Mathematics Education Research Journal 

About: Mathematics Education Research Journal is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Teaching method & Connected Mathematics. It has an ISSN identifier of 1033-2170. Over the lifetime, 791 publications have been published receiving 16452 citations.

Mathematics teachers’ beliefs and curriculum reform

Abstract: This paper discusses the role of mathematics teachers’ beliefs and their impact on curriculum reform. It is argued that teachers’ beliefs about the teaching and learning mathematics are critical in determining the pace of curriculum reform. Educational change is a complex process in which teachers hold strong beliefs about the quality and the process of innovation. Curriculum implementation may only occur through sufferance as many teachers are suspicious of reform in mathematics education given its equivocal success over the past decades. It is not surprising then that many teachers, when they come to enact the curriculum in their classes, rely more on their own beliefs than on current trends in pedagogy. These beliefs, conservative as they might be, have their own rationality in the practical and daily nature of the teaching profession, and in the compelling influence of educational systems from which these teachers are paradoxically the social product. The literature indicates that many of these teachers hold behaviourist beliefs, a fact that has strong implications for the success of constructivist-oriented curriculum reform. In general, studies of teachers’ pedagogical beliefs reveal the extreme complexity of bringing about educational change, and largely explains the failure of many past reform endeavours.

Awareness of pattern and structure in early mathematical development

Abstract: Recent educational research has turned increasing attention to the structural development of young students’ mathematical thinking. Early algebra, multiplicative reasoning, and spatial structuring are three areas central to this research. There is increasing evidence that an awareness of mathematical structure is crucial to mathematical competence among young children. The purpose of this paper is to propose a new construct, Awareness of Mathematical Pattern and Structure (AMPS), which generalises across mathematical concepts, can be reliably measured, and is correlated with general mathematical understanding. We provide supporting evidence drawn from a study of 103 Grade 1 students.

The Transition to Formal Thinking in Mathematics

Abstract: This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts towards a formal framework of axiomatic systems and mathematical proof. In this paper, the transition in thinking is formulated within a framework of ‘three worlds of mathematics’- the ‘conceptual-embodied’ world based on perception, action and thought experiment, the ‘proceptual-symbolic’ world of calculation and algebraic manipulation compressing processes such as counting into concepts such as number, and the ‘axiomatic-formal’ world of set-theoretic concept definitions and mathematical proof. Each ‘world’ has its own sequence of development and its own forms of proof that may be blended together to give a rich variety of ways of thinking mathematically. This reveals mathematical thinking as a blend of differing knowledge structures; for instance, the real numbers blend together the embodied number line, symbolic decimal arithmetic and the formal theory of a complete ordered field. Theoretical constructs are introduced to describe how genetic structures set before birth enable the development of mathematical thinking, and how experiences that the individual has met before affect their personal growth. These constructs are used to consider how students negotiate the transition from school to university mathematics as embodiment and symbolism are blended with formalism. At a higher level, structure theorems proved in axiomatic theories link back to more sophisticated forms of embodiment and symbolism, revealing the intimate relationship between the three worlds.

The beliefs/practice connection in broadly defined contexts

Abstract: The findings of a study that examined the connection between the beliefs of secondary mathematics teachers and their classroom practices are reported in this article. Classroom practice was defined in terms of the extent to which classroom environments could be characterised as constructivist. Cluster analysis was used to group teachers according to their responses to a beliefs instrument and to group their classes according to their average responses to a classroom environment survey. Associations between the two sets of clusters were found, suggesting some consistency between broad relatively decontextualised teacher beliefs and student perceptions considered at the whole class level.

Pedagogic Discourse and Equity in Mathematics" When Teachers' Talk Matters

Abstract: In this paper, we discuss the role and nature of pedagogic discourse. We argue that teachers’ talk plays a much more important role in students’ learning than is often considered—particularly in the learning of racially, ethnically, and linguistically diverse students. We present one teacher who has a record of assisting her fifth grade Latino students to make significant academic gains in mathematics, and we examine the way she uses her talk in teaching and how students in her class develop control over the mathematics discourse. To help make our point, we contrast this teacher with another teacher whose instructional talk is not as mathematically rich.