M-ProSE

Making Mathematical Problem-Solving Accessible to the General Student Population

Watch: What is M-ProSE? (2:11)

  • Nurtures students’ confidence and ability to handle unfamiliar math problems

  • Complements existing Math curriculum and provides practical lesson plans, math problems and assessment guides

  • Helps math teachers develop a shared language in the area of math problem-solving, facilitating long-term professional collaboration in school

Understanding how to tackle math problems like a professional mathematician is a powerful way to get students comfortable with handling challenging problems.

To enable students to learn the process of problem-solving more effectively,
M-ProSE provides teachers with a suite of engaging and practical lessons and resources. Based on Pólya’s 4-step model of problem solving, M-ProSE ingeniously introduces math “practical” lessons into the curriculum. In these lessons, students are given interesting and challenging problems and are scaffolded to solve them using the Pólya framework.

M-ProSE has been successfully rolled out to four mainstream secondary schools, where participating students showed they could learn to apply all the steps of problem-solving. Students’ performance in the problem-solving module was also significantly correlated with their score on their school mathematics achievement test.

M-ProSE helps bring the explicit teaching and learning of problem-solving skills into classrooms by introducing math “practical” lessons based on Pólya’s model of problem solving.

In these math practical lessons, analogous to science practicals, teachers encourage learners to go through the entire mathematical problem-solving process. This is facilitated by a specially designed practical worksheet, together with an assessment rubric, that highlights each step of the process.

The problem-solving approach draws out students’ ability to think about math problems in both logical and imaginative ways. The process of solving is prioritised, instead of mere drill and practice often seen in classrooms.

Question-Icon
What is Pólya's model again?

Pólya’s model is a 4-step problem-solving approach that scaffolds students through the problem-solving process.

Stage 1: Understand the problem - Does your student understand the question? Is there enough information to enable your student to find a solution?

Stage 2: Devise a plan - What methods can your student use? Diagrams? Formulas? Drawings?

Stage 3: Carry out the plan - Students implement the chosen methods to solve the question.

Stage 4: Check and expand - Did your student manage to solve the question? If not, what went wrong? What worked? What didn't?

Question-Icon
The M-ProSE package includes
  • A module, consisting of 10 lessons and practical worksheets, to teach students how to use Pólya’s model and mathematical heuristics to solve mathematics problems.
  • An assessment rubric to accompany the use of the worksheets, to help teachers and students to understand the important steps in attempting to solve a mathematical problem.
Question-Icon
How did students respond?
  • A high percentage of the students completed Pólya stages 1-3 and applied heuristics when solving a problem.
  • Many students demonstrated Pólya Stage 4 to some extent.
  • Stage 4: Checking and Expanding is within the reach of the general student population.
Question-Icon
In addition, teachers who participated in the research noted:
  • M-ProSE can help enhance students’ confidence and ability to handle unfamiliar problems.
  • Teachers who received professional development in math problem-solving could employ a shared language to talk about problem-solving with the students as the students moved through different classes and levels of the school.
  • Teachers could also use the shared language and way of thinking to facilitate professional collaboration within their school.
  • Remember that when math problems are intriguing enough, extendable and generalizable for most students, students are motivated towards solving it.

  • You may consider practising sample problems (available under Classroom resources and at the M-ProSE website) before bringing them to the classrooms. This will give you greater confidence as you experience learning from students’ standpoints.

  • You may consider awarding marks for students’ work done according to Pólya’s framework. What gets assessed, gets done.

  • For more information on implementing M-ProSE in your classroom, visit the M-ProSE website.

Classroom resources

Three math sample problems that scaffold the problem-solving process for secondary students.

For teaching tips, sample problems and more, visit the M-ProSE website.

Question-Icon
Further readings

For educators interested in understanding and implementing M-ProSE, these titles serve as ideal handbooks:

futher_readings_book futher_readings_book

Toh, T. L., Quek, K. S., Leong, Y. H., Dindyal, J., Tay, E. G. (2011). Making Mathematics Practical: An Approach to Problem Solving. Singapore: World Scientific [Amazon]

Leong, Y. H., Tay, E. G., Quek, K. S., Toh, T. L., Toh, P. C., Dindyal, J., . . . Yap, R. A. S. (2014). Making mathematics more practical: Implementation in the schools. Singapore: World Scientific. [Amazon]

Research projects

The following projects are associated with M-ProSE research:


Question-Icon
Research team

To learn more about M-ProSE, please contact the Principal Investigator A/P Toh Tin Lam at tinlam.toh@nie.edu.sg.



