Manipulation of physical models such as tangrams and tiles is a popular approach to teaching early mathematics concepts. This pedagogical approach is extended by new computational media, where mathematical entities such as equations and vectors can be virtually manipulated. The cognitive and neural mechanisms supporting such manipulation-based…

Almost twenty years ago, the National Council of Teachers of Mathematics (NCTM) published "Principles and Standards for School Mathematics" (2000), which recommended that teachers should incorporate more writing into their math lessons, claiming that writing helps students "consolidate their thinking" (p. 402) by causing them…

How children play around with new numerical concepts can provide important information about the structure and patterns they notice in number systems. In this chapter, we report on data from 243 second graders who were asked to fill in missing numbers on a number path (encouraging them to play around with numbers less than zero) and to solve…

Engineering educators are being challenged to create learning environments that not only teach technical skills, but also foster higher-order thinking skills and instill professional attributes. Problem-based learning has been proposed as an effective method to prepare our future engineers. However, pedagogical innovations, like PBL, disrupt…

Different approaches to the use of "clickers" (also known as student response systems) were introduced to a cohort of 127 students over a two-year period with the aim of making students think more deeply in-class about their chemistry knowledge. Student performance was monitored, and individual, anonymous student feedback was frequently…

This case study investigates how preservice primary school teachers describe their experiences with digital story-based problem solving applications and their plans for the future integration of this technology into their teaching. Totally 113 preservice primary school teachers participated in the study. Data collection tools included a…

The current study evaluated the effects of modified schema-based instruction on the mathematical word problem solving skills of three elementary students with autism spectrum disorders and moderate intellectual disability. Participants learned to solve compare problem type with themes that related to their interests and daily experiences. In…

Searching for loci belongs to classical topics of school curricula at schools of different levels all over the world. In the text investigation of loci by GeoGebra using the command "LocusEquation," the tool which has recently been implemented into GeoGebra and which brings a new approach in searching for loci of points, is given. This…

The aim of this paper is to propose a method for solving head-on elastic collisions, without algebraic complications, to emphasize the use of the fundamental conservations laws. Head-on elastic collisions are treated in many physics textbooks as examples of conservation of momentum and kinetic energy.

What "gamification" means and what it doesn't has been addressed and described by many researchers from a variety of different perspectives in the past. Similarities and differences of the methods between "gamification" and "games" (as well as "gamification" and "game based learning") have also…

In recent years most text books utilise either the sign chart or graphing functions in order to solve a quadratic inequality of the form ax[superscript 2] + bx + c < 0 This article demonstrates an algebraic approach to solve the above inequality. To solve a quadratic inequality in the form of ax[superscript 2] + bx + c < 0 or in the…

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…