This article considers the rise of generative Artificial Intelligence (GenAI) in the context of secondary mathematics education, focusing on its responses to cognitively demanding tasks and the pedagogical implications of these interactions. Using tools such as ChatGPT (OpenAI) and Gemini (Google), we investigate how GenAI engages in complex…

The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…

This article presents several mathematics problems on the same theme that can be used in class or for independent study. It is very difficult to show students how mathematics research is done by mathematicians, so the author first introduces a problem that can be tackled solely by arithmetic and then gives an idea of how a mathematician might…

For over a decade, Which One Doesn't Belong? (WODB; Danielson, 2016) has been a beloved classroom routine that invites students to engage in mathematical decision-making and justification. In the WODB routine, four related figures are shown to students, and they are asked to decide which of them doesn't belong with the other three. The beauty of…

Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

Metacognition supports students in successfully working through struggle by equipping them with the tools to maintain an awareness of what they are doing and to change directions when needed to overcome obstacles. Thus, it is of little surprise that effective problem solvers spend a significant amount of time analyzing tasks relative to the amount…

In teaching bi/multilingual students, translanguaging underscores "what students know and can do (speak two languages) instead of what they do not know (English)" (Phakeng & Moschkovich, 2013, p. 125). Employing translanguaging strategies in the mathematics classroom can create an inclusive learning environment that values students'…

This article presents a task providing college students opportunities to build on their high school knowledge of trigonometry to explore parametric equations and inverse trigonometric relationships within a contextual learning ladder problem.

Providing students with opportunities to build, and test and revise ideas, can help them develop critical thinking and problem-solving skills. In this article, the authors describe how core measurement and geometry concepts were embedded within a "Model It!" task. They replicate an industry-based, interdisciplinary problem, but only…

As a distinct mode of mathematical representation and communication, geometry diagrams are both signs that represent abstract geometric concepts and visual images that offer graphical-spatial properties. Dynamic geometly environment offers a wide range of tools for its users to create and interact with geometry diagrams. In this paper, I propose a…

Solving word problems is a large part of algebra coursework and statewide testing. However, solving secondary mathematics word problems is difficult for most students and extremely challenging for students with specific learning disabilities (SLD). In recent meta-analyses, two problem solving strategies emerged as effective for secondary students…

Representations are used throughout school mathematics for students to both think through a problem and communicate their ideas. Students also often come to mathematics class with a repertoire of representations. This article presents the ideas of different and multiple representations with conceptual connections as their underlying distinguishing…

Increasing the performance of secondary students with learning disabilities (LD) in mathematics on word problem-solving tasks involving ratios and proportions is challenging for secondary math teachers. Teachers must use evidence-based practices to enhance secondary students' problem-solving proficiency and math achievement. Schema-based…

Quadratic equations are a notorious topic for the challenge it provides to students in secondary mathematics. Despite this, there is limited research, particularly in the Australian context, that explains why such challenges persist. This article details the causes of Year 11 students' difficulties in solving quadratic equations. Observing…

We propose some generalizations of the classical Division Algorithm for polynomials over coefficient rings (possibly non-commutative). These results provide a generalization of the Remainder Theorem that allows calculating the remainder without using the long division method, even if the divisor has degree greater than one. As a consequence we…