*(Psychology Press), suggested to us by our colleague and provision fellow Prof.James Allen, I skipped straight to Chapter 9 on Development of Problem-Solving Skills.Well, you may be tempted to say, “Jump over that line! Halpern examines the stages in the model of problem solving proposed by the English psychologist Graham Wallas (1858 – 1932), which is commonly known as the model of the process of creativity.*

Many students come to college ill-equipped to problem solving in mathematics as well as in other disciplines.

Problem solving requires critical thinking and both are fundamental to learning mathematics.

Two models that are worth noting are the Polya’s and Wallas’ problem-solving models.

In his best-selling classic How to Solve It (Princeton University Press, 1945), George Polya (1887 – 1985), a Hungarian mathematics educator, identifies the four main steps that form the basis of any problem solving.

This practice not only helps the students to develop critical thinking skills, but also allows them to increase their confidence, inspire and engage them in the subject.

When I first started reading Diane Halpern’s (2014) text Thought and Knowledge: An Introduction to Critical Thinking, 5 ed.Mathematics can be either analysis or synthesis, and sometimes both depending on the math topic.Nonetheless, both require critical thinking in problem solving. Some of these models are specific to a given discipline while others are all-purpose models.In fact, students must learn how to think critically to be able to acquire mathematical knowledge through problem solving.This is why NCTM advocates that mathematics instruction should include problem solving, quantitative reasoning, and critical thinking.id=23273) While critical thinking has several definitions depending on the discipline, there is a strong consensus that critical thinking is the ability to use knowledge to conceptualize, apply, analyze, and synthesize information to successfully solve problems (Hence, for the students to be critical thinkers, they need to be able to both analyze and synthesize information.These steps are: understanding the problem (identifying what is being asked), devising a plan (formulating a set of strategies), carrying out the plan (executing the selected strategies), and looking back (checking and interpreting the results).Polya also argued that a mathematics problem should not end just because the answer has been found, instead, there should be a constant probing related to the problem.Halpern describes how psychologists think of the word problem as “a gap or a barrier between where you are and where you want to be.” She also gives a nice visual illustration of a “problem” in Fig.9.1 p.453: one long rectangle/box divided by a vertical line into two blocks “X” and “Y” – you are at “X” (box left of vertical line) and want/need to get to “Y” (right box), how do you that?

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