Reflection On Chapters 12 & 13

I still remembered my astonishment when my eight year old daughter showed me how she did her addition computation. I couldn’t understand a thing and so did her. And because I couldn’t understand, I didn’t know how to teach her and in the end, I resorted to the tradition algorithms method. After reading chapter 12 and 13 of the book ‘Elementary and middle school mathematics’, I was surprised to learn that the teaching of mathematics have moved towards teaching children to compute mentally. Children are encouraged to use ‘invented’ strategies to do addition, subtraction and even multiplication and division. It is beneficial because the person using his or her own ‘invented’ strategies can then understand how the answer is derived rather than merely following the steps in standard algorithms. Upon reflecting, although I was taught to use algorithms to do math computation in schools, I believe that I did not quite develop mathematical thinking or understanding. Because despite hours of instruction and practice, I often fail to apply them correctly in problem solving situations. And hence, I grew up thinking that that mathematics is a collection of mysterious formulas and procedures that have to be memorized and practiced.  

I believe that in supporting children to develop their own strategies, children can be more aware of the place values and have less conceptual errors. Moreover, there is a real understanding through creating their own strategies, hence they are more willing to solve unfamiliar problems in the future.

The process of developing invented strategies needs support from the adults. Both teachers and parents then play an important role. Teachers have to allow ample time to guide children, facilitate the sharing of various solutions, listen carefully to their ideas, and make explanations about the math ideas presented in the invented strategies.