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From: Katie <firstname.lastname@example.org> To: Teacher2Teacher Public Discussion Date: 2012091714:41:40 Subject: Re: The Potential Dangers of Teaching Touch Math I am currently looking into the various strategies for teaching basic math facts (simple addition and subtraction) to children, and I came across this article regarding the dangers of teaching touch math. I have numerous questions, however, about the stated harmfulness of touch math: 1. "It is an artificial, contrived, synthetic program..." How is this a problem, necessarily? 2. "It encourages rote, mindless, “pencil tapping." As far as I can see, the "pencil tapping" is not mindless - it's counting. 3. "The method forces students to think of every number as “in the ones column” and, as a result, it inhibits understanding of place value concepts, thus deterring number sense." As I understand it, math is first introduced with manipulatives. Obviously, we don't want children to continue to need physical manipulatives forever, so eventually, I assume, "number sense" must develop? With touch math, it seems to me that a manipulative becomes buried within the number, and that, in a very visual sense, the number is seen as "being worth" that much or becoming its actual value. For example, the number 5 contains five touchpoints. The touchpoints seem to me to be a simple visual representation, right on the number itself, of what the number 5 "means" or stands for. 4. "It is rule bound, and teacher lead. There are no strategies taught – only rules remembered." I'm not sure I'm entirely understanding the distinction or, again, why this is inherently a problem. I can understand how this is a problem if the touchpoint system is NOT working, but if it's working to assist with basic computation, I'm not sure how being "rules remembered" is a problem. When basic math facts are memorized (as seems to be the current "method" of teaching them?), there are also no strategies involved - only facts remembered. And math is, on the whole, a lot of rules to remember. There's not much creativity within basic math and the knowledge of what numbers mean and how they work! 5. "Students cannot manipulate them in any way. They can only touch them on paper." In my opinion, the students ARE manipulating the dots or points - within their mind - as a transition between physical manipulatives and simple memorization, and this actually contributes to a greater understanding of the "sense" of the numbers. 6. "Another problem with Touch Math™ is that teachers who use this system are so impressed with the speed and accuracy resulting from teaching this method..." Again, I see how never moving beyond this method or doing most memorization of basic math facts is a problem - however, if a child has most facts memorized, and reaches a problem where they suddenly cannot remember, for example, 7+4, it seems to be that touchpoints offers an actual strategy for finding an answer - something that cannot be obtained with memorization. 7. "With Touch Math™, the foundational concepts of addition, subtraction, multiplication or division are ignored" At their simplest, the foundational concepts of addition, etc, are counting. This is exactly what touchmath reinforces. 8. "Think about numerals as representations of quantity. The number 38, for example is not thought of as “almost 40”, which would be helpful for estimating an answer, or as 3 tens and 8, which would be helpful for understanding place value concepts. Instead 38 is thought of as an 8 which requires 8 taps and a 3 which required 3 taps." This kind of problem seems to be an issue only if math concepts are taught out of order or to children who are not ready for the concepts, but not an actual problem with the touchpoint system. Ultimately, my question is: What are the STRATEGIES you recommend kids use for basic addition/subtraction, especially when they cannot remember a memorized fact (ie, 7+4)?
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