I have really been enjoying the CGI text just because of all of the examples it gives of the many ways that students approach various math problems. Chapter 4 is a continuation of the principles established in the previous chapters but it applies to multiplication and division instead. I remember when I first came across partitive and measurement division I was an adult and I had difficulty figuring out what the difference between the two of them were and why it was even important because with my background the math in them seemed to be the same. Since this is my second experience learning about the differences I can now grasp that partitive and measurement division are uniquely different for children learning about math and that needs to be kept in mind. If you try to solve the problem by using counters or drawing pictures the difference becomes immediately obvious. I also liked the idea that the text raised about introducing simple multiplication and division problems in as low as K-1 so that students get used to the idea of using math in this way.
I also also surprised when the book addressed the common misconception that students should have a good grasp of base-ten in order to be able to work with two and three digit numbers. They raised the point that as long as students can count they can solve problems with two digit numbers. Of course, this is sped up immensely once students realize they can count in groups of 5 or 10, etc. Many of the students in my second grade class are in the process of refining their knowledge of the base ten system. They spend a lot of time with a chart they have that lists ones, tens, and hundreds and they have cubes they use to model problems that are two digit addition and subtraction. Most of the students can make blocks of 10 cubes and use them that way while other students still prefer to count out each block.
I also was interested in reading about the various strategies that students use when working with multi-digit numbers such as incrementing, combining tens and ones, and compensating. These are all still strategies that I use in mental math but I've grown so used to it that I don't spend much time thinking about what exactly goes into solving a math problem anymore. When working with students to have an awareness of all the different ways students can do something is helpful so you can help a student find the strategy that works the best for them.
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Anne,
ReplyDeleteI really like the very last point you made in your post. "When working with students to have an awareness of all the different ways students can do something, it is helpful so you can help a student find the strategy that works the best for them." I think this is key. As we have been reading, there are numerous strategies that can be put to use when computing addition, subtraction, multiplication, and division problems. Counting up, using manipulatives, using facts deriving from base ten, and trial and error are just a few of these strategies. It is so important that we, as teachers, recognize the plethora of strategies that exist and understand that a strategy that may work for one child, will not necessarily work for another. Individualized instruction is increasingly important both within general and special education settings in order to ensure academic success.