This dissertation case study examines how teachers' levels of units coordination afford their ability to reason multiplicatively and fractionally, as well as use their mathematics knowledge for teaching to analyze student multiplicative and fractional reasoning, when a two-year intervention is put into place to evoke new mathematical reasoning.…

This study explores components of ambitious teaching practices for teaching multiplicative properties that can give teachers opportunities to learn through a quick images activity in a cycle of enactment and investigation. Throughout the cycle, it is found that the participants have opportunities to learn the following components of ambitious…

A journey into multiplicative thinking by three teachers in a primary school is reported. A description of how the teachers learned to identify gaps in student knowledge is described along with how the teachers assisted students to connect multiplicative ideas in ways that make sense.

An important decision that professional development (PD) facilitators must make when preparing for activities with teachers is to select an appropriate tool for the intended learning goals of the PD (Sztajn, Borko, & Smith, 2017). One important and prevalent tool is artifacts of student thinking (e.g. Jacobs & Philipp, 2004). In this paper…

Ratio and proportion have many daily life applications and hence form an important part of the Mathematical Literacy (ML) curriculum in South African schools. The purpose of this study was to explore ML teachers' application of ratio in an assessment task with multiple measure spaces set within the real-life context of the need to establish the…

Lesson study cultivates teachers' capacity for formative assessment by placing student thinking front and center throughout. Lesson study is a form of professional development in which a team of teachers determines a mathematical focus, collaboratively studies student thinking about the topic, designs a lesson about this content, implements the…

The complex nature of multiplicative thinking can be challenging for students and teachers to navigate. We report on the impact on student learning of school-based professional learning that targeted teachers' pedagogical content knowledge related to Multiplicative Thinking. Analysis of Year 4 students' longitudinal data indicated greater growth…

We examine a 4th grade teacher's development of a constructivist-based, adaptive pedagogy (AP) approach--and its contribution to student multiplicative reasoning and outcomes, mixing qualitative analysis of segments from her interviews with quantitative analysis of her student outcomes on the state-mandated test. Her reflections indicate a shift…

Background: The research on diagrammatic representations highlights their importance for the teaching and learning of mathematics. However, the empirical evidence to support their use in the classroom is mixed and somewhat lacking. Purpose: The aim of this study was to develop the use of diagrammatic representations of mathematical concepts in…

This submission contains the Proceedings of the 2015 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the Université de Moncton in Moncton, New Brunswick. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…