This paper is concerned with developing a new class of generalized numbers. The main advantage of this class is that it generalizes the two classes of generalized Fibonacci numbers and generalized Pell numbers. Some new identities involving these generalized numbers are obtained. In addition, the two well-known identities of Sury and Marques which…

Success in Algebra I often predicts whether or not a student will pursue higher levels of mathematics and science. However, many students enter algebra holding persistent misconceptions that are difficult to eliminate, thus, hindering their ability to succeed in algebra. One way to address these misconceptions is to implement worked-examples and…

During collaborative learning, computer-supported or otherwise, students balance task-oriented goals with the interpersonal goals of relationship-building; these goals may conflict, negatively impacting learning. In peer tutoring, for instance, tutors may avoid providing feedback to their partners to avoid the face-threat to their tutee. In this…

Background: Integration of engineering into middle school science and mathematics classrooms is a key aspect of STEM integration. However, successful pedagogies for teachers to use engineering talk in their classrooms are not fully understood. Purpose/Hypothesis: This study aims to address this need with the research question: How does a middle…

Higher education institutions (HEIs) are drivers of social change embedded in a society which is experiencing increasingly complex and multifaceted crises. This is partly attributable to the use of conventional and deterministic problem-solving curricula. A combination of a transdisciplinary approach and indigenous knowledge (IK) as transformative…

The probability is exceptional in the teaching of mathematics because students often have difficulties to understand the basic terms and the problem solving strategies. Understanding lacks of the probability concept and various types of misconceptions arise from the misleading intuition and misinterpretations of experience with the stochastic…

We compared students' learning gains in authentic seventh-grade classrooms (N = 144) in 4 different interventions that incorporated a computer game that aims to teach players to solve linear equations. Significantly higher learning gains were measured in the implementations that were specifically designed to mediate the attribution of algebraic…

This study examined effects of the Polya's problem solving Technique (POPSOT) as observed by Shaibu (1987) in Atadoga (2010) and conventional problem-solving Technique (CONPSOT) on cognitive achievement of physics students. A pre-test post-test quasi experimental design used adopted for the study. The sample comprised of 102 senior secondary two…

Increasing and decreasing functions can be combined into a quadratic to explore the competing demands of number of sales, price points and profit (or loss). An interesting application of taxation rates is also explored.

In this article, the authors present the use of digital tape diagrams--implemented using GeoGebra (2001) dynamic mathematics software--as a support to static diagrams to pose and solve proportional reasoning tasks. They show how dynamic sketches can allow students to explore standard tasks in proportional reasoning in ways that emphasise…

This informal essay is based on a presentation James Tanton gave at the Australian Association of Mathematics Teachers (AAMT) 'Why Maths?' Conference in 2019. It begins by offering two first steps to problem-solving that Tanton believes are key for finding success--and joy--in doing mathematics: (1) Be human! Have an emotional reaction to the…

The spectrum of Teaching Styles (TS) provides a solid theoretical foundation for teaching Physical Education. It is common for teachers to use directive styles that do not meet program requirements. This is further accentuated in the case of dance, to the detriment of the development of emotional and cognitive factors. This study investigates the…

With the advance of engineering education research and scholarship, there has been an increased focus on amending chemical engineering courses to increase student learning, engagement and enjoyment. These approaches are often incorporated in project-based courses such as capstone design courses and laboratory courses, providing opportunities to…

Collaborations and partnerships across disciplines are becoming increasingly recognized as valuable endeavors toward solving emerging global challenges in our rapidly changing world. Thus, it is crucial to create STEM educational strategies that infuse diverse and interconnected perspectives among scientists, policymakers, and the general public.…

When teaching through problem solving, effective mathematics teachers need to lead discussions that assist students in making connections between different solution strategies. However, while teaching a methods course for preservice teachers (PSTs), we noticed that after solving a problem and presenting various solution strategies, many PSTs…