This paper explains how an original conceptual framework model for mathematics pedagogy, the Australian Curriculum Conceptual Rubric (ACCR), has continued to be used successfully by the author in pre-service and in-service teacher education programs over the past ten years or more. Now further enhanced by a deeper reflection upon Peter Sullivan's…

We use a narrative framework to investigate how mathematics textbook lessons can promote sustained student inquiry. Our analysis of four high school textbook lessons on the SSA congruence property, three of which contain explorations, reveals how explorations can promote problem-solving perseverance by inspiring readers to raise mathematical…

Fostering conceptual understanding in mathematics classrooms is an important goal in mathematics education. To support this goal, we need to be able to diagnose and assess the extent to which students have conceptual understanding. In this study we employed a problem-posing task and a problem-solving task in order to diagnose and assess preservice…

When examining success in mathematics education, it should be taken into consideration that it is important to examine teachers' work with their resources. In this study, it is aimed to examine this work through the processes of using and transforming the resources into documents. In this context, the "Documentational Approach to…

Mathematics education can be positioned as fertile ground for societal change. This article deconstructs the complex work of supporting students' positive mathematical identities by introducing pedagogical fluency to embody equitable beliefs and practices. Embodying equitable beliefs and teaching practices can systematically build a transformative…

Area models are an important strategy for representing and solving multiplication problems under the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010). The hands-on task presented in this article, featuring differentiation and open-ended learning, sets up students to discover area models for themselves. Organized around…

Wenger's theory of learning proposes the concepts of "participation" and "reification" as dimensions of educational design. Based on this proposal, this position paper looks at the design of one Mathematics Professional Development Program (MPDP) through the lenses of these concepts. We argue that the "reification"…

Students' success in learning is inseparable from their high level of fighting power or the Adversity Quotient (AQ) they have. This study examines whether there was an Adversity Quotient (AQ) difference between Boarding Schools (BS) and NonBoarding Schools (NBS) students through the application of metacognitive learning Think-aloud cooperative…

Feedback provided by mathematics teachers usually addresses procedural skills and, to a much lesser extent, other competencies such as conceptual understanding or engagement in mathematical practices. As most previous literature has studied feedback provided on homework or video prompts, how teachers provide such feedback in the classroom is…

Research has shown that students' beliefs related to mathematics are connected to their affect and motivation as well as their mathematical thinking and activity. Moreover, high parental expectations have been shown to play a role in students' positive beliefs and self-efficacy. This paper reports on two studies investigating parental expectations…

The purpose of the study was to see the effect of quizzes on anxiety and performance in mathematics at middle-level students. Seventy-two participants from a public sector high school were chosen carefully. In experimental designs, the Pretest Posttest Non-equivalent Control Group Design was selected for the study. The instruments for measuring…

Mathematics teachers make a number of decisions that shape their lessons, which therein impact their students' opportunity to learn mathematics. Past research has often focused on teachers, students and the mathematical content as key classroom elements that drive teachers' decisions. In this article, we propose that a fourth element -- the…

In this paper we introduce the reader to a foundational topic of differential geometry: the curvature of a curve. To make this topic engaging to a wide audience of readers, we develop this intuitive introduction employing only basic geometry without calculus and derivatives. It is hoped that this introduction will encourage many more to both…

In undergraduate mathematics, deductive reasoning plays important roles in teaching and learning various ideas, and is primarily characterized by the concept of logical implication. This comes up whenever conditional statements are applied, i.e., one checks if a statement's hypotheses are satisfied and then makes inferences. In calculus, students…

Mathematics education needs measures that can be used to research and/or evaluate the impact of professional development for constructs that are broadly relevant to the field. To address this need we developed the Priorities for Mathematics Instruction (PMI) survey consisting of two scales focused on the constructs of Explicit Attention to…