Active Learning

The effective teaching and learning of mathematics occurs through the alignment of evidence-based active learning teaching practices (ALPs) within the classroom with supports available outside the classroom, and an institutional climate that promotes increased mathematical understanding. ALPs come in many forms at K-16 levels and may go by other names such as cooperative learning, group think, etc. This broad range of active learning techniques are available for use in a wide variety of class sizes, each of them helping students to understand the material more deeply while not requiring more class time to implement.  Most importantly, there is an increase in retention of information and deep understanding when ALPs are utilized.


The information contained on this page is meant for the novice active learning user, hoping to give you a glimpse at how you can begin to incorporate active learning in your own classroom. The list of resources is in no way comprehensive; I have personally found these resources to be useful. If you would like to see something added, please don’t hesitate to send me a link. (


Here are the PowerPoint presentations for two of my recent presentations on active learning:

1)      Panel Session at the MAA Joint Meetings in Atlanta, GA: Panel #6 - Roadblocks for Implementing Active Learning Strategies in Calculus Courses

Faculty members who would like to begin implementing active learning strategies in their Calculus course(s) may become overwhelmed by apparent roadblocks, often quitting before going very far. Panelists will discuss roadblocks they have encountered through their own journey towards integrating active learning in calculus courses, as well as successful models for implementation. Ample time will be given for questions from the audience. [Link to Panel PPt]


2)      Workshop at the MAA Joint Meetings in Atlanta, GA: Implementing and Orchestrating Active Learning Strategies in Calculus

In this workshop, participants will engage in pedagogical discussions focused on developing practical strategies for incorporating active learning strategies (e.g. student presentation, inquiry-based learning activities, writing to learn, etc.) into their Calculus courses. The emphasis will be on using existing curricular materials (e.g. activities from Active Calculus (Boelking, Austin, Schlicker, 2015), classroom voting questions, concept tests, etc.) to support active learning. Active learning strategies are those that engage students in activities that promote analysis, synthesis and evaluation of course content. This workshop, intended for the novice user, will include small group discussions and interactive discussions with the organizers centered upon helping participants move beyond the initial difficulties tied to first time implementation of active learning strategies. [Link to Workshop PPt]


What the research says

There is a growing body of research supporting active learning in STEM fields; I believe that the most compelling evidence is given by Freeman et. al. (2014). This analysis found that “active learning leads to increases in exam performance that would raise average grades by half a letter….” and that “failure rates under traditional lecturing increases by 55% over the rates observed under active learning.” 


Setting the Stage for Success

There are a number of elements to contemplate as you consider incorporating active learning in your classroom – department culture and/or perspective, socio-cultural norms, and general classroom culture in your classroom. From the department or institutional perspective, are there institutional incentives on teaching excellence? What are the expectations? Is there a teaching and learning center on your campus? Look in your department, and beyond, to find colleagues to support your work. It is hard to take the first steps if you are unsure of how these pedagogical techniques are viewed in the world in which your work.


As you know, students always come to our classrooms with preconceived ideas and expectations. I have started beginning every semester with a discussion in each class about mindset and student expectations as well as professor expectations. There are several great resources for thinking about Mindset; my favorites are Dweck (2006) and Good (2016). I then talk about the Study Cycle around Week 3 of each class, after the first exam. See the LSU web site for interesting information about the Study Cycle ( I have found that each of these conversations help to build a positive environment within the classroom, one of mutual respect and growth.


Above all, remember that YOU get to set the tone for the class and the culture of cooperation that you are hoping that they develop. Be transparent about why you are using active learning; this will help to overcome student resistance. Give students a heads-up in the prior class about what you will be doing next time; many students do not like to be surprised, especially introverted or ELL students. Prior notification will give them time to mentally prepare themselves for class. Throughout their time with you, classroom participation norms will need to be reinforced by reminding students of your expectations for the way that they interact with each other and with the content. Soliciting feedback about specific activities throughout the semester is a great way for you to give students the opportunity to vent their concerns; it is important, though, to respond to that feedback with planned changes based upon student comments. You do not need to respond to every comment; but, it is important to make a plan moving the class forward and describing to students how you will address their needs. You will be amazed at how small changes in a class based upon student feedback can make the difference in compliance when you are transparent about working to meet student needs. This is especially helpful when asking students to work on active learning activities that lie outside of students’ comfort zone.


Being Materialistic!

When thinking about utilizing active learning practices, you do need to think about the structural set up on the class session from a materials standpoint – what do you give to students to get started on an activity in order to promote productive active learning? As much as possible, you want to use mathematically rich tasks in your class, especially if you are using groups. To deal with the variety of ability levels in your class, prepare enough problems or tasks so that no one will finish but everyone will get through (what you believe are) the most important pieces in the allotted time.


