Barbara Waxman
Nancy M. Robinson
Swapna Mukhopadhyay

Talent in mathematical reasoning is highly valued in this society and yet very little is known about its early course. This book is an outgrowth of a two-year study of children discovered during preschool or kindergarten to be advanced in their thinking about math. In addition to psychometric and cognitive testing conducted at the beginning, middle, and end of the study, half of the children were randomly assigned to biweekly intervention (Saturday Club) for a total of 28 weeks over the two years. Among other findings, the study revealed that, as a group, the children remained advanced in math over the two-year period, that their spatial reasoning related more closely to their math reasoning than did their verbal reasoning (although they were ahead in all three domains), and that the math scores of the boys started and remained somewhat higher than those of the girls. The Saturday Club intervention proved effective in enhancing mathematical reasoning.

This book discusses ways of identifying very young math-advanced children as well as a variety of educational strategies to meet their needs. Its primary emphasis is on creating an open-ended approach to teaching mathematics that provides an opportunity for children at different levels of advancement and different personal styles to engage with mathematical challenges in a playful way, to conceptualize math broadly, to pose problems, and to make sense of the mathematical system. Also emphasized are the importance of representing and communicating mathematical ideas in multiple ways in order to deepen children’s understanding. A variety of engaging activities such as the Fibonacci series, the Vedic square, and chip-trading are described. Most of these activities emanate from “big ideas” such as the nature of numerals and the number system, equivalence, visualizing and graphing numbers, measurement, estimation, and so on. Job cards for various mathematical tasks are included, as well as ways to integrate mathematics into other aspects of the curriculum. The approach to mathematics portrayed in this book is one that creative teachers can flexibly adapt to meet the needs of math-advanced children in a regular or specialized classroom.

Reference:

Teachers Nurturing Math-Talented Young Children
Barbara Waxman
Nancy M. Robinson
Swapna Mukhopadhyay
 

Guidelines

1. Mathematically advanced children should be given an appropriate and a challenging math curriculum.
2. Teachers should explore options for meeting the needs of mathematically talented children in their classrooms including: compacting the curriculum, using advanced curriculum, organizing mentoring opportunities, and creating math enrichment activities.
3. Options to meet the needs of mathematically talented children between classes include: cross-grade grouping, cluster grouping, ability grouping within the classroom, multi-age classrooms, early entry to kindergarten or first grade, grade-skipping, pull-out programs and resource rooms, and special classrooms.
4. For many mathematically talented children, out-of-level assessment measures are needed, along with teacher observations of a child’s true conceptual mastery, to determine if acceleration is an appropriate option.
5. Teachers should serve as facilitators, guides, designers of challenging problems, and probing questioners.
6. Manipulatives should be viewed as tools for problem-solving and as a way to represent mathematical thinking.
7. Mathematically talented children should be exposed early on to the “big ideas” and themes in mathematics: infinity, zero, number systems, reversibility, equivalence, measurement, negative numbers and fractions, estimating, data, and probability.