Cognitively Guided Instruction

In many college level courses students find the reading to be useless, unneeded, or boring. For me, this was not the case when reading about Cognitively Guided Instruction. When reading the first three chapters of the book I became excited know that I could use some of this information in my future classrooms. The author of the book states, “Over time, direct modeling strategies give way to more efficient counting strategies, which are generally more abstract ways of modeling a problem” (Carpenter, 3). I was struck by this quote, not because I did not realize that children moved from direct modeling to more abstract thinking of mathematical concepts, but because I questioned if all students do this on their own time or if some need more direct instruction on how to begin to think abstractly (for example: doing mental math). This quote also reminded me of the subtle things teachers need to be looking for during mathematical thinking. An observer may think a child who gets the answer right by using direct modeling has a better understanding of mathematics than a child who uses mental math and gets the answer incorrect. In reality the teacher needs to think about the student’s mathematical thinking and where they need to grow from there.

In the book the authors state, “Variations in the wording of the problems and the situations they depict can make the problem more or less difficult for children to solve” (Carpenter, 10). I found this extremely interesting. I had never thought about how a word problem can be manipulated to change its difficulty. In the book the example the authors gave (in case you do not remember) was:

Janice had 9 cookies. She at 3 of them. How many cookies did Janice have left?

Janice just ate 3 cookies. She started with 9 cookies. How many cookies does Janice have now?

The problems are the exact same, just worded a little differently. This information visually showed me how a teacher needs to be careful when writing his or her own word problems, or when picking word problems from a book. This is because the ways the word problems are written affect the way a person perceives the problem. Another way a teacher can use these two word problems are by using one or the other for an extension or simplification. Depending on the needs of the child the same word problem can be written in a harder or easier way.

I also really enjoyed learning about the different types of word problems. I had never thought of word problems as having so many different types. I am not sure if I have completely memorized what each of the word problem types are called, but I know have an idea that when teaching a classroom a teacher can not just pick a word problem arbitrarily. A good teacher has to plan ahead!

Overall, I really thought this book had a lot of helpful information. I am interested to see what others thought about the book and the information they found important. The only thing I am worried about is being able to spend enough time to pick the correct word problems for my students. I am also questioning myself on how I will be able to remember all the different types of word problems and recognize them by sight. Hopefully this will come from experience and time, but as of now I feel that this task may take a lot of time and effort for beginners.