Making it Your Own

No one strategy is going to work the same for everyone. Learning to adapt strategies to your own personal style and student audience is the key to integrating active learning in the classroom. Of course, that is easier said than done! I recommend you first work through the mindset and community building ideas talked about in the sections above; it will give you a strong foundation. The next step is thinking about risk-taking.


The issue for many faculty comes when you realize that research shows that having students sitting quietly waiting for you to fill their heads with wisdom is no necessarily the best way for students to learn. Their first thought is, now what!?!? The answer is active learning strategies. Part of moving towards active learning is also moving away from lecturing by taking more risks as an instructor. Risks occur when you step into areas in which you are somewhat unsure, using techniques that you’ve never before tried. How do you develop a sense of risk-taking? How do you manage that sense of loss-of-control when there is so much talking and action occurring in the classroom that it seems you have lost all control? How do you manage the ebb and flow of a classroom that is seemingly out of control? And, is being less in control not necessarily a bad thing?


So, faculty need to learn how to release control of the classroom, gradually picking and choosing active learning strategies that will fit into their own teacher toolbox. This process will take time. Think of it as playing the long-game in teaching; doing small new things one at a time and continuing to grow semester by semester. The most difficult piece of this process is managing your own expectations and concerns. You do not have to get it completely right when trying something new! Try it. Get feedback. Figure out what you need to change. And, then, try it again. The key is to have an iterative process for change. Be strategic and collect activities that work for you.  


Some Resources

A partial list of active learning strategies that are available to classroom teachers are shown in the table; those shown here were chosen only to illustrate the variety of student groupings and communication means that are possible.


SELECTED ACTIVE LEARNING Practices – Research Results

Minute papers – a one minute response to a prompt

·   Increases recall of statistics knowledge (Das, 2010)

·   Increase conceptual understanding (Mansson, 2013; Nilson, 2010; Millis, 2012)

·   Gives students the opportunity to make connections between key ideas and allowed them to apply that knowledge to other scenarios, prompting students to ask questions and improved student writing. Anderson and Burns (2013) and Stead (2005)

Small-group discussions – discussion of problem solving or content questions to encourage peer interaction

·   Challenge students’ understanding of the material and helps them to better learn the material, and retain it longer, by requiring them to interact with both classmates and the material. (Ambrose, 2010; Cavanagh, 2011; Hamann, Pollock, Wilson, 2012; Millis, 2012; Prince, 2004)

Group learning – groups of students are given problems to solve

·   Improves conceptual understanding, creates more complex critical-thinking skills - varying group sizes is impactful (Cooper, MacGregor, Smith, Robinson, 2000)

Exploratory writing assignments – response to a writing prompt

·   Increases students’ conceptual understanding of key concepts and building on existing knowledge, when those assignments are aligned with learning outcomes. (Lumpkin, 2015)

·   Transforms the way students study and makes active critical thinking about subject matter part of each day’s homework. Bean (2011)


More Sample Active Learning Activities

Exit Tickets: Exit tickets are your opportunity to gather feedback from your students to either gauge their understanding of the day’s material or to determine how well students liked a particular class activity. Either way, being transparent about why you are requesting (and using!) feedback will help you to gain student buy-in. Remember to refer to student feedback during the next class so that students know you are listening. If you would like more information on different kinds of prompts to use for Exit Tickets (prompts that 1: provide formative assessment data, 2: stimulate student self-analysis, 3: focus on instructional strategies, and 3: are open communications to the teacher), see Marzano (2012). To get some informal (anonymous) feedback at the end of each class on the first day I asked students to give me three adjectives to describe me as a professor; in other words, what was their first impression of me? I then copied their responses into the WordSalad app and created a word cloud, making the most frequently used words larger. It gave me a wonderful picture of how my students viewed me after one class meeting! I repeated the activity at the end of the semester and was pleasantly surprised that many of the same adjectives were used.


Socrative: This is a (free) online polling web site. I use it because it is super easy to use and has an app for both teacher and student use. Quizzes can be created to be anonymous (for general feedback, Exit tickets, etc.) or students can be required to type in their ‘ID’, whatever you want that to be. Sadly, there is a limit on class size, so I had to pay the fee ($30) to get the Pro version in order to use it in my larger classes. A colleague and I have been sharing tips on using the program and have shared some feedback with the author’s in hopes of getting some refinements to the data in MS Excel format (currently NOT alphabetical and absentees are omitted instead of getting zeros).


