In each educational curriculum, trigonometry is an important subject at upper secondary schools and pre university level that apply in many other subjects such as algebra, calculus, geometry and physics. Many of students have serious problem in learning the trigonometric materials because usually mathematics educators transfer the trigonometric…

In 2014 NCTM advocated for productive struggle by expressing the need for teachers to allow their students the time necessary to grapple with their mathematical "uncertainties." We posit pre-service teachers need opportunities to productively struggle when learning and applying their mathematical understanding in order to understand how…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

Eye tracking enables the reconstruction of eye movements and thus the analysis of visual information selection and integration processes during problem solving. In this way, learner-specific difficulties can be identified and problem-solving process can be adapted accordingly. For such an adaptation, the prediction of response behavior plays a…

There is little empirical research related to how elementary students develop computational thinking (CT) and how they apply CT in problem-solving. To address this gap in knowledge, this study made use of learning trajectories (LTs; hypothesized learning goals, progressions, and activities) in CT concept areas such as sequence, repetition,…

Since formal mathematics is discussed in terms of abstract symbols, many students face difficulties to acquire a clear understanding of mathematical concepts and ideas. Transforming abstract or dis-embodied representations of mathematical concepts and ideas into embodied representations is a strategy to make mathematics more tangible and…

The number and variety of educational mathematics mobile applications (EMMAs) make it difficult to select mobile applications for mathematics learning and teaching. Therefore, in this study, multi-criteria decision-making (MCDM) techniques, which are effectively used in a wide variety of disciplines, were applied to choose among alternative…

This article aims to show some activities based on non-routine problems with different levels of difficulty and from different classes that are integrated into the curriculum, additionally two spaces were opened for students to interact with recreational mathematics activities with the purpose of providing opportunities to all students access the…

In this paper, we consider mathematical competitions for pre-university students, such as the "International Mathematical Olympiad" (IMO) and many national and regional Olympiads following a similar model. The problems proposed in these contests must be solvable by 'elementary' methods (i.e., without using calculus) and belong…

Historically, police educators delivering academy programs have overused traditional or teacher-centred methods as part of an authority driven command and control culture. In addition to being educationally unsound, this teaching approach has limited the development of the critical thinking skills needed for effective reform in the community…

Three studies examine a novel pathway by which the perseverance component of the personality trait "grit" might predict college students' behavioral persistence when solving challenging math problems. Specifically, we focus on the intervening role of what we refer to as "math-specific self-perceptions of perseverance," which…

In this paper, we present an overview of a series of 1-credit applied problem solving courses. The goal of these courses was to help students develop their oral and written communication skills, ability to work as a team, and general problem solving skills through preparation and participation in the Mathematical Contest in Modeling (MCM) and…

The United Arab Emirates' vision of the 2021 National agenda aimed that its students rank among the best in the world in mathematics and the sciences. However, fractions remain a challenging topic for both teachers and students. The purpose of this study was to investigate the impact of using digital games-based learning (ABACUS) on students'…

The static equilibrium properties of a spool, resting on an incline and subject to the tension exerted by a string wrapped around the core cylinder, are studied by means of Newtonian mechanics. The overall behaviour of this system is imagined to be similar to that of a doggie kept on a leash. Starting from the well-known mechanical properties of…

This paper seeks to evaluate learning based on the competency approach, taking a didactic experience to evaluate a possible improvement in the ability to solve problems and for autonomous learning in general. For the didactic development, the theme "gases" was taken, which is generally enunciated: Corpuscular kinetic theory of matter;…