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Professional noticing of learners’ mathematics reasoning is a crucial ingredient of a mathematics teacher’s set of teaching competencies. Research lessons in the lesson study process, with its focus on learner reasoning, provide a structured environment for the building of mathematical knowledge as well as for reflection and the development of teacher professional noticing and sense-making. This paper reports on the depth and growth in noticing of three pre-service teachers during research lessons in their third and fourth years, using the Van Es noticing framework. The study showed that two of these teachers’ noticing shifted to higher levels over the two years, with greater focus on learners’ mathematical reasoning and sense-making than on teacher actions and teaching. Prospective teachers need well-structured and focused opportunities, individually as well as in groups, to learn to notice and make sense of learner thinking and reasoning.

Script-writing is a novel pedagogical approach and research tool in mathematics education. The goal of this chapter is to introduce the approach and exemplify its implementation. A script-writing task presents a prompt, which usually includes an incomplete argument or erroneous claim of a student. Prospective teachers address the prompt by creating a script for a dialogue—presenting an imaginary interaction between a teacher and her students, or among different students. In this chapter I exemplify several results of implementing script-writing tasks and discuss advantages of this approach. In particular, I focus on the concepts related to elementary number theory, prime numbers and factors of a number, and demonstrate how the understanding of these concepts can be explored and refined, as script-writers create characters who discuss particular claims. I suggest that engaging prospective teachers in script-writing is one possible way to support and improve preparation of mathematics teachers.

Equity in education has been a concern of almost all countries, whether developed, transitional, or in the progress of developing. It is believed that unequal education implies that human potential is being wasted. The present study focused on students with different characteristics as aggregate groups in an examination of similarities and differences in mathematics learning. The information analyzed here was mainly based on data from TIMSS and PISA databases. This investigation aims to paint an overall picture about gender equity, socioeconomic status, and indigenity equity in mathematics education over the last twenty years. It is hoped that the study can provide useful insights to individual education systems and further help them to identify more promising practices to narrow or even eliminate the existing between-system as well as within-system gaps.