Editorial for Teaching with Technology Special Issue of PRIMUS

In 1974, the National Council of Teachers of Mathematics (NCTM) issued a far-reaching statement urging the use of calculators in K-12 mathematics education, saying that with the cost of such devices decreasing rapidly, their power and potential was too omnipresent to ignore [6]. This observation is true many times over today: we live in a world in where technology is ubiquitous and omnipresent, where computers masquerade as phones and everyone is always online. In this environment, the NCTM’s endorsement of the use of calculators—over 40 years ago—suggests that if we are not now considering how technology changes the teaching and learning of college mathematics we are behind a curve set decades ago.

The goal of this issue of PRIMUS is therefore to reflect on how different components of our technology-saturated environment influence the teaching and learning of undergraduate mathematics. We highlight some of the many different ways that technology is being used in collegiate mathematics instruction today, say something about its effectiveness, and describe some of the strategies used to obtain that level of effectiveness.

Obviously, in the face of the breadth of the types of technology available to today’s instructors and students, it is not possible to undertake (in a single journal issue!) a complete survey of available technologies and their uses, nor even to present a comprehensive analysis of the effectiveness of the uses we are able to discuss here. Instead, we explore a representative sample of some of the different technologies available and how they may be used, from computers used in a laboratory setting, to classroom response systems and computer tablet use in the classroom. In this exploration we also investigate the impact the technology use has on student learning and instructor effectiveness.

However, “effectiveness” in this context is not easy to define, and less easy to quantify. The assessment of some of the most obvious techniques for increasing student learning illustrate this difficulty: for example, while there are many analyses that show that something as simple as homework (not online!) facilitates student learning (e.g., [1, 4]), there are others that suggest that much of the statistical analysis presented in these is more ambiguous than we might expect [8]. However, although different studies can, and do, illustrate that the use of technology or other pedagogical techniques can improve student learning—with varying degrees of statistical validity or strength of argument—their real power lies in the replication of results and the accumulated weight of the research record.

A specific example of a research area in which there is now an accumulation of research that is clear and persuasive is the research on the impact of student engagement and collaborative work on student learning. Here the evidence is already clear, with ever–increasing support: student engagement with the material being learned and students’ cooperative work with their peers are fundamental to students’ learning of mathematics [5]. And this is great news: these are not things that are unique to any choice of pedagogy or course structure. They are generally applicable to anything we do in our instructional efforts. Thus, the question of effectiveness of a type of technology for the mathematics learner may be the wrong one: instead, we should be asking how it may be used to promote students’ engagement with the material and with each other, and this is one of the things echoed in the articles in this special issue. In this context, the NCTM’s statements endorsing the thoughtful use of calculators [6] and graphing calculators [7] because they may enhance student learning and understanding of mathematical concepts [2, 3], which are based on a research record that does have significant replication and weight, appear readily applicable to other technology.

For all of these reasons we firmly believe that technology can enhance our teaching and our students’ learning, even as we believe that, in any form, it will never be a panacea or silver bullet that creates a perfect environment for learning. As such, there will be studies considering the impact of technology that do not provide concrete evidence of its effectiveness, but this does not mean that it is not effective, and there will be many more studies that indicate that it is effective and show how we may use it effectively. The work we present here includes articles that explore new technology or new techniques, that consider effective use of established tools, and which add data to the evaluation of the improvement of learning. In short, they explore the goals we have set forth for the issue, and we hope they inspire readers to think about how technology may enhance student learning, and to consider how it may be appropriate in their own classrooms.

The articles that follow span a wide range, from student work to assessment, and from there to instruction in a range of formats. Sullivan and Melvin’s article, “Enhancing Student Writing and Computer Programming with LATEX and MATLAB in Multivariable Calculus,” directly considers issues of student learning through the use of typesetting and visualization technology. Lunsford and Pendergrass discuss how the use of an assessment tool (online homework) may be formative, promoting student learning, in their article “Making Online Homework Work,” and Callahan investigates the learning that may be measured through the use of such homework in his article “Assessing Online Homework in First-Semester Calculus.” Online homework serves as a platform to implement gamification to promote student engagement and learning in Goehle and Wagaman’s article “The Impact of Gamification in Web Based Homework,” and as a vehicle for collecting, promoting and assessing student work in Engelke, Karakok, and Wangberg’s “Engaging Students in the Classroom with WeBWorK Class.”

The use of online video to promote and assess student learning is explored in Shroeder and Dorn’s article “Enabling and Integrating Online Formative Assessment in a Flipped Calculus Class.” We consider technology for instruction in Latulippe’s article “Clickers, iPad, and Lecture Capture in One Semester: My Teaching Transformation,” and then conclude with an investigation of an issue that looms large at many institutions, that of MOOCs and large online courses, with “Using a MOOC Format for a Precalculus Course,” by Townsley.

In aggregate, these articles span an impressive range of technology and use-cases, affording insight on how they work and on the issues that we need to consider when using them. We hope you enjoy reading them all as much as we did in compiling them for this issue.

Additional information

Notes on contributors

P. Gavin LaRose

P. Gavin LaRose is a Lecturer IV and instructional technology program manager in the Department of Mathematics at the University of Michigan. He received a B.A. from Grinnell College, and M.S. and Ph.D. in Applied Mathematics from Northwestern University. He is involved in many aspects of the department’s undergraduate curriculum, from its new instructor training program to instruction and course (re)development. As instructional technology progam manager he develops and maintains homework, tutorial, and database systems that support the department’s undergraduate program. He is the 2012 recipient of the Michigan MAA Section’s Award for Distinguished Teaching of College of University Mathematics, and in 2014 received the MAA’s Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics. E-mail: [email protected]

Robert Talbert

Robert Talbert is an Associate Professor in the Mathematics Department at Grand Valley State University in Allendale, Michigan USA. He holds a B.S. degree in Mathematics from Tennessee Technological University and M.S. and Ph.D. degrees in Mathematics from Vanderbilt University. His scholarly interests lie in the scholarship of teaching and learning, especially at the intersection of mathematics, teaching, and technology. He is on Twitter at @RobertTalbert and writes on his blog (rtalbert.org/blog), and for re:Learning, a blog for the Chronicle of Higher Education. He lives with his wife and three young children in Allendale, Michigan. E-mail: [email protected]