The 1989 good old days' quote from the "Field of Dreams" by Kevin Costner that "If you build it, he or they will come" is no longer going to be attractive, especially in the field of mathematics education. One such challenging subject in the field of mathematics education is the teaching and learning of geometry. It is the aim…

Much important research on the learning of mathematics with technology-supported inquiry has been devoted to learning with multiple-linked representations (MLR) as a mode of feedback. Like a mirror, MLR feedback helps students see their actions in one representation "reflected" in another. Yet, research has followed learning episodes…

Students enrolled in introductory math courses, such as college algebra, deserve to do more than find answers and fix mistakes. We present one interactive digital activity, the Cannon Man "Techtivity," which we developed to provide opportunities for students to develop an understanding of function, beyond just applying a rule, such as…

Emergent graphical shape thinking (Moore & Thompson, 2015) is a way of reasoning that is critical across numerous STEM fields. However, evidence indicates that the underlying component ideas for emergent thinking are underdeveloped in school mathematics education (e.g., Thompson & Carlson, 2017), and few studies directly report on…

This study sets for itself the task of constructing a learning trajectory for the fundamental theorem of calculus (FTC) that takes into account the interaction with an educational digital tool. Students were asked to explain the connections between interactive and multiple-linked representations in an educational digital tool, and to conjecture…

Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the…

Statistics is a domain that is taught in Mathematics in all school levels. We suggest a potential in using an interdisciplinary approach with this concept. Thus the development of the understanding of a situation might mean to use both mathematical and statistical reasoning. In this paper, we present two case studies where two middle school…

There is a recognised need in mathematics teaching for new kinds of tasks which exploit the affordances provided by new technology. This paper focuses on the design of prediction tasks to foster student reasoning about exponential functions in a mathematics software environment. It draws on the first iteration of a design based research study…

Students' development of an understanding of covariation was the focus of a research project that investigated the way in which 12 Year 5/6 students engaged with the learning environment afforded by the graphing software, "TinkerPlots." Using data generated from individual interviews, the results demonstrate that upper primary students…

Often, quantitative and mathematical models are used to study complex dynamic systems--where collections of individual components interact to produce an emergent pattern of behavior. To interpret such models involves 'unpacking' the collective behaviors and interactions that underlie a given pattern. We investigate what representational supports…

No person, place, or thing can capture the attention of a class of sixth graders like "man's best friend." To prompt students' interest in a series of lessons on proportional relationships, the authors brought in a unique teaching aid--a dog. A family dog was used to supply the measurements for scatter plots and variables so that students could…

The new Common Core State Standards for Mathematics have been formulated to provide students with instruction that will help them acquire a thorough knowledge of math at their grade level, which will in turn enable them to move on to higher mathematics with competence and confidence. "Hands-on Activities for Teaching the Common Core Math…

Evolving technology has played an important part in a common quadratic-function lesson. Having been mentioned repeatedly in numerous reform documents, a recurring lesson has involved changing the parameters in f(x) = ax[superscript 2] + bx + c and studying the effects on the graph. In both NCTM Yearbooks and NCTM Standards documents, technology is…

In this article, the author suggests a framework for developing lesson ideas involving variation. This idea was demonstrated by Rebecca Davey at a conference bringing together teachers from the seven schools participating in the TI-"n"spire pilot research project overseen by Alison Clark-Wilson of the University of Chichester. It uses information…

The universities and faculties which educate teachers of mathematics for teaching pupils/students of any age group from pre-school age to higher education carefully monitor and compare valuable results of this research, detect the areas in which the mathematical achievements of pupils should be improved at the national level and propose the ways…