{"id":939,"date":"2015-09-10T00:01:39","date_gmt":"2015-09-10T04:01:39","guid":{"rendered":"http:\/\/blogs.ams.org\/matheducation\/?p=939"},"modified":"2015-12-28T07:17:04","modified_gmt":"2015-12-28T12:17:04","slug":"active-learning-in-mathematics-part-i-the-challenge-of-defining-active-learning","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/matheducation\/2015\/09\/10\/active-learning-in-mathematics-part-i-the-challenge-of-defining-active-learning\/","title":{"rendered":"Active Learning in Mathematics, Part I: The Challenge of Defining Active Learning"},"content":{"rendered":"

By Benjamin Braun, Editor-in-Chief<\/a>, University of Kentucky; Priscilla Bremser, Contributing Editor<\/a>, Middlebury College; Art Duval, Contributing Editor<\/a>, University of Texas at El Paso; Elise Lockwood, Contributing Editor<\/a>, Oregon State University; and Diana White, Contributing Editor<\/a>, University of Colorado Denver.<\/span><\/i><\/p>\n

Editor\u2019s note: This is the first article in a series devoted to active learning in mathematics courses. \u00a0The other articles in the series can be found here<\/a>.<\/span><\/i><\/p>\n

\u201c…if the experiments analyzed here had been conducted as randomized controlled trials of medical interventions, they may have been stopped for benefit.”<\/span><\/p><\/blockquote>\n

So strong is the evidence supporting the positive effects of active learning techniques in postsecondary mathematics and science courses that Freeman, et.al, made the statement above in their 2014 Proceedings of the National Academy of Science (PNAS) article <\/span>Active learning increases student performance in science, engineering, and mathematics<\/span><\/a><\/em>. \u00a0Yet faculty adoption of active learning strategies has become a bottleneck in post-secondary mathematics teaching advancement. \u00a0Inspired by the aforementioned PNAS article, a landmark meta-analysis of 225 studies regarding the positive effects of active learning, we will devote a series of posts to the topic of active learning in mathematics courses. \u00a0<\/span><\/p>\n

An immediate challenge that arises when discussing active learning in mathematics is that the phrase \u201cactive learning\u201d is not well-defined. \u00a0Interpretations by mathematics faculty of this phrase range broadly, from completely unstructured small group work to the occasional use of student response systems (e.g., clicker) in large lectures. \u00a0In this article we discuss several descriptions from the literature, including what we will take as our working understanding throughout this series of posts, discuss important considerations in the adaptation of such methods, and highlight some important aspects of the PNAS article.<\/span><\/p>\n

What is Active Learning?<\/b><\/p>\n

The core tenet of active learning is that providing students with opportunities to actively engage with content during their classes leads to positive learning outcomes. \u00a0In mathematics, the phrases \u201cactive learning\u201d and \u201cinquiry-based learning\u201d (IBL) are closely related, though opinions vary regarding the extent to which they are related or overlap. \u00a0Here are some particularly insightful descriptions of active learning and IBL from the literature.<\/span><\/p>\n

Active learning is generally defined as any instructional method that engages students in the learning process. In short, active learning requires students to do meaningful learning activities and think about what they are doing. While this definition could include traditional activities such as homework, in practice active learning refers to activities that are introduced into the classroom. The core elements of active learning are student activity and engagement in the learning process. Active learning is often contrasted to the traditional lecture where students passively receive information from the instructor.
\n<\/span>— Does Active Learning Work? A Review of the Research, Michael Prince, J. Engr. Education, 93(3), 223-231, 2004<\/span><\/i><\/p>\n

In the context of mathematics, IBL approaches engage students in exploring mathematical problems, proposing and testing conjectures, developing proofs or solutions, and explaining their ideas. As students learn new concepts through argumentation, they also come to see mathematics as a creative human endeavor to which they can contribute. Consistent with current socio-constructivist views of learning, IBL methods emphasize individual knowledge construction supported by peer social interactions.
\n<\/span>— Assessing Long-Term Effects of Inquiry-Based Learning: A Case Study from College Mathematics, Marina Kogan & Sandra L. Laursen, Innov High Educ (2014) 39:183\u2013199<\/span><\/i><\/p>\n

A student-centered instructional approach places less emphasis on transmitting factual information from the instructor, and is consistent with the shift in models of learning from information acquisition (mid-1900s) to knowledge construction (late 1900s). This approach includes<\/span><\/p>\n