The Consequences of Experimentalism in Formulating Recommendations for Policy and Practice in Mathematics Education
In this response to Foundations for Success: The Final Report of the National Mathematics Advisory Panel (2008), the authors argue that the Panel's assumption that only experimental research studies can pro duce scientific evidence limits the power of the Panel's recommen dations to improve mathematics teaching and learning. The authorsfirst discuss the theoretical underpinnings, potential contributions, and limitations of experimental studies. Against this background, they focus on three issues that are central to improving mathematics learning and teaching, those of equity, the nature and content of text books, and graduate education. In doing so, the authors illustrate thelimitations of developing implications for policy and practice by rely ing exclusively on research conducted using a single methodology Keywords: equity; mathematics education; research methodology The National Mathematics Advisory Panel's (2008) recent report sought to synthesize the '"best available scientific evidence' to [recommend] ways to foster greater knowledge of and improved performance in mathematics among American students'" (p. xiii). We support the effort to develop recommendations for policy makers and teachers that are based on high-quality research. The Panel produced a comprehensive report with an impressive array of supporting documents. Unfortunately, the Panel took an overly narrow view of what counts as scientific evidence, thereby failing to capitalize on much of what is known about mathematics learning and teaching.
As a consequence, the Panel's report is less effective than it would oth erwise have been in supporting policy makers and teachers to make substantial improvements. In this response to the report, we first discuss the theoretical underpinnings and the potential contributions and limitations of experimental research studies. We go on to argue that other methodologies produce different forms of knowledge that complement the findings of the Panel and would have increased the usefulness of the Panel's report for policy and practice. Against this background, we then focus on The Approach the Panel Used to Produce Its Recommendations The trustworthiness of research findings depends on the sound ness of the method used to produce those findings (Bernstein, 1983; Lakatos, 1970; Popper, 1972). Similarly, the value of the Panel's recommendations depend on the soundness of the method the Panel used to (a) discriminate between trustworthy and suspect research findings and (b) synthesize findings judged to be trustworthy. In our view, there is good reason to be con cerned about both of these steps in the Panel's approach. The Panel used three categories to discriminate between trust worthy and suspect studies. The first category of high-quality sci entific evidence is reserved for "studies that test hypotheses, meet the highest methodological standards (internal validity), and have been replicated with diverse samples of students under conditions that warrant generalization (external validity)" (p. 7-4). The Panel assumed that only one methodology can produce high-quality scientific evidence: experimental and quasi-experimental studies. The studies in the Panel's second category of promising or suggestive findings "represent sound, scientific research that needs to be fur ther investigated.
The Theoretical Grounding of Experimental Research
Slavin (2004) succincdy described the forms of knowledge experi mental studies produce under the best of circumstances when he can contribute to the establishment of causal claims about the effec tiveness of instructional interventions. We follow Maxwell (2004) in arguing that this assumption is unwarranted. Maxwell distin guishes between two complementary treatments of causal explana tion. The first of these two treatments, which Maxwell terms the regularity type of causal description, is central to the experimental methodology and is based on observed regularities across a num ber of cases. Maxwell calls the second treatment process-oriented explanation and clarifies that it "sees causality as fundamentally referring to the actual causal mechanisms and processes that are involved in particular events and situations" (p. 4). Process-oriented explanations are therefore concerned with "the mechanisms through which and the conditions under which that causal rela tionship holds" (Shadish, Cook, & Campbell, 2002, p. 9, cited in Maxwell, 2004, p. 4). In contrast to the regularity conception of causality, viable explanations of this type can be developed based on a relatively small number of purposefully selected cases (Maxwell, 2004). For example, studies employing the design research methodology have been conducted to develop process oriented causal explanations of the relations between teachers' instructional practices, instructional tasks as they are actually enacted in the classroom, the learning opportunities that arise for students as they engage in the tasks, and students' resulting learn ing in particular mathematical domains (P. Cobb, McClain, & Gravemeijer, 2003; Confrey &C Smith, 1995; Lehrer & Sch?uble, clarified that well-designed studies of this type are not limited to x versus y comparisons but can "also characterize the conditions under which x works better or worse than j/, the identity of the stu dents for whom x works better or worse than y, and often produce
rich qualitative information to supplement the quantitative com parisons" (p. 27). The key point to note for our purposes is that knowledge claims associated with experimental studies reflect a par ticular conception of the individual. The knowledge claims refer to an abstract, collective individual or statistical aggregate that is con structed by combining measures of psychological attributes of the participating students (e.g., measures of mathematics achieve ment). This statistically constructed individual is abstract in the sense that it does not correspond to any particular student.
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