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…

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…

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…

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…

Evidence suggests that some students have learned procedures with little or no underpinning understanding while others have a much more connected and conceptual levels of understanding. In this article, the work of four primary students is discussed in terms of their contextual understanding of multiplicative concepts. The difference between…

In this article we describe and evaluate processes utilized to develop an online learning module on mathematical modelling for pre-service teachers. The module development process involved a range of professionals working within the STEM disciplines including mathematics and science educators, mathematicians, scientists, in-service and pre-service…

Considering that learning belongs primarily to the student, student self-regulation capacity is essential to ensure mathematics learning. Poor self-regulation limits students' mathematical performance and their ability to participate fully in classroom discourse. By enhancing self-regulation it is possible to improve students' equitable…

Teachers' inquiry-based mathematics teaching (IBMT) competence is often acquired and developed through participation in professional development programs (PDPs), but researchers have not established an effective method of assessing teachers' performance in this area. Moreover, the definition of IBMT, and the relationship between teachers'…

Questioning has an important role in teaching mathematics. There is current research about questioning, especially related to class discussion and students' responses. Some researchers suggest teachers pose any kind of questions in mathematics classroom regarding problem solving and mathematical creativity. This research focused on a teacher's…