Searching for the center on the mathematics-science continuum

School Science and Mathematics, Oct 1998 by Roebuck, Kay I, Warden, Melissa A

The history of mathematics and science integration in American schools can be illustrated through the use of a continuum which runs from math for math 's sake at one end to science for science 's sake at the other. True integration occurs at the center point. While published examples of integration focusing on process skills are common, those featuring integration of content are less often found. Two such lessons, developed around radioactive decay and efficiency in nature, are presented as examples of science and mathematics concepts taught in concert. Changes in preservice and in-service teacher training must occur if the potential for this type of integration is to be realized.

Calls for the integration of science and mathematics instruction are not new. In a 1901 address to the Royal College of Science in London, John Perry called for a laboratory approach to the teaching of mathematics, decrying the practice of "teaching boys elementary mathematics as if they were all going to be pure mathematicians" (Mock, 1963). As Kullman (1966) noted, "if science depends on mathematics for the formulation and solution of many of its problems, mathematics also must acknowledge that it acquires meaning as it is used to describe the physical world" (p. 645). Brown and Wall (1976) characterized the connections between mathematics and science in this way: There is a continuum from mathematics for the sake of mathematics to science for the sake of science. Between these two extremes lie at least three points of importance: (1 ) mathematics for the sake of science, (2) mathematics and science in concert, and (3) science for the sake of mathematics. Any program that does not include all five points on this continuum is not representative of both disciplines and the related aspects of both fields of study. Unfortunately, only the two categories at the ends of the continuum have a long history in U.S. education programs. (p. 552) This continuum (Figure 1) provides a framework for considering levels of integration of mathematics and science in schools.

Two methods for considering the connections between mathematics and science are to consider the nature of mathematical skills needed for the solution of science problems or to use real-world, science-related scenarios to give mathematical computations contextual meaning. These approaches represent the second and fourth points on the continuum. Cain and Lee (1963) analyzed this approach to integration by examining secondary mathematics and science programs of the late 1950s and early 1960s to determine the extent of correlation, identifying such skills as solving and graphing equations, evaluating formulas, and using trigonometric functions. Laper (1961) also quantified the extent to which these skills were used in general science, chemistry, and physics in roughly the same time period. Kren and Huntsberger (1977) later investigated the effects of integrated instruction on elementary grade students' abilities in measuring and constructing angles and constructing linear graphs.

Integration Through Process Skills

True integration of mathematics and science is found on the center point (3) of the continuum. Suggestions for this true integration of science and mathematics have more recently focused on the "process skills" common to both fields. Cooney and Henderson (1972) did so by identifying the strategies classifying, analyzing, characterizing, explaining, implicating, and abstracting and generalizing as means by which students structure knowledge in both mathematics and science.

Similarly, Brown and Wall (1976) identified sorting and classifying, measuring, and collecting and interpreting data as appropriate points for the integration of mathematics and science in the elementary school. Basic skill areas common to mathematics and science, according to Gallagher (1979), are acquiring information through observation, counting and measuring, interpreting information through the use of tables, charts, and graphs, and going beyond given information by inferring, predicting, and estimating. Berlin and White (1995) identified basic and integrated process skills common to mathematics problem solving and science as observing, inferring, measuring, communicating, classifying, predicting, controlling variables, formulating hypotheses, interpreting data, and experimenting.

A number of curricula projects, such as AIMS (Activities to Integrate Mathematics and Science) and GEMS (Great Explorations in Mathematics and Science), focus on this view of integration. Many of these projects feature activities in which students gather data by observation or measurement and then analyze the data using graphs or tables. This view of integration is certainly in keeping with the standards movements in both mathematics and science. The Curriculum and Evaluation Standards for School Mathematics include problem solving, building mathematical connections, and reasoning processes as standards at each grade level. The topic area standards (geometry, number sense, algebra, etc.) make frequent use of words such as explore, describe, investigate, and predict (National Council of Teachers of Mathematics [NCTM], 1989).