Information about "mastery-based" courses in mathematics?
November 21, 2016 11:55 AM   Subscribe

My department is interested in transitioning to a "mastery-based" precalculus class at the college level. The basic idea is that students would be allowed (somehow) to work at their own pace, and success in the class would be by demonstrating mastery of most of the material (80%?). Somehow. Does anyone have any experience with this sort of teaching, in any discipline?

I don't have a sense of what a "mastery-based" course would/should entail. It's maybe related to the "emporium"-style descriptions that were cool a couple years ago.

Have you taken a mastery-based course? How did it work, logistically?

Have you taught a mastery-based course? Did students have infinite time to complete the material, or only one semester? What happened in the classroom? Outside the classroom?

Can anyone point me to web resources? Syllabi? Descriptions? So far, I haven't had much luck finding anything useful.

Are we behind the times? Has current math pedagogy progressed beyond mastery-based and the new hotness is something else? Currently we're still mostly at the lecturing/quizzes/exams with the occasional worksheet level...
posted by leahwrenn to Education (8 answers total) 3 users marked this as a favorite
Does anyone have any experience with this sort of teaching, in any discipline?
Not directly, but it's a thing at the university where I work. As I understand it, the math department buys a product from a textbook company. (We use ALEKS. I don't know if there are other versions of the same thing.) The product is software that first administers a test of algebra and trigonometry. The test identifies areas of weakness. Students are then required to work on modules on each area of weakness. They meet in a classroom, and there is a teacher to help them, but they spend most of the time working through their modules and doing problems. When they get a certain number of problems right, they can move on to the next module, which corresponds to their next area of weakness. At the end of the semester, they take the placement test again and hopefully place out of pre-calculus. I think the idea is that the students who take this class have initial placement test scores that suggest that they should be able to complete all the necessary modules by the end of the semester. Students who score below a certain score on the initial placement test get a different remedial algebra class before they can take the mastery-based online one.

Some students really like this, and some students truly hate it. I haven't quite been able to figure out what determines whether a student will thrive or not in this style of class.
posted by ArbitraryAndCapricious at 12:20 PM on November 21, 2016 [1 favorite]


I teach a partially mastery-based course in middle school (English/History). Basically, I choose the concepts that students HAVE to master and I build my timeline in around those. Things like "writing an objective summary" and "supporting claims with evidence" - and I make it work by having students practice those skills with whatever content I'm teaching (usually History content).

For me, that means that the skills are repeated until mastered, but the content keeps moving on. For supporting claims with evidence, it may take us the whole year! But I give lots of opportunities to practice, and lots of repetition - so they may have 20 assignments in a month on that skill, but they're all a bit different and they're all pretty low-stakes.

Lots of reps, lots of variety.

But in Math, you don't have the same kind of freedom with content and the concepts build, so it's not practical to have a model like the one I use.

However, I know a few really good math teachers who do self-paced or mastery based learning. They are all high school teachers, but most of them teach Advanced Math and/or Calculus.

Stacy Roshan - high school AP Calculus teacher (YouTube, Blog)
The Algebros (website)
Zach Cresswell (blog post about how his classroom works)
Graham Johnson (blog, YouTube)
La Cucina Matematica (website - mostly aimed at 9th/10th grade math, but they have some GREAT ideas about how to get students engaging with math in a fun and authentic way)

I do personally know all of those people, and I know that they are always willing to talk about what they do in their classrooms. Most have contact info on their blogs, and most will respond via Twitter as well.

Other search terms that may help you:
Flipped Learning, Flipped Mastery, Mastery-based Learning

Good luck!
posted by guster4lovers at 12:20 PM on November 21, 2016 [2 favorites]

I have a colleague who does this (in Math at the college level). My understanding from talking to her is that there are some number of core concepts that students have to master by the end of their time in the course. They get as many chances during the term as they want to demonstrate mastery of those concepts (in a test setting, in her case, but you could just as easily imagine it being in some sort of project-based class). I can ask her more about the exact logistics of this, but I think it means that there are questions on every test that some students don't have to answer if they've already demonstrated mastery over the topics.

