Young Mathematics at Work: Chapters 5 and 6

Overall, on thing I think that has really struck me about this book is how the problems which are posed to a class of students are relevant. The children become emotionally attached to the problem and want to find the right answer. They are not just doing the problem because the teacher said to do it. The “Pizza Patterns” problem in this chapter really caused the children to become involved in mathematics in a way that was exciting and fun. Also, this type of problem allows for a lot of small group and large group discussion. For example, one group began noticing that the whole matters. One child snipped a little off of his paper to make the thirds equal but noticed the whole matters when comparing it to another students work. On page 77 of Young Mathematics at Work they state, “The whole matters – you can not change the whole by snipping off a little bit – it changes everything!” This is not something that comes naturally to students, but through problem solving and discussion this one particular child began to understand this concept more fully.

Another interesting point that I found in chapter 5 is that people use models as a tool to help them mathematize. People have to work through the problem to gain a greater understanding of the concepts within the problem and models are a way of doing this. In chapter 5 the authors also stated that people have to move from models of thinking to models for thinking. At times people solve the problem and then create a model for their thinking, but as teachers we have to move our students to using models as a way to help them through their thinking process.

Chapter 6 in Young Mathematics at Work was very different from Chapter 5, but it caught my interest because of the different algorithms which were used. I feel that we live in a world where the “traditional” algorithms are what is accepted and known. Before reading this chapter I had no clue that there were other algorithms that worked and people used hundreds of years ago. Even though the algorithm we use today may be the most efficient the beauty of all algorithms is “that they [are] generalized procedures that [can] be used as efficient computation strategies for all problems” (p. 99). It is important to remember that there is no correct way of solving a problem, the most important thing is that people understand that mathematics they are doing and why they are doing it.

At the end of chapter 6 the authors state, “ Teaching algorithms is in fact harmful to children’s mathematical development” and “ when algorithms are taught as procedures to use for any and all problems children necessarily give up their own meaning making in order to perform them” (p 105). I feel that both of these quotes are something to think about when working with children and choosing the different mathematical task to teach to your students.