Inclusion and differentiation--hallmarks of the current educational system--require a paradigm shift in the way that educators run their classrooms. This article enumerates the need for techno-kinesthetic, visually based activities and offers an example of a calculator-based programming activity that addresses that need. After discussing the use…

The aim of this study was to examine prospective mathematics teachers' proof processes for algebraic concepts. The study was conducted with 10 prospective teachers who were studying at the department of secondary mathematics teaching and who volunteered to participate in the study. The data were obtained via task-based clinical interviews…

The study investigated teacher knowledge of error analysis in differential calculus. Two teachers were the sample of the study: one a subject specialist and the other a mathematics education specialist. Questionnaires and interviews were used for data collection. The findings of the study reflect that the teachers' knowledge of error analysis was…

As learning technologies proliferate, it is important for research to address how to best align instruction to educational goals. For example, recent evidence indicates that working collaboratively may have unique benefits for facilitating the acquisition of conceptual understanding, as opposed to procedural fluency (Mullins, Rummel & Spada,…

We examine a 4th grade teacher's development of a constructivist-based, adaptive pedagogy (AP) approach--and its contribution to student multiplicative reasoning and outcomes, mixing qualitative analysis of segments from her interviews with quantitative analysis of her student outcomes on the state-mandated test. Her reflections indicate a shift…

Several researches showed that students had difficulty in understanding the concept of Least Common Multiple (LCM) in Elementary School. This underlies the researcher to design a learning of LCM using storytelling, Legend "Putri Dayang Merindu" (LPDM), which contains situational problem related to LCM. The purposes of this study are to…

Somewhere in a programme of study for mathematics in Key Stages 3 and 4 you would expect to find the terms mean, mode, median, and range. You might even find the terms central tendency, and variation. Many students following such a programme will be able to calculate the mean, most will be able to quote the mode, and some students will be able to…

Asked to complete a decimal-ordering task, several preservice teachers were unable to arrange the values from smallest to largest. Even more surprising to the authors were the number who could solve this task correctly but could not justify their solution by representing each decimal in an area model using a decimal grid. Their preservice teachers…

Effective instruction is multifaceted, dependent largely on the context and, consequently, on numerous variables. Although "effective instruction" is difficult to define, in the author's experience--and as the work of mathematics education specialists and researchers indicates--three key features of quality instruction stand out: (1) Teaching…

The purpose of this paper is to analyze in detail the process in which a 5th grade student learned proportion and percent using double number lines and to obtain insights into how his use of those representations supported his learning. A series of lessons were designed and conducted in a class and the whole learning process of one student was…

Composition has been described as essential for understanding functions (Carlson, Oehrtman, & Engelke, 2010; Cooney, Beckmann, & Lloyd, 2010). Studies of students' understanding of function composition have shown that students use multiplication and other operations in place of composition (Carlson et al., 2010; Horvath, 2010). While…

Teachers' ability to elicit and build on students' mathematical thinking during instruction is critical in order to support students' mathematical growth. An emerging hypothesis in the field is that the construct of a "learning trajectory" (LT) has the potential to support teachers in making sense of and using student…

The purpose of this study is to present some of the classical concepts, definitions, and theorems of calculus from the constructivists' point of view in the spirit of the philosophies of L.E.J. Brouwer and Errett Bishop. This presentation will compare the classical statements to the constructivized statements. The method focuses on giving…

This paper reports on a design experiment regarding young children's concepts of mass measurement. 119 year one and two children were interviewed using a clinical interview both before and after the teaching period comprising five lessons that offered rich learning experiences regarding concepts of mass. The results of the interviews were that the…

This paper examines spatial metaphors in the English language associated with the number line, in particular metaphors of direction and motion, and how these are manifested in actual spatial practices associated with number. It considers how these metaphors are culturally influenced, and how the influences of other cultures, such as Arabic,…