Q&A #17459

Teachers' Lounge Discussion: Who "invented" touch point math?

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From: Susan Olander <solande@ucls.uchicago.edu>
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
>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
>adults how to perform basic operations of additions, subtraction,
>multiplication and division.  These students, who found memorizing
>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
>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™ 
>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. 
>touch points are not manipulatives, but rather arbitrary symbols
>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.
>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
>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
>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
>their own thinking and follow the rules of Touch Math™ is harmful to
>children’s autonomy and separates students from their own thought
>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
>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
>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
>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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