Teaching toward mastery

I’ve been inspired by a recent series of education-related talks and papers regarding the disconnect between modern classrooms and achieving subject mastery. The demands placed on today’s college graduates include a higher degree of creativity, breadth, and collaboration. To prepare students for the future, their classroom experience must evolve away from the enormous and impersonal lecture hall. Team-based, project-centered learning is an excellent model but it doesn’t go all the way toward teaching subject mastery. I’ve given this some thought recently, and have some ideas on how to realign the classroom experience to accomplish mastery. From Sir Ken Robinson, Jeri Ellsworth, and Dr. Tae, the following three videos kick-started my thought process:

In general, teachers know what they expect their students to be able to do at the end of a course. Some are good at articulating this to the students by setting and communicating their “intended learning outcomes.” The difficult step is teaching the course in a way that actually achieves these goals. It is one thing to set the bar, it is quite another to jump over it. One difficulty in reaching these goals is in the popular assumption that telling someone how to solve a problem is sufficient for them to know how to solve the same problem later in the future. Even worse, we (teachers) go one step further and assume that telling students how to solve a new problem is sufficient for them to know how to solve a different new problem that synthesizes new ideas with old ones.

Why do we think this works?

This approach has worked in the past, especially for the first two thirds of the 20th century where many skills were mechanical in nature and could be taught with a “watch one, do one, teach one” method. Mechanical tasks are easily extended from a few basic steps into more complicated processes. Unfortunately for today’s students, many careers that rely on these skills have been outsourced overseas. What is left for college graduates are careers that require creative thinking and analytical problem solving skills. Neither of these abilities are taught in lectures, nor can they be taught by telling.

A solution

Creating active learning environments and providing students with opportunities to solve real-world problems can better prepare them for future demands. These ideas are supported by recent education research and have been implemented with success in many disciplines throughout the country. In introductory physics, the results of these revisions can be quantified using tools such as the Force Concept Inventory (FCI) or the Force and Motion Concept Evaluation (FMCE). These tests measure gain; the improvement in each student’s score from a pre- to a post-test, calculated as follows:


Many studies have shown an improvement in FCI/FMCE gain with an increase in active-learning activities and other approaches that emphasize concept understanding along with quantitative accuracy.

The rest of the story

While concept gain is better in active learning environments, the level of mastery still has room for improvement. Gains of 0.60-0.70 (60-70%) are common and a vast improvement over 20-30% shown in traditional lecture classrooms. However, to reach mastery requires a different level of exposure and a different level of involvement from the students.

This is where Dr. Tae’s approach comes in. The video above presents his explanation of why school should be more like skateboarding. In learning a skateboard trick, failure is to be expected for at least the first dozen attempts. Learning from failure is the essence of mastery. This is the disconnect: even struggling students are given only a few opportunities to fail in a typical classroom. Now, I should be clear that “fail” means to experience a situation where the first attempt is not successful. Some may argue that every homework problem is an opportunity to fail. I disagree, students have substantial support from peers, profs, and other resources to ensure that before they even start solving a problem, they know how to do it. This approach can never lead to mastery simply because there are no mistakes to learn from.

The inspiration for a new approach came from the mutual realization that my wife and I had during an 8-hour drive to our Christmas destination. We realized that even ten years out of college, we still remember the answers to exam questions that we got wrong. This is important from a retention standpoint, but it also points to a serious amount of learning. We could probably answer some of the same questions correctly again, but we’ve certainly forgotten some of what we once knew. What is remarkable is that we actually learned how to solve a problem by getting it wrong in a high-pressure situation. The learning happened because we got it wrong, we didn’t like that feeling, and we learned how to do it right. Somehow, that part of our brains is still hardwired correctly ten years later.

Some specific examples: I will never be able to forget the formula for the airy disk diffraction angle because it was something I failed to answer correctly in my Ph.D. prelim exam. I will also always remember how to explain circular polarization in my waves and optics class… because I failed at that the first time I tried!

