This paper aims to characterize critical events noticed by novice mathematics teacher-educators (NMTEs) while they facilitate teacher education sessions. Twenty-four NMTEs enrolled in a university course on teaching teachers were asked to facilitate a series of three sessions with preservice teachers, identify critical events from those sessions…

Example-generation tasks have been suggested as an effective way to both promote students' learning of mathematics and assess students' understanding of concepts. E-assessment offers the potential to use example-generation tasks with large groups of students, but there has been little research on this approach so far. Across two studies, we…

We describe here a low-cost experiment for introductory physics students where they compare the physical properties of aluminum and steel by means of cantilever oscillations. This, in turn, allows the students to improve their physical intuition about these materials. Further, the students can apply their physics and mathematics knowledge and…

This pilot study examined the feasibility of using worked examples as a mechanism to improve verbal explanations of fractions concepts among Grade 5 students with mathematics difficulties in a small-scale randomized controlled trial (RCT) before scaling up to a large-scale RCT. Students (N = 49) were randomly assigned to a business-as-usual (BAU)…

State exams frequently use word problems to measure mathematics performance, making difficulties with word problem solving a barrier for many students with learning disabilities (LD) in mathematics. Based on meta-analytic data for students with LD, five empirically validated word-problem strategies are presented, with components of model-based…

Most mathematicians state mathematics is a field of beauty, creativity, and innovation, yet what is echoed by students is not how mathematics allows students to explore, but rather the ways in which it constrains and does not necessitate creativity. In comparison, many students associate coding with freedom, and the ability to create and express…

Considering the importance of mathematics in modern society, it is crucial to understand the cognitive processes involved in the acquisition of complex mathematical competency. As a new generation of evaluation theory, cognitive diagnosis has its unique advantages in personalized evaluation. Based on the mathematical cognitive framework of Trends…

Understanding negative numbers can be challenging for many students, as these concepts may seem less tangible than counting objects, which are commonly represented by positive numbers. In addition, the multiplication of two negative numbers resulting in a positive might appear inconsistent and puzzling to young learners who are used to seeing the…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

The research entitled The Development of Learning Activity through KWDL Technique Combined with BAR Model to improve problem-solving Ability in Math for Secondary 1 (Grade 7) Students made use of a quasi-experimental design wherein the experimental group was exposed to learning activities through the KWDL technique combined with BAR model while…

Mathematical "magic," or experiences of beauty and creativity for K-12 mathematics students, can contribute to deepened content understanding. However, creating opportunities for mathematical "magic" in mathematics classrooms has been a challenge for classroom practitioners. To support development of these experiences in…

While the importance of collaborative problem-solving has been highlighted as an important skill by the OECD (Organisation for Economic Co-operation and Development), no specific model exists for mathematics facilitators to implement when engaging their students in group problem-solving. In this paper, we introduce the CoPs model for Collaborative…

DE programming in higher education should be designed to increase student success, and well-designed corequisite models have shown great potential as an accelerated option for completion of the first college-level course in math. With the support of a Texas Higher Education Coordinating Board grant, Tarleton State University, a member institution…

Examining the effect primary school teachers' preferred teaching method has on primary school students' mathematics achievement is important. In this context, the purpose of the research is to determine whether the worked example method is effective on students' ability to learn fundamental knowledge about fractions and their success in solving…

Each level on van Hiele's model has its characteristics, such as terminology, concept, and reasoning strategies. This study attempts to reveal epistemological obstacles on all van Hiele's levels of geometric thinking in the topic of geometric transformation. Thus, a student could overcome the epistemological obstacles in transformation geometry…