This article presents a curricular reasoning model developed based on research conducted with middle grades teachers as they planned, taught, and reflected on a geometric transformations unit. Teachers can use the model to become aware of their own curricular reasoning to make key mathematical decisions as they plan and teach their lessons. While…

Discrete time models, one linear and one non-linear, are investigated, both with a herbivore species that consumes a basal food source species. Results are presented for coexistence of the species and to illustrate chaotic behaviour as parameters are varied in the non-linear model. The results indicate the benefit of fertilization in terms of the…

Nicolas Senior shows how EMC3 's Launch-Explore-Summarise/Review model for mathematics lesson structuring sets the conditions to get the most out of both dialogic and direct instruction. He argues that this model will help teachers walk the balance between order and chaos.

The aim of this study is to investigate the change of prospective mathematics teachers' pedagogical content knowledge (PCK) on the linear equation and slope subject based on the lesson plan development and implementation process based on the 4MAT model. The concept of PCK was discussed in three components as content knowledge, knowledge of student…

The present study, carried out in the context of a Teacher Professional Development (TPD) Program on mathematical modelling and digital technologies, focuses on how Italian mathematics teachers refer to digital technologies in designing their lessons and investigates to what extent the TPD program impacted the way by which teachers design their…

This paper studies the knowledge developed by a group of sixty-two pre-service primary teachers during a training session on the definition of a polygon and the mathematical practice of defining. We explore the knowledge developed by pre-service teachers when they carry out a series of training tasks oriented around the practice of defining with…

In this article, the authors explore how the 3C Model can be used to integrate other curriculum areas with mathematics, namely digital technologies. To illustrate the model, they provide a practical example of a teaching sequence. T he 3C Model is designed to create opportunities for applying reasoning and problem-solving skills and learning…

This article presents an extension of the well-known TPACK model to describe the professional digital competencies of mathematics teachers. The extension leads to what we want to call MPC-model (Media-Pedagogy-Content) in the following. It additionally includes (1) the consideration of competencies instead of knowledge for a holistic description,…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…

Purpose: This study aimed to explore how an adapted theoretical framework by networking two theories could help document teachers' collective learning through lesson study. Design/methodology/approach: Interconnected Model of Teacher Professional Growth (IMPG) and Documentational Approach to Didactics (DAD) has been used individually to document…

Effective planning lays the foundations for effective teaching in mathematics (Smith & Stein, 2018). The planning decisions made by teachers are many and varied and ultimately inform what, how and why students learn mathematics (Kilpatrick et al., 2001). Critically, these decisions affect students' opportunities to engage with mathematics in…

Analogical reasoning has played a significant role in the development of modern mathematical concepts. Although some perspectives in mathematics education have argued against the use of analogies and analogical reasoning in instructional contexts, some attempts have been made to leverage the pedagogical power of analogies. I assert that with a…

In response to increasing teacher interest in how to design and implement effective challenging tasks, James presents the Launch/Explore/Discuss model that builds on the work of leading Australian educators and researchers Peter Sullivan, Doug Clarke, and Charles Lovitt.

Lesson planning is a crucial component of effective mathematics instruction. However, existing lesson planning frameworks and design models do not explicitly foreground equity and inclusion within instructional planning which are necessary in teaching every student. The What-How-Who structure frames the planning process by foregrounding who the…

In this paper, we propose an analytic tool for describing the mathematics made available to learn in a "textbook lesson". The tool is an adaptation of the Mathematics Discourse in Instruction (MDI) analytic tool that we developed to analyze what is made available to learn in teachers' lessons. Our motivation to adapt the use of the MDI…