The purpose of this article is to describe and illustrate learning trajectories (LTs) and introduce a new, comprehensive set of resources that support teaching meaningfully and joyfully. An LT for a topic has three parts: (1) a mathematical goal; (2) a developmental progression of levels of thinking; and (3) teaching practices (environments,…

The aim of the study is to conduct a bibliometrical analysis on the published articles related to RME. Accordingly, Scopus database was scanned using the keywords "realistic mathematics education" or "realistic mathematic education" or "realistic maths" or "realistic mathematical education" and a total…

In this paper, drawing on the philosophy of dialectical materialism, we present an elaboration of two concepts that tend to remain backstage in debates in the field of history in mathematics education, namely, the concept of "mathematics learning" and the concept of classroom "mathematics knowledge." The elaboration of these…

This manuscript contributes to research on how algebraic thinking about operations and properties can develop, and relevant forms of curricular activity. The key question asked is: how can students' early algebraic activity be fostered through focusing on relations involving operations and properties? We adopt Radford's three aspects of algebraic…

Mathematical representations are 'visible productions' that embody mathematical ideas. The author guides teachers with suggestions for the use of representations in mathematical problem solving with students. Representations can be used to help make abstract mathematical ideas accessible, allowing teachers and students to interpret, communicate,…

This paper introduces tools for converting circular-featured-waste into polygonal construction parts and then 3D polyhedra. The tools, including diagrams, 3D printable joiners and mathematical formulae are designed for mathematics-related play, re-use, learning, design and improvisation. Activities for students include making assemblies, gathering…

Counting is an intellectual activity that is usually identified with the assignment of positive whole numbers ("1, 2, 3, 4, ...") in one-to-one correspondence with a collection of items in one's attentional field. Taking into account a broader, "combinatorial" meaning of the term, counting extends far beyond this description.…

Math anxiety negatively affects student learning and academic performance. Students with high math anxiety exhibit physical, mental, and emotional symptoms. As a result, they tend to avoid mathematics and mathematics-related situations, perform poorly, and exhibit deficiencies in working memory. Research studies have shown that inquiry-based…

In this article, we state an interesting geometric conservation property between the three angle bisectors of three similar right triangles and provide a proof without words for its justification. A GeoGebra applet is also presented to help with the understanding of the progression of the proof from inductive to deductive stage.

The aim of this study was to determine how 5-year-old children identified the functional relationship of correspondence, and whether or not they generalized when working on a task that involved programmable robots. We conducted this study with 15 children (9 girls and 6 boys) in their last year of preschool education. The study was designed around…

How do task experiences support proximal and longer-term desires to reengage? Central to this question is the interplay between perceptions of task difficulty and the situational interest. This interplay is increasingly researched but not yet well understood. Micro-analytic, latent studies are important tools for replicating past findings and…

Although numbers are universal, there are great differences between languages and cultures in terms of how they are represented. Numerical notation can influence number processing. Two well-known types of notational systems are sign-value, such as the Roman numeral system, and place-value systems, such as the Indo-Arabic numeral system. What is…

The hanging rope problem is considered. The rope is subject to rotation with the rotation axis being parallel to the rope. Using a continuum model and the basic principles of dynamics, the differential equation governing the motion is derived. The dynamic equilibrium case without vibrational motion is assumed in deriving the equation. The equation…

Noticing is a momentary act. Enriching the possibility of noticing something specific in the future marks the beginning of an action labelled "professional development". Thus, what happens as a result of noticing is what matters for the teacher, but what really matters is what happens for the learner. Whether something noticed enables a…

Scholars paid attention to the relationship between homework frequency and academic performance, however, fewer of them noticed that the relationship might be nonlinear and may vary across different types of homework. This study aims at exploring the nonlinear relationship between the different types of homework frequency and mathematical academic…