Recent reform efforts state the importance of providing students with opportunities to persevere with challenging mathematics to make meaning. We posit translanguaging practice as a vital option by which Latinx bilingual students can sustain collective perseverance during problem solving. In this paper, we employ a constant-comparative overlay…

Many literature studies point out how the process that moves the student from personal reasoning to the arrangement of fruitful argument could help them in the development of mathematical argumentative thinking. Starting from the above assumptions, in this paper we investigate the interaction among teacher/researcher and students in a Digital…

In quantum mechanics courses, students are often asked to solve bound and scattering state problems. The use of an ordinary differential equation is a standard technique to solve these questions. Here, we investigated students' problem-solving processes for two typical problems of a single particle in one spatial dimension: a bound state problem…

In 2017, the mathematics assessments that are part of the National Assessment of Educational Progress (NAEP) program underwent a transformation shifting the administration from paper-and-pencil formats to digitally-based assessments (DBA). This shift introduced new interactive item types that bring rich process data and tremendous opportunities to…

This research deals with a possible use of history of mathematics in mathematics education. In particular, history can be a fundamental element for the introduction of the concept of integral through a problem-centred and intuitive approach. Therefore, what follows is dedicated to the teaching of mathematics in the last years of secondary schools,…

This study investigated relations between the distribution of practice problems in textbooks and students' learning of decimal arithmetic. In Study 1, we analyzed the distributions of decimal arithmetic practice problems that appeared in 3 leading math textbook series in the United States. Similar imbalances in the relative frequencies of decimal…

One method of proof is to provide a logical argument that demonstrates the existence of a mathematical object (e.g., a number) that can be used to prove or disprove a conjecture or statement. Some such proofs result in the actual identification of such an object, whereas others just demonstrate that such an object exists. These types of proofs are…

This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…

Metacognition is vital for a student's academic success. Gifted learners are no exception. By enhancing metacognition, gifted learners can identify multiple strategies to use in a situation, evaluate those strategies, and determine the most effective given the scenario. Increased metacognitive ability can prove useful for gifted learners in the…

In this article, the authors first present the Hands Together! task. The mathematics in this problem concerns the relationship of hour and minute durations as reflected in the oft-overlooked proportional movements of the two hands of an analog clock. The authors go on to discuss the importance of problem solving in general. They then consider…

The aim of this article is to shift the notion of 'sites' as places of work peculiar to continuous professional development (CPD) to a theoretical level, independent of, yet intimately connected to, their physical meanings, for example universities and schools. Most CPD initiatives have to contend with at least one of these two sites, in which…

Mathematical achievement in problem solving is not yet as expected. This is due to strategies that have not accommodated the situation of students. Adversity quotient is the state of the student who needs to get the attention of the teacher so that the learning strategy is expected to be appropriate. This research aims to describe the thinking…

The Three-Square Puzzle shows a remarkable relationship between three angles. What happens when the number of squares increases? This article explores that question and brings in Fibonacci and Lucas sequences.

We recognise that though teachers may participate in various forms of professional development (PD) programmes, learning that they may have gained in the PD may not always lead to corresponding perceivable changes in their classroom teaching. We offer a theoretical re-orientation towards this issue by introducing a construct we term…

A core aim of contemporary science, technology, engineering, and mathematics (STEM) education is the development of robust problem-solving skills. This can be achieved by fostering both discipline knowledge expertise and general cognitive abilities associated with problem solving. One of the most important cognitive abilities in STEM education is…