Current international curriculum frameworks and research advocate for K-12 mathematics to emphasize proof and argumentation. This review synthesizes literature related to conceptions, content, and supportive actions for proof and argumentation across four grade-level bands: K-2, 3-5, 6-8, and 9-12. Our systematic search and subsequent screening…

The purpose of this review is to determine the evidence base classification of schema-based instruction (SBI) as an intervention to improve word problem-solving outcomes in mathematics for students with learning or mathematics disabilities in Grades K-12. Using the Council for Exceptional Children's quality indicators (QIs) and standards, we…

This study examined if and how thinking time, defined as the time from the start of the problem to the students' first action to solve, influences their problem-solving efficiency, defined as the number of steps taken to solve the problem, using Graspable Math, a web-based mathematical tool. We found that: (1) students who took longer to think…

Front camera data from tablets used in educational settings offer valuable clues to student behavior, attention, and affective state. Due to the camera's angle of view, the face of the student is partially occluded and skewed. This hinders the ability of experts to adequately capture the learning process and student states. In this paper, we…

Project BRIDGE was launched as a response to the underrepresentation of English learners in gifted education. Through Project BRIDGE, high-ability English learners were able to access the same rigorous academic content as their native English-speaking peers. The present study compared intervention and comparison teachers' instructional behaviors…

The aim of this study is to investigate both the planning and implementation process of a modelling task by a middle school mathematics teacher. The participant of the study, which was conducted as a single case study, is a middle school mathematics teacher who have knowledge and experience in modelling. The data collecting tools of this study…

The purpose of this study is to explore elementary educators' perceptions regarding what it means to conceptually understand mathematics, the emphasis teachers place on utilizing evidence-based teaching processes, as identified as effective by National Council of Teachers of Mathematics (NCTM), and how these perceptions influence their…

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

The radius of curvature formula is usually introduced in a university calculus course. Its proof is not included in most high school calculus courses and even some first-year university calculus courses because many students find the calculus used difficult (see Larson, Hostetler and Edwards, 2007, pp. 870- 872). Fortunately, there is an easier…

This article focuses mainly on two key mathematical processes (representation, and reasoning and proof). Firstly, we observed how teachers learn these processes and subsequently identify what and how to assess learners on the same processes. Secondly, we reviewed one teacher's attempt to facilitate the learning of the processes in his classroom.…

The important role that metacognition plays as a predictor for student mathematical learning and for mathematical problem-solving, has been extensively documented. But only recently has attention turned to primary grades, and more research is needed at this level. The goals of this paper are threefold: (1) to present metacognitive framework during…

One of the foundational topics in first-year algebra concerns the concept of factoring. This article discusses an alternative strategy for factoring quadratics of the form ax[superscript 2] + bx + c, known as "factoring for roots." This strategy enables students to extend the knowledge they used when the leading coefficient was 1 and…

Students learn mathematics by solving problems. Mathematics textbooks are full of problems, and mathematics teachers use these problems to test students' understanding of mathematical concepts. This paper discusses how problem-solving skills can be fostered with a geometric tiling problem.

We explored the effectiveness of a flipped active learning pedagogy in a liberal arts mathematics course without video or interactive preparation. In both control and active learning classes, students were required to respond to a reading before class and take a quiz after class. During the active learning class, students worked together in groups…

This article examines the work of 30 in-service teachers engaged with modelling activities during a course within an Ecuadorian master's degree program in mathematics teaching. These teachers experienced a sequence of activities designed to explore imaginative aspects of mathematical modelling and problem solving, inviting perspectives from life…