Adding failure to the classroom

Now for the counter-intuitive part. We’re so used to helping our students succeed that, like new parents, new teachers often prevent failure and thereby prevent mastery. So how do we add failure, and what is the right amount? It would be bad to add so much failure that students lose motivation, and there is obviously a balance between motivation and failure tolerance. The same students that give up after one try at a physics problem, spend hours mastering the next level of the latest video game. Like Dr. Tae, many will try a skateboard trick 58 times in order to land it even once. The challenge is that the old fashioned motivators—like grades and deadlines—don’t instill a high failure tolerance. What does create failure tolerance is letting students see their abilities and inabilities in an honest way. Everyone wants to avoid failure and move toward mastery, what has to be overcome is the fear of failure.

Fear of failure is more dangerous than actual failure

This is the essence of a new approach. Rather than quantifying (i.e. grading) based on failure, we need to grade based on fear of failure, or courage and perseverance in the face of potential failure. Ideally this approach can be integrated with a system that rewards true mastery and provides opportunities for active learning and failure.

My crude vision for how to integrate these ideas into a active-learning course includes the following:

  • a specified set of mastery problems, ~50 in total, that encompass the intended learning outcomes. The mastery problems should be chosen by completing the statement “by the end of this course you should be able to…”
  • a daily “quiz” that consist of:
    • 1 or 2 problems taken from the mastery problems
    • any exam problems from the past 3 days that the student has not yet correctly answered. This repetition provides the opportunity for mastery, but prevents a huge backlog of work if mastery isn’t achieved. Maybe after 3 days, the missed questions become homework problems? (I’m still working on these details).
    • The quizes will not be returned, instead students will be able to view their solution during office hours with me, and ask me questions. They can also ask each other questions at any time, but they will do so with mutual memory of the question(s) because they will not have copies of the question(s). This will require a higher level of attentiveness during and after each quiz.
    • The quiz is an attempt at a “trick”. Fail at a trick and you fall down. Each time you get closer to landing it, you’ve learned more of the process. Forget a sign in your answer, and you better remember it next time or you’ll “fall down”. It’s important that failing a quiz isn’t something to fear. The quiz grade isn’t recorded, the quiz is only practice for the midterm and final.
  • 6 or 7 in-class projects for groups of 3 students; project timeline is half-semester
    • each week 1 student from each project rotates to a new project, the other two remain on the same project as the previous week. This gives everyone a taste of each project, but maintains continuity. Additionally, each student is accountable for each project, so peer instruction gets them up to speed after each rotation.
    • After the first half-semester, groups are assigned, and each group chooses one project for the remainder of the semester. This is their “final project”. Projects are vetted by the instructor, but otherwise up to the group.
  • Class time is used for
    • micro-lectures (short lessons on specific topics)
    • group discussion of project elements in the group-meeting style
    • progress presentations by each project
    • group-teach: one project team presents a topic they recently learned for their project
  • Grades are determined by:
    • Project progress and particpation
    • Quiz questions answered (credit is given for passed questions, regardless of the number of attempts).
    • Midterm and Final exams (questions are taken directly from the mastery problems or lightly modified mastery problems).
    • Final project (progress, presentation, teamwork, and participation).

There is obviously a lot more to figure out but I would be happy to hear feedback on these ideas. In particular if you do anything similar, let me know how it went (good or bad). I’m sure similar ideas have been presented, so if there are better names for these ideas, I’d love to find out who else is working on similar ideas. I’m hoping to tie this together by Fall 2011 for my electronics class. There will probably be 12-15 students, sophomores through seniors, and not necessarily physics majors. I welcome your thoughts, and thanks for reading about these early ideas.


3 thoughts on “Teaching toward mastery

  1. Love the ideas here! But, how would this scale up to a class of 30, 50, or larger? Especially getting students to come into office hours?

    • A large course is definitely something that would take some work. Of course, the mastery problems would be the same, and the quiz/exam setup could be too. Obviously projects get more involved and would require additional bodies in the classroom/lab (TAs etc). You are right that office hours definitely don’t scale to larger classes.

      One option in a large class is to invoke peer-instruction and appoint students as “problem experts” for problems they have solved correctly. This would have to be done carefully to respect privacy but also to distribute the work, otherwise the top few students might be bombarded by requests for help (although, it may already be that way in regular classes). Serving as a problem expert could have a positive impact on their grade sort of like the service component of the tenure process.

      Thanks for your support, I’m happy to have some folks out there to bounce ideas with.

  2. Pingback: The Educational Benefit of Ugly Fonts? « The Daily Photon

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