The shift from additive to multiplicative thinking is challenging for students. A professional learning program was developed that focused on an identified area of need by teachers, namely multiplicative thinking. Program content focused on concepts underpinning multiplicative thinking, pedagogical approaches, challenging tasks, and application to…

Over the past four years, Skyline Middle School (SMS) has implemented high-quality instructional materials and made numerous attempts to create a school-wide Response to Intervention (RtI) program to support students struggling with classroom mathematics instruction. Despite these efforts, students' mathematics proficiency levels as measured by…

Visualising positive and negative numbers on a number line is helpful for exploring problems involving operations with positive and negative numbers. This is because number lines lend themselves to exploring problems involving continuous linear contexts such as travelling distances and temperature. Teachers in a professional development program…

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.

This paper reports on a pilot study that incorporated an alternative professional learning model that was school-based and focused an identified area of need: multiplicative thinking. The shift to multiplicative thinking can be challenging for both students and teachers due to its multifaceted nature. The study involved the delivery of six modules…

This study examines how a PD program to promote teachers' shift toward a student-adaptive pedagogy impacts students' multiplicative reasoning. We describe the underpinnings of this pedagogy and main components of the PD program. Then, we present key features of participants, data collection/analysis methods, and the written assessment used to…

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…

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…

The National Mathematics Advisory Panel, established under the Bush Administration, was created to improve teaching and learning of mathematics in the United States. One component of the study was focused on teachers and professional development opportunities. They found that the majority of professional development studies available were mostly…

Identifies the types of reasoning involved in middle grade mathematics with regard to multiplicative structures and the difficulties students have with the concepts, why these difficulties might occur, and the interconnections within this content area. Offers four recommendations for the preparation and professional development of teachers.…