Mathematics skills are crucial in the current job market; however, many students with disabilities are graduating high school with limited mathematics knowledge and skills. Mathematics skills are fundamental for navigating the complexities of everyday life after high school, extending their importance beyond the workplace to community engagement.…

This paper investigates the connection between the spiral teaching method and mathematical rigor in K-12 education. Defining rigor as a balanced integration of conceptual understanding, application, and procedural fluency (contrasting it with rote learning), the paper posits that the spiral approach cultivates this rigor. By revisiting…

Students need to create mental models for different types of addition and subtraction situations in order to develop a broad and viable understanding of these operations. Although most students succeed when changing or combining sets, situations that demand a quantitative comparison of sets seem considerably more difficult in the first school…

In calculus, related rates problems are some of the most difficult for students to master. This is due, in part, to the nature of the problems, which require constructing a nuanced mental model and a solid understanding of the function. Many textbooks present a procedure for their solution that is unlike how experts approach the problem and elide…

The more ambitious an educational innovation, the greater the challenge in scaling up. In this paper, we focus on the scaling up of an ambitious pedagogical practice--mathematics problem solving as a regular feature in the classroom. We adopt a long-term approach to continual professional development (CPD) that began with intensive work with one…

Since problem solving became one of the foci of mathematics education, numerous studies have been performed to improve its teaching, develop students' higher-level skills, and evaluate its learning. While these studies usually study specific aspects of problem solving, further research is needed to understand how to address problem solving from a…

Comparison is a powerful and important way that we learn. To support teachers in the use of comparison in their instruction, the authors developed an instructional routine called compare and discuss multiple strategies (CDMS). Similar to other instructional routines, CDMS is a structured, specific, repeatable minilesson that teachers can use to…

The purpose of this project was to understand how implicit views of authority support or limit prospective elementary teachers' (PTs) mathematical activity of justifying and to understand how the experience of justifying might support a development of an internal source of authority. In this case study of 18 PTs, we coordinate an analysis of (1)…

This work seeks to understand the emergent nature of mathematical activity mediated by learners' engagement with multiple artifacts. We explored the problem solving of two learners as they aimed to make sense of fraction division by coordinating meanings across two artifacts, one being a physical manipulative and the other a written expression of…

This study compared the problem-solving abilities of ChatGPT and 58 pre-service teachers (PSTs) in solving a mathematical word problem using various strategies. PSTs were asked to solve a problem individually. Data was collected from PSTs' submitted assignments, and their problem-solving strategies were analyzed. ChatGPT was also given the same…

Identifying the knowledge resources teachers productively and unproductively draw upon can provide a means by which to create support structures to develop a more robust understanding of the content. To provide more informed grade-level support structures in teacher education programs, this study examined the knowledge resources 20 secondary…

Assessment plays a crucial role in the learning process and significantly impacts students' understanding of tasks and their engagement. With the increasing popularity of e-learning, cognitive assessment methods are becoming more prevalent, and they can help develop students' high-order thinking skills (HOTS). Thinking-Aloud Peer Assessment (TAPA)…

Research shows that when students engage with mathematical inquiry their problem-solving skills are strengthened. Demands in the revised Australian curriculum raised problem-solving of new senior secondary mathematics assessment, specifically in Queensland Problem-solving and Modelling Tasks (PSMTs). The challenge for Queensland was to scale…

Problems presented in mathematics classrooms often focus on routine tasks with students practicing mathematical techniques demonstrated by the teacher. However, this does not reflect the problem-solving process in the real world, and students often find it difficult to connect school mathematics with authentic contexts. This paper discusses…

The purpose of this study was to examine the effects of an online, multi-component intervention (video modeling, online mathematical games, self-monitoring checklists, and least to most prompting) in teaching mathematics skills to autistic secondary school students using a multiple probe design across skills. This study is unique from previous…