is used before singular countable nouns, plural countable nouns and uncountable nouns. Uncountable nouns do not have plural forms, e.g. we cannot say ‘sugars’, we will say ‘the sugar’.

‘The’ is used

• While talking about a particular person or thing or one already referred to (that is, when it is clear from the context which one we mean), e.g. The book you want is not available.
• When a singular noun represents the whole class, e.g. The dog is a faithful animal.
• Oceans and seas e.g. the Pacific, the Arabian Sea
• Rivers e.g. the Ganga, the Thames
• he Suez Canal
• Deserts e.g. the Thar, the Sahara
• Group of islands e.g. the West Indies, the Netherlands
• Mountain ranges e.g. the Himalayas, the Satpura
• A few names of countries, which include words like states, Republic or Kingdom e.g. The People’s Republic of China, the United Kingdom, the USA, the Republic of Korea, the Hague etc
• Before the names of religious, mythological e.g. the Vedas, the Puranas, the Mahabharata (but we say Homer’s Iliad, Valmiki’s Ramayana).
• Before the names of things which are unique or one of their kind. e.g. the Sun, the Moon, the Pacific Ocean
• Before a proper noun, when it is qualified by an adjective or a defining adjectival clause. e.g. The Great Caesar, the King of Rome. The Mr Verma whom you met last night is my boss.
• With superlative degrees. e.g. This is the worst performance I have ever seen.
• With ordinals. e.g. He was the first man to walk on the Moon.
• Before musical instruments. e.g. He can play the tabla rhythmically.
• Before an adjective when the noun is understood, e.g. The rich always exploit the poor. Here the word ‘people’ is understood.
• As an adverb with comparatives. e.g. The more money we have, the more we want.

Omission of Article ‘The’

• Before material, abstract and proper nouns used in a general sense. e.g. (a) Honesty is the best policy, (not The honesty….) (b) Sugar tastes sweet, (not The sugar….) (c) Paris is the capital of France, (not The Paris….)
• Before plural countable nouns used in a general sense. e.g. Children like toys.
• Before names of people e.g. Rohit.
• Before names of continents, countries; cities etc e.g. Europe, Pakistan, Nagpur.
• Before names of individual mountains e.g. Mount Everest.
• Before names of meals used in a general sense, e.g. Dinner is ready.
• Before languages and words like school, college, university, church, hospital. e.g. (a) I learn English at school. (b) My uncle is still in hospital.
• Before names of relations, like father, mother etc. e.g. Father is still not at home.
• In certain phrases consisting of preposition followed by its object. e.g. At home, in hand, by night, in case, on foot, by train, on demand etc.

2. Demonstrative Adjectives

This, that, these and those are used before nouns and point to the objects denoted by the nouns; as— This car is very beautiful. Aditi lives in that house. These books are yours. Distribute these mangoes among those children. (i) ‘This’ and ‘These’ point to the objects which are near while ‘that’ and ‘those’ point to the ‘distant’ objects. (ii)   ‘This’, and ‘that’ are used before singular nouns while ‘these’ and ‘those’ are used before plural nouns.

Check Point 1

Question 1. Fill in the blanks with ‘a’ ‘an’ or ‘the’:

• ………… auditorium has been built in our school.
• Honesty is ……………….. best policy.
• The Ganges is ……………….. holy river.
• Hari is ………………… honourable man.
• I saw ……….. one-eyed sailor.
•  …………. sun is bigger than ……………….. earth.
• ………..umbrella is ………………. useful thing.
• This is ……………….. first time I have visited ……………….. big city.
• This car can be driven at ……………….. speed of 180 kilometres ……………….. hour.
• Mount Everest is ……………….. highest peak in ……………….. Himalayas.

Question 2. Fill in the blanks with suitable Demonstrative/Possessive Determiners—this, that, these, those, my, our, your, his, her, their, one’s:

• He is a good boy ………… father is a doctor.
• Aditi wants me to lend her ………….. car.
• All ………….. mangoes are rotten.
• The child has broken ………….. toy.
• Would you like to have ………… book or ………….. one?
• Are there any girls in ………….. class?
• What was ………….. noise?
• The gardener waters ………….. plants every day.
•   ………….. boys will soon join us.
• Who is ………….. fellow?

3. Quantifiers ‘Some’, ‘many’, ‘a lot of’ and ‘a few’ are examples of quantifiers. Quantifiers can be used in affirmative sentences, questions, requests or commands with both countable and uncountable nouns. e.g.

• There are some books on the desk.
• He’s got only a few dollars.
• How much money have you got?
• There is a large quantity of fish in this river.
• He’s got more friends than his sister.

Some quantifiers can go only with countable nouns (e.g. friends, people, cups), some can go only with uncountable nouns (e.g. sugar, tea, money, advice), while some can be used with both countable and uncountable nouns.

Examples of quantifiers are given below

Usage of quantifiers are as follows

I. Use of few/a few and little/a little (a) Few and a few. Few emphasises the lack of something, e.g. There are few sweets left in the jar. (We should be careful not to eat them too quickly because they are almost finished.)