    Principal Investigator
  • A/P Toh Tin Lam, Mathematics and Mathematics Education (MME), NIE

    Co-Principal Investigators
  • A/P Tay Eng Guan, MME, NIE

  • A/P Leong Yew Hoong, MME, NIE

  • Dr Quek Khiok Seng, Psychological Studies, NIE

  • Ast/P Toh Pee Choon, MME, NIE

  • A/P Dindyal Jaguthsing, MME, NIE

  • Mr Ho Foo Him, MOE

Research led by
Author
Principal Investigator
A/P Toh Tin Lam
Author
Co-Principal Investigator
A/P Tay Eng Guan
Author
Co-Principal Investigator
Ast/P Leong Yew Hoong
Author
Co-Principal Investigator
Dr Quek Khiok Seng
Author
Co-Principal Investigator
Ast/P Toh Pee Choon
Author
Co-Principal Investigator
A/P Dindyal Jaguthsing

Researchers above are from NIE

Co-Principal Investigator

Mr Ho Foo Him, MOE

To learn more about M-ProSE, email: tinlam.toh@nie.edu.sg

    Collaborators

  • A/P Ng Pak Tee, Policy and Leadership Studies, NIE
  • Dr Hang Kim Hoo, MOE
  • Ms Yen Yeen Peng, MOE

This research on M-ProSE was funded by Singapore Ministry of Education (MOE) under the Education Research Funding Programme (OER 32/08 TTL & OER 22/12 TTL) and administered by National Institute of Education (NIE), Nanyang Technological University, Singapore. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Singapore MOE and NIE.

This knowledge resource was written by Tan Minying, Bernadine W. Sengalrayan and Tan Giam Hwee.

What teachers say

“Ever since we implemented M-ProSE into the lesson plans… I noted [students] are more resilient; they are not so afraid when it comes to handling ambiguous or difficult problems.”

- HOD Mathematics
Participants

500 students (approx.)

Mathematics teachers

5 secondary schools

Contents

Research led by
Author
Principal Investigator
A/P Toh Tin Lam
Author
Co-Principal Investigator
A/P Tay Eng Guan
Author
Co-Principal Investigator
Ast/P Leong Yew Hoong
Author
Co-Principal Investigator
Dr Quek Khiok Seng
Author
Co-Principal Investigator
Ast/P Toh Pee Choon
Author
Co-Principal Investigator
A/P Dindyal Jaguthsing

Researchers above are from NIE

Co-Principal Investigator

Mr Ho Foo Him, MOE

To learn more about M-ProSE, email: tinlam.toh@nie.edu.sg

M-ProSE

Making Mathematical Problem-Solving Accessible to the General Student Population

Question-Icon
How M-ProSE can help your students
  • Nurtures students’ confidence and ability to handle unfamiliar math problems
  • Complements existing Math curriculum and provides practical lesson plans, math problems and assessment guides
  • Helps math teachers develop a shared language in the area of math problem-solving, facilitating long-term professional collaboration in school
Question-Icon
Why M-ProSE?

Understanding how to tackle math problems like a professional mathematician is a powerful way to get students comfortable with handling challenging problems.

To enable students to learn the process of problem-solving more effectively,
M-ProSE provides teachers with a suite of engaging and practical lessons and resources. Based on Pólya’s 4-step model of problem solving, M-ProSE ingeniously introduces math “practical” lessons into the curriculum. In these lessons, students are given interesting and challenging problems and are scaffolded to solve them using the Pólya framework.

M-ProSE has been successfully rolled out to four mainstream secondary schools, where participating students showed they could learn to apply all the steps of problem-solving. Students’ performance in the problem-solving module was also significantly correlated with their score on their school mathematics achievement test.

Question-Icon
How does M-ProSE work?

M-ProSE helps bring the explicit teaching and learning of problem-solving skills into classrooms by introducing math “practical” lessons based on Pólya’s model of problem solving.

In these math practical lessons, analogous to science practicals, teachers encourage learners to go through the entire mathematical problem-solving process. This is facilitated by a specially designed practical worksheet, together with an assessment rubric, that highlights each step of the process.

The problem-solving approach draws out students’ ability to think about math problems in both logical and imaginative ways. The process of solving is prioritised, instead of mere drill and practice often seen in classrooms.

