This paper presents a series of basic computational problems that are mathematically and/or graphically appealing, and provides an idea of places one might go in trying to understand what is happening, integrating mathematics, computation, and graphics. The real point of this paper is to make a case, through those examples, for computation as an…

Industrial-scale models require considerable setup time; hence, once built, they are used in myriad ways to consider closely related cases. In practice, the code for these models frequently evolves without appropriate notational choices, largely as a result of the lengthy development time of, and the number of individuals contributing to, their…

In this paper we develop a case for introducing a new teaching tool to undergraduate mathematics. Lean is an interactive theorem prover that instantly checks the correctness of every step and provides immediate feedback. Teaching with Lean might present a challenge, in that students must write their proofs in a formal way using a specific syntax.…

We are interested in understanding how university students learn to use programming as a tool for "authentic" mathematical investigations (i.e., similar to how some mathematicians use programming in their research work). The theoretical perspective of the instrumental approach offers a way of interpreting this learning in terms of…

R is becoming the standard for teaching statistics due to its flexibility, and open-source nature, replacing software programs like Minitab and SPSS. The main driver for reform within Scottish statistical undergraduate programs is the creation of the Scottish Qualification Authority's Higher Applications of Mathematics course which has statistics…

Computer programming and mathematical algorithms are natural partners in the development of programming skills, logical thought, and a deeper understanding of mathematical concepts. We present the details of a course which blends the two at the sophomore level. This course is required of our mathematics majors, but attracts mathematics minors from…

The instrumental approach is a useful theoretical lens for understanding students' learning processes with a main focus on the transformation of an artefact (a human design for a goal-directed activity) into a meaningful instrument (i.e. an artefact and schemes developed by the student). In this paper, we articulate the instrumental approach for…

This paper presents a case study that is part of a research studying how university statistics teachers integrate digital tools in their practice. The case study is of a teacher who claims to follow constructionist ideas for her teaching of statistics, using the R programming language. The teacher developed a series of activities with R, aiming to…

The goal of this paper is to promote the use of R and Python as high-level, free, open-source programming environments that can be used as a computational and visualization tool for teaching differential equations. Both R and Python also allow for creating reproducible dynamic documents using Markdown, which combines live code, plain text, and…

We have integrated computer programming instruction into the required courses of our mathematics major. Our majors take a sequence of four courses in their first 2 years, each of which is paired with a weekly 75-minute computer lab period that has a dual purpose of both computationally exploring the mathematical concepts from the lecture portion…

In this paper, we discuss the Experimental Mathematics course taught at Valparaiso University since 2009. We focus on aspects of the course that facilitate students' abilities to ask and explore their own research questions.

Programming with Computer Algebra Systems (CAS) has become an important tool as a support in Computer lectures in Mathematics subjects aimed at Engineering degrees. In this paper, the authors present their teaching experience within the concept "Line Integration" with the help of two specific CAS: DERIVE and MAXIMA. When introducing the…

We have adapted our two laboratories at our department based on our research results, which were presented at the conference CADGME 2014 in Halle and published in the journal. In this article we describe the hardware and software structure of the Laboratory 1: LabIT4KT-1: Laboratory of Computer Modelling and the Laboratory 2: LabIT4KT-2:…

Biostatistics courses are integral to many undergraduate biology programs. Such courses have often been taught using point-and-click software, but these programs are now seldom used by researchers or professional biologists. Instead, biology professionals typically use programming languages, such as R, which are better suited to analyzing complex…

In this work, we review and share some useful technology for mathematics educators that can help to enhance their pedagogical practices to motivate students to improve their further understanding of differential equations after an initial exposure to the topic in an undergraduate class. In particular, we present some innovative ways to employ…