Academic journal article Childhood Education

Whole Math through Investigations

Academic journal article Childhood Education

Whole Math through Investigations

Article excerpt

Ken Goodman (1986) says it is easy to learn language when: "It's real and natural. It's whole. It's sensible. It's interesting. It's relevant. It belongs to the learner.... The learner chooses to use it. It's accessible to the learner. The learner has power to use it". This observation is not just applicable to language and literacy. In this article, the authors describe some of the ways children in a K-1-2 combination class learn math by choosing to do it in real, sensible and interesting ways. For example, when a child decides to estimate how much her classmates weigh, then checks and records their actual weights, she has chosen a real measurement activity that interests her and that belongs to her.

There are strong parallels between the whole in whole language and the whole in a child-centered approach to learning mathematics. For several years, educators in New Zealand and England have been exploring more "natural learning processes" for teaching mathematics. Central to the natural learning processes, as described by Stoessiger and Edmunds (1992), are open-ended problem-solving challenges similar to the investigations described in this article.

Many adults approach mathematics with a feeling of panic and fear (Buxton, 1991). Children, on the other hand, begin school confident in their abilities and interested in learning about numbers. By later elementary school, however, math is not a favored subject (Boling, 1991). The way math is taught in the early years of school affects not only math achievement and skill development, but also a child's disposition to learn (National Association for the Education of Young Children, 1988). Continued exploration of mathematics requires a feeling of competence and a favorable disposition toward problem-solving.

Many theorists insist that the only meaningful and genuine learning is that which is constructed by the learner from within (Baroody, 1987; Elkind, 1989). Kamii (1985) states that in order to understand and enjoy mathematics, children must literally reinvent it through their own daily explorations and with number games. Traditional math instruction with drills, flash cards and work sheets may, in fact, lead to math anxiety. The following account describes a class where, instead of disliking math, children develop a disposition to enjoy problem-solving and mathematical activities.


Louise Burrell has been teaching for more than 20 years in a small rural school in the mountains of western North Carolina. She has developed a unique classroom for kindergarten, 1st- and 2nd-grade children. Instead of desks in rows, tables and centers are full of learning materials. Children learn to read, write and use mathematics through rich experiences that engage them in problem-solving and real life applications.


Investigations are the official math activities in Burrell's class. Every day each child is expected to design and carry out some form of investigation that varies week by week. The areas for investigation are based on North Carolina Standard Course of Study (North Carolina Department of Public Instruction, 1989) as well as National Council of Teachers of Mathematics standards (1989), including geometry, numeration, estimation, measurement, patterns, classification, sequencing and money. The class focuses on a different area of concentration each week. Many strands of mathematics, however, are evident throughout the day. As the children grasp the concepts, the topic is expanded. Occasionally, children are expected to work on areas where they feel they need improvement. In order to choose the areas that need work, children must practice self-evaluation.

During large group meetings, Burrell introduces a specific topic and gives sample investigations that can be done in that area. Investigations combine math, science, problem-solving, reading and language arts. As one child in the class explained, "Investigations would be like what you call a kinda mix of math and science together. …

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