# Shallow understanding of mathematics

Today I try this journal prompt with my students. Write a word problem with the answer as 5x.

As this is the first time the students are doing it, I try to give them an example with the algebraic expressing (x+5). Explain to them now we are “doing the opposite”. Usually, you are to solve the problem. Now , you are to create a problem with the answers provided.

Sensing that the students are at a loss as to what to do, I decide to provide them with scaffolding by giving them some key words to use. They can either use “each” or “as much as”.  I would have though that these keywords are a “give away” but I am proven very wrong.

Looking at their journal entries, only about half of them seem to know how to create word problem. From their entries,  it seems that they do not have a deep understanding the use of “each” and “as much as”.  They may seem able to solve the word problem but they might be just doing mechanically without any real understanding (e.g., see “each” and “as many as”, just times …)

I can see their shallow understanding in solving geometry word problems. In getting them to articulate the property used, they would just say “angles in a straight line” when they see 180.

From these various episodes, it appears that my students are simply “hatuming” .  They are not thinking deep enough. How to make them think “deep deep”? Here are some of the activities that I can think of :

(1) Get them to look at their friend problem and identify the mistake

(2) Modelling the problem-solving process. I need to show them how I try to understand the word problem through a series of questioning.

(3) Make them verbalize their problem solving process (e.g., using screencasting)

There is lots of work to be done but I will continue to strive on. Why? Because they are my students and I would always do what I can for them.