In this paper, we present brief summaries of research literature on topics related to the teaching and learning mathematics and mathematics education online. We also describe the process the Task Force utilized to conduct the summary of the selected research. We agreed with the above cited authors that conducting a review of all of the literature in online education is daunting, but we initially felt that focusing on topics related to mathematics teacher education online might help “downsize” the task as earlier reviews done by members of the Task Force found the research to be somewhat sparse. As we began conducting our initial searches, we noted that research in online mathematics education is still limited, but for online education overall, there is an expanding literature base. We begin the paper with a description of our “sifting” and review process and then share our summary.

Where and how to start?

We began our selection of topics with the Task Force brainstorming what we believed to be important issues relative to mathematics teacher education online such as doing mathematics online, teaching mathematics vs teaching mathematics methods (modeling best practices of face to-face mathematics teaching in online environments), asynchronous teaching and learning, etc. Individuals chose topic areas closest to their own current work and began their review.

The review process took on both a traditional “look backward” approach of searching the mathematics education research literature databases given specific key words as well as a “forward-looking” approach of citation tracing. Citation tracing is a method of measuring the impact of research studies by analyzing the subsequent citations of the research in terms of number, the authors who have cited the particular research, and the topics represented. We then summarized the research that was connected to a selected seminal work for a given topic. This forward-looking trace based on a seminal piece of work we were familiar with, allowed us to find online mathematics teacher education research in sources that we might not normally consider.

A Task Force member selected a seminal work relative to their chosen topic of interest. An article could be thought of as seminal for one of several reasons, such as a study that changed how we think about a topic, provided a new synthesis of ideas, highlighted a new research method, or introduced a new theory that is gaining heavy scholarly interest. The seminal works generated more thought and work in the research area, growing the research in a variety of ways that can be analyzed to show and describe the impact of the seminal work. We also considered the dates of the subsequent citations, to assess the impact or influence of ideas of the seminal article, working from the assumption that a seminal piece would have some current citations.

We examined the subsequent citations of the seminal works and recorded descriptive information, including title, author, date of publication, abstract, etc. We then determined the articles that were relevant to our focus on the teaching of mathematics or mathematics methods online. For example, some citations included references with other foci such as nursing or business, which were excluded. We focused on peer-reviewed work published in English (or translated into English when possible), excluding dissertations and theses. From the “filtered” list of citations, we summarized the articles, highlighting major ideas from the collective works, focusing on the question of “so what do we know now that can help us understand how to teach mathematics teacher education at a distance?”

Summary topics?

Since we are posting this document online, we see it as a “living” document that can be updated overtime, adding additional summaries as they are completed. In our initial posting, we share our summaries on the following topics: how the AMTE Standards for Preparing Teachers of Mathematics emerge in research on online mathematics teacher education, grappling with what it means to do or learn mathematics online, and asynchronous teaching and learning.