Research Basis of Everyday Mathematics

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During the 1980s, a consensus emerged among mathematics educators about how best to teach mathematics to children in school. The NCTM Standards (1989) expressed that consensus and communicated it to a broader audience. Everyday Mathematics is based largely on the same body of research that led to the Standards consensus. In this paper we describe the research findings that were most influential in the original development of Everyday Mathematics.1

Infant’s and Young Children’s Mathematical Knowledge

Before 1980 many people believed infants to be fairly passive and unaware of the world around them. Thanks to the work of Starkey and Cooper (1980), Strauss and Curtis (1981), and others, a very different view emerged, one that showed infants to be active, alert to the world, and aware of differences in numbers of objects and certain additive or subtractive relationships. That pioneering work has been expanded in recent years (e.g., Wynn, 1992) and shows the crucial importance of early experience in building cognitive abilities.

Research in the late 1970s and early 1980s also revealed that preschool children have much richer and more active mathematical minds than had been suspected (Gelman and Gallistel, 1978; Gelman, 1982; Resnick, 1983; Fuson & Hall, 1983; Gelman, Meck, & Merkin, 1986). They found that young children are capable of absorbing a great deal of new material, sometimes more rapidly than adults &ndash for example, in the learning of language&ndash but that neurological windows for learning appear to close at certain points in the development of the brain, making later learning of concepts more difficult. Also during the 1980s, certain supposed constraints on what and when children could learn, hypothesized by Piaget and others, were shown to be artifacts of the research tasks and not truly indicative of the capabilities of children (Walsh, 1991).

Many studies confirmed that young children, regardless of social-economic background, possessed considerable informal mathematical knowledge, which the curricula in use at the time failed to use (Riley, Greeno, & Heller, 1983; Carpenter & Moser, 1984; Hiebert, 1984; Cobb, 1985; Baroody & Ginsburg, 1986; Bell & Bell, 1988; Resnick, Lesgold, & Bill, 1990; Carpenter, Ansell, Franke, Fennema, & Weisbeck, 1993). For example, even without instruction, most kindergarten children are capable of solving a wide range of simple addition and subtraction story problems by their own methods (Riley, Greeno, & Heller, 1983; Carpenter and Moser, 1984). Multiplication, division, and fraction problems are also within their reach when manipulatives are available (Carpenter, Ansell, Franke, Fennema, & Weisbeck, 1993). In brief, children know much about addition and subtraction and other operations before formal instruction begins. Research on children’s informal solution methods revealed a typical developmental progression from simple counting of objects, to use of more sophisticated counting strategies and relationships, to derived fact strategies, to use of arithmetic facts and number relationships (Bergeron & Herscovics, 1990; Fuson, 1992).

In extensive interviews with children, Max Bell and Jean Bell, developers of Everyday Mathematics, showed that knowledge of counting, reading and writing numbers, and problem solving among kindergarten children far exceeded the expectations of kindergarten programs of the time (Bell & Bell, 1988). For example, while most programs spent the entire year focused on counting to 10 or 20, 84% of children beginning kindergarten could already count 13 dots, nearly half could count beyond 30, and many could count to 100, read and write numerals such as &ldquol;57” or “100”, act out “equal sharing” division problems, and name common geometric objects.

Typical first grade textbooks of the time expected children to count only to 100 and to read and write numbers to 20, but interviews revealed that many beginning first graders already had whole-number capabilities beyond those and could actually solve simple fraction problems. Even children’s “errors” showed substantially greater capabilities than had been supposed. For example, many beginning first graders wrote “four hundred ninety-eight” from dictation as “40098” or “4098” and read the numeral “5004” as “five hundred and four” –wrong answers to be sure, but indicative of readiness for work well beyond the content offered in standard textbooks of that time.

Algorithms

Researchers working in the 1970s and 1980s showed that U.S. children often learn standard computational algorithms with very little understanding (Brown & Burton, 1978; Van Lehn 1983, 1986). Other researchers found that the traditional approach to teaching computation engenders beliefs about mathematics that impede further learning (Hiebert, 1984; Cobb, 1985; Baroody & Ginsburg, 1986).

On the other hand, Kamii and others demonstrated that students are capable of inventing their own effective and meaningful methods for computation (Kamii, 1985; Madell, 1985; Kamii & Joseph, 1988; Cobb & Merkel, 1989; Resnick, Lesgold, & Bill, 1990; Carpenter, Fennema, & Franke, 1992). Furthermore, these experiences were found to improve understanding of place value and enhance estimation and mental computation skills.

Learning in a Social Context

During the 1970s and 1980s, the work of Lev Vygotsky (1962) began to be more widely known in the United States. Vygotsky’s research promoted a view of learning based on both individual and social construction, and showed the importance of social functions in supporting and extending learning. Language, tools, and social interactions all assist children in acquiring skills and concepts. For example, a problem that seems beyond the capabilities of a child working alone with paper and pencil can often be solved when appropriate manipulatives are available. When children interact with each other or with adults, then their learning potential, what Vygotsky called the “zone of proximal development,” is extended, increasing both the types of tasks that can be accomplished and the amount of learning that takes place. Early learning appears to be greatly enhanced by ongoing interactions between children and their world, including adults in that world. Talking about ideas, with informal error corrections by adults and peers, is often as important as thinking about ideas, and conversations can gradually become internal dialogues that guide the child’s progress through a problem.

Footnotes

  1. Everyday Mathematics was developed over a period of more than ten years beginning in about 1985, a time frame that is reflected in the dates of the references in this paper. More recent research has confirmed and extended the findings discussed here.

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