Teacher2Teacher |
Q&A #17459 |
From: Susan Olander
To: Teacher2Teacher Public Discussion
Date: 2010042613:10:48
Subject: Re: The Potential Dangers of Teaching Touch Math
On 2007092616:47:36, Angela G. Andrews wrote: > >"Touch Math ™" is a system for assigning a touch point to each number. >The number 1 has one touch point; the number 2 has 2 touch points, >etc. Students are taught to touch these points and count to get an >answer. Later students are taught a series of rules for using touch >points to obtain answers to problems involving the operations of >addition, subtraction, multiplication and division. > >Where did Touch Math ™ come from? >Touch Math ™ was originally developed to teach cognitively challenged >adults how to perform basic operations of additions, subtraction, >multiplication and division. These students, who found memorizing the >facts to be extremely difficult, were given an acceptable process for >arriving at the correct answers needed to pay for small purchases or >receiving correct change. Some LD teachers picked it up and began to >teach it to their students. When LD students were able to compute >more accurately and quickly than their “regular” education >counterparts in the classroom, some classroom teachers began to teach >it. Because it produces quick, accurate answers, teachers are often >enthusiastic about the system. They don’t have to worry about their >students knowing their basic facts, and their students perform well on >timed tests. > >Why is it so harmful? >Although it is certainly true that students who use the touch point >system arrive at accurate answers quickly, the use of Touch Math™ and >it underlying philosophy goes completely counter to the vision of the >NCTM Principles and Standards for School Mathematics. It is an >artificial, contrived, synthetic program, which has no connections to >anything in mathematics or in the real world. It encourages rote, >mindless, “pencil tapping”. 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. >It is rule bound, and teacher lead. There are no strategies taught – >only rules remembered. In this sense, it is a giant leap backward and >puts the student, says Bob Wright of Southern Cross University, >founder of Math Recovery, “on the path to nowhere. Touch Math™ forces >the child to perform computations at Stage 3 (count on) of Early >Arithmetic Learning, when even those students who qualify for and >receive intervention services are capable of leaving first grade >exhibiting much more sophisticated Stage 4 and 5 behaviors.” > > >Why is using touch points any different than using manipulatives? >An argument used to support using Touch Math™ is that it is like any >manipulative that is used to make connections to concepts then >discarded when no longer necessary. This argument is in error. First, >touch points are not manipulatives, but rather arbitrary symbols added >to the numbers. Manipulatives are real concrete materials that are >used to help students make connections to abstract mathematical >concepts. Dots on paper are not real, nor are they concrete, but >simply additional abstract markings of abstract number symbols. >Students cannot manipulate them in any way. They can only touch them >on paper. 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 that they tend not to see a need for >manipulatives. Instead, they replace cognitively valuable models that >truly represent the operations, with the pencil tapping method. > >Can’t I teach Touch Math™ along with other strategies? >With Touch Math™, the foundational concepts of addition, subtraction, >multiplication or division are ignored. The method ignores the >student’s need to: >• Develop a visual image of how sets are joined and separated. >• Develop non-counting strategies for adding and subtracting, such as >partitioning, using doubles, using the commutative principle, etc. >• Develop strategies for doing mental mathematics. (Without visible >“touch points” children trained in this system have few options for >solving mental problems.) >• Develop the concept of multiplication as repeated addition or as an >array of objects. >• Understand both the subtractive and partitive concepts of division. >• Understand the relationship of numbers as defined by our base ten >place value system. This technique bases computation on arbitrary >rules rather than on the foundations of the base ten number system. In >fact, the authors of Touch Math™ state that they have no intention to >teach place value, which should, they say, be taught only after >students master computation skills. In reality, by the time students >master the increasingly complex Touch Math™ rules, they have little >patience for learning to understand place value. >• 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. > >The Touch Math™ system is comprised of a series of rules or contrived >methods that students must follow in order to get the correct answer. >The teaching of such arbitrary rules to get correct answers is harmful >to children’s learning of arithmetic because the rules go counter to >children’s natural way of thinking. These rules “unteach” the >intuitive understanding that students have of place value, thereby >depriving them of opportunities to develop number sense. The history >of computational procedures suggests that students would understand >algorithms better if they were allowed to go through a constructive >process. (Kamii) However this process is time consuming and requires >cognitive effort on the child’s part. Giving the child the option of >“not thinking, just doing” is seductive, especially for a teacher >frustrated by students’ difficulties in understanding mathematics or >learning facts. However, it should not be considered by primary >teachers. Forcing, encouraging, or even allowing students to give up >their own thinking and follow the rules of Touch Math™ is harmful to >children’s autonomy and separates students from their own thought >processes. > >Won’t students discard this method when they become more proficient? >To be fair, this scenario is possible. To be truthful, all available >evidence indicates that it is not likely. Manipulatives or the natural >finger counting strategies that young children use are discarded when >their use becomes unavailable or cumbersome to a child who has >internalized the concept with the help of such manipulatives, or who >has learned non-count by one strategies, or math facts. On the other >hand, "touch points" never become too cumbersome, because using this >system is quicker than thinking and always available. Students who are >addicted to Touch Math™ then have no incentive to either understand >math concepts or learn number facts. Touch Math™ becomes a “nasty >addiction” which has proven to be practically impossible to break. >Teachers all over the country tell horror stories about how difficult >it is to break students of the “touchpoint” habit, and more >importantly, how little number sense and place value understanding >these students have. Parents, who may be impressed initially with >their child’s ability to compute so quickly and accurately, are later >alarmed when they realize the damage done to their children’s >mathematical health. As a pre-service university instructor of math >methods, I observe the crippling effects of Touch Math™ on students >each term as they try to break this tiresome habit and, at the same >time, develop the missing number sense they know they need to teach >mathematics themselves. > >At best, Touch Math™ is an unnecessary handicap to impose on those >students who are capable of building an understanding of mathematics, >given adequate time and experience. At worst, Touch Math™ fails to >encourage strategic, logical, and autonomous thinking, replacing it >with a mechanical, non-thinking process, which will not prepare our >students for the challenges of the 21st century. > >Teachers who are considering using Touch Math™ or who currently use >this system are urged to reflect on the following questions about the >possible long term effects of teaching Touch Math™: > >• While Touch Math™ is easy to teach and easy to use, does it actually >promote mathematical understanding? > >• Can I be assured that I am not "saddling" my students with a system >that produces quick, accurate answers in the short term, but has the >potential for doing permanent harm? > >
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