Problem Solving

Exploring a challenge for which a resolution is not obvious.

PISA defines problem-solving as: …an individual’s capacity to engage in cognitive processing to understand and resolve problem situations where a method of solution is not immediately obvious. It includes the willingness to engage with such situations in order to achieve one’s potential as a constructive and reflective citizen.

Simply put, Problem solving is what you do when you don’t know what to do.  This implies problem solving is a set of skills or methods that are applied when a new issue is encountered.

Frequently, we think students are problem solving when they are merely practicing methods they have been shown in class.  True problem solving requires analyzing the problem, generating and selecting possible solutions, carrying out the plan,choosing and using a method, and reflecting on the results.  From PISA:

Exploring and Understanding

This involves exploring the problem situation by observing it, interacting with it, searching for information and finding limitations or obstacles; and demonstrating understanding of the information given and the information discovered while interacting with the problem situation.


Representing and Formulating

This involves using tables, graphs, symbols or words to represent aspects of the problem situation; and formulating hypotheses about the relevant factors in a problem and the relationship between them, to build a coherent mental representation of the problem situation.


Planning and Executing

This involves devising a plan or strategy to solve the problem, and executing it. It may involve clarifying the overall goal, setting subgoals, etc.


Monitoring and Reflecting

This involves monitoring progress, reacting to feedback, and reflecting on the solution, the information provided with the problem, or the strategy adopted.


PISA problem solving

PISA Problem Solving Questions

This fifth volume of PISA 2012 results presents an assessment of student performance in creative problem solving, which measures students’ capacity to respond to non-routine situations in order to achieve their potential as constructive and reflective citizens. It provides the rationale for assessing problem-solving skills.

To try sample PISA problem solving questions, click the image to the right.



problem solving matrix



Additional links and resources:

University of Waterloo Teaching Problem Solving Skills Teaching Problem Solving Skills
 Levels of Problem Solving from Ontario Skills Passport Problem Solving Rubric

Literacy Numeracy Secretariat monograph


Problem Based Learning in Mathematics
Literacy Numeracy Secretariat monograph  Asking Effective Questions


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