Before I read the first three chapers of CGI I had never really stopped to think about how children learn math. I have always just thought of math as something you get or you don't. It was very informative to read about the different ways in which students learn math such as; join, separate, part-part whole, and compare (graph page 12). I thought it was neat how the book stated how strategies such as counting come naturally to young children. Children do not have to be taught that a particular strategy goes with a particular type of problem. I thought this little fact was so cool and it got me thinking about the students I work with and how each of them use different strategies for the same problem. One student isn't more right than the other, it just shows how children learn things in different ways. Another thing that I found particularly interesting was the effort that goes into creating story problems for students. I had never stopped to think about how the wording in word problems can make a problem harder or easier for a student. Problems are easier if their wording corresponds to the action sequence. For example:
Janice had 9 cookies. She ate 3 of them. How many cookies does Janice have left? VSJanice just ate 3 cookies. She started with 9 cookies. How many cookies does Janice have not? Clearly the first one is easier because the starting quanity is given first. All in all I really enjoyed these three chapters and learned a lot about math, however I do have one question and that is at what age do you try to get students to stop counting up or down and just doing the math? How do you teach students to SOLVE a math problem, rather than just counting up or down?
Kate,
ReplyDeleteJust like you I enjoyed reading the CGI book. I feel that as pre-teachers this book will help us see that it is okay for students to be at different stages of mathematics development. This book also makes you realize that the students use of different strategies allows a teacher to have a greater understanding of the developmental level a child is at. With that said, I feel that overtime children begin to move from one strategy to another with scaffolding. It isn't that a teacher has to try to get the students to stop counting up or down so they are just doing the math. It is the idea that through time the students begin to find strategies which make the mathematics problems quicker and more efficient. This can be seen in the many examples of different students using different strategies to solve the same problem. Overtime the students use number facts, but they first have to know these number facts. With that stated, do you now feel that students will learn at their own pace? Or do you still feel that there is a specific time when students need to stop using manipulatives to solve mathematics problems?
In my opinion all children learn at different paces and therefore there is no specific time when children need to stop using specific strategies.