From my (albeit) limited understanding of this, it doesn't sound too different from what good faculty already do. I suppose the one exception is that students get to keep going back to things they missed and take another shot at demonstrating mastery of said topics. In principle, this makes a lot of sense - you shouldn't go on to the next topic until you've mastered the previous one. In reality, I'm not entirely sure how well this can be managed in a large classroom.

Their end-of-term evaluations and grades are based on how many concepts they demonstrated mastery over. Again, I don't think this is so different from what grades are based on in a traditional classroom.
posted by Betelgeuse at 12:28 PM on November 21, 2016

I TAed a biology course intended for freshmen that was based around this concept. There were many modules (10 I believe), each of which were based around certain readings in the textbook as well as a few hands-on exercises. The students were given time to read the material at their own pace, ask questions of TAs and the instructor. There were some discussion sessions, but fewer than for a regular course.

The core of the class was based around oral examinations for each module. For each of these exams, the TAs had to come up with questions which were then carefully calibrated across TAs and discussed. The questions were designed such that it would be very difficult for a student to just memorize the material and pass - you had to be able to explain the concept in different words, answer questions that required you to apply the concept in a different context, respond to further questions delving deeper. We used Bloom's Taxonomy as a guide. The students could retry the exam how many ever times they liked (though not on the same day and with a different TA).

There were some students who breezed through the modules, working well ahead of the average of the rest of the class. And there were some students who seemed to slack off, suddenly discovering that they had to pass 8 modules within 2 weeks. The saddest were those who made an effort to pass, but weren't able to achieve "mastery" and so fell behind the pace. Students were only given the semester to pass - if they did not pass all modules (plus the final exam and lab) - they failed the class. This happened to about 10 students in my 80 person class, so it was not exactly rare.
posted by peacheater at 12:50 PM on November 21, 2016

The University of Michigan math department's "gateway" test program might be interesting to you?: link, more.

These were just one part of the class, which also had traditional tests and exams.

One issue is that if give students multiple chances to pass a test, then you have to be able to quickly generate and grade new tests. In fact, UM's gateway tests are generated and graded by software. That's easier to do with some skills than others.
posted by bfields at 12:50 PM on November 21, 2016

I actually did the coursework described by ArbitraryAndCapricious. It was to prepare me to take calculus and it was voluntary and entirely online. You took a long assessment test and the online system assigned you problems to work on based on that assessment. The goal was to do the problems you were assigned to "pass out" of that area.

My experience was pretty meh. I think it would be a good refresher but the model is not that good at teaching you a concept you need guidance with.

It was entirely up to you to internalize the material and that's not easy without any guidance of any kind. Self-discovery learning is great and all but math wasn't a subject I could do like that. I ended up dropping out of calculus after the first test the next semester. I moved and ended up at a college that had a traditional precalculus class that I got an A in. I went on to get a B in a calculus course where most people got C's or below, so, traditional was much better for me. I have been successful at other subjects where you have to self-guide through a lot of material, namely analytical chemistry, but math was a no-go. As a disclaimer, math and physics are my roughest subjects.
posted by Foam Pants at 2:18 PM on November 21, 2016

We also tried ALEKS for this years ago for elementary and intermediate algebra.

Plus - You have to keep reviewing stuff all the way till the end. So, you do really have to master the material to finish the program.

Minus - I have the same problem with ALEKS that I have with all online computer programs - I think they promote Learning and Purging. I am a bit skeptical that "mastery learning" actually is any better than what we do traditionally.
posted by wittgenstein at 3:46 PM on November 21, 2016

If you haven't tried this already, googling "mastery grading" and "standards based grading" should lead you to some helpful information.
posted by kayram at 5:33 PM on November 21, 2016

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