Abstract
An exploration of factor analytic structure of the conceptions of mathematics scale among pre-service mathematics teachers in South-West Nigeria was conducted as evidence suggests paucity of research on psychometric properties of the conceptions of mathematics scale in Nigeria.This article through instrumentation research methodology reports the reliability and validity of the Conceptions of Mathematics Scale based on the responses of 228 pre-service mathematics teachers from five public universities in South-West Nigeria. The reliability assessed as internal consistency produced a Cronbach alpha of .88. A principal components exploration with varimax gyration established the validity of the scale as two-component archetypal accounting for 48.9% of the total variance. The dimensions were taken as Patchy Formations and Unified Formations of mathematics, as explicated in the original and other replicating studies. The factor solution could be compared to that recounted in the previous studies; hence the outcome showed the need to adopt the scale in the Nigerian context, as the pedagogy implemented during the teaching and learning of mathematics can influence students’ conceptions of mathematics. Thus, teaching mathematics with rules-based and algorithm-dependent teacher-centered pedagogies might result into rote memorization thereby leading to patchy formations while teaching mathematics as a meaningful subject full of applications to the real life could engender conceptual understanding leading to unified formations. The implication of this study is that students with patchy formation are connected with surface approaches to learning while those with unified formation of mathematics are connected with deep approaches to learning and engaging mathematics.
Highlights
School mathematics primarily deals with rules, formulas, and algorithms apply to solve problems
Students who hold patchy formations see mathematics subject matter as comprising figures, guidelines and formulas, while students with unified formations describe mathematics as a multifarious, rational system that provides insight for comprehending the universe. It follows that a person with patchy formations of mathematics would focus on constituent parts rather than on the whole, and another that views mathematics cohesively would focus on the whole rather than on the parts
A value of .885 recorded for the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy was within tolerable range. This led to the conclusion that the 19-items of the Conception of Mathematics Scale was apt for PCA
Summary
School mathematics primarily deals with rules, formulas, and algorithms apply to solve problems. Students who hold patchy formations see mathematics subject matter as comprising figures, guidelines and formulas, while students with unified formations describe mathematics as a multifarious, rational system that provides insight for comprehending the universe It follows that a person with patchy formations of mathematics would focus on constituent parts rather than on the whole, and another that views mathematics cohesively would focus on the whole rather than on the parts. It is proposed that how students conceive mathematics directly or indirectly influences how students engage with cognitive activity in mathematics This has been shown to influence students’ learning approaches and learning outcomes that relate to their performance in mathematics (Crawford, 1992; Crawford et al, 1998b). The prospective teachers of mathematics who view mathematics as being rulesbased and formulae-dependent were more apprehensive of mathematics
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