A few emphasises that something still remains, e.g. We still have a few minutes left before the class gets over. Do you have any questions? (We still have some time, so we should use it.)

(b) Little and a little Little emphasises the lack of something, e.g. We have little money right now; we should go out for dinner another day. (We should be careful and use the money wisely because we don’t have much.)

A little emphasises that something still remains, e.g. e.g. There’s a little ice-cream left; who will eat it? (There’s not enough ice-cream left to put back in the freezer, so it should be eaten.)

II. Use of much and many (a) We use much with singular uncountable nouns and many with plural nouns.

• I haven’t got much change; I’ve only got a hundred rupee note.
• Are there many campsites near your place?

(b) We usually use much and many with interrogative sentences and negative sentences.

• Is there much unemployment in that area?
• How many eggs have not been used in this cake?
• Do you think many people will come?
• The rain was pouring down in torrents but there wasn’t much wind.

III. Use of more, less and fewer (comparative determiners) We use more or less before singular uncountable nouns by adding than after it, or for an additional or lesser quantity of something, e.g.

• I do more work than Suresh.
• Please give me some more salad.
• Satish does less work than me.
• I want less salad than Mahesh.

We use fewer before plural countable nouns to refer to a group of things smaller than another. e.g.

• Fewer students succeeded in passing than last year.
• We had fewer computers a year ago.
• of each and every (distributive determiners)

We use each for two or more than two items and every for more than two items. Both of these are followed by singular countable nouns and singular verbs,  e.g.

• Each of the two boys has won a prize.
• Every student in the school is present today.

We use each when the number in the group is limited or definite, but every is used when the number is indefinite or unknown. e.g.

• Each student in my class was promoted.
• Every person in the world has a parent.

V. Use of most, several and all (a) We usually use most with plural uncountable nouns, e.g.

• Most of the people can be trusted.
• Most of the time I am not at home.

(b) We usually use several with plural nouns, but it refers to a number which is not very large, (i.e. less than most)

• Several people were crushed by the stampede.
• Several people lost their lives in the Tsunami.

(c) All requires a plural verb when used with a countable noun, but requires a singular verb with an uncountable noun, e.g.

• All are going to Delhi.
• All that glitters is not gold.

VI. Use of another and other We use another only with singular countable nouns, whereas others can be used with singular countable, plural countable or uncountable nouns. e.g.

• Bring me another knife, as this one is blunt.
• I would prefer the other house.
• The other students went back home.
• He is a better human being than most others.

VII. Use of either and neither (a) We use either to refer to two things, people, situations etc. It may mean one or the other of two or each of the two. e.g.

• I don’t agree with either Ram or Shyam.

(b) We use neither with only singular countable nouns and a singular verb. Neither is the negative of either, e.g.

• Neither of the two boys passed the exam.

4. Possessives ( My, Your, His, Her, Its, Our, Their, etc.) Possessive determiners or possessive adjectives tell us who owns something. We use a possessive determiner before a noun to show who owns the noun we are talking about. They come in front of any other adjectives, e.g.

• This is your book.
• That is our beautiful house.

We use different possessive determiners depending on who owns the thing we are talking about.

My, her, his, and its are used with singular nouns, while ours and they are used with plural nouns. You can be used with either singular or plural nouns, depending on the sense, e.g.

• This is my book.
• The dog licked its paw.
• Which is their car?
• All three of you, have you done your homework?

Determiners and Kinds of Nouns With Which They are Used

• A, an, each, everyone, another, and either are used with singular countable nouns.
• This and that are used with uncountable nouns/singular countable nouns.
• These and those are used with uncountable nouns/plural countable nouns.
• A little, a lot of, a great deal of, much are used with uncountable nouns.
• More, most, a lot of, enough, adequate, some are used with uncountable nouns/plural countable nouns.
• A few, several, many, both are used with plural nouns.
• The, some, any, my, her, your, our, their, its, which, whose, what are used with any type of noun.

Check Point 2 1. Fill in the blanks using suitable quantifiers. (a) Class XI students have had ……….. of homework in mathematics recently. (b) How ……….. time do you need to finish the work? (c) There are too ……….. students in the library. (d) Have you visited ……….. foreign countries recently? (e) Although he’s very ill, he didn’t take ……….. medicine. Answer: (a) lots (b) much (C) many (d) any (e) any

2. Fill in the blanks with quantifiers from the options given. Hints are given in brackets to guide you. (i) There’s hard……….. sunlight in London in the winter. (I expect you will say ‘yes’, because Lodon is too much cold.) (a) some (b) any (c) many (d) few Answer: (b) any

(ii) Could you give me ……….. your time and your money? (A request -1 expect you will say ‘yes’.) (a) each (b) little (c) enough (d) both Answer: (d) both

(iii) Did you buy ……….. butter? (I expect you will say ‘yes’, because we talked about it before.) (a) some (b) any (c) little (d) less Answer: (a) some

