Students' proficiency in the language of instruction is essential for their mathematical learning. Accordingly, language-responsive instruction, which includes adapting teaching material to students' language needs, is thought to promote mathematical learning, particularly for students with lower levels of proficiency in the language of…

Curriculum materials have a substantial influence on mathematics instruction and, consequently, students' learning opportunities. Many curriculum programs provide instructional notes for teachers and tasks for students as a means of accommodating particular student groups, such as those identified for English language learners. The presence of…

It is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing…

Facilitators, i.e., individuals who lead professional development (PD) programs, play a crucial role in providing high-quality PD to teachers, which is particularly relevant in the context of teaching mathematics with technology given the ubiquitous calls to exploit the potential of digital mathematical tools (DMT). However, quantitative research…

Mathematics content courses for prospective elementary teachers (PTs) should provide them with opportunities to deepen their understanding of and develop productive dispositions toward mathematics. Supporting mathematics teacher educators (MTEs) to learn how to develop practices that create rich learning opportunities for novice teachers comprises…

We study in this article mathematics teachers' "documentation work": looking for resources, selecting/designing mathematical tasks, planning their succession, managing available artifacts, etc. We consider that this documentation work is at the core of teachers' professional activity and professional development. We introduce a distinction between…

Students mainly perceive the transition to secondary school as an opportunity to start their school career anew. Reality often proves them wrong, especially in the case of mathematics. In our paper, we briefly discuss children's transition to secondary school as both an opportunity and a problem, with reference to the Greek context. In discussions…

This paper outlines some theoretical categories (i.e. the "meso-", "topo-", "chrono-geneses," the "milieu," the didactical contract and the learning games), providing a "model" to study mathematics teacher's action. In order to show what this model brings to the didactical analysis, we present the…

Focuses on the process by which children develop a formal mathematical concept of the circle by using various instruments to draw circles within the context of a goal-directed drawing task. Concludes that the use of the compass in circle drawing structures the circle-drawing operation in a radically different fashion than circle tracers and…

This study investigates how four prospective teachers interpret and use textbooks while learning to teach mathematics during university coursework and practicum teaching. Results indicate that prospective teachers had varied approaches to using textbooks ranging from adherence, elaboration, and creation. Factors influencing how they engaged with…

This paper summarizes our analysis of the complexity of ratio problems at Grades 6 and 7, and reports a two-year experiment related to the teaching and learning of rational numbers and proportionality in these grades. Two classes were followed and observed. Part of the teaching material was common to both classes, mainly the objectives and the…

Identifies factors affecting problem solving strategies in the case of a multiplicative comparative situation involving three unknown quantities whose sum is known, and in which comparison relations between two pairs of the quantities are given. Proposes a model of the complexity of a word problem about such situation to analyze solution…

The interplay among and connections between objects (structured or unstructured), images, language and symbols that lead to mathematical reasoning and the stating of mathematical propositions of very wide generality is well worth closer study. I believe that the subtle distinction between the way mathematical ideas are constructed from objects and…

This paper reflects on the use of didactic material in mathematics classes. It focuses on the mathematical activities of students and the didactical activities of teachers. Its point of departure is a critique of technical-managerial approaches to teaching, learning, and innovation. Based on this critique, fundamental tensions between the…