A one-degree angle would certainly be difficult to draw accurately, especially without the aid of other tools like a protractor. However, mentally making a one-degree angle in visualized imagination is not only possible, but it is important for students' emergent understandings of angular measure. When students begin learning about length,…

Tentativeness is often framed as a deficit, synonymous with timidity or a lack of confidence. In this article, I situate the notion of tentativeness in an enactivist framework and describe its role as both a strategy and affordance in a spatial visualization exercise. Drawing on insights from mathematics education and ecological psychology, I…

The article uses dynamic visualizations in Excel to examine a variety of ways in which students can attain a much greater depth of understanding of optimization problems in introductory calculus. The topics discussed include a variety of common optimization problems that appear in virtually every calculus textbook that can all be enhanced…

Visualising positive and negative numbers on a number line is helpful for exploring problems involving operations with positive and negative numbers. This is because number lines lend themselves to exploring problems involving continuous linear contexts such as travelling distances and temperature. Teachers in a professional development program…

There is a large body of research that suggests a sound understanding of rational number is vital for success in all areas of mathematics, at school and beyond. In the Australian Curriculum, fractions are formally introduced from Year 1, yet there is evidence to suggest that current approaches are not leading to deep understanding in later years.…

In this article, Rebecca Seah and Andrew Beencke explore the importance of developing critical thinking and spatial reasoning skills. They explore a series of activities designed to develop the visualisation and critical thinking skills with Year 4 students.

Typical difficulties in learning probabilistic subjects are concerned with big data, complicated formulas and inconvenient figures in statistical analyses. The present research considers the usage of innovative teaching methods (e.g. electronic summary of lectures, presentations of lecture courses, task solution templates, electronic training…

In this paper I analyze students' conceptual understanding of the quality of polynomial approximation. In particular, I analyze to what extent the interactive play with various methods of interpolation enables the students to build visual pictures that help understanding the formal mathematical statements. The role of the Mathematica software in…

Launching a problem is critical in a problem-based lesson. We investigated teachers' perspectives on the use of a problem that was analogous to the one provided during a launch. Our goal was to identify teachers' underlying assumptions regarding what should constitute a launch as elements of the "practical rationality of mathematics…

Admittedly, the Fundamental Theorem of Calculus-TFA holds an important role in the Complex Analysis-CA, as well as in other mathematical branches. In this article, we bring a discussion about the TFA, the Rouché's theorem and the winding number with the intention to analyze the roots of a polynomial equation. We propose also a description for a…

This paper shows how GeoGebra--a dynamic mathematics software--can be used to experiment, visualize and connect various concepts such as function, first derivative, slope, and tangent line. Students were given an assignment to determine the first derivative of the exponential function that they solved while experimenting with GeoGebra. GeoGebra…

The author reviews research on working memory and short-term memory abilities of deaf individuals, delineating strengths and weaknesses. Among the areas of weakness that are reviewed are sequential recall, processing speed, attention, and memory load. Areas of strengths include free recall, visuospatial recall, imagery, and dual encoding.…

Many students find it difficult to engage with mathematical concepts. As a relatively new class of learning tools, visualization tools may be able to promote higher levels of engagement with mathematical concepts. Often, development of new tools may outpace empirical evaluations of the effectiveness of these tools, especially in educational…

In the Netherlands, as in many other countries, the algebraic expertise of students graduating from secondary education is an issue. The use of digital tools for algebra education is expected to change epistemologies, activity structures and student achievement. Therefore, a study was set up to investigate in what way the use of ICT in upper…

A random sample of middle school special education teachers from various classroom settings completed a survey asking them about what instructional practices and materials they used to teach students with disabilities how to solve word problems, how much time they allocated to problem solving instruction, and what type of problems they gave their…