The aim of this study is to describe the mathematical thinking process of autistic students in terms of gesture, using a qualitative approach. Data collecting is conducted by using 3 (three) audio-visual cameras. During the learning process, both teacher and students' activity are recorded using handy cam and digital camera (full HD capacity).…

The purpose of this study is to evaluate the relationship of mathematics calculation rate (curriculum-based measurement of mathematics; CBM-M), reading rate (curriculum-based measurement of reading; CBM-R), and mathematics application and problem solving skills (mathematics screener) among students at four levels of proficiency on a statewide…

Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…

Contemporary research has suggested that in order for students to compete globally in the 21st century workplace, pedagogy must shift to include the integration of science and mathematics, where teachers effectively incorporate the two disciplines seamlessly. Mathematics facilitates a deeper understanding of science concepts and has been linked to…

In this paper, we describe our learning progressions approach to early algebra research that involves the coordination of a curricular framework, an instructional sequence, written assessments, and levels of sophistication describing the development of students' thinking. We focus in particular on what we have learning through this approach about…

What is the meaning of absolute value? And why do teachers teach students how to solve absolute value equations? Absolute value is a concept introduced in first-year algebra and then reinforced in later courses. Various authors have suggested instructional methods for teaching absolute value to high school students (Wei 2005; Stallings-Roberts…

This study aims to examine the modes of representation used by prospective teachers, taking the physics-I (mechanics) course of the primary mathematics education program in the Faculty of Education. The teachers' opinions were elicited about circular motion and the awareness of the instructors delivering the physics-I course regarding these modes…

Trigonometry is a well known branch of Mathematics. The study of trigonometry is of great importance in surveying, astronomy, navigation, engineering, and in different branches of science. This paper reports on the discovery of flaws in the traditional definitions of trigonometric ratios of an angle, which (in most cases) make use of the most…

We present background and an activity meant to show both instructors and students that mere button pushing with technology is insufficient for success, but that additional thought and preparation will permit the technology to serve as an excellent tool in the understanding and learning of mathematics. (Contains 5 figures.)

This article explores how a focus on understanding divisibility rules can be used to help deepen students' understanding of multiplication and division with whole numbers. It is based on research with seven Year 7-8 teachers who were observed teaching a group of students a rule for divisibility by nine. As part of the lesson, students were shown a…

Middle-grades students have a concept image of a circle, but they lack experience in the act of defining. The structure of definitions needs to include conditions that are necessary and sufficient. Most students are able to identify necessary conditions, but they have trouble determining if sufficient conditions are met. How do teachers engage…

We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…

Inversion is a fundamental relational building block both within mathematics as the study of structures and within people's physical and social experience, linked to many other key elements such as equilibrium, invariance, reversal, compensation, symmetry, and balance. Within purely formal arithmetic, the inverse relationships between addition and…

Recent research on children's conceptual and procedural knowledge has suggested that there are individual differences in the ways that children combine these two types of knowledge across a number of mathematical topics. Cluster analyses have demonstrated that some children have more conceptual knowledge, some children have more procedural…

Designing quality continuing professional development (CPD) for those teaching mathematics in primary schools is a challenge. If the CPD is to be built on the scaffold of five big ideas in mathematics, what might be these five big ideas? Might it just be a case of, if you tell me your five big ideas, then I'll tell you mine? Here, there is…