The overall purpose of this study was to investigate the role of personal relevance in conceptual change. First, we used an experimental design to investigate the role of augmented activation--which directly implicated teachers' personal prior beliefs about mathematics learning and instruction--and refutational text manipulations on short and…

This article explores the effectiveness of the pedagogical practices associated with the cognitive load theory and the van Hiele theory, which are two theories from cognitivism and constructivism perspectives, respectively. Following a quasi-experiment, the quantitative analysis of 157 high school students' responses to pre, post, and retention…

The main focus of the study was to identify the the effects of the ACE teaching cycle approach on students' engagement in learning of Elementary Linear Algebra. The Elementary Linear Algebra course was delivered at the Mathematics Education Study Program of State University of Padang, Indonesia. An action research methodology was adopted for the…

Subitising, a quick apprehension of the numerosity of a small set of items, has been found to change from an individual's reliance on perceptual to conceptual processes. In this study, we utilised a constructivist teaching experiment methodology to investigate how the subitising activity of one preschool student, Amy, related to her construction…

Certain aspects of theoretical frameworks in mathematics education can remain unexplained in the literature, hence unnoticed by the readers. It is thus interesting to participate in a dialogue where they can be discussed and compared in terms of the aims, objects studied, results and their relation to teaching. This study is focused on how APOS…

In this chapter, I propose a stance on learning fractions as multiplicative relations through reorganizing knowledge of whole numbers as a viable alternative to the Natural Number Bias (NNB) stance. Such an alternative, rooted in the constructivist theory of knowing and learning, provides a way forward in thinking about and carrying out…

Teacher knowledge of students' mathematical thinking has been a growing research area in mathematics education. Although researchers have made substantial progress in understanding students' mathematical thinking and created research programs and curricula tailored to the research findings, teacher education programs have, by and large, not been…

Communicating their thinking in mathematics is challenging for young children. This research studied the change in six-year old students' oral and written solution explanations before and after six problem-based mathematics lessons that focused on developing conceptual understanding of adding or subtracting a 2-digit number and a multiple of ten.…

The purpose of this paper is to account for the advancement of questioning in mathematics education. Four sections focus on: (1) Importance of Questioning in Education (a historical perspective of questioning from the 1960s through the 1990s); (2) Cognitive Classification of Questions (Costa's Levels of Thinking, Webb's Depth of Knowledge, and…

In this paper, we put Basil Bernstein's theory of pedagogic discourse to work together with additional theoretical resources to interrogate knowledge and practice in mathematics teacher education. We illustrate this methodology through analysis of an instance of mathematics teacher education pedagogic practice. While the methodology itself is…

In this paper, we report a pilot study on engaging a group of undergraduate students to explore the limits of sin(x)/x and tan(x)/x as x approaches to 0, with the use of non-graphic scientific calculators. By comparing the results in the pretest and the post-test, we found that the students had improvements in the tested items, which involved the…

This study of "Preservice Secondary Mathematics Teachers' Beliefs about Teaching Geometric Transformations (GTs) using Geometer's Sketchpad (GSP)" aimed to explore the beliefs hold by preservice secondary mathematics teachers about teaching geometric transformations with Geometer's Sketchpad. In this study, I applied three methodological…

Teaching experiments have generated several hypotheses concerning the construction of fraction schemes and operations and relationships among them. In particular, researchers have hypothesized that children's construction of splitting operations is crucial to their construction of more advanced fractions concepts (Steffe, 2002). The authors…

Some intensive quantities, such as slope, velocity, or likelihood, are perceptually privileged in the sense that they are experienced as holistic, irreducible sensations. However, the formal expression of these quantities uses "a/b" analytic metrics; for example, the slope of a line is the quotient of its rise and run. Thus, whereas students'…

This study by Lio Moscardini of the University of Strathclyde shows how a group of 24 children in three Scottish primary schools for pupils with moderate learning difficulties responded to word problems following their teachers' introduction to the principles of Cognitively Guided Instruction (CGI). CGI is a professional development programme in…