Q&A #17459

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

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From: Angela G. Andrews

To: Teacher2Teacher Public Discussion
Date: 2007092616:47:36
Subject: The Potential Dangers of Teaching Touch Math

"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

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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