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## Supporting school maths

https://nzmaths.co.nz/supporting-school-maths

## Supporting school maths (TKI85585)

Pat (progressive achievement tests).

http://assessment.tki.org.nz/Asse...rces/Commonly-used-assessments/PAT

## PAT (Progressive Achievement Tests) (TKI83722)

## How parents and whānau can help at home – mathematics

http://assessment.tki.org.nz/Repo...hanau-can-help-at-home/Mathematics

## How parents and whānau can help at home – mathematics (TKI83970)

## NZ Maths: Going Bananas

http://nzmaths.co.nz/content/going-bananas

## NZ Maths: Going Bananas (TKI82590)

## Problem Solving - NZ Maths

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## Problem Solving - NZ Maths (TKI85594)

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## Learning from home resources: Maths memory

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## Learning from home resources: Maths memory (TKI85920)

https://arbs.nzcer.org.nz/resources/some-maths-problems

## Some maths problems - NM1333 (TKI80813)

## NZ Maths: Safe landings

http://nzmaths.co.nz/content/safe-landings

## NZ Maths: Safe landings (TKI82598)

## NZ Maths: The Big Splash

http://nzmaths.co.nz/content/big-splash

## NZ Maths: The Big Splash (TKI82599)

## People also looked at

- 1 School of Education, Shanghai International Studies University, Shanghai, China
- 2 Faculty of Education, Beijing Normal University, Beijing, China

## Introduction

## Literature review

Significance and value as goals of mathematics teaching.

## Mathematical problems and problem-solving

## Psychological analysis of the process of mathematical problem-solving

## Influencing factors of mathematical problem-solving

## Evaluation of mathematical problem solving ability at home and abroad

## Analysis framework

## Materials and methods

## Instruments

## Mathematical problem-solving test paper

## Questionnaires on factors influencing the performance of mathematical problem-solving

## Data collection and test procedure

## Data processing

## Overall proficiency of students’ mathematical problem-solving ability

## Background differences in the benchmark of students’ mathematical problem-solving performance

Table 2 . The compliance rate of middle school students’ mathematical problem-solving performance.

## Students’ mathematical problem-solving ability and influencing factor model setting

## Hierarchical linear model analysis

## Overall performance of students’ mathematical problem-solving ability

## Differences in the benchmark of middle school students’ mathematical problem-solving ability in mainland China

## The predictive effect of student-level and school-level factors on mathematical problem-solving ability

## Limitations

## Author’s note

## Data availability statement

## Ethics statement

## Author contributions

## Conflict of interest

## Publisher’s note

1. ^ φ represents the effect size of the Chi-squared test.

PubMed Abstract | CrossRef Full Text | Google Scholar

Blake, J. (1981). Family size and the quality of children. Demography 18, 421–442.

CrossRef Full Text | Google Scholar

Duncker, K. (1945). On problem solving. Psychol. Monogr. 58, i–113. doi: 10.1037/h0093599

Kilpatrick, J. (2009). The mathematics teacher and curriculum change. PNA 3, 107–121.

Lumbelli, L. (2018). Productive thinking in place of problem-solving. Gestalt Theory 40, 131–148.

Mayer, R. E. (1992). Thinking, Problem Solving, Cognition . 2nd Edn. New York: Freeman.

Neisser, U. (1967). Cognitive Psychology. New York: Appleton-Century-Crofts.

Newell, A., and Simon, A. (1972). Human Problem Solving. New Jersey: Prentice Hall.

OECD (2013). PISA 2012 Assessment and Analytical Framework. Paris: OECD Publishing.

Polya, G. (1957). How to Solve it . 2nd Edn. New York: Doubleday Publishing.

Schoenfeld, A. H. (1985). Mathematical Problem Solving. New York: Academic Press.

Wang, P. (2020). The application of heuristic teaching in modern teaching. Global Market. 6:215.

Wang, K. (2021). On problem solving and mathematics curriculum reform. Educ. Rev. 7, 141–147.

Zhang, D. (1991). Mathematics Education . Nanchang, China: Jiangxi Education Press.

Received: 12 September 2022; Accepted: 21 October 2022; Published: 11 November 2022.

*Correspondence: Chunxia Qi, [email protected]

## This article is part of the Research Topic

Advances in the Contributions of Mathematics in the Field of Education and Psychology

EVERYTHING YOU NEED FOR THE YEAR >>> ALL ACCESS

## Math Problem Solving Strategies

Grab your Problem Solving Strategy Freebie Here !

## 1. C.U.B.E.S.

- Why I like it: Gives students a very specific ‘what to do.’
- Why I don’t like it: With all of the annotating of the problem, I’m not sure that students are actually reading the problem. None of the steps emphasize reading the problem but maybe that is a given.

## 2. R.U.N.S.

- Why I like it: Students are forced to think about what type of problem it is (factoring, division, etc) and then come up with a plan to solve it using a strategy sentence. This is a great strategy to teach when you are tackling various types of problems.
- Why I don’t like it: Though I love the opportunity for students to write in math, writing a strategy statement for every problem can eat up a lot of time.

