What Counts as Active Learning?

by Justin Skycak on

True active learning requires every individual student to be actively engaged on every piece of the material to be learned.

This post is part of the book The Math Academy Way: Using the Power of Science to Supercharge Student Learning (Working Draft, Jan 2024). Suggested citation: Skycak, J., advised by Roberts, J. (2024). What Counts as Active Learning?. In The Math Academy Way: Using the Power of Science to Supercharge Student Learning (Working Draft, Jan 2024). https://justinmath.com/what-counts-as-active-learning/

It is a common misconception that the fastest way to learn math is by watching videos, attending lectures, reading books, or re-reading notes.

This is false.

As hundreds of studies have shown, passively consuming educational content leads to significantly worse educational outcomes than active learning, where students are actively performing learning exercises (Freeman et al., 2014).

In a passive learning scenario like watching a video, students may believe they are effectively learning if they can understand the video and follow along. However, following along and understanding the video’s contents isn’t learning, even if students claim that it is.

Learning is a positive change in long-term memory. In order for students to have learned something, they need to be able to consistently reproduce that information and use it to solve problems. None of these things happen when students watch a video, even if they understand it perfectly. The same reasoning applies to attending lectures, reading books, re-reading notes, and all other passive learning techniques.

The superiority of active learning is so robust across subjects and experimental methodologies that a highly-cited meta-analysis states, verbatim (Freeman et al., 2014):

  • "...[C]alls to increase the number of students receiving STEM degrees could be answered, at least in part, by abandoning traditional lecturing in favor of active learning.
    Given our results, it is reasonable to raise concerns about the continued use of traditional lecturing as a control in future experiments."

Like lecturing, re-reading does not count as active learning either. As Brown, Roediger, & McDaniel (2014, pp.10) describe:

  • "The finding that rereading textbooks is often labor in vain ought to send a chill up the spines of educators and learners, because it's the number one study strategy of most people -- including more than 80 percent of college students in some surveys -- and is central in what we tell ourselves to do during the hours we dedicate to learning.

    Rereading has three strikes against it. It is time consuming. It doesn't result in durable memory. And it often involves a kind of unwitting self-deception, as growing familiarity with the text comes to feel like mastery of the content. The hours immersed in rereading can seem like due diligence, but the amount of study time is no measure of mastery."

What Counts as Active Learning?

It’s important to realize that true active learning means every individual student is engaged in activity, not just the class as a whole.

For instance, although a class-wide discussion might seem like active learning on the surface, it does not immediately follow that each student is active. Often, it is only a proportionally small number of enthusiastic, vocal students who participate in all parts of the discussion and can be considered truly active. Even if the instructor cold-calls on students who have not been participating, most students will only pay attention enough that they won’t look foolish or be embarrassed if called upon.

Moreover, true active learning requires every individual student to be actively engaged on every piece of material to be learned. Divide-and-conquer group projects do not count as fully active learning because each student is only actively learning the material that corresponds to their individual responsibility in the division of labor. The rest of the project, they observe only passively, if at all.

To get a clear, concrete picture of what active learning entails and why it is so beneficial, it’s helpful to go through a case study in what is perhaps the most familiar setting for active learning: learning a new sport.

Suppose that you want to learn how to play tennis. You go to your local tennis club, where there is a coach who used to play tennis professionally. They offer personal lessons for a pricey $100/hour, but you really want to learn from the best, as efficiently as possible, so you fork over the money for a lesson the following week.

The next week, you show up for your lesson. The coach greets you and begins the hour-long session. It proceeds as follows:

  • [5 minutes] Coach talks about the beauty of tennis and why it's a great sport to learn.

    [5 minutes] Coach demonstrates a tennis stance and explains the specific components of the stance: bent knees, forward lean, racket in front of you, etc.

    [5 minutes] Coach demonstrates the ideal place to stand when receiving a volley: near the baseline, in the middle of the court, so that you're back far enough that your opponent can't hit the ball behind you, but you're close enough to the net to launch forward towards any shorter volleys.

    [10 minutes] Coach demonstrates a forehand swing, explains how the force should come from the legs and the twisting of the body (rather than the arm) and emphasizes the importance of "follow through" on the swing.

    [20 minutes] Coach demonstrates a backhand swing, breaks down the components, and shares stories about historic moments in tennis when a player had no time to position themself for a forehand and therefore had to rely on their backhand to win the game. Coach demonstrates a one-arm backhand, an advanced move that looks particularly cool.

    [15 minutes] Coach demonstrates serving and shows off some lightning-fast, precisely targeted serves that seem impossible to return. Again, these are advanced moves that look really cool.

When the session ends, the coach asks if you want to schedule another session the following week.

What do you do? Are you a happy customer? Do you want to schedule another session?

Heck no!

The coach just waxed philosophical and showed you moves the whole time. You didn’t actually learn anything. You might as well have just watched tennis on TV. You signed up for a tennis lesson to become a better tennis player – not to watch the coach hit the ball. You just wasted $100 on a complete waste of time and you want your money back.

Of course, this situation is unlikely to occur in real life athletic training because coaches know that continued employment depends on their ability to make students learn. They are held accountable for improving the performance of their students. They need to get real, demonstrable results, and get them fast – and if they can’t, then they’re going to lose a client and develop a reputation as a grifter who tricks people into paying a lot of money for a service that just doesn’t work.

In real life athletic training, a coach is going to have their students actively performing moves within the first couple minutes of the session. Sure, the coach might take a minute to demonstrate and break down a new move as the student watches, but for the next 10+ minutes after that, the student is going to be actively practicing that new move.

