While the ideas of Dewey and E. H. Moore undoubtedly spurred R. L. Moore into thinking about pedagogical strategies, he developed his method of teaching in isolation, and as such the ‘Moore Method’ is seen as distinct from a range of pedagogies with which it has a lot in common. Taxonomically, the Moore Method is a type of problem-based learning, though its proponents such as the Educational Advancement Foundation refer to it as Inquiry-based Learning; we point the reader back to Section 3.2 and, in particular, Hmelo-Silver et al. (2007)’s comments on the lack of clear distinction between EBL and PBL.
The roles of the written material, the class, and the teacher combine to ensure that the Moore Method is clearly not ‘minimally guided’, though before they present to the class each student has the opportunity to direct their own investigations into a problem. It is this lack of discussion before the presentation that best sets apart the Method from other PBL pedagogies, and something that requires the complicity of students taking a Moore Method course.
The emphasis on writing mathematics further defines the method as different from other PBL pedagogies. Neither aspects of independent study nor a concentration on proof writing are necessarily absent in other methods of PBL, and at its heart the Moore Method has much in common with other student-centred PBL pedagogies. The strong culture surrounding the teaching of the Method, at the University of Texas at Austin in particular, has helped it to remain a distinct pedagogy over a century of educational reform.
Given this relationship to other student-centred PBL pedagogies, much of the research discussed in the previous part of the thesis is relevant to the Moore Method. The central principle of student discovery relates directly to the work of Bruner (1961, p. 26) and so research on discovery learning, combined with that on constructivism, may be used in support of the efficacy of the Method.
Brousseau (1997, p. 229) notes the importance of working alone in learning mathematics:
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One of the fundamental contributions of the modern didactique consists of showing the importance of the role played in the teaching process by the learning phases in which the student works almost alone on a problem or in a situation for which she assumes maximum responsibility.While there is an amount of indirect support of the Moore Method in the literature, there exists a dearth of studies aimed directly at it. Smith (2006) compared the Moore Method with traditional direct instruction methods of teaching and their effects on approaches to proofs.
The author asserts that there were marked differences in the approaches of the students in the two groups, though they were only two students and three students in size, respectively, and:
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the [Moore] students’ approach to proof is reminiscent of Weber and Alcock (2004, p. 210)’s notion of a semantic proof production: “a proof in which the prover uses instantiation(s) of the mathematical object(s) to which the statement applies to suggest and guide the formal inferences that he or she draws”. The students’ use of initial strategies, notation, prior experiences, and examples could be considered as such instantiations of mathematical concepts, meaningful ways of thinking about mathematical objects.Perhaps one reason for the lack of research on the Method is the way it has spread. The Moore Method is still centred around the University of Texas in Austin, and its dissemination has largely taken place by passing the Method from teacher to student. Often these teachers are mathematics researchers who may not have the time or inclination for scrutiny as part of an educational study. By means of an example, of the four authors of Coppin et al. (2009), Coppin was a student of Hubert Stanley Wall, a colleague of Moore and a leading proponent of the method, while the other three authors were students of John Neuberger, another student of Wall’s. Mahavier’s father, furthermore, was a student of Moore. Smith (2006) is also based at Austin. At the Annual Moore Legacy Conference held each June, presenters describe their position in the Moore family tree; grandson, or grand-niece, for example. Students who subsequently become teachers themselves are generally predisposed to teach in the manner in which they were taught, and so the way in Moore Method has propagated through the mathematical community is natural:
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The student’s learning about teaching, gained from a limited vantage point and relying heavily on imagination, is not like that of an apprentice and does not represent acquisition of the occupation’s technical knowledge. It is more a matter of imitation, which, being generalized across individuals, becomes tradition. Lortie, 1975, p. 63Chapter 6
Determining the Effectiveness of
the Moore Method at Improving Mathematics Performance
6.1 Introduction
This chapter is a longitudinal study of “1Y”, a first year Moore Method module in the School of Mathematics at the University of Birmingham. In the chapter we demonstrate a correlation between participation in 1Y and performance in a number of other first- and second-year modules in the School.
Entitled “Developing Mathematical Reasoning”, the optional module started in the academic year 2004/05 and is taken by roughly a dozen students each year. Its aim is to improve students’
problem solving in a process driven by the students themselves. The data for the study are the module marks of students over the period 2005/06–2011/12; 99 students who took 1Y in that
time are compared to their peers in the rest of the cohort.