Division. The word instantly brings an image of long division into my mind, but done using an alternative algorithm (the scaffolding method.) As a student, I used this method as a tool to make division a neater, tidier process for myself. My teacher at the time was not so pleased with my problem solving skills: she would not allow me to use my algorithm on an exam, nor was I allowed to teach other students my way of solving division problems. I was deeply confused by her reasoning and frustrated with my inability to fully understand the standard algorithm.

As an educator, we could embrace students’ problem solving skills and exploratory methods used to solve a problem given in class. **Does it really matter how a student solves a problem?** I feel as long as said student can show how they solved the problem and be able to explain their method, their mathematical understanding is just as good (if not better) than if using a standard algorithm.

This concept is demonstrated in this week`s chapter, where the reader is introduced to Mac, a student who has not been taught formal division. Jennifer`s focus is to set up Mac`s mathematics side by side, so that he “…opens a space of his own where he relates and integrates the equations in ways that most definitely speak (mathematically) to one another.“

By allowing Mac to explore his knowings of 18, he learns to develop different ways of seeing and expressing his own mathematics:

18-3-3-3-3-3-3=0

6×3=18

18-6-6-6=0

0+6+6+6=18

3×6=18

In doing so, Mac can clearly see that division involves groups and sharing these groups. He can also see that division and multiplication are related to one another: they are opposites.