Question-Icon
What is Pólya’s model again?

Pólya’s model is a 4-step problem-solving approach that scaffolds students through the problem-solving process.

Stage 1: Understand the problem - Does your student understand the question? Is there enough information to enable your student to find a solution?

Stage 2: Devise a plan - What methods can your student use? Diagrams? Formulas? Drawings?

Stage 3: Carry out the plan - Students implement the chosen methods to solve the question.

Stage 4: Check and expand - Did your student manage to solve the question? If not, what went wrong? What worked? What didn’t?

Question-Icon
The M-ProSE package includes
  • A module, consisting of 10 lessons and practical worksheets, to teach students how to use Pólya’s model and mathematical heuristics to solve mathematics problems.
  • An assessment rubric to accompany the use of the worksheets, to help teachers and students to understand the important steps in attempting to solve a mathematical problem.
Evidence from M-ProSE research
Question-Icon
How did students respond?
  • A high percentage of the students completed Pólya stages 1-3 and applied heuristics when solving a problem.
  • Many students demonstrated Pólya Stage 4 to some extent.
  • Stage 4: Checking and Expanding is within the reach of the general student population.
Question-Icon
In addition, teachers who participated in the research noted:
  • M-ProSE can help enhance students’ confidence and ability to handle unfamiliar problems.
  • Teachers who received professional development in math problem-solving could employ a shared language to talk about problem-solving with the students as the students moved through different classes and levels of the school.
  • Teachers could also use the shared language and way of thinking to facilitate professional collaboration within their school.
Question-Icon
How can teachers get started?
  • Remember that when math problems are intriguing enough, extendable and generalizable for most students, students are motivated towards solving it.
  • You may consider practising sample problems (available under Classroom resources and at the M-ProSE website) before bringing them to the classrooms. This will give you greater confidence as you experience learning from students’ standpoints.
  • You may consider awarding marks for students’ work done according to Pólya’s framework. What gets assessed, gets done.
  • For more information on implementing M-ProSE in your classroom, visit the M-ProSE website.
Question-Icon
Related links
Question-Icon
Further readings

For educators interested in understanding and implementing M-ProSE, these titles serve as ideal handbooks:

futher_readings_book futher_readings_book

Toh, T. L., Quek, K. S., Leong, Y. H., Dindyal, J., Tay, E. G. (2011). Making Mathematics Practical: An Approach to Problem Solving. Singapore: World Scientific [Amazon]

Leong, Y. H., Tay, E. G., Quek, K. S., Toh, T. L., Toh, P. C., Dindyal, J., . . . Yap, R. A. S. (2014). Making mathematics more practical: Implementation in the schools. Singapore: World Scientific. [Amazon]

Research projects

The following projects are associated with M-ProSE research:


Question-Icon
Research team

To learn more about M-ProSE, please contact the Principal Investigator A/P Toh Tin Lam at tinlam.toh@nie.edu.sg.



    Principal Investigator
  • A/P Toh Tin Lam, Mathematics and Mathematics Education (MME), NIE
    Co-Principal Investigators
  • A/P Tay Eng Guan, MME, NIE
  • A/P Leong Yew Hoong, MME, NIE
  • Dr Quek Khiok Seng, Psychological Studies, NIE
  • Ast/P Toh Pee Choon, MME, NIE
  • A/P Dindyal Jaguthsing, MME, NIE
  • Mr Ho Foo Him, MOE
    Collaborators

  • A/P Ng Pak Tee, Policy and Leadership Studies, NIE
  • Dr Hang Kim Hoo, MOE
  • Ms Yen Yeen Peng, MOE

This research on M-ProSE was funded by Singapore Ministry of Education (MOE) under the Education Research Funding Programme (OER 32/08 TTL & OER 22/12 TTL) and administered by National Institute of Education (NIE), Nanyang Technological University, Singapore. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Singapore MOE and NIE.

This knowledge resource was written by Tan Minying, Bernadine W. Sengalrayan and Tan Giam Hwee.

What is M-ProSE? (2:11)

Classroom resources

Three math sample problems that scaffold the problem-solving process for secondary students.

For teaching tips, sample problems and more, visit the M-ProSE website.

What teachers say

“Ever since we implemented M-ProSE into the lesson plans… I noted [students] are more resilient; they are not so afraid when it comes to handling ambiguous or difficult problems.”

- HOD Mathematics
Participants

500 students (approx.)

Mathematics teachers

5 secondary schools