Board work in groups: Building learning communities within each of my classes is an important personal goal, driving me to be innovative in my approach. Students come to my classes typically either having had a bad experience with math or hating math; I am very open about my desire to do everything within my power to help them not only pass my course while not insisting that they come to love the subject, but also for them to reach their own potential. In every one of my classes I separate students into groups during the first weeks of the semester, having students introduce themselves during the first few sessions so that they can learn a little bit more about each other. One activity that I use to bolster community spirit, while also increasing students’ engagement with the content for high-impact practice is to use what I call Pink Sheets, 2’x2’ Sticky Notes on the classroom walls. Students are randomly placed into groups for this activity and each group is given a problem to complete together while standing at the Pink Sheets. Once they are done their individual problem they are then required to go to another groups’ Pink Sheet to double check the work and give assistance. There has been an overwhelmingly positive response from students for this activity, even in my 55 seat classes. Recently, one student said, wow, Dr. G, I never thought that standing up and doing math would help me figure out what’s going on… Can we do Pink Sheets again? Overall, I have found that the learning communities that have been created within the classroom have extended to groups meeting outside of the classroom, a great extension of our work together. I have also found that getting students out of their seats is an opportunity to rejuvenate a class session. Having students present solutions alone can sometimes be very stressful for them; Pink Sheets are just one way to help address that issue.



Ambrose, S.A. (2010). How learning works: Seven research-based principles for smart teaching. San Francisco, CA: Jossey Bass.

Anderson, D., S. Burns. (March 2013). One-minute paper: Student perception of learning gains. College Student Journal, 47(1): 219.

Bean, J.C. (2011). Engaging ideas: The professor’s guide to integrating writing, critical thinking, and active learning in the classroom (2nd ed). San Francisco, CA: Jossey Bass.

Cavanagh, M. (2011). Students’ experiences of active engagement through learning activities in lectures. Active Learning in Higher Education 12(1): 23-33.

Conference Board of the Mathematical Sciences (CBMS). (7/15/2016). Active Learning in Post-Secondary Mathematics Education. Retrieved online on 1/3/2017 from

Cooper, J.L., J. MacGregor, K.A. Smith, P. Robinson. (2000). Implementing small-group instruction: Insights from successful practitioners. New Directions for Teaching and Learning, 81(1): 63-76.

Das, A. (2010). Econometric assessment of ‘one minute’ paper as a pedagogic tool. International Education Studies, 3(1): 17-22.

Dweck, Carol. (2006). Mindset: The new psychology of success. New York: Random House Publishers.

Freeman, et. al. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences of the United States of America, 222:23. Retrieved online on 1/3/2017 from

Good, C. (2016). 7 Things Growth Mindset is Not. The 180 Blog. Retrieved online on 1/3/2017 from

Hamann, K., P.H. Pollock, B.M. Wilson. (2012). Assessing student perceptions of the benefits of discussions in small-group, large-class, and online learning contexts. College Teaching, 60: 65-75.

Lumpkin, A., R.M. Achen, R.K. Dodd. (2012). Student perceptions of active learning. College Student Journal, 1: 121-133.

Mansson, D.H. (2013). Assessing student learning in intercultural communication: Implementation of three classroom assessment techniques. College Student Journal, 47: 343-351.

Marzano, R.J. (2012). Art and science of teaching / The many uses of exit slips. Educational leadership, 70(2): 80-81. Retrieved online on 1/3/2017 from

Millis, B.J. (2012). IDEA Paper No. 53: Active learning strategies in face-to-face courses. Manhattan, KS: The Idea Center. Retrieved online on 1/3/2017 from

Nilson, L.B. (2010). Teaching at its best: A research-based resource for college instructors. San Francisco, CA: Jossey Bass.

Prince, M. (2004). Does active learning work? A review of the research. Journal of Engineering Education, 93(3): 223-231. Retrieved online on 1/3/2017 from

Smith, C.V., and L. Cardaciotto. (2011). Is active learning like broccoli? Student perceptions of active learning in large lecture classes. Journal of the Scholarship of Teaching and Learning, 11(1): 53-61. Retrieved online on 1/3/2017 from

Stead, D.R. (2005). A review of the one-minute paper. Active Learning in Higher Education, 6(2): 113-131. Retrieved online on 1/3/2017 from,%20read,%202005.pdf

Yeager, D.S., and C.S. Dweck. (2012). Mindsets that Promote Resilience: When Students Believe that Personal Characteristics can be Developed. Educational Psychologist, 47(4): 203-314. Retrieved online on 1/3/2017 from