As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.

"Flatland: A Romance of Many Dimensions" is an 1884 novella written by English schoolmaster Edwin Abbott. He describes what it would be like to live in a two-dimensional (2D) world--Flatland. It is fascinating reading that underscores the challenge of teaching three-dimensional (3D) mathematics using 2D tools. Real-world applications of…

The author shares the lesson that he used to introduce the quadratic unit to students in an extended second-year algebra class, demonstrate why it was appropriate for his struggling learners, and discuss possible future modifications to this lesson.

In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students' difficulties when treating…

Admittedly, the notion of generalized integrals in one parameter has a fundamental role. En virtue that, in this paper, we discuss and characterize an approach for to promote the visualization of this scientific mathematical concept. We still indicate the possibilities of graphical interpretation of formal properties related to notion of…

The authors provide a dynamic Ferris wheel computer activity that teachers can use as an instructional tool to help students investigate functions. They use a student's work to illustrate how students can use relationships between quantities to further their thinking about functions.

The process of prime factor splicing to generate home primes raises opportunity for conjecture and exploration. The notion of "home primes" is relatively new in the chronicle of mathematics. Heleen (1996-97) first described a procedure called "prime factor splicing" (PFS). The exploration of home primes is interesting and…

This paper describes a classroom experiment where students use techniques found in the history of mathematics to learn about an important mathematical idea. More precisely, sixth graders in a primary school follow Archimedes's method of exhaustion in order to compute the number p. Working in a computer environment, students inscribe and…

There are at least five different equivalent definitions of the absolute value concept. In instances where the task is an equation or inequality with only one or two absolute value expressions, it is a worthy educational experience for learners to solve the task using each one of the definitions. On the other hand, if more than two absolute value…

Mathematics teachers continually look for ways to make the learning of mathematics more active and engaging. Hands-on activities, in particular, have been demonstrated to improve student engagement and understanding in mathematics classes. Likewise, many scholars have emphasized the growing importance of giving students experience with the…

In this paper we describe a touchscreen application called "TouchCounts," which is designed to support the development of number sense in the early years. We first provide an a priori analysis of its affordances. Then, using Sfard's communicational approach, augmented by a focus both on the role of the body--particularly the fingers…

This paper offers an account of what early mathematics education could look like in an age of young digital natives. Each "Tubby," as the tablets are called, presents Nicole (our generic little child) with stimulating mathematics microworlds, from which, beginning at age 3, she can learn basic math concepts, as well as methods of…

Many delegates at "conference" relish the opportunity, and the space, to "do some mathematics". Opportunity and space help to make the experience memorable, but how often is the quality of the starting point, or question acknowledged? Here is a set of starting points or problems that invite the reader to "do some mathematics". Deliberately, no…

In short, this is a "master class". The learning and teaching of mathematics can be revolutionised with the creative use of dynamic software is an oft quoted mantra. Here, this mantra is exemplified through the documented experiences of using Autograph to enliven, to extend, and to foster the understanding of differentiation and integration. The…

This article explicates the development of top-view numeric coding of 3-D cube structures within a design research project focused on 3-D visualization skills for elementary grades children. It describes children's conceptual development of 3-D cube structures using concrete models, conventional 2-D pictures and abstract top-view numeric…