In this issue

Using a problem-solving model to solve the early math problem

Pat Stokes reports on a successful early (K-2) math program that she developed and tested in a public grammar school in New Jersey.

By Patricia D. Stokes, PhD

The early math problem is that children are not fluent in numbers, symbols and patterns. My problem-solving model, which is based on paired constraints, was used to create a solution. The solution is called Only the NUMERS Count©. Its structure is shown below. The initial state was current curricula; the goal state, a new curriculum designed to promote fluency. The preclude column lists aspects of current curricula; the promote column indicates their replacements.

Table 1. Problem Space for Only the NUMERS Count©

Problem Space for Only the NUMERS Count©

The new count is explicit in that it (like the Asian counts) names the place value of each digit. For example, the number 11 is called “ten-one,” 21 is “two-ten-one” and 31 is “three-ten-one.” The single manipulative (like the abacus), called the count-and-combine chart, represents numbers as combinations of other numbers. By the end of kindergarten, children solve place value and single-digit addition and subtraction problems. By the end of first grade, they solve double-digit problems.

The multi-operation chart was designed to teach multiplication, division (which undoes multiplication) and fractions (which involve multiplication and division) simultaneously. Instead of chanting the chart as addition (2, 4, 6…), second and third graders chant it as multiplication (two 2s are 4, two 3s are 6…). They also chant it in reverse (two 3s are 6, three 2s are 6). In third grade, they include fractions (1/3 of 6 is 2, ½ of 6 is 3) as part of the pattern.

Deliberate practice, used in all grades, is continuous and focused on specific aspects of a skill to be developed. It is also highly variable with children switching between solutions (as opposed to split practice, during which they switch between kinds of problems).

The photo shows my two lab assistants with this year’s third grade class. The two children wearing Columbia University T-shirts won them for having won the most multiplication-division bees during the school year. (Although the children are wearing uniforms, this is a public school in New Jersey.)

Nadira Rahman and Maria Ahwa (my lab assistants) with the third-grade math class.