The coach will observe the student and point out areas where they need to correct their form to be more effective – and as the student gets better at the new move, they will experience a real, demonstrable improvement in their athletic performance. Maybe they’ll be able to hit the ball faster or more precisely. Maybe they’ll be able to return a tricky volley that originally kept going past them at the beginning of the session. Whatever the improvement, it will be tangible and reproducible.

It’s worth emphasizing: in a personal coaching session, when does the learning occur? It’s not when you pay the coach the money. It’s not when you watch the coach demonstrate a move. It’s when you actually start doing things that you weren’t able to do before. It’s when you attempt a move, the coach corrects your form, and you attempt the move again with better results. The learning is the incremental gain in your ability to perform a skill. If you’re not getting those gains, you’re not learning.

The same reasoning applies if you’re getting a lesson on piano or guitar. You’re not just absorbing information – you’re developing skills. Mathematics, too, is skill-based. Learning how to solve a new type of equation is totally different from, say, learning some new history about the life of Napoleon. At the core, the keys to effective training in mathematics are the same as the keys to effective training in athletics or music.

Why are People Still Confused About This?

Why do misconceptions about active and passive learning persist, despite clear intuition and decisive evidence supporting active learning?

Several reasons are obvious:

  1. Passive learning is more convenient for students and teachers alike. Teachers don't have to spend time and effort implementing learning activities, and students don't have to spend time and effort engaging those activities. Most teachers are happy to lecture about the beautiful intricacies of their field of study and believe that their students are learning, and most students are happy to lean back, relax, pay half attention (if that), and believe that they are learning. (In general, it is always tempting to believe that which is most convenient.)
  2. It's easy to mistakenly believe that you have learned a concept well enough to reason and solve problems when you are not actually made to attempt those things. (For the same reason, many people mistakenly believe that they can outrun a bear.)
  3. Some teachers resist active learning methods like cold-calling out of fear that it will make students uncomfortable -- even though research has shown that cold-calling not only heightens engagement but also increases voluntary participation and comfort over time (Dallimore, Hertenstein, & Platt, 2013).

A fourth, less-obvious reason was discovered by a study (Deslauriers et al., 2019) on Harvard physics classes, which not only measured educational outcomes in active versus passive learning settings, but also measured students’ perceptions of their learning. As quoted in the study:

  • "Compared with students in traditional lectures, students in active classes perceived that they learned less, while in reality they learned more.

    Students rated the quality of instruction in passive lectures more highly, and they expressed a preference to have 'all of their physics classes taught this way,' even though their scores on independent tests of learning were lower than those in actively taught classrooms.
    When students experienced confusion and increased cognitive effort associated with active learning, they perceived this disfluency as a signal of poor learning, while in fact the opposite is true."

In other words, active learning produced more learning by increasing cognitive activation, but students mistakenly interpreted that extra cognitive effort as an indication that they were not learning as well, when in fact the opposite is true. Active learning creates a desirable difficulty that makes class feel more challenging but improves learning. Passive learning, on the other hand, promotes an illusion of competence in which students (and their teachers) overestimate their knowledge because they are not made to exercise it.

That said, it’s dubious whether students and teachers – at their core – truly believe these misconceptions, given that their behavior quickly changes to an active learning model of working through practice questions with direct and immediate feedback when they are held accountable for demonstrating learning, such as when preparing for a standardized test like an AP exam.

In a similar way, one might question whether students – at their core – actually dislike active learning. Tharayil et al. (2018) note that students’ perceptions of active learning have not been consistent across studies and are often positive:

  • "Although much of the published literature suggests that students often respond positively to active learning strategies (Arce 1994; Armbruster et al. 2009; Carlson and Winquist 2011; Hoffman 2001; Leckie 2001; Oakley et al. 2007; O'Brocta and Swigart 2013; Reddy 2000; Richardson and Birge 1995), there are counterbalancing studies which show mixed student responses (Bacon et al. 1999; Brent and Felder 2009; Goodwin et al. 1991; Hall et al. 2002; Kvam 2000; Rangachari 1991; Wilke 2003) or negative student responses (Lake 2001; Yadav et al. 2011)."

People often do not look forward to workouts, yet they don’t mind it once they actually begin exercising, and then they feel proud of their efforts afterwards. If active learning is similar to physical activity, then students may prefer passive to active learning simply because it’s easier (a typical human behavior), but they may feel much more engaged during active learning (whereas passive learning is pretty boring for students), and they may feel better about themselves after doing actual work and knowing that they made real progress.


Brown, P. C., Roediger III, H. L., & McDaniel, M. A. (2014). Make it stick: The science of successful learning. Harvard University Press.

Dallimore, E. J., Hertenstein, J. H., & Platt, M. B. (2013). Impact of cold-calling on student voluntary participation. Journal of Management Education, 37(3), 305-341.

Deslauriers, L., McCarty, L. S., Miller, K., Callaghan, K., & Kestin, G. (2019). Measuring actual learning versus feeling of learning in response to being actively engaged in the classroom. Proceedings of the National Academy of Sciences, 116(39), 19251-19257.

Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), 8410-8415.

Tharayil, S., Borrego, M., Prince, M., Nguyen, K. A., Shekhar, P., Finelli, C. J., & Waters, C. (2018). Strategies to mitigate student resistance to active learning. International Journal of STEM Education, 5, 1-16.

This post is part of the book The Math Academy Way: Using the Power of Science to Supercharge Student Learning (Working Draft, Jan 2024). Suggested citation: Skycak, J., advised by Roberts, J. (2024). What Counts as Active Learning?. In The Math Academy Way: Using the Power of Science to Supercharge Student Learning (Working Draft, Jan 2024). https://justinmath.com/what-counts-as-active-learning/