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Activating Your Young Child's Potential in Mathematics

by Marsha Landau, Ph.D.

Identifying Your Child's Aptitude for Mathematics
Early reading is easy for parents to detect. A gift for verbal expression is apparent in story-telling and imaginative or dramatic play. What clues should parents be watching for to identify a special aptitude for mathematics in their young children?

Many parents look for signs of skills with numbers, such as: early facility with counting; knowledge of basic facts; and mental computation. Some parents actively teach their children to "count" almost as soon as the children can speak–but what they are really doing is simply memorizing the counting word string as though it were a poem. A genuine understanding of counting is much more complex than simply being able to recite "one, two, three,..."

Pepper (1998) describes characteristics of five levels of counting development in young children. For example, does your child require physical units for successful counting, or can she count pictorial representations, or motor representations (such as claps)? How does she manage counting when some of the objects are visible and some are not? Can she order sets of objects according to the number in each set?
If your child knows addition and subtraction facts, you can present real-world questions such as the following:

  • I had some pennies in my pocket. Emily gave me 3 more. Then I counted and found out I have 11 pennies. How many did I start with?
  • Twelve children were invited to the birthday party. I have 8 party hats. How many more are needed?

Probe your child's understanding of number by asking questions that get at underlying patterns and relationships. For example:

  • If 100 - 60 = 40, find 100 - 62. Tell how you got the answer. Here you are looking for a reasoned rather than a computational response. The reasoning might go like this: The answer is 38, because if I subtract 2 more, the answer should be 2 less. A child who looks for paper and pencil and computes the result correctly using regrouping is showing competence in arithmetic, but not a "mathematical turn of mind."

Of course, mathematics is much more than computation.

  • Does your child notice patterns and relationships in geometric objects, measurement, or data? Does your child love mathematical puzzles or games? (See references below for suggestions.)


A talent for mathematics is often expressed by a child's seeing the world through "mathematics colored" glasses–wondering about the world in a way that is mindful of mathematics. Any of the following would be a clue that your child has a special aptitude for mathematics:

  • Deliberately finding a path through the supermarket that covers every aisle
  • Questioning advertising, e.g. "three out of four doctors recommend..."
  • Asking, in a restaurant, when the hostess tells you that you'll have to wait 20 minutes for a table, how did she know that? (And having some ideas about an answer)
  • Exploring relationships among measuring spoons, cups, containers, etc.

These indicate a tendency to mathematize the real world. A child who engages in such activities is not likely to ask, "When am I ever going to use this?" Real situations are important representations of mathematical ideas, along with concrete manipulatives–spoken and written symbols, language, and pictures.


School mathematics is too often restricted to textbook representations of mathematical ideas. They consist of lots of symbols, some pictures,and much written language. Some ways you can enrich your child's mathematical experiences are by providing opportunities to represent ideas in the real world by using manipulatives and to encouraging translations within and between all the representations.


Mathematics, School, and Teachers
Is math your child's favorite school subject? Clearly, this could indicate a special interest that should be fostered. Curiously, though, not liking mathematics at school, even when grades are good, may be an indication that your child is gifted in the subject.


If your child reports "boredom," you must investigate. One possibility is that she is having trouble learning new material and is hiding behind "boredom." Perhaps she is gifted in other areas and is embarrassed about her perception that she is less capable in math. There are many potential sources for difficulties–recent absences, poor teaching, incomprehensible materials, a bewildering sequence of topics, inattention, and so on.


On the other hand, your child might be bored because mathematics in her classroom is genuinely boring–endless repetition and drill, too much emphasis on computation, or not enough challenge. Does the math program include geometry, measurement, data and chance, patterns and relationships? Do the students use manipulatives to develop underlying concepts? Check the type of work your child is expected to complete. If the assignment requires doing 25 exercises that are all the same and at the lowest cognitive levels, you need to speak with the teacher about the appropriateness of this math program for your child.


Your child's teacher may agree that your child has talent in mathematics. What happens next? Beware the teacher who wants to "let your child proceed at her own pace"–this means no instruction from the teacher and little interaction with peers. This plan deprives your child of the social learning that is an important element in a good mathematics program, as well as ignoring entirely the spoken modes of representation.


Further, if your child completes the material in a second grade textbook on her own and then moves into a third grade textbook, look it over carefully– the first three or four chapters are likely to be review of second grade. If the teacher agrees, and your child starts somewhere in the middle of the third grade book, she may complete that before the end of the school year. Where does this acceleration lead?


Do not permit the teacher or the school to put your child on a path that leads to a point at the end of grade 5 or 7 or 10 where there is no teacher and no curriculum to meet her needs. Acceleration is certainly a viable option for a child gifted in mathematics, but only when a comprehensive long-range plan is in place at the outset (even for your second grader). Some of the questions that must be answered satisfactorily include:

  • Will my child be permitted to take pre-algebra before middle school, if she is ready? Who will teach it? Will she learn individually, or as part of a group?
  • Will my child be permitted to take algebra in grade 6 or 7 if she is ready?
  • What happens in subsequent years, before she is attending high school, if she is ready to take high school math courses? If she will be taking courses at the high school while still attending middle school, who provides transportation? Will her grades contribute to her high school GPA and class rank?
  • At the high school, are there courses after calculus for students who complete it before grade 12? What courses? Taught by whom?

Parent Options
Consider enriching your child's mathematics experiences with books, games, toys, manipulatives, World Wide Web resources, classes, or individual time with a math mentor.

Online Resources for Parents


Sites Designed for Students

Sites for Teachers

Reference
Pepper, K. L. (March 1998). Preschoolers' Counting and Sharing. Journal for Research in Mathematics Education, 29(2), 164-183.

Marsha Landau, Ph.D., is a mathematics education specialist in Evanston, Illinois. She mentors gifted children in mathematics and has developed a Web site that links excellent Internet lessons, activities, and resources to specific mathematics curriculum descriptors covering the fundamentals through algebra. Dr. Landau can be contacted at mlanwhe2@yahoo.com
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