Connection to Multiplication Fluency
As I have mentioned several times above, understanding multiplication is a major focus of mine for my third graders. However, I do not force my students to memorize facts or practice through timed tests. In contrast, I focus on helping my students develop number sense as they interact with numbers and learn to use numbers flexibly. If memorization and speed are in control, students begin to cling to formulas or formal procedures. A student who relies on memorization may have no problem recalling the fact 8x6=48, however, they then struggle to solve 8x16=128. A student who has a strong number sense mindset may quickly see one solution as 8x10+8x6=128.
In Jo Boaler’s book Mathematical Mindsets, she explains a brain process called compression.3 Learning new aspects of mathematics that you have no previous experience with takes up a large amount of space in your brain. You need to spend a lot of time thinking about how it works and how these new ideas relate to each other. Mathematics that you have learned completely and know well, such as addition, take up small, compact space in your brain. You can use it without thinking about it. (insert citation) My goal is to help my students see mathematics conceptually and to enjoy “playing” with numbers. Compression will happen with increased familiarity and understanding.
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