Quality science and mathematics education research: Considerations of argument, evidence, and generalizability

School Science and Mathematics, Jan 2003 by Yore, Larry D

Science and mathematics educators-and educators in general-frequently question why research results are not used to influence, make, and justify educational policies and instructional decisions at the national, state/provincial, and local levels (Kennedy, 1997). Kilpatrick (2001) captured much of the central issue with "Where's the evidence?" He questioned whether education research was rigorous enough to be trusted, whether the data collected related to the central focus of the study, whether the research questions were worthy of inquiry, whether researchers were selecting research approaches that matched the research questions, and whether the results could be applied generally by decision makers and politicians.

The issue of quality science and mathematics education research is not an issue of quantitative vs. qualitative methodologies! The critical issues regarding quality research are identifying important problems, selecting research designs that match the question being considered and the developmental stage of the exploration, applying disciplined inquiry, and artfully reporting the results. Above all, educational research-like science and mathematics research-- involves the construction of knowledge claims that can be evaluated against the available evidence and the canonical understandings.

Argumentation is a fundamental tradition of the science and mathematics education research communities. Each research approach within these communities has an associated view of knowledge, plausible reasoning, patterns of argumentation, and variation in the evidence used to establish or justify claims. Futhermore, generalization is and has been a major limitation to educational research across the disciplines and has led many politicians, decision makers, and teachers to question the value of research results. The issues of research rigor and generalized application are not new concerns, but lingering ones that have plagued education research over the last 102 years of School Science and Mathematics.

Argument

Discourse communities, research disciplines, and cultures influence how research reports are developed and structured. Discourse within the contemporary science research community "critically examines and evaluates the numerous and at times iterative transformations of evidence into explanations" to produce an argument about descriptive or causal claims (Duschl & Ellenbogen, 1999, p. 1). Arguments have three generally recognizeable forms: analytical, dialectical, and rhetorical. Duschl and Ellenborgen stated:

* Essentially in the analytical approach an argument proceeds inductively or deductively from a set of premises to a conclusion. For analytical arguments of categorisation, the form is the syllogism [a = b, b = c, therefore a = c]. For the analytical argument of causation, the form is material implication: If p then q; p therefore q.

* Dialectical arguments are those that occur during discussion or debate and involve reasoning with premises that are not evidently true.

* Rhetorical arguments are oratorical in nature and are represented by the discursive techniques employed to persuade an audience. (p. 1)

Analytical and dialectical arguments focus on the burden of support, presumption, and plausibility to determine probable claims or actions where "evidence is paramount" (Duschl & Ellenbogen, 1999, p. 1). Dialectical arguments are not totally based on knowledge and probability but on the refutation of the counterclaims and rebuttals. Rhetorical arguments focus on persuasion by presenting a more compelling case than the alternative cases.

Many international English-language science, mathematics, and education research journals utilize a hybrid research report genre (function-form) that reflects rhetorical and dialectical features, as well as analytical features of an argument. The authors make claims and try to persuade the audience that their claims are justified by the supportive evidence and the warrants and backings established and are more plausible than the alternative claims. The specific structure, conventions, and logic of the argument may vary; but effective research reports allow readers to identify the plausible reasoning used and the components of the argument.

Plausible Reasoning

Toulmin's (1969) models of the evidence and the transformation process illustrate an argument's logic, components, and discourse pattern. Developing an argument requires a limited introduction to set the problem, the logic to be used, and the basic grounding of the argument. The plausible reasoning used in science, mathematics, and education research are abduction, induction, deduction, and hypothetico-deduction.

Not all types of plausible reasoning are equally problematic or difficult for the reader to comprehend. But abduction and induction deserve special consideration based on their use in experimental, interpretative, and grounded theory approaches. Abductive reasoning involves extracting a pattern from observations, measurements, or events in a holistic manner. Abduction involves perception of the whole in the form of a gestalt-a unified whole, a configuration, a pattern, or an organized field having specific properties that cannot be derived from the summation of its component parts-or a metaphor-an application of an idea to another idea that does not literally denote the second idea in order to suggest comparisons and potential relationships. Reporting gestalts and using metaphors requires special attention to ensure that these creative insights are noted, the metaphor connects with the reader, and the limitations of metaphor are considered. It is not enough for the writer to state, "Being a teacher is like being a rugby referee." The researcher must provide a context for the metaphor that enables the reader to comprehend the connections, like the fact that there is one referee for 30 players on the rugby pitch (field) and that most players are intent on avoiding, stretching, or breaking the laws governing this rather unstructured, physical game meant to be played by polite, upstanding people-much like the idealized assumptions of a classroom. But, unlike the teacher, the rugby referee is sole judge of fact or law.