CGI Chapters 1-3 Ideas

After reading the first three chapters of "Children's Mathematics" I already know that I will like this book. It's so interesting to watch a child count on their fingers for a particular problem and then go back and understand why this was helpful to them. Throughout the three chapters, I found multiple ideas and strategies that stood out but I found two of them most helpful and interesting. The idea of direct multiple modeling strategies seemed to be most helpful for younger and less advanced students. Since I am placed in a kindergarten class at this time, I was able to relate to these strategies better. Although the student's rarely do addition or subtraction, they are currently working on counting. I can see using physical objects being the best way to instruct them with join problems. The other theory I found really interesting was the whole idea of the join, separate, part-part-whole and compare problems. I never really realized there were so many ways to write simple math and addition problems. It is helpful to know these ways though so we can have variation in our work. It also helps us as teachers know that our students truly understand the multiple ways of performing addition and subtraction problems. Through the three chapters I only really came across one question. On page 22, we see two students performing the "counting down to" strategy. Both of the children were sure to either not count the first one or not count the last one to reach the correct answer. It had me wondering if this was a practice taught to the students or whether it was something the realized through trial and error. If it was taught, how would you teach something like that?