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Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when…
Mathematical reasoning with algebraic and graphical representations is essential for success in physics courses. Many problems require students to fluently move between algebraic and graphical representations. We developed a freely…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
The subject of Polynomiography deals with algorithmic visualization of polynomial equations, having many applications in STEM and art, see [Kal04]. Here we consider the polynomiography of the partial sums of the exponential series. While…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…
This study examines the potential of using math-themed postage stamps in mathematics lessons as a tool to engage students and integrate the subject with history, art, and culture. Since the first mathematical stamps appeared in the early…
We are convinced of the usefulness of sketches and diagrams during mathematical work but the observation is made in our practices that they are not spontaneously used by students. In order to study the understanding and use of sketches by…
Comics is emerging as a popular medium for providing visual explanations of programming concepts and procedures. Recent research into this medium opened the door to new opportunities and tools to advance teaching and learning in computing.…
In this paper we present our experience in using visualization in mathematics education. The experience with our university courses: "Computer tools in matematics" and "Symbolic algebra" provides the basis for mathematics teacher education…
Bubble Sort is simple. Yet, it seems a bit difficult for high school students. This paper presents a pedagogical methodology: Using Design Sketch to visualize the concepts in Bubble Sort, and to evaluate how this approach assists students…
Creative coding is a rapidly expanding domain for both artistic expression and computational education. Numerous libraries and IDEs support creative coding, however there has been little consideration of how the environments themselves…
Recent work investigated the potential of comics to support the teaching and learning of programming concepts and suggested several ways $coding$ $strips$, a form of comic strip with its corresponding code, can be used. Building on this…
Gauss' and Stokes' theorems are fundamental results in vector calculus and important tools in physics and engineering. When students are asked to describe the meaning of Gauss' divergence theorem, they often use statements like this: "The…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
Learning vector calculus techniques is one of the major missions to be accomplished by physics undergraduates. However, beginners report various difficulties dealing with the index notation due to its bulkiness. Meanwhile, there have been…
At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics,…
Quantum theory is often regarded as challenging to learn and teach, with advanced mathematical prerequisites ranging from complex numbers and probability theory to matrix multiplication, vector space algebra and symbolic manipulation within…
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a give problem into a representation that is easier to exploit for solving it. A major focus while helping introductory physics students learn problem…
Image tracing is a foundational component of the workflow in graphic design, engineering, and computer animation, linking hand-drawn concept images to collections of smooth curves needed for geometry processing and editing. Even for clean…