Problem decomposition into sub-problems or subgoals and recomposition of the solutions to the subgoals into one complete solution is a common strategy to reduce difficulties in structured problem solving. In this study, we use a datadriven graph-mining-based method to decompose historical student solutions of logic-proof problems into Chunks. We…

The more researchers understand the subtleties of teaching practices that productively use student thinking, the better we can support teachers to develop these teaching practices. In this paper, we report the results of an exploration into how secondary mathematics teachers' use of public records appeared to support or inhibit their efforts to…

Covariational reasoning and the creation and interpretation of graphs of covariational situations are important skills in math and science. Unfortunately, research shows that students often struggle to make meaningful connections between graphs and the covariational situations they represent. Educational activities designed to help students…

This article explores the effectiveness of the pedagogical practices associated with the cognitive load theory and the van Hiele theory, which are two theories from cognitivism and constructivism perspectives, respectively. Following a quasi-experiment, the quantitative analysis of 157 high school students' responses to pre, post, and retention…

Probability is generally considered one of the most challenging areas to teach in mathematics education due to its intricate nature. However, the simulation-based teaching method can increase students' accessibility significantly to the probability problems because it enables students to resolve the problems with minimal mathematical skills. By…

We explored primary pre-service teachers' beliefs about challenging mathematical tasks and the role they perceived their initial teacher education played in influencing those aspects. Fifty-seven pre-service teachers completed an online questionnaire, and four participants were individually interviewed. Results showed that most participants…

In this paper, we explore how students' algebraic noticing's and explanations changed across a two-year period with the introduction of designed instructional material. The data in this report is drawn from n=53 Year 7-8 students' responses to a free-response assessment task across two different years. Analysis focused on how students noticed and…

In this paper, we extend our previous work on challenges teachers face when engaging with proportional reasoning contexts to investigate two contexts that included four problems for middle grades teachers to solve as well as eight student solutions. Analysis included coding for correct solving of the problem as well as making sense of and…

The purpose of this study was to implement a student response system-Kahoot to find out whether the inclusion of Kahoot in the teaching-learning process affected pre-service teachers' perceptions of the classroom environment in a compulsory Educational Sciences course. This study employed an experimental research design and the participants of the…

Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually…

Decades-old research has demonstrated the effects of virtual space on perception mostly with adult samples. Little is known about children's ability to utilize spatial-temporal qualities from computerized settings. Past research with primary school children suggested that the ability to utilize spatial-temporal information is crucial for inferring…

Block building activities help develop students' spatial reasoning, but few studies focus on the development of block building skills beyond preschool. We worked with four kindergarten, four first grade, and four second grade students to learn more about their Lego block building. We compared students' accuracy, building strategies, and spatial…

Our paper details the ways teachers understand and navigate equity-oriented dilemmas (Berlak & Berlak, 1981) when teaching mathematical modeling and how mathematics teacher educators can support teachers' learning of culturally responsive mathematics teaching. Using Zavala and Aguirre's (in press) framework for culturally responsive…

The aim of research was validation of a method for the assessment of cognitive complexity of chemical technology problem tasks. The method included an assessment of the difficulty of concepts and an assessment of their interactivity. As a research instrument for assessing performance, test of knowledge was used. Each task in the test was followed…

Conventional coordinate systems are often considered representational tools for reasoning about mathematical concepts. However, researchers have shown that students experience persistent difficulties as they engage in graphing activity. Using examples from research and textbooks, we present a framework based on a conceptual analysis of the use of…