What Educators Can Learn from the Fact that I Almost Failed Calculus 24 Years Ago

I’ve always enjoyed learning new things. There is little that I enjoy more than discovering some new idea or possibility. This is not to suggest that I was a skilled learner. In fact, my obsession with new ideas was what led me to sometimes struggle in school. As a student in high school, I was far more interested in experiencing a new idea than doing the hard work of mastering a concept enough that I could recall and use it.

This served me well in classes where my interest in comparing and contrasting ideas was rewarded. I was generally curious enough to that my emotional connection with new ideas embedded them in my memory, but practicing was another thing. It was not until I took calculus as a college freshman that I discovered the limitation of my approach. I would learn about a new concept in the calculus class, be excited about it, and want to talk about what was next. Of course, that isn’t how math works. Once you are introduced to a new concept, you need to practice it, and I didn’t do practice…not that much.

This limitation with my approach to learning didn’t show up as much in a history or English courses because I could always cram for the tests. You can’t cram for calculus tests, at least most of us can’t do that with effectiveness. You might be able to do so with the first unit or two, but as concept builds upon concept, you are quickly lost, and your grade reflects that by the second test in the class.

Much of my problem had to do with the fact that I didn’t understand the difference between mass and distributed practice. Mass practice is also known as cramming. You cram in all the studying for a big event into a single marathon study session, often the night or two before the big assessment. Deceptively, it actually works for some of us in the short-term. The problem is that mass practice has very poor results when we look at long-term retention and recall. So, cramming for the first test will do little to prepare me for the next, and almost nothing to help me recall and use that knowledge six months or two years after the class ends. Cramming causes mental fatigue and decreases the efficiency of studying. The result is possible evidence of a gain in the short-term, but abysmal long-term results.

Distributed practice is when there is space between studying, rehearsing and/or reviewing a concept or skill. It requires setting aside time to review and practice concepts over an extended period. The body of research is hard to deny. Distributed practice results in better retention and recall.  If you want to remember something from a class four or five years after taking it, then that requires reviewing and/or using what you learned over time, with breaks between reviewing sessions. As you extend the time between the rehearsals (to a reasonable extent), this increases your learning.

The research is clear. For most purposes, distributed practice rules. The one exception that I’ve seen is when we need to prepare people to function under fatigue. That is where a coach might use mass practice to get players fatigued and then have to perform…simulating an end of game performance. Apart from that, distributed practice gets at the long-term results that most of us want from our learning.

This contract of mass versus distributed practice is a simple concept, one that most education students had to at least read about at some point. However, perhaps that was when many of us were trying to get by on mass practice strategies in our courses. Perhaps that explains why we persist with the following.


  • One-day training workshops with no intentional plan for ongoing practice, rehearsal and review.
  • Massive investments in attending conferences and webinars, sometimes taking voracious notes; and then forgetting about it all, thinking perhaps the exposure was enough for us to be influenced or transformed by what took place.
  • Course designs that introduce ideas and then move on, never using, applying or referencing them again.
  • Recognizing people for diplomas earned years or decades ago with little evidence that any of that prior work reflects current capabilities;
  • Assessment plans that seem to reward mass practice, failing to build in formative assessment that serve to promote distributed practice.
  • Emerging competency-based programs that ignore these realities and provide credentials on the basis of a single performance or product that may never be reviewed again.
  • Some Universities cutting courses lengths down to as short as 2-5 weeks, but arguing that they are “covering” the same amount of content, when there are not enough hours in the day for a learner to engage in distributed practice with all the key concepts during such a short time.
  • People (myself included) getting addicted to scanning and skimming mass amounts of information in the web; but failing to take the time to practice with these ideas in a way that they will stick and be of use in six months or longer.

These are real problems. We invest massive time, money and resources on learning experiences that have little chance of benefitting us down the road. They fail to be high-impact experiences. At the same time, we have wonderfully promising practice that seem to align quite well with the benefits of distributed practice.

  • Online communities of practice where people learn new ideas, put them into practice in their life and work, and continue to reflect and review with the group over months, years, even decades.
  • The slow learning movement, which is pushing back against the unrealistic demands of immediate results from contemporary society.
  • Project-based learning that invites a person to grapple with a narrow topic over an extended period, representing a form of natural and authentic distributed practice.
  • Personal learning networks that invite people to remain in perpetual conversation, application and reflection about what we are learning.
  • Learning In Depth projects that have students focus upon a narrow topic for years.
  • Competency-based approaches that require performance over extended time, perhaps using gamification concepts like levels, macro-badges, and the scaffolding of learning (new knowledge building upon prior knowledge…which also happens to involve a review of the prior knowledge).
  • Game-based learning models that are designed with this idea of distributed practice in mind. The learning happens within the game, with ample spaced practice incorporate right into the experience.
  • Blended learning models that can be designed to create space between practice.
  • Emerging learning analytic tools that allow learners and teachers to track progress over months and years.
  • Adaptive learning software that monitors learner progress and helps design personalized lessons that incorporate ample opportunities for distributed practice.
  • Training for critical knowledge and skills that requires renewal and re-certification processes, calling for long-term retention and recall.
  • Fields like heutagogy that emphasize the development as a self-directed learner who discovers and leverages successful strategies and heuristics for lifelong learning, including understanding things like distributed versus mass practice.
  • Conferences and webinars that are extended through social media, remote collaborative projects, and other forms of ongoing connections. These all represent authentic forms of distributed practice with ideas that might first be learned about at the initial event.

