This article presents a series of open-ended tasks exploring the development of algebraic expressions suitable for exploration with Year 7 students. The tasks use a familiar tool, the hundreds chart, to aid the transition between representational tools and abstract ways of working. The tasks outline a developmental progression of patterns and…

As early as first grade, some children are more likely than others to perform arithmetic using inefficient or other overt counting strategies. To partially address this problem, the primary investigator developed a skill hierarchy with procedures based on applied behavior analysis. The novel early-intervention program included a combination of…

Background: ChatGPT, an AI-based chatbot, supports learning by accurately interpreting and responding to user inputs. Despite its potential, few empirical studies have examined its influence on college students' mathematical problem-solving processes. Objectives: This study aimed to introduce a ChatGPT-facilitated scaffolding to investigate its…

Achieving meaningful educational outcomes requires scalable strategies for mastering mathematical concepts and skills, with student engagement at the core. This paper examines the use of comprehensive, technology-enhanced activities designed to promote active learning and deeper conceptual understanding. Specifically, it focuses on the integration…

Evidence of positive associations between the frequency of home math activities and preschool children's math skills is mixed, and the operationalization of home math activities varies across studies. We test whether home math activities can be grouped by activity factors based on the math subdomain they target (i.e., counting and cardinality,…

This essential handbook is a must-have for anyone teaching mathematics and statistics in Aotearoa New Zealand, from student teachers to experienced educators. It offers a comprehensive resource for both primary and secondary school teachers, filled with classroom-ready activities designed to engage diverse learners and foster positive mathematics…

This article describes how the authors developed the activity Speaqual to enable their students to "speak" about the "equal" sign and foster communication of their reasoning. The article explains how to play Speaqual and how the students were thoroughly engaged in a friendly competition, centralizing algebraic concepts and…

Currently, there is a rapid development of artificial intelligence systems that can solve and explain the solution of mathematical problems in the same way as students do. The problem of organizing interaction of artificial and human intelligence which does not lead to the degradation of the student's thinking skills arises. The article proposes…

Educators often argue that students should engage in activities such as conjecturing, proving, and deductive reasoning. The underlying principle is that learning mathematics means doing as mathematicians do. However, "mathematician" implicitly refers to a pure mathematician at university. "The aim of our paper is to critically…

Taking a socio-cultural perspective, in this study we explored the challenges toddlers might face as they practice 1-1 correspondence in the playful context of setting a table, and how different individuals may participate in this playful activity. Findings indicated that toddlers' competence in carrying out one-to-one correspondence may be…

Several articles deal with tilings with squares and dominoes on 2-dimensional boards, but only a few on boards in 3-dimensional space. We examine a tiling problem with coloured cubes and bricks on a (2 × 2 × "n")-board in three dimensions. After a short introduction and the definition of breakability we show a way to get the number of…

This article focuses on the experience of viewing polyhedra in modified kaleidoscopes, highlighting the perceptive acts that take place. It presents aspects of geometry, such as concepts and ideas involved in the visualization of polyhedra in kaleidoscopes, through an analyticalmathematical study of the reflection of images in mirrors and…

This paper reports on the design, implementation, and evaluation processes of an activity that focused on the comparison meaning of the subtraction of integers and included the number line model as the primary representation. Finding the answer and determining the sign of the answer in the subtraction questions were targeted as the learning…

Understanding and supporting students' development of graph literacy is important. We studied how aspects of graph literacy might be supported (or hindered) in middle school by analyzing the content in textbooks. Specifically, we conducted a content analysis of tasks involving two-dimensional Cartesian graphs presented in grade 6-8 US textbooks.…

In studies over recent years, there has been an increasing interest in teachers' predicting middle school students' thinking processes. However, as far as we are aware, there are no studies examining students' thinking in terms of mathematical thinking components. This study primarily aimed to determine the mathematical thinking of middle school…