Abstract
Psychological theory indicates that human use heuristics, the psychology of mental shortcuts, to make decisions, solve problems, or learn new knowledge. In this article, I will discuss how some common mathematical mistakes generate from the heuristics process while students learn mathematics or solve mathematics problems, and how we may help students avoid the hurdle of heuristic bias. Constructing heuristics ability of non-linear thinking will be discussed to shed light on teaching students high order of mathematical thinking.
Highlights
Psychological theory indicates that human use heuristics, the psychology of mental shortcuts, to make decisions, solve problems, or learn new knowledge
I will discuss how some common mathematical mistakes generate from the heuristics process while students learn mathematics or solve mathematics problems, and how we may help students avoid the hurdle of heuristic bias
In my preservice elementary content courses, often when being asked Pythagorean theorem, some students immediately replied “a2 + b2 = c2”, but they were not able to answer the follow-up questions: what do a, b, c represent? Can you explain in what situation this happens? This is a typical example that it does not help mathematics learning if students only memorize mathematical formula without understanding the mathematical meaning
Summary
Psychological theory indicates that human use heuristics, the psychology of mental shortcuts, to make decisions, solve problems, or learn new knowledge. Without any experience of hunting, none of them answered correctly. Without a doubt, this is an easy question for a person who often hunts in forest. Since I never hunt anywhere, the right answer for this question is definitely beyond my imagination. This event reminds me of mathematics teaching/learning. The thinking process of the small house question is analogous to that of solving a math problem or learning mathematics. When students are given a mathematics problem, they would start with searching the relevant knowledge they are familiar with, which could be a number, a formula, a problem solved before, a life experience that related to the given problem, etc. THE LITERATURE AND THE OBSERVATIONS FROM TEACHING PREACTICE area of square B and the volume of square A doubles the volume of square B too
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