3. Replace the personal pronouns (in brackets) with possessive determiners from the options given in brackets after the blanks. (a) Sunita likes (she) ……….. (her / its / my / his) dog. (b) She goes to college with (she) ……….. (their / our /her / his) brother. (c) (It) ……….. (Your / Our / Her / Its) name is Tommy. (d) (He) ……….. (His / Her / Our / Its) favourite hobby is collecting matchbox labels. (e) (I) ……….. (Your / My / His / Her) husband and I want to go to Mumbai. (f) Where is (I) ……….. (their / its / my / our) school bag? (g) We want to see (ii) ……….. (their / these / her / our) historical monuments. (h) (You) ……….. (My / Your / His / Her) laptop is very expensive. (i) Here is (we) ……….. (our / their / your / his) professor. (j) (They) ……….. (Its / Their / Her / His) father works in the government. Answer: (a) her (b) her (c) Its (d) His (e) My (f) my (g) its (h) Your (i) our (j) Their

Error Correction

Detect the error or determiners in the sentences given below and correct them:

• I am going to post office. It is near the central park.
• She lives near temple on Civil Road.
• He is a boy who helps me in need.
• There is little milk in the jug. You may use it.
• Much of the people who went there lost their belongings.
• Avoid eating too many butter.
• Sarojini wrote much of her poems when she was young.
• Their all efforts went up in smoke.
• All of the playground was waterlogged.
• Neither of us did not knew the answer.
• Almost all her time is spent on buying clothes and cosmetics.
• All person have to shape his own destiny.
• Don’t pay some attention to what that silly hag says.
• Everyone takes little time to settle down at a new place.
• I phoned her many times but each time there were no answers.
• I am going to the post office . It is near the central park.
• She lives near the temple on Civil Road.
• He is the boy who helps me in need
• There is a little/(some) milk in the jug. You may use it.
• Avoid eating too much butter .
• Sarojini wrote many of her poems when she was young.
• All of their efforts went up in smoke.
• The whole of the playground was waterlogged.
• Neither of us knew the answer.
• Almost all of her time is spent on buying clothes and cosmetics.
• Every person has to shape his own destiny.
• Don’t pay any attention to what that silly hag says.
• Everyone takes a little time to settle down at a new place.
• I phoned her many times but every time  there was no answer.

Editing Tasks The following passage has not been edited. There is an error in each line against which blanks are given. Write the incorrect word and the correction in the spaces provided. Remember to underline the word that you have supplied.

Editing Task for 11th Class CBSE 1

Answer: (a) Much – Many (b) a – the (c) many – much (d) their – its (e) a – the (f) none – no (g) an – the (h) the – a

Editing Task for 11th Class CBSE 2

Answer: Incorrect – Correct (a) an a – a (b) A The – The (c) the a – a (d) a the – the (e) the a – a (f) its – my

Reordering of Sentences

Look at the following sentences given in a disorderly form. Reorder (Rearrange) them to form meaningful sentences.

• each/last/it/week/rained/day.
• city/a few/have/this/in/I/friends
• mangoes/ripe/all/are/these
• write/she/with/can/hand/either
• stock/sugar/there is/the/in/much ..
• sisters/the/to marry/refused/both
• there/news/is/any?
• milk/jug/some/the/in/is/there
• do/money/want/much/you/how?
• class/boys/your/in/many/are there/how?
• It rained each day last week.
• I have a few Mends in this city.
• All these mangoes are ripe.
• She can write with either hand.
• There is much sugar in the stock.
• Both the sisters refused to marry.
• Is there any news?
• There is some milk in the jug.
• How much money do you want?
• How many boys are there in your class?

Transformation of Sentences

Select the option which transforms the given sentence without changing its meaning.

1. Lead is the heaviest of all metals. (a) Lead is heavier than other metals. (b) Lead is heaviest all than other metals. (c) Lead is heaviest than all other metals. (d) Lead is heavy than all other metals. Answer: (c) Lead is heaviest than all other metals.

2. Who can count the stars? (a) Can one count the stars? (b) None can count the stars. (c) Someone can count the stars. (d) Anyone can count the stars. Answer: (b) None can count the stars.

3. Delhi is one of the biggest Indian cities. (a) Delhi is biggest than most other Indian cities. (b) Delhi is bigger than any other Indian cities. (c) Delhi is big than most other Indian cities. (d) Delhi is bigger than most other Indian cities. Answer: (d) Delhi is bigger than most other Indian cities.

4. Was Bhuvnesh a coward? (a) Wasn’t Bhuvnesh a coward? (b) Bhuvnesh was no coward. (c) Bhuvnesh is not coward. (d) Bhuvnesh was coward. Answer: (b) Bhuvnesh was no coward,

5. Only Mukesh was present in the hall. (a) None but Mukesh is present in the hall. (b) None but Mukesh presents at the hall. (c) None but Mukesh was present at the hall. (d) Only Mukesh was present. Answer: (c) None but Mukesh was present at the hail.