Facility
in math is recognized by educators as being key to later success in life. The
National Council of Teachers of Mathematics (NCTM) has set ten content standards
for the teaching and learning of mathematics from prekindergarten through
twelfth grade.
The standards in this series refer to the entire range of grades.
Examples, however, are for prekindergarten to second grade, which includes the
grade I teach.
The NCTM publication Principles and Standards for School Mathematics
has complete explanations of these. For more information, you may visit NCTM at
www.nctm.org.
Bullet points are quotations from the publication. Underneath them are my
suggestions for parents.
Math
principles and standards, part 10
Representation
Standard
The instructional programs should enable all students to:
 Create
and use representations to organize, record, and communicate mathematical
ideas;
 Select,
apply, and translate among mathematical representations to solve problems;
 Use
representations to model and interpret physical, social, and mathematical
phenomena.
When a child holds up two fingers to show how old he is, he is probably
showing his first representation of a number with a physical object. Moving into
the early school years, children learn to represent numbers in other ways as
well: by speaking, writing, gesturing, and drawing. Some use numbers that we can
easily recognize because they are standard; others invent their own symbols to
get their point across.
Parents can be most helpful by listening carefully to what their children
say about their mathematical observations. In the event that their children have
math homework, parents can encourage their children to find a way to put their
thoughts onto paper as they figure out math problems. Then, after this is
completed, parents ask the kids to use what they wrote to explain their thought
process to the adult.
When family members are trying to figure out a mathematical situation as
a group, parents explain to the older siblings the need to respect the budding
math talent of the younger ones. There has to be a safe environment in which all
can explain the various ways of doing the math. Children at different stages of
development will find ways to solve problems that reflect their own level of
understanding.
For example, a thirdgrader who has learned times tables may easily
understand and explain that 6 X 5 = 30. At the same time a first grader may show
her understanding by writing 5 + 5 + 5 + 5 + 5 + 5 and then counting, “5, 10,
15, 20, 25, 30” and come up with the same answer, or by adding pairs of the
fives into three separate tens, then counting, “10, 20, 30.” Parents would
do well to respect that there are many ways  not just one “right” way  to
express oneself mathematically and come up with answers to questions in these
situations.
Jay Davidson lives in Palo Alto and has been teaching in San Francisco
for 31 years; he teaches first grade. His book, Teach Your Children Well: A Teacher’s
Advice for Parents, is available for $12.95 at
Amazon.com. Each part of this series is archived and available on his website,
www.jaydavidson.com.
