This study focuses on connections between linear functions and their graphs that were made by tertiary remedial algebra students. In particular, we describe students' work on a Task designed to examine the connection between points on a graph and the equation of a line. The data consist of 63 responses to a written questionnaire and individual…

In this paper, we examine mathematicians' views on the value of advanced mathematics for secondary mathematics teachers. The data comprise semi-structured interviews with 24 mathematicians from 10 universities. The findings indicate that the value of advanced mathematics courses for prospective secondary mathematics teachers lies in their…

Backward transfer refers to the influence on prior knowledge of the acquisition and generalisation of new knowledge. Studies of backward transfer of mathematical knowledge have focused on content that is closely related in time and in curricular sequencing. Employing the notion of thickening understanding, we describe instances of transfer that…

Acknowledging the contribution of mathematicians to the mathematical education of teachers, we explore mathematicians' perspective on an envisioned Calculus course for prospective teachers. We analyzed semi-structured interviews with 24 mathematicians using the EDW (Essence-Doing-Worth) framework (Hoffmann & Even, 2018, 2019); and…

We believe that professional mathematicians who teach undergraduate mathematics courses to prospective teachers play an important role in the education of secondary school mathematics teachers. Thus, we explored the views of research mathematicians on the mathematics that should be taught to prospective mathematics teachers, on how the courses…

In this paper, we highlight a further use of scripting tasks in the work of researchers-teacher-educators, which we present in two parts. In Part 1, we study prospective secondary school mathematics teachers' responses to a scripting task on the topic of functions. The generated examples for a function that satisfies certain constraints provide a…

We investigate responses of prospective secondary school teachers to a task related to the inverse function concept. We utilize ideas of fuzzy logic as a theoretical lens in analyzing the participants' demonstrated avoidance of refuting the existence of an inverse to a quadratic function. The analysis is based on 29 responses to a scripting task,…

This study examines future secondary physics teachers' knowledge related to the teaching of sound waves, and specifically the topics of sound level and sound intensity. The data is comprised of future teachers' responses to a task in which they had to compose a script for an imaginary dialogue between a teacher and a group of students and to…

Script writing by learners has been used as a valuable pedagogical strategy and a research tool in several contexts. We adopted this strategy in the context of a mathematics course for prospective teachers. Participants were presented with opposing viewpoints with respect to a mathematical claim, and were asked to write a dialogue in which the…

This paper elaborates the notion of a personal example space as the set of mathematical objects and construction techniques that a learner has access to as examples of a concept while working on a given task. This is different from the conventional space of examples that is represented by the worked examples and exercises in textbooks. We refer to…

In this article we introduce a usage-goal framework within which task design can be guided and analyzed. We tell a tale of one task, the Pentomino Problem, and its evolution through predictive analysis, trial, reflective analysis, and adjustment. In describing several iterations of the task implementation, we focus on mathematical affordances…

Discussed is a project promoting "thinking about what students did" in an Israeli high school. Five examples of the project are described with LOGO commands. Several educational ideas are provided. (YP)