NumberTheoryChapter3FollowUp

W A R N I N G ! ! What you are about to read can be quite addictive. Try it out at your own risk.

If you ever see students' papers with dots all over the numbers, it's possible they are using "dot math." It's an actual system that's been taught for a long time that helps kinesthetic learners be able to accurately do addition. It's also good for students who aren't developmentally ready for the abstractness of memorizing addition facts. There is now a company selling training videos and resources to teach "[|Touch Math]." It looks like the founder of the company may actually be the inventor of what I was introduced to as "dot math."

Enjoy the Peanuts cartoon in which [|Touch Math helps Peppermint Patty feel confident in her math.]. It will give you insights into how it works as well as the frustration that some of your students may feel about math. If you dare, try the technique out on a few addition problems.

You'll possibly have students who know their addition facts but will use dot math because it's "faster." This is not dissimilar from students who learn touch typing but aren't willing to invest the time it takes to practice it or maybe they don't "believe" in it, and so they continue to hunt and peck. It's actually similar to someone who knows how to doggy paddle across a body of water. When you first learn the American Crawl or freestyle swimming, it's scary to put your face in the water. In that first swimming lesson, that person swallows a lot of water and this new style of swimming isn't as fast as the way that he/she is comfortable with. Anyone who masters freestyle swimming would probably recognize that this new way is much faster and more efficient than the old way. But when you're "on the other side" it's hard to believe that will be true.

You will find that you have students who never mastered their addition facts. Some never had to, some tried and chose not to, some had a great alternative method (like dot math) and never felt the need to. Is it necessary that they do memorize those facts now that they're in your high school class? If so, how will you help them?

For students that were developmentally ready, I would ask them, "What's 9 + 7?" Once they said 16, I would ask, "And tonight when you go home, how much will 9 + 7 be?" And often, I would have to wait for them to recalculate the answer. Then I would ask, "Tomorrow morning when you are eating breakfast, how much will 9 + 7 be?" Wait... Keep asking the questions for different situations and times. After a while, they start to laugh and they "get" that it's 16. My last question is, "What will always be the answer to 9+7?" This would usually motivate them. Of course, every time I saw that student, I would ask, "What's 9 + 7?" It became our inside joke and sometimes they would even see me and say "16!" before I could even ask the question. You can continue to do this, one addition fact at a time if you want. ;-)

Is it necessarily bad to not have facts memorized? What if the non-memorized method is actually faster for calculations? The student on the left in this video has learned to use an abacus and then learned a method that allows you to visualize an abacus and solve the problem without the physical abacus.

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 * There is very little that's abstract about working with an abacus as long as your understanding of place value is strong.
 * [|Abaci and similar instruments are known to have been used by ancient Romans, Indians, Native Americans, Russians, Koreans, Chinese, and Japanese.]
 * [|In Japan, there is a movement to bring the abacus back into the classroom] as a teaching model and to aid students in truly understanding arithmetic as well as a way to bring back an appreciation of an important part of Japanese culture/heritage.