## 3. U.P.S. CHECK

U.P.S. Check stands for understand, plan, solve, and check.

- Why I like it: I love that there is a check step in this problem solving strategy. Students having to defend the reasonableness of their answer is essential for students’ number sense.
- Why I don’t like it: It can be a little vague and doesn’t give concrete ‘what to dos.’ Checking that students completed the ‘understand’ step can be hard to see.

## 4. Maneuvering the Middle Strategy AKA K.N.O.W.S.

UPDATE: IT DOES HAVE A NAME! Thanks to our lovely readers, Wendi and Natalie!

- Know: This will help students find the important information.
- Need to Know: This will force students to reread the question and write down what they are trying to solve for.
- Organize: I think this would be a great place for teachers to emphasize drawing a model or picture.
- Work: Students show their calculations here.
- Solution: This is where students will ask themselves if the answer is reasonable and whether it answered the question.

## 5. Digital Learning Struggle

## Printable and Digital Math Performance Tasks

Check out these related products from my shop.

## Reader Interactions

Great idea! Thanks so much for sharing with our readers!

LOVE this idea! Will definitely use it this year! Thank you!

I would love an anchor chart for RUBY

That’s brilliant! Thank you for sharing!

Going off of your idea, Natalie, how about the following?

I’m doing this one. Love it. Thank you!!

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## Problem Solving

## NRICH - Mathematics Resources for Teachers, Parents and Students to Enrich Learning

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## Primary and EY Teachers

Find more rich tasks, with teacher support, at the Primary and EY teacher homepages

## Secondary Teachers

You can find more rich tasks, with accompanying teacher support, at the Secondary Teacher Homepage

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## THE FOUR-STEP PROBLEM SOLVING PLAN

Overview of “Four-Step Problem Solving”

- “What is the main idea in the question of this problem?”
- “What are we looking for?”
- “What do we want to find out?”

- “What are the details needed to answer the question?”
- “What are the important details?”
- “What is going on that can help me answer the question?”
- “What details do I need?”

- use or draw a picture
- look for a pattern
- write a number sentence
- use actions (operations) such as add, subtract, multiply, divide
- make or use a table
- make or use a list
- work a simpler problem
- work backwards to solve a problem
- act out the situation

- “What am I going to do to solve this problem?”
- “What is my strategy?”
- “What can I do with the details to get the answer?”

Benefits of Using “Four-Step Problem Solving Plan”

Educational Research Supporting “Four-Step Problem Solving”

- Teachers need to investigate how their students arrive at answers. Correct answers don't necessarily equate to correct thinking.
- Students need to explore various ways to think about math problems and their solutions.
- Students need to learn to analyze and solve problems on their own.
- Students' discourse in a mathematics classroom should focus on their thinking process as they solved a problem.

Relationship of “Four-Step Problem Solving” and the TEKS

- The student applies mathematics to solve problems connected to everyday experiences and activities in and outside of school.
- Identify the mathematics in everyday situations.
- Solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.
- Select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.
- Use tools such as real objects, manipulatives, and technology to solve problems.
- The student communicates about mathematics using informal language.
- Explain and record observations using objects, words, pictures, numbers, and technology.
- Relate informal language to mathematical language and symbols.
- The student uses logical reasoning to make sense of his or her world.
- Make generalizations from patterns or sets of examples and nonexamples.
- Justify why an answer is reasonable and explain the solution process.

Instructional Methods Behind “Four-Step Problem Solving”

- model use of the “Four-Step Problem Solving Plan” with graphic representations as they guide students through the four-step problem-solving process;
- use a think-aloud method to share their reasoning with students;
- employ questioning strategies that provoke students to higher levels of thinking; and
- foster rich dialogue, both in whole-class discussions and for partner/table activities.

Students Using “Four-Step Problem Solving”

Putting “The Four-Step Problem Solving Plan” into Action

In class, students will use “Four-Step Problem Solving” in a variety of circumstances.

- Students will participate in whole-class discussion and completion of “Four-Step Problem Solving” pages as the teacher explains math problems to the group. To guide students through the steps, teachers may place a “Four-Step Problem Solving Organizer” transparency on the overhead, affix a “Four-Step Problem Solving Organizer” visual aid to the white board, use a “Four-Step Problem Solving Organizer” poster, or simply draw a “Four-Step Problem Solving Organizer” on the board to fill in the areas of the graphic organizer so that students observe how to solve the problems.
- Students will work in pairs to complete daily work with a partner using four-step problem solving. Having a partner allows the students to discuss aspects of the problem-solving process, a grouping arrangement which helps them develop the language skills needed for completing the steps of the problem-solving process.
- Students will complete assignments on their own using the four steps, allowing teachers to gauge their ability to master the steps needed to complete the problem-solving process.

Assessment and Grading with “The Four-Step Problem Solving Plan”

## What IS Problem-Solving?

## Written by Donna Boucher

I would LOVE to hear your comments about problem-solving!

I do professional development for district and schools, and I have online courses.

I think we’ve ALL been there! We learn and we do better. 🙂

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