In mathematics, the expectation to set up and solve word problems emerges as early as kindergarten; however, many students who experience mathematics difficulty (MD) and dual-language learners often present with specific challenges in this area. To investigate why these populations experience word-problem difficulty, we examined the word, problem…

There have been recent pushes for more active learning in mathematics classrooms, especially at the undergraduate level. To incorporate more active learning, there is a need for tasks that explicitly support this type of instruction, attention to student reasoning and whose ideas are publicly acknowledged, and awareness of differences in students'…

This article proposes a practical method of teaching the addition of unit fractions using a series of mirror equation experiments.

This article elaborates a new direction for studying the construction of novel strategies that enables researchers to model the conceptual underpinnings of students' observable strategic actions during episodes of mathematical problem solving. The nature of the relationship between conceptual and procedural knowledge has been persistently debated…

An interesting Sangaku problem was chosen and a multidirectional study was performed, which included finding the locus of a circle's center moving while being tangent to two circles. It also included finding the radius of that circle given the datum that it is also tangent to the side of an isosceles triangle. Two different proofs are presented of…

Geometrography, "alias the art of geometric constructions" was proposed by Emile Lemoine between the late 1800s and the early 1900s. It consisted originally of a system to measure the complexity of ruler-and-compass geometric constructions, capable of: designate every geometric construction by a pair of values that manifests its…

This study aims to introduce a method that is based on the relationship between numbers and geometry, which can be used to show the exact location of rational numbers on the number line, compare rational numbers, make calculations, and examine rational numbers conceptually through parallel lines. It is believed that this method will to contribute…

Recently, Gauthier introduced a method to construct solutions to the equations of motion associated with oscillating systems into the mathematics education research literature. In particular, Gauthier's approach involved certain manipulations of the differential equations; and drew on the theory of complex variables.Motivated by the work of…

The mathematics education field recognizes the importance of noticing children's mathematical thinking as a means for supporting children in learning mathematics (Sherin et al. Mathematics teacher noticing. Routledge, New York, 2010). Using the existing literature base around teachers' knowledge of children's mathematical thinking and…

The mathematics standards for many countries include teaching and learning ratios, typically with efficient algorithms and strategies (Australian Curriculum: Mathematics, Assessment and Reporting Authority, 2017; National Council of Teachers of Mathematics, 2014). In the 1990s, Cramer and Post (1993) claimed that school mathematics mostly involves…

Technology has an inseparable role in contemporary educational systems. Recent demands consider its informed integration in classrooms. The current study aims to investigate whether informed use of Interactive Whiteboard (IWB) technologies affects students' real-time emotions in mathematics classes, through an integrative research model that…

Understanding the proof problem is necessary in the development of geometric proof in schools. This paper discusses findings from a qualitative case study which explored the mathematical work done by teachers in helping students to understand geometric proof problems. Data were generated from two teachers through video-recorded observations of 30…

The purpose of this study is to investigate pre-service elementary teachers' realistic considerations and difficulties in solving "division with remainder" type of problems which focus on the measurement meaning of division operation. The qualitative research method of case study design was used for the study. The purposive sampling…

Solution representations can reveal how problem solvers communicate mathematical thinking and reasoning in problem-solving process. The present study examined the solution representations used by 20 pre-service teachers for the percentage change problems. The pre-service teachers were invited to solve a combination of simple and complex percentage…

This research is based on an individual case finding, where the response from individuals in answering the mathematical problems is initiated with perplexity to proceed with the new finding by reflecting on the previous experience. This research aimed at contributing practically on the indicators causing a perplexity on students which described…