Distributed PracticeI almost failed Calculus in college before I discovered the importance of distributed practice over mass practice. Despite some wonderful teachers along the way, I made it through thirteen years of an educational system without discovering this truth. The exciting part is that we have an opportunity to make experiences like mine a rarity. We do it by embracing some of these emerging practices that help us leverage the power of distributed practice in a digital age.

Posted in assessment, blog, education

About Bernard Bull

Dr. Bernard Bull is an author, professor of education, Vice Provost of Curriculum and Academic Innovation, podcast host, and blogger. Some of his books include Missional Moonshots: Insights and Inspiration for Educational Innovation, What Really Matters: Ten Critical Issues in Contemporary Education, The Pedagogy of Faith (editor), Adventures in Self-Directed Learning, and Digitized: Spiritual Implications of Technology. He is passionate about futures in education; educational innovation; and social entrepreneurship.

4 Replies to “What Educators Can Learn from the Fact that I Almost Failed Calculus 24 Years Ago”

  1. David Black

    I would be interested in hearing your thoughts about how to address one of the cultural elements of secondary and post-secondary education — the Final — from a mass vs. distributed practice perspective. It seems as if this is set up for the mass practice world.

    • Bernard Bull Post author

      There is nothing that I’ve seen to indicate that a final can’t work in promoting long-term retention and recall, granted that it is supported with solid instructional designer throughout a course. This would seem to suggest that a cumulative final is better; but adding a number of small ungraded quizzes that are gradually larger (also cumulative) throughout the class would increase long-term retention and recall. It would require students to return to the same knowledge multiple times over a course, thus engaging in more distributed practice. The same would be true for a final project. It would seem as if breaking the project down in a way that students have to review and revisit ideas in the project over an extended period of time (and to reflect and debrief what is done) would add more distributed practice with the content. I’m just thinking about the logical applications. There may be specific research to support or negate this.

  2. Julie Gaskey Faulkner

    Your post supports my argument that I’ve had for years with completely structured academic learning. Education should allow for authentic, relevant, personalized learning within the confines of the lesson. (Especially higher level learners in an academic setting)

    I agree with your statement, “We invest massive time, money and resources on learning experiences that have little chance of benefitting us down the road. They fail to be high-impact experiences.”

    As an educator, why would we NOT want our students to succeed in their education as it immediately impacts them? This nurturing of learning begins in my kindergarten classroom. However, as students progress, often their round peg must fit perfectly in the hole given to them by their teacher….either on a test, by a rubric, or by made-up guidelines. That’s not learning. That’s certainly not teaching.

    I enjoyed Calculus. Still do! Thinking and reasoning using the beautiful structure of mathematical modeling to solve real life problems. Problems: (Or learning opportunities) most of which involve unknown or difficult to measure quantities or functions that change with or depend on other variables that may be measurable.

    Is there a connection with Calculus and educators?
    Is this why teachers want everyone to fit into the round hole? Is it because the students’ learning outcomes would be difficult to measure? There would not be a simple test key to follow.
    Not everyone would have the same questions or problems in their classroom assignments.
    Is it because the variables are all different or the functions change? Did many teachers have to cram for Calculus too and miss the beauty of practicing and finding different ways to reach a conclusion?

    A teacher would have to use Calculus….the students’ learning and the answers might be dependent on the student, not just the teacher, and how they are using the information presented to them in a course and how it applies to their learning.

    So, what happened? And how can we get high level of authentic, relevant learning experiences back? Who needs to step up and demand more? Improved teaching from the educators? Absolutely.
    More learning from the students? Yes.
    Who goes first?

    Julie Faulkner

    • Bernard Bull Post author

      Thanks for the post, Julie. Reading my blog, you know that I share your interests in authentic learning, project-based learning, self-directed learning, etc. With that said, this post is really about distributed practice versus mass practice. There is ample research to support the effectiveness of highly structured lessons with clear outcomes, rubrics, and the like as being effective for long-term retention and recall. Some (but not all) of this research on distributed versus mass practice, for example, comes from military training, where there is need to have very clear desired outcomes that everyone must meet (sometimes as a matter of life and death). In terms of retention and recall research, I’ve seen few studies that looked at this in less structured environments, simply because it is hard to measure whether one retains something unless there is a clear idea of what is desired to be retained and recalled. So, whether highly structured and teacher-directed or more student-directed, retention and recall can take place. In either environment, one is likely to retain more (in the long-term) if there is space between practicing with the knowledge rather than cramming it all in a marathon study session. So, perhaps it is desired that every student know how to tie her shoes. Mass practice would be sitting her down for a 5-hour marathon session, practicing over and over for 5 hours. The research would indicate that such a student would not retain the skill in the long-term as well as 10 distributed 30-minute sessions.

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