Mastery Learning in Developmental Mathematics

I have never met somebody who used Mastery Learning in their classroom, nor have I heard of anybody using this method. Like all absolute statements, this statement has a ‘if … then’ clause within it. More properly stated, I would say that “Nobody understands what mastery learning is”.

Mastery Learning is not about a minimum performance level on one assignment; that is unrelated to the theory and conception. Mastery learning is about the entire learning environment, and is based on two goals and a belief. The goals are to create a learning environment with flexible and adaptive learning resources so that essentially all students (>95%) are able to learn at a high level (‘masters’), and to reduce the learning variation observed among groups of students. The belief is that almost all (>95%) of students are capable of learning at the master level if provided the appropriate learning resources and instruction. For some information on Mastery Learning, see http://www.nathanstrenge.com/page5/files/formative-classroom-assessment-0026-bloom.pdf — it is a good summary. In the original model, ‘enrichment’ was part of the design for students who achieved the master level quickly — they would have time to explore and investigate, create and design.
Mastery Learning is hard work for the faculty and administration involved. No excuses … if a student does not understand, you find another way to learn and reinforce. Mastery Learning is likely to be ‘more expensive’ than other models for that reason. Of course, ‘more expensive’ depends on your point of view — are we talking about the cost per enrolled student, or are we talking about the cost per passing student?

People often confuse Competency Standards with Mastery Learning. With online homework systems, people set ‘mastery’ levels — but this has nothing to do with Mastery Learning. If the instructional system is limited to software and tutoring, this can not be Mastery Learning. Mastery Learning involves the entire learning process, not just ‘homework’.

What would a course look like in a Mastery Learning model? Here is a brief sketch, based on a program at my College (long since evolved and eventually closed).

Students begin with a standard assignment
Students take an assessment (skills, applications, concepts — including novel situations)
Those who perform at a master level proceed to the next unit (we were not able to design ‘enrichment’ in to the course).
Students who performed below master level had a diagnostic interview with an instructor. Options included:
1. Media (video and/or audio) help
2. Tutoring
3. Computer tools (either custom written programs, or packaged, or both)
4. Hands-on activities
5. Small groups
Students initially below master level then took the assessment again. If not at master level, prior step repeated (with longer diagnostic interview)
All units completed at master level
Cumulative final exam, also done in the same master manner.

People using the ‘mastery’ label are generally only referring to the first step (assignments); however, this is not even an assessment — and Mastery Learning is all about assessments (formative and summative). In Mastery Learning, we aim for the goal of 95% of the students achