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White Rose Maths Year 6: What Students Learn And The Resources To Support Them

Emma Johnson

Here we look at the White Rose Maths Year 6 scheme of learning, the topics it covers across the year and provide lots of sample questions and White Rose Maths resources for those following White Rose in Year 6.  

About White Rose Maths 

Year 6 autumn term, year 6 spring term, year 6 summer term, recommended white rose maths year 6 resources, place value year 6.

• Addition, subtraction, multiplication and division Year 6

Fractions Year 6

Fractions b year 6, converting units year 6, ratio year 6, algebra year 6, decimals year 6, fractions, decimals and percentages year 6, area, perimeter and volume year 6, read more: mean median mode, shape year 6, looking for more year 6 maths resources and guidance.

Year 6 Maths Test

Download this free Year 6 maths test to check that your class is on track with their Year 6 maths curriculum.

The White Rose Maths scheme of learning follows the national curriculum with a mastery approach to maths with a range of fluency, reasoning and problem solving elements. They also encourage concrete, pictorial and abstract representations to develop deep understanding of mathematical concepts. 

Read more: White Rose Maths

It is thought that approximately 70% of schools in the UK follow the White Rose Maths scheme and this is reflected in the thousands of young mathematicians Third Space Learning tutors every week. Our tutors are highly skilled maths and pedagogy experts, well trained in the language, representations and approach used by White Rose. They are therefore able to deliver a one to one lesson that feels familiar to students who are also used to White Rose. 

Throughout this article you’ll see example maths lesson slides and example questions from Third Space Learning’s Year 6 maths curriculum that exemplify best practice teaching to the White Rose Maths Year 6 scheme. 

We’ve also provided lots of links to White Rose Maths Year 6 resources that are suitable for use for each topic.In addition to the links provided, Third Space Learning also offers libraries for White Rose Maths Year 1 , White Rose Maths Year 2 , White Rose Maths Year 3 , White Rose Maths Year 4 , and White Rose Maths Year 5 . 

About the White Rose Maths Year 6 Scheme of Learning

The primary school White Rose Maths scheme of learning has gone through several iterations and versions up to the current version 3. The scheme of learning SOL is designed as guidance and it is not necessarily intended for each small step to take one lesson. As with all teaching, it is important that teachers adapt this SOL for their class/ pupils. 

Topics covered in Year 6 White Rose Maths scheme of learning work

The White Rose Maths Year 6 SOL outlines which topics are taught, and when, throughout the autumn, spring and summer terms of Year 6. 

The breakdown for Version 3 of the scheme of learning is as follows 

• Place value
• Addition, subtraction, multiplication and division
• Fractions A
• Fractions B
• Converting units of measurement
• Fractions, decimals and percentages
• Area, perimeter and volume
• Position and direction
• Themed projects, consolidation and problem solving

​​Third Space Learning has created several collections of White Rose Maths aligned resources for all primary year groups from early years through to Year 6. These resources can provide a different perspective on a topic and so help pupils spend the time needed to fully embed a concept.

Here is a summary of the different collections available for schools following Year 6 White Rose Maths, many of them are free resources and some are premium resources, all can be downloaded from our maths hub. Links to the topic specific versions are provided within each termly breakdown below:

Ready to go lesson slides

These ready-to-go lesson slides come in the form of editable powerpoints with related worksheets that are designed for everyday teaching. The lesson slides cover both version 2 of the White Rose scheme of learning (in blue) and version 3 of the SOL. They also include support slides that can be used to support pupils who need a little extra  pre/ post teaching to support their understanding.

Year 6 ready-to-go lesson slides

Code Crackers 

Our Code Crackers resources are aligned to the version 2 SOL. These are summative resources designed as a retrieval activity for the end of the place value block.

Maths Code Crackers Year 6

Pre and Post Diagnostic Questions 

These tests can be used before starting the place value block to assess gaps, and after teaching the place value block to identify progress. 

Diagnostic Assessments Year 6

Worked Examples

Pupils check over completed questions to identify errors (or identify correct answers). Pupils are encouraged to explain the errors they find, not just ‘mark’ work. These worked examples help to solidify understanding by getting the pupil to discuss errors and how to avoid them. 

Year 6 Worked Examples

Rapid Reasoning 

These reasoning problems go alongside our Fluent in Five resource. One question each week has a model answer so teachers can understand what the question is asking and how to solve it. 

Rapid Reasoning Year 6

All Kinds of Word Problems

Test your class’ problem solving skills with these place value word problems.

All Kinds of Word Problems Year 6

White Rose Maths Year 6 autumn term

In the autumn block, Year 6 focuses on place value; addition, subtraction, multiplication & division; fractions and converting units of measurement.

As  with all year groups, place value is the first block to be covered in the Autumn term. By Year 6, this is only a short unit of work; reading and writing numbers to 10,000,000 and exploring powers of 10.

Example year 6 place value questions

1. Write the following number in digits: twenty seven million, three hundred and forty eight thousand, five hundred and 6.

Answer: 27,348,506

2. Identify the value of each underlined digit

a) 7 3 ,640,328

b) 25, 6 04,713

c) 17,3 9 4,801

a) 3 million

Addition, subtraction , multiplication and division Year 6

Addition, subtraction, multiplication and division is the largest block of Year 6. Unlike the other year groups, the four operations are all covered in one block, rather than being separated into two separate blocks. By this stage, pupils are expected to be confident using formal written methods for addition and subtraction. Focus is on securing confidence with long multiplication and division, and applying this knowledge to solving more complex multi-step problems. Learners also build on their understanding of factors, multiples, prime, square and cube numbers.

Example year 6 addition, subtraction, multiplication and division questions

1. 196,877 ÷ 37 = 

Answer: 5,321

2. Which number is a factor of 24, but not a multiple of 8?

Answer: d) 12

Fractions in Year 6, are also split into two blocks, with both Block A and Block B being covered in the Autumn term. 

Fractions A in Year 6

Pupils continue to develop their understanding of equivalent fractions in Year  6; utilising this knowledge to be able to compare and order fractions, and add and subtract fractions and mixed numbers with different denominators.

Example year 6 fractions A questions

1. Order the following fractions from largest to smallest

\frac{1}{2}, \frac{2}{3}, \frac{9}{12}, \frac{5}{6}

Answer: \frac{5}{6}, \frac{9}{12}, \frac{2}{3}, \frac{1}{2}

2. 4\frac{3}{4} + 5\frac{4}{12}

Answer: 10\frac{1}{12}

In this second fractions block of Year 6, pupils build on the concepts introduced in Year 5; including multiplying and dividing fractions. They also continue to focus on calculating fractions of an amount

Example year 6 fractions B questions

1. 2\frac{1}{2} × 3\frac{1}{4} =

Answer: 6\frac{1}{8}

2. What is \frac{7}{8} of 336

Answer: 294

Converting units is a short topic at the end of the autumn term. In this block, pupils build on their understanding of converting metric measures and are introduced to converting between metric and imperial measures (For example, between miles and kilometres).

Example year 6 converting units questions

1. Write 7,532m as km

Answer: 7.532km

2. If 1 mile = 1.6km, how far in kilometres is 8 miles?

Answer: 12.8 miles

White Rose Maths Year 6 spring term

In the spring term term, Year 6 focuses on ratio; algebra; fractions, decimals & percentages; area, perimeter & volume and statistics

Pupils are introduced to ratio for the first time in Year 6. In this block pupils learn to use ratio language and the symbol. They also look at the connection between ratio and fractions and scale drawings.

Example year 6 ratio questions

1. Gemma is making a necklace. The ratio of purple beads to blue beads she uses is 3:1. If she uses 5 blue beads, how many purple beads does she use?

Answer: 15 purple beads

2. The ratio of counters was 4:1 (red:yellow). If there were 20 counters altogether. How many red and yellow counters were there?

Answer: 16 red and 4 yellow

Year 6 is the first time pupils are introduced to algebra. Students begin the block investigating 1-step and 2-step function machines, followed by forming expressions, formulae and equations. This progresses to solving 1-step, then 2-step equations. 

Example year 6 algebra questions

1. An x was input into the following function machine. What would be the output expression?

Answer: 2 x + 4

2. Solve the following equation: 2x + 2 = 12

Answer: x = 5

In Year 6, pupils focus on decimals in two blocks. Firstly as an independent unit, followed by a unit covering fractions, decimals and percentages. In this first block, understanding of place value within a decimal number is reinforced, followed by rounding and adding & subtracting decimals and finally building on knowledge from year 5 to multiply and divide by 10, 100 and 1000.

Example year 6 decimals questions

1. Round 3.765 to 2 decimal places

Answer: 3.77

2. Divide 32.7 by 10, 100 and 100

32.7 ÷ 10 = 3.27

32.74 ÷ 100 =0.327

32.74 ÷ 1000 =0.0327

In this block, pupils build upon the concepts learnt in Year 5; exploring and using equivalence between fractions, decimals and percentages. At this stage, students are also introduced to the concept of calculating a percentage of an amount. Initially pupils are introduced to  one-step problems, such as finding 10% of an amount. They then progress to solving multi-step problems, such as calculating 37% of an amount.

Example year 6 fractions, decimals and percentages questions

1. Write \frac{7}{25} as a decimal and a percentage

Answer: \frac{28}{100} = 0.28 = 28%

2. Use the < > or = symbol for each question below:

\frac{4}{10}   ______  45%

\frac{3}{4} ________ 70%

\frac{6}{20} ______  60%

\frac{4}{10}   < 45%

\frac{3}{4}   > 70%

\frac{6}{20} <  60%

In Year 6, pupils explore how to calculate the area of different shapes; including triangles and parallelograms. They also build on their knowledge of volume from Year 5; calculating, estimating and comparing volume of cubes and cuboids, using standard units, including cubic centimetres and cubic metres.

Example year 6 area, perimeter and volume questions

1. Calculate the volume of the cuboid below

Answer: 72cm ^{3}

2. Draw 2 different cuboids with a volume of 60cm ^{3}

Answer: 2 x 5 x 6 and 3 x 4 x 5

Statistics Year 6

In Year 6, pupils continue to focus on drawing and interpreting line graphs. They are also introduced to pie charts for the first time, learning how to interpret and construct them. Students also learn how to calculate and interpret the mean as an average.

Example year 6 statistics questions

1. A man walks up a hill. It takes him 15 minutes to reach 800m. He then stops for 10 minutes before walking back down. It takes him 10 minutes to reach the bottom of the hill. Plot the graph to show what happens.

White Rose Maths Year 6 summer term

In the summer term, Year 6 focuses on shape; position & direction, followed by themed projects, consolidation and problem solving.

Pupils build on their understanding of shape and properties of shape; drawing 2D shapes, using given dimensions. Students also learn to recognise, describe and build simple 3D shapes, including making nets. In Year 6, there is a significant focus on angles, with pupils learning how to calculate a range of angles, including: vertically opposite angles; angles in triangles, quadrilaterals and other polygons.

Example year 6 shape questions

1. Calculate the size of angle a below:

Answer: Angle a = 180°

2. A triangle has the angles: 45° and 65°. Calculate what the 3rd angle will be:

Answer: 70°

Position and direction Year 6

In Year 4 and 5, pupils learn to plot coordinates in the first quadrant. In Year 6, pupils progress to reading and plotting points in all four quadrants and solving problems with coordinates. Students also draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

Example year 6 position and direction questions

1. On the grid below, plot the following coordinates. What shape do they make?

(4,3) (-2,3) (-2, -2) (3,-2)

They make a square

• Year 6 Maths Test (Year 6 content only)
• Year 6 Maths Questions (with answers)
• Year 6 Maths Sats Papers

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White Rose Maths Reasoning & Problem Solving Kit

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Technical Summary

Helping to support teaching and learning.

Collaborative Design

White Rose Maths partnered in the development of this kit, enhancing the teaching of reasoning and problem solving across multiple key stages.

Versatile Teaching Tool

This kit is designed to enhance reasoning and problem-solving skills across Key Stage 1 and Key Stage 2, making it a practical addition to enhance mathematical learning.

Comprehensive Resource Set

Ensures comprehensive support for children's mathematical development through a variety of resources including Dip n Pick and Graded Problem Solving Cards.

Practical Storage Solution

The kit includes a Gratnell Storage Tray with a lid, ensuring that all resources stay organised and secure, aiding quick setup and safe storage.

Key Stage 1 and 2 Focus

Specifically supports 'Number - addition and subtraction' in Key Stages 1 and 2, helping children solve multi-step problems effectively.

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White rose maths reasoning & problem solving kit.

Enhance reasoning and problem-solving skills with collaborative resources from White Rose Maths.

This kit enriches the mathematical experience for children across Key Stages 1 and 2, by offering targeted support in critical areas such as number processing, geometrical reasoning, and algebraic operations.

Each resource within the kit, including Problem Solving Cards and Bar Model Teacher Version, is meticulously selected to promote an in-depth understanding and application of mathematical concepts. These resources assist children in working through complex, multi-step problems using strategic, thought-provoking approaches.

Integrating these resources into daily maths lessons can significantly enhance children's analytical and reasoning capabilities, thereby supporting structured learning and assessment alignment with educational standards across various key stages.

Read more about our fantastic White Rose Maths Kits here.

Supports the National Curriculum

Mathematics, Key Stage 2, Number - Addition & Subtraction

Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

Mathematics, Key Stage 3, Working Mathematically

Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems.

Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.

Product includes

1 x Dip n Pick Problem Solving Cards Group Set,1 x Graded Problem Solving Cards Group Set,1 x Making Maths Connections Activity Cards Group Set,1 x Bar Model Teacher Version,1 x Tray Lid,1 x Gratnell Storage Tray

Year Six White Rose Supporting Resources

Supporting white rose maths hub.

Welcome to our Supporting White Rose Maths hub! Discover fun, engaging and teacher-approved resources that perfectly align with the White Rose Maths framework and the maths mastery approach.

Ever since White Rose Maths set out on their mission to help every child master maths, the organisation has taken the world of primary education by storm. Through resources, Schemes of Learning and yearly frameworks detailing small steps to progression, White Rose Maths has been helping teachers and parents turn children into confident young mathematicians. At the heart of White Rose Maths is  maths mastery , an approach that’s sparked a positive,  growth mindset  towards mathematics in teachers, parents and pupils.

Here at Master the Curriculum, we’re thrilled to see so many primary school teachers and parents using White Rose Maths to enhance their lessons and get children engaged and excited about maths. Whether you’re using White Rose Maths resources, following the Schemes of Learning and the small steps to progression and/or taking a mastery approach to mathematics, White Rose Maths can transform children’s learning experience and attitude towards numeracy.

That’s why we offer resources aligned with the White Rose Maths framework and the National Curriculum. Each of our resources is designed to help children work towards maths mastery and have fun while doing so — because enjoyment can make a world of difference to children’s engagement with education.

Year 6 Version 3.0 White Rose Maths Resources

Year 6 version 2.0 white rose maths resources, using white rose maths to help children master maths.

The White Rose Maths mastery approach has seen tremendous success in schools all over the UK, helping children learn with a can-do attitude and embrace maths challenges with a smile. Lessons and resources influenced by White Rose focus on three concepts that help children work towards mastery.

Problem Solving

Through problem-solving lessons and activities, children are encouraged to use their mathematical skills and understanding to solve problems unfamiliar to them.

Maths reasoning tasks get children thinking about number problems logically so they can reach conclusions, find solutions and decide which methods to use and why.

Fluency tasks help children strengthen their foundational knowledge. They practise applying their skills and understanding to different number problems with varying contexts and levels of complexity, while independently choosing the method they use to tackle number problems successfully. Fluency brings together problem-solving and reasoning.

Discover Resources That Follow the White Rose Maths Small Steps to Progression

Maths mastery is a journey and to help youngsters on their way, so White Rose Maths has created “Small Steps to Progression”. These small steps break down which learning objectives children need to master, and in what order, to gain a deep understanding of maths topics, and gradually develop their reasoning and problem-solving skills.

There are small steps for each year group, sorted into blocks of weeks. For example, block one for Year 1 covers what children should learn between weeks one to three of the Autumn term. By following these steps, you can make sure children gain all of the foundational skills and knowledge they need to progress onto more complex and challenging lessons.

To help you work through the small steps with your class or with your child, we offer weekly resources that align with them. When you browse our maths resources by year group, you’ll find weekly packs of worksheets, teaching slides and lesson plans. These packs make it easy for you to follow the White Rose steps, save time on lesson planning and find resources that perfectly match your lessons and where children are in terms of progress.

Why Use Our White Rose Style Resources?

Designed with Mastery in Mind — We offer a huge range of primary maths resources that combine fluency, reasoning and problem-solving activities to help children on their journey to maths mastery.

Follow Clear Learning Objectives  — Each one of our resources is designed to help children meet learning objectives that align with the White Rose Small Steps. You’ll have peace of mind knowing our resources suit your lessons perfectly and will help children build on their maths skills and understanding.

Assess Children’s Progress — We offer assessments and mini-assessments to help you check children have a firm understanding of the steps you’ve already covered. This way, you can make sure your class is ready to move on to more advance lessons.

Fun and Engaging Resources  — Fun is at the heart of our White Rose style resources. Our learning materials engage children in maths and get them excited about learning with fun visual imagery, creative contexts and imaginative maths problems.

Explore Topics in Depth with Differentiated Resources  — Our resources are differentiated by complexity so children can explore topics in-depth and improve their fluency.

Free and Premium Membership Options  — We want to make sure everyone has access to high-quality, White Rose style resources. So we offer hundreds of free resources you can download instantly with a free membership. Or if you’d rather have unlimited access to all of our resources, you can sign up for a premium membership.

The Benefits of White Rose Maths for Schools: Transforming Lessons with a Mastery Approach

Help all children master maths at a similar pace.

White Rose inspired lessons meet the needs of all children and focus on helping them keep up, not catch up. The small steps for progression make sure all pupils master the same learning objectives and progress at a similar pace. No children should fall behind, and none should speed through content ahead of their classmates. Instead, children of all levels of attainment get the support they need to grasp topics and explore concepts in depth. Only once the whole class has a good understanding of one learning objective do teachers move onto more advanced lessons.

Build Children’s Confidence and Competence in Maths

Every teacher wants to see their class excel in all subjects and White Rose Maths resources and frameworks can help whole classes work towards maths mastery. A big part of the mastery approach is teaching children to adopt a growth mindset. Maths lessons should show pupils that anyone can become a master of maths if they put in the effort and get the support they need to succeed.

When children stop believing that they can’t do maths and adopt a more positive, proactive attitude to this subject, that’s when they can reach their full mathematical potential. They’re likely to feel more confident and engaged in lessons, and the more they embrace maths challenges, the easier it will be for them to develop skills and understanding.

Streamline Lesson Preparation

White Rose Maths takes a weight off your shoulders when it comes to lesson planning. With Schemes of Learning, yearly frameworks and detailed small steps to progression, you won’t have to worry about planning what to cover in lessons each day, week, month and term.

The clear learning objectives outlined in the small steps to progression also make it easy for you to find resources to complement lessons and help children progress.

Enhance Your Maths Lessons with White Rose Maths Resources

Explore our primary maths resources by year group and discover a wide range of resources that support White Rose learning and the small steps to progression. Enhance your lessons, make learning fun and teach for mastery with maths worksheets, teaching slides, lesson plans, reasoning booklets and more.

White Rose Maths for Parents: Get Children Engaged in Learning at Home

The White Rose approach isn’t just for teachers to use in the classroom. You can also use  White Rose Maths in your home learning  to help your little one improve their confidence in mathematics. Practice makes perfect, and if your children are learning at home as well as at school, they’ll have a chance to delve deep into maths topics and develop a firmer understanding of the lessons covered in school. This knowledge and understanding can pave the way for more advanced maths.

White Rose Maths also makes it easier for you to support your child with their home learning tasks. As a busy parent, you don’t want to spend time trying to figure out exactly what children are learning at school, and you don’t have the time to learn topics for yourself so you can guide your child through it. You can use the White Rose Maths  small steps  as a schedule for your home learning sessions and you can find endless White Rose resources right here on the Master the Curriculum website. As homework will often be fluency or consolidation tasks, you won’t have to guide your child through number problems.

Help Little Ones Master Maths with Our White Rose Maths Resources

We are currently updating the 3.0 table. If you cannot find the resources needed, please use the 2.0 table.

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Year 2 - Problem solving and reasoning - Summer - Block 2 - White Rose

Subject: Mathematics

Age range: 5-7

Resource type: Unit of work

Last updated

11 October 2019

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This problem solving pack contains resources that challenge children’s reasoning, investigative and problem solving skills. They include problems involving number, money, shape, position and direction, statistics and fractions.

All resources have answers provided. The pack contains:

• Worksheets – Problem solving 1 • Worksheets – Problem solving 2 • Worksheets – Problem solving 3 • Activity – Compare durations • Activity – Cut and glue fractions • Activity – Let’s go shopping • Activity – Number square - Missing numbers • Game – Shape loop cards • Game – Treasure hunt

Children can use concrete resources to help investigate and find solutions to the problems on the worksheets.

PDF format (please set print option to fit).

The resources support a mastery approach to encourage a deeper understanding of the topics taught. It follows a CPA (Concrete, Pictorial, Abstract) approach to ensure all children can access learning. The pack provides pictorial and abstract representations, along with reasoning, problem solving and open-ended investigations. Details of this can be seen in the contextual overview provided.

I hope you find them useful.

If you have any questions, please email [email protected] .

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PERSPECTIVE article

Problem solving is embedded in context… so how do we measure it.

• 1 Language Variation and Academic Success (LVAS) Lab, School of Education, University of California, Irvine, Irvine, CA, United States
• 2 Science of Learning (SoL) Lab, School of Education, University of California, Irvine, Irvine, CA, United States
• 3 Culture and Social Action Lab (CaSA), Department of Psychology, California State University, Fullerton, Fullerton, CA, United States

Problem solving encompasses the broad domain of human, goal-directed behaviors. Though we may attempt to measure problem solving using tightly controlled and decontextualized tasks, it is inextricably embedded in both reasoners’ experiences and their contexts. Without situating problem solvers, problem contexts, and our own experiential partialities as researchers, we risk intertwining the research of information relevance with our own confirmatory biases about people, environments, and ourselves. We review each of these ecological facets of information relevance in problem solving, and we suggest a framework to guide its measurement. We ground this framework with concrete examples of ecologically valid, culturally relevant measurement of problem solving.

1 Introduction

As of writing this perspective piece, there exist pockets of the world with ubiquitous internet, fingertip access to generative artificial intelligence, and engagement with global news and commerce, while other humans grapple more regularly with local subsistence farming, climate change, and family social relationships. These are abstracted points of comparison among the incredibly varied social and cultural contexts in which human reasoners must draw from information in their environments to notice problems that need resolution, find relevant information from which to make inferences, and execute problem solutions. This wide variance highlights the deep theoretical and practical challenges of characterizing and measuring problem solving as a pragmatically-grounded, cognitive construct.

In this perspective piece, we focus on measurement theory for gathering data on the complex cognition that governs humans’ everyday lives, focusing on problem solving in specific. Problem solving broadly encompasses human goal-directed behaviors ( Newell and Simon, 1972 ). Though problem solving may include a variety of goal structures in everyday living (from solving a mathematical problem in a formal educational setting to identifying the need for housework in one’s family context), it is often measured with highly abstracted tasks that attempt to decontextualize problems from the specific in favor of the universal ( Jukes et al., 2024 ).

We posit that measurement of problem solving with recognition of the deeply intertwined nature of reasoning with one’s context necessitates that we must center (a) the experiences and perceptions of the problem solver, (b) the context in which problem solving is being observed, and (c) the lens through which we as observers are interpreting problem solving. Each of these ecological facets influences our interpretations of problem-solving behavior, and each is socioculturally bound. Without situating problem solvers, problem contexts, and our own experiential partialities as researchers, we risk intertwining the research of information relevance with our own confirmatory biases about people, environments, and ourselves. We review each of these ecological facets of information relevance in problem solving, and we suggest a framework to guide ecologically valid, culturally relevant measurement.

2 Centering the relevant experiences and perceptions of the problem solver

We naturally use our problem-solving resources to attend to experientially relevant information, and thus, problem-solving tasks are socioculturally bound to problem solvers ( Oyserman, 2011 , 2016 ). Our measures of problem solving broadly reflect different attentional patterns that are based on prior developmental experiences which differ depending on socialization ( Newell and Simon, 1972 ; Ericsson et al., 1993 ). Broadly speaking, this means that the measurement of problem-solving tasks is closely tied to the particular experiences of problem solvers.

Consider, for example, the famous marshmallow experiment ( Mischel, 1961 ; Mischel and Metzner, 1962 ; Mischel and Ebbesen, 1970 ). In this lab-based experimental task, children are given a marshmallow and told that they may eat the treat immediately or wait an unspecified amount of time and receive additional marshmallows as a reward. Performance on the marshmallow task has typically been interpreted to indicate ability to delay gratification, (i.e., inhibitory control), and it has been linked to later academic performance, self-confidence, likelihood of subsequent substance abuse, and a variety of other outcomes ( Mischel et al., 1988 , 1989 ; Shoda et al., 1990 ; Ayduk et al., 2000 ). Thus, the researcher-identified problem of the marshmallow task is (1) the identification of the marshmallow as a reward, (2) the decision to engage in a desired goal-oriented behavior (waiting) to obtain the reward, and then (3) the execution of the desired goal-oriented behavior (engaging inhibitory control in order to wait).

However, some researchers have raised concerns about the interpretation of performance on the marshmallow task, in particular, questioning what we might reasonably infer about the relevant pieces of information that children use to execute decision-making about whether or not to wait. For example, Kidd et al. (2013) found evidence that children’s rational decision-making about the reliability of the experimental environment (and by implication, their prior experiences with reliable and unreliable environments) may also influence their decisions to delay gratification comparably to their individual differences in capacity for self-control.

Other researchers have noted that the “The Marshmallow Test” may simply be a culturally loaded problem-solving task with narrow expectations about children’s behavior and ways of solving the problem. For example, Yucatec Maya children are often engaged in real-life productive activities, are motivated to contribute, and allowed to take the initiative to solve problems they encounter ( Gaskins, 2020 ; Cervera-Montejano, 2022 ). When encountering novel problems, they are expected to be attentive and learn by observing others and not just by listening to verbal instructions ( Alcalá et al., 2021 ). However, when Gaskins tried to replicate this study with Yucatec Maya children, she found that none of the six children she tested earned the second marshmallow ( Gaskins and Alcalá, 2023 ). Two of them ate the treat, and four of them left the room. Gaskins attributes their marshmallow task performance differences to the cultural assumptions in the methodology, such as the expectation that children will obediently attend to and follow adult’s instructions. The children who left the room did not leave because they were tempted to eat the marshmallow – which assumes poor self-regulation – but they left because “they saw no ‘good reason’ to sit alone in a room for a long time doing nothing, rejecting the basic premise of the task.” (p. 8). Gaskins and Alcalá (2023) results illustrate that participants’ perceptions about adult authority, expectations for child compliance, and familiarity with verbal instructions are also relevant and often overlooked aspects of the marshmallow experiment.

The marshmallow task illustrates that the same contextual cues may be interpreted very differently by different experimental participants because prior experiences influence our expectations, beliefs, and ultimately, our mental representations of the problems we are solving. Lab-based problem-solving tasks like the marshmallow task have the advantages of being tightly controlled, but they are also decontextualized, adult-generated, and assume child compliance based on the lived experiences and rules familiar to White, middle-class children ( Jukes et al., 2024 ). Examining psychological constructs and tasks across contexts can help illuminate characteristics of problem-solving tasks that may be reflecting culturally-derived experiences and socialized expectations.

3 Centering the sociocultural context in which problem solving is being observed

The sociocultural context in which problem solving is being observed helps define the parameters of the problem being solved, which in turn influences the pieces of information that may be relevant to its effective solution. Consider, for example, the sociocultural norms that contextualize children’s helping behaviors in their homes and communities. Helping behaviors are also goal-oriented, problem-solving behaviors that are prosocial in nature – they require the identification of a social problem (the need for help to occur), the formulation of a solution (selecting the kind of help that will remedy the identified issue), and the execution of a solution (engaging in helping until a desired goal has been reached). In many Western, educated, industrialized, rich, and democratic (WEIRD) societies, children are viewed as the recipients of help rather than as independent, helpful agents in their communities ( Ochs and Izquierdo, 2009 ). However, in communities where children are socialized to provide substantial contributions to their families, taking the initiative to help with complex household tasks and to assist during community celebrations, the contextual expectations around problem solving might be quite different ( Rogoff, 1990 ; Chavajay and Rogoff, 2002 ).

During a visit to Yucatan, Alcalá (2023) observed how children are given extensive amounts of autonomy to decide how to spend their time, including helping with household work and engaging in unstructured play activities. In this context, children are expected to notice when there is a problem and act accordingly to find the appropriate solution ( Alcalá and Cervera, 2022 ). Mothers state that children need to learn to be autonomous because they might not always be with adults or others that can help them, and need to learn to solve the problems they encounter.

Alcalá et al. (2021) asked children why they help at home and the majority of them reported that they help because helping is a shared responsibility of all family members, they help because they like to help, or they help because they notice work that needs to be done. The cultural expectations to be attentive to their surroundings, to be autonomous and self-directed in choosing activities, and to notice work and problems in need of solution is key in how children in this community learn to solve problems. For example, children notice that there are some dirty dishes and will go and wash the dishes, or they might notice that the plants need to be watered.

The shared responsibility to help and solve problems, opens other opportunities for children to identify and solve problems in their communities. For example, children might notice or hear about a family member who is ill, and they volunteer to help with chores that would normally be done by the ailing adult as illustrated by “ Soledad ” (Chan Cah, age 10) “my mom’s foot hurt and that is why I help” ( Alcalá et al., 2021 , p.).

Furthermore, when asked what would happen if they do not help, about half of the participants responded in a way that reflected a community-minded way of solving problems. Children indicated that if they do not help, for example with washing the dishes, then the pile of dirty dishes will get bigger and then someone else would have to wash the dishes. Likewise, if a child does not help with the milpa (corn field) there might not be enough corn for the family.

In this context, where children are allowed to be present and observe almost all of the activities of the household and community, children are expected to become interested and notice when someone needs help ( López Fraire et al., 2024 ). Children are trusted enough to solve certain problems on their own, or know when to find help, as they are becoming competent members of their communities.

The sociocultural context helps to dictate what is a problem, who is affected by the consequences of the problem, and who is allowed, expected, and empowered to solve the problem. Importantly, the sociocultural context also determines the level at which problems exist - Not all problems belong to the individual as is often assumed in highly individualistic societies ( Oyserman et al., 2002 ; Arieli and Sagiv, 2018 ). In many problem-solving contexts across the world, problems, their consequences, and the responsibility for solving them belong to groups and communities of problem-solvers ( Lasker and Weiss, 2003 ).

4 Discussion

4.1 how do we measure problem solving: considering the lens of the research observer.

For many researchers, the measurement of problem solving may appear to be a primarily methodological issue at first glance ( Messick, 1981 ). We create tasks, observe individual differences in task performance, and assign interpretations for those differences. The measures are assumed to be objective, empirical, quantitative metrics of performance – Child X ate marshmallow Y after Z minutes of waiting, therefore failing to delay gratification with additional marshmallows (see Mischel et al., 1988 ). However, without the guidance of strong theoretical postulates about constructs, and without clear links between theoretical postulates and the measures designed to capture constructs of interest, we are asking our measures to do the work of specifying larger theoretical models ( Borsboom, 2005 ).

Our measures reflect our theoretical dispositions, and our theories reflect ourselves. The lens through which we generally interpret cognitive development is culturally misaligned with the majority of the world’s problem solvers and problem-solving contexts, and our measures of problem solving reflect that epistemological misalignment. As researchers who are primarily from Western, educated, industrialized, rich, and democratic societies, our lens for understanding and measuring human behavior is WEIRD ( Henrich et al., 2010 ). Problem solving is no exception and has traditionally been measured in WEIRD ways with WEIRD problem solvers, which can misrepresent developmental phenomena that may not replicate with children from other sociocultural backgrounds or lived contexts (e.g., for evidence of this in the above marshmallow task, see Watts et al., 2018 ). These traditional measures of problem solving do not account for potential sociocultural differences in information processing that can derive from the nature of the task requirements to the cultural context of how children should speak with adults. For problem solving measures, one must step back to consider that even the definition for what constitutes a problem that a participant has the authority to solve is cultural, with measures tending to be based on WEIRD researchers’ known context, which can lead to bias then in solution rates and participants’ engagements. Thus, it is unsurprising that children who are not from WEIRD communities or who are marginalized within WEIRD societies may perform differently on traditional measures of problem solving (see for example, Miller-Cotto et al., 2022 ).

If our aim is to capture problem solving in ways that have meaningful implications for the real world information processing, we need to measure problem solving in ways that are culturally relevant for broad populations of children. This aim is critical for problem-solving research, and it necessitates an epistemological (and possibly an ontological) recentering of our measurement of problem solving.

4.2 Framework for ecologically valid, culturally relevant measurement

There is a growing push to measure human problem solving “in context,” in ways that are ecologically valid (see for example Burgess et al., 2006 ; Miller and Scholnick, 2015 ); however, contextualized tasks can still evidence the same biases that create validity issues for traditional, abstract, decontextualized tasks. The field has a pressing need for a framework that helps researchers to evaluate problem-solving tasks in ways that consider their relevant features from the perspective of diverse learners. To support an evolution in the fields of reasoning and problem solving that better centers tasks and measurement on the abilities executed by reasoners in their everyday worlds, we propose a set of questions that researchers can ask when developing a task to better ensure relevance and alignment between test participants, researchers, and the interpretation of empirical data.

4.2.1 Understanding problem solvers’ relevant experiences

4.2.1.1 how are reasoners perceiving the problem.

✓ Assume that the problem solver’s solution is predicated on the kind of mental representation she has formed about the problem.

⃠ Avoid assuming that problem solvers perceive the same goal-structure, have the same mental representation of the problem, or have the same reasoning and approach to solving the problem. Problem solvers are NOT necessarily attending to the researchers’ desired matrix of information when thinking about the problem.

★ Forexample, Rhodes et al. (under review) research on the mathematical problem solving of African American children who use African American English dialect (AAE; a cultural dialect of American English) explored the types of errors that children make on various arithmetic problems as a function of both item formatting and the density of children’s AAE dialect usage. The very exploration of this research question runs counter to the assumption that word formatting and children’s home language would have no impact on African American children’s mental representations of problems and strategic approaches to solving them. Results suggested that children’s strategic errors occurred as a complex interaction between word problem formatting and children’s AAE dialect density, effectively challenging the assumption that word problems would elicit language neutral mental representations with African American children whose home and community language systems were linguistically distanced from them.

4.2.1.2 What does unexpected or “non-normative” task performance mean?

✓ Assume that divergence from a normative expectation is not necessarily indicative of pathology or lack of skill.

⃠ Avoid assuming that we manage attentional resources during problem solving in one, normative way. In particular, avoid the assumption that problem solving is maladaptive – instead, look for the adaptive response in the way that you interpret the problem solving.

★ Forexample, a child who does not concentrate fully on a problem solving task they have been given, but instead is also directing attention toward monitoring the experimenter’s actions and conversations with another child, may be exhibiting highly culturally appropriate and intentional resource allocation to ensure they are not missing a need to learn new relevant information or assist the experimenter (e.g., Correa-Chávez et al., 2005 ). Challenging the assumption that the management of attentional resources should happen in one, normative, culturally-sanctioned way, creates the opportunity for researchers to recognize important sources of cultural variance in otherwise invisible aspects of task construction (i.e., prosocial attentional engagement as a means of identifying information relevance).

4.2.2 Considering socio-cultural contexts of problem solving

4.2.2.1 where do problems occur.

✓ Assume that there are no neutral contexts for problem solving. The “lab” (a tightly controlled experimental context) is not, in fact, neutral.

⃠ Avoid assuming that the most meaningful problems we solve occur in formal educational settings or in tightly controlled experimental settings.

★ Forexample, in his landmark study of Brazilian child candy sellers, Saxe (1988) used a multimethod paradigm to observe and query the naturalistic mathematical behaviors of children in- and out-of-classroom mathematics problem-solving contexts. In challenging the assumption that normative mathematical problem solving only develops in formal educational contexts, he observed that the skills children used in their street vending activities did not necessarily transfer to their school contexts and vice versa, and importantly, that children who were quite adept at using mathematics in their real-world vending activities were not necessarily able to translate their skills toward high-achievement on formal educational tasks ( Saxe, 1988 ).

4.2.2.2 For whom is the problem consequential? and relatedly, who is empowered to solve the problem in this context?

✓ Assume that problem solving is not necessarily an individual sport - individuals, groups, and communities may identify problems, problem consequences, and problem solvers very differently.

⃠ Avoid assuming that problem solving should only be conceptualized and measured at the individual level. Similarly, avoid the assumption that cultural expectations for problem solving converge around efficiency (i.e., quickly and accurately; careless mistakes may have important consequences beyond an individual).

★ Forexample, when asked why they help with household chores, most Yucatec Maya children mentioned that if they did not do the chore, this would create more work for their parents or cause harm to others including younger siblings or aging adults ( Alcalá and Cervera, 2022 ). In challenging individualistic assumptions about measuring problem solving, these researchers were able to capture children’s mental representations of problems and problem consequences as belonging to the entire household, rather than assigning the responsibility for problem solving to a household’s individual members.

4.2.3 Evaluating researchers’ perspectives of problem solving

4.2.3.1 how does the observer’s positionality influence the evaluation of problem solving.

✓ Assume that positionality is something we can and should acknowledge, particularly if we are evaluating the problem-solving abilities of others.

⃠ Avoid assuming that researchers have the same positionality as research participants or groups to whom research is generalized (see for example, Bilgen et al., 2021 ; Patton and Winter, 2023 ).

★ Forexample, Patton and Winter (2023) provide a detailed and reflexive account of researcher positionality and decision-making in engaging in an observational study with preschool-aged children. These researchers consider the use of a teddy bear named “Ted” as an elicitation tool for gathering information about children’s perspectives and contextual experiences of early childhood educational settings. In examining their own positionalities, the authors were able to interrogate the inherent power structure between adults and children in traditional research participation paradigms. This consideration of positionality helped inform the researchers’ decision to embed “Ted” into children’s preschool contexts in meaningful ways that allowed children to engage with him as a peer, including him in activities and songs, helping him, or even explaining mistakes to him in the role of experts.

4.2.3.2 What can we infer from a reasoner’s problem-solving actions?

✓ Assume that the interpretation of problem-solving actions will be influenced by the problem solver, the context for problem solving, and the research observer.

⃠ Avoid assuming that a particular measurement instrument is contextually neutral or culturally unbiased. It is critical that we acknowledge the fact that measurement instruments are also NOT free of positionality. They exist in the context of larger epistemologies that influence their design, application, and interpretation.

★ Forexample, many laboratory tasks assume that children are familiar with and willing to follow adults’ instructions, even if the tasks do not accomplish readily apparent goals such as care or feeding. These tasks then may yield biased conclusions when used with children from communities which value autonomy over decision-making, specifically where respect for children’s ability to decide about their participation in activities means they are not required to obey adults; such children may perform poorly on these types of tasks or refuse to follow the researcher’s instructions ( Jukes et al., 2024 ).

5 Conclusion

We argue that problem solving is fundamentally and inextricably tied to deeper, often implicit, questions of epistemology, which need to be made explicit to facilitate its meaningful measurement. This philosophical work cannot be undertaken during methodological decision-making alone. Rather, if we hope to validly and reliably measure problem solving, we must also formulate strong theoretical positions about what it is, how it operates across various contexts of interest, and how we may observe it – all of which must be integrated and mapped onto specifications of our models of measurement. For as illustrated by the difficulties in interpreting performance on the marshmallow task, children with various prior experiences, in various sociocultural contexts, may have vastly different experiences of problem-solving the same task.

To be clear, rigorous measurement of information relevance in problem solving does not require that we abandon the empirical tenets of modern measurement theory. Nor does it require the rejection of the thoughtful positionality critiques of critical theorists. Rigorous research of problem solving requires the careful consideration of these seemingly irreconcilable epistemologies and, where possible, the integration of them in research design and interpretation.

Measuring problem solving “in context” does not necessarily remedy the issue of culturally biased measurement because contextualized for one group may be decontextualized (and biased) for another group. The wide variance in our experiences and contexts may necessitate admission that there may not be a perfect, unbiased measure of human problem solving, and the best measure for one’s particular research perspective will likely have shortcomings. Still, rigorous measurement of information relevance in problem solving demands that we acknowledge these shortcomings and interpret performance with sensitivity to them. The authors recognize that this process is not easy. We grapple with this in our own work; however, we believe that the process of grappling with these epistemological issues is central to the evolution of our research.

Data availability statement

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

Author contributions

KR: Conceptualization, Funding acquisition, Methodology, Project administration, Resources, Validation, Visualization, Writing – original draft, Writing – review & editing. LR: Conceptualization, Funding acquisition, Methodology, Project administration, Resources, Validation, Visualization, Writing – original draft, Writing – review & editing. LA: Conceptualization, Funding acquisition, Resources, Validation, Visualization, Writing – original draft, Writing – review & editing.

The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. This material is based upon work supported by the National Science Foundation under Grant no. NSF 2141411.

Acknowledgments

We are grateful to Suzanne Gaskins, Ella Rose, and Lina Brodsky for substantive conversations that supported the development of these arguments.

Conflict of interest

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

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Keywords: problem solving, measurement, information relevance, ecological validity, cultural relevance

Citation: Rhodes KT, Richland LE and Alcalá L (2024) Problem solving is embedded in context… so how do we measure it? Front. Psychol . 15:1380178. doi: 10.3389/fpsyg.2024.1380178

Received: 01 February 2024; Accepted: 26 April 2024; Published: 17 May 2024.

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Copyright © 2024 Rhodes, Richland and Alcalá. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Katherine T. Rhodes, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.