This article documents differences between novice and experienced undergraduate students' processes of reading mathematical proofs as revealed by moment-by-moment, think-aloud protocols. We found three key reading behaviors that describe how novices' reading differed from that of their experienced peers: alternative task models, accrual of…

"Wheel spinning" is the phenomenon in which a student fails to master a Knowledge Component (KC), despite significant practice. Ideally, an intelligent tutoring system would detect this phenomenon early, so that the system or a teacher could try alternative instructional strategies. Prior work has put forward several criteria for wheel…

Mathematics curricula are often the primary resource used in the teaching and learning of mathematics--in particular, they represent mathematical knowledge for teachers and students. Yet, there seems to be a discrepancy between the curricular materials written for teachers and students (e.g., more variety in the semiotic choices in text provided…

This study sought to analyse, using the Mathematics Discourse in Instruction framework, teachers' explanatory talk when introducing standard units of length in standard 4 in Malawi. The study analysed teachers' use of content and pedagogical practices for introducing standard units of length and how that made the concept of standard units of…

In this work, we examined mathematical knowledge mobilised by mathematics teachers while interpreting students' answers, which we denote as Interpretative Knowledge (IK). In particular, we analysed the IK of prospective mathematics teachers (PTs), who were students of a Mathematics Education course for the Master's Degree in Mathematics. In order…

Background: Poor mathematics performance in South Africa is well known. The COVID-19 pandemic was expected to exacerbate the situation. Aim: To investigate Grade 7 learners' mathematical knowledge at the end of primary school and to compare mathematical performance of Grade 7 and 8 learners in the context of the pandemic. Setting: Data were…

This study aimed to investigate the effect of instruction based on metacognitive strategies on geometrical problem-solving performance of mathematics preservice teachers. Geometrical problem-solving tests developed by the researchers were applied as pre-test and post-test before and after the experimental instruction. Preservice teachers predicted…

This article highlights the main ideas that underlie the differences in potential pragmatic knowledge constructs students experience when solving problems, between the zone of proximal development (ZPD) and the zone of potential construction (ZPC). This qualitative research is based on a phenomenological approach to finding the meaning of things…

The aim of the study is to examine whether classroom teachers' Pedagogical Content Knowledge (PCK) on numbers develops in the period from their university education to their active teaching profession. Cross-sectional comparative study method was used in this research in order to examine what kind of development classroom teachers? pedagogical…

This study examines the impact of the Primarily Math Elementary Mathematics Specialist program on K-3 teachers' mathematical content knowledge for teaching, attitudes toward learning mathematics, and beliefs about mathematics teaching and learning. Three cohorts of teachers participating in the program were compared to a similar group of…

The flipped classroom is a growing trend within the education field; specifically at the colligate level. When examining the flipped classroom, teachers assign students material to review prior to attending class. Such materials could be videos, lecture notes, reading assignments, or work/activity sheets. During class time, students collaborate…

Virtual Manipulatives (VMs) are computer-based, dynamic, and visual representations of mathematical concepts, provide interactive learning environments to advance mathematics instruction (Moyer et al., 2002). Despite their broad use, few research explored the integration of VMs into mathematics instruction (Moyer-Packenham & Westenskow, 2013).…

For children with persistent mathematics difficulties, research and practice espouses that an altered kind of mathematics instruction is necessary due to sustained performance differences. Yet, a critical issue in mathematics education rests in the question of why research locates the problem within these children. In this paper, we challenge a…

The study investigates the mathematical and the pedagogical content knowledge among in-service and pre-service first- and second-grade mathematics teachers. The sample of 300 subjects consisted of 150 first- and second-grade in-service teachers and 150 pre-service teachers studying in a college of education, 75 of whom were first-year students and…

This research analyses preservice teachers' knowledge of fractions. Fractions are notoriously difficult for students to learn and for teachers to teach. Previous studies suggest that student learning of fractions may be limited by teacher understanding of fractions. If so, teacher education has a key role in solving the problem. We first reviewed…