The National Council of Teachers of Mathematics's "Principles to Actions" (NCTM, 2014) cites posing purposeful questions and eliciting and using evidence of student thinking as effective mathematics teaching practices. Interviewing students creates opportunities for teachers to develop these practices. Through interviewing, they can try…

This paper describes our work to determine the naturalistic images that first-time second-semester university calculus students possess for series convergence. We found that the students we interviewed most frequently determined whether a series converged by imagining a process of appending summands into a running total and examining whether this…

The aim of this paper is on the one hand to discuss from an APOS (Action-Process-Object-Schema) theory perspective the mental constructions involved in the learning of linear algebra, through examples concerning the linear transformation concept and related notions. On the other hand, methodological issues related to the design of research…

In order to develop a deeper understanding of mathematics teaching expertise, in this study we use the Documentational Approach to Didactics to explore the resource systems of three Chinese mathematics "expert" teachers. Exploiting the Western and Eastern literature we examine the notion of "mathematics teaching expertise", as…

This study is motivated by the issues found in observations at school, where the daily teaching activities carried out by teachers show that: teaching and learning activities are classical, the teacher only stands or sits in front of the class, the direct relationship between the teacher and students is rare, and students tend to behave passively,…

Mathematics assessment is integral in enabling teachers to implement specially designed instruction for students with disabilities. This article presents an overview of an underutilized form of assessment, the clinical interview. A type of diagnostic assessment, clinical interviews are critically important when designing individualized instruction…

Action-Process-Object-Schema (APOS) theory and tools resulting from dialogue with the Anthropological Theory of the Didactic (ATD) were used to analyse data from semi-structured interviews and teaching materials to study students' understanding of the relationship between tangent planes and the total differential. Results of the study show…

Researchers have argued teachers and students are not developing connected meanings for function inverse, thus calling for a closer examination of teachers' and students' inverse function meanings. Responding to this call, we characterize 25 pre-service teachers' inverse function meanings as inferred from our analysis of clinical interviews. After…

This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…

It is widely acknowledged that the transition from informal, everyday knowledge to formal, school-taught knowledge is a critically important stage in children's mathematical development. Research highlights the importance of making connections between the different representations of mathematics and the value of children's own mathematical…

This research aims to reveal the importance of science and mathematics education, children's natural curiosity towards science, and teachers' deficiencies and opinions in this area. In this study, where the qualitative method is preferred, the special case method, which enables in-depth research within a specific subject, is used. The study group…

We examine teachers' use of resources as they prepare to teach the topic of numerical series of real numbers, in order to identify how their "personal relationship" with mathematical content--and its teaching--interacts with their use of a commonly used textbook. We describe this interplay between textbook and personal relationship, a…

Dennis Pearl is Professor of Statistics at Pennsylvania State University and Director of the Consortium for the Advancement of Undergraduate Statistics Education (CAUSE). He is a Fellow of the American Statistical Association. This interview took place via email on November 18-29, 2016, and provides Dennis Pearl's background story, which describes…

Creativity has a significant role in individuals' lives. This research aims to examine the reflection of the learning process of analytic geometry concepts through GeoGebra software and its effect upon the development of preservice mathematics teachers' creative thinking skills. This effect is expected to make a significant contribution to the…

In a rural elementary school, characterized by high poverty levels in Appalachian Ohio, school personnel were concerned that student literacy and math proficiency levels remained low during 2005-2015 and teachers had not been able to close the achievement gap between economically disadvantaged students and non-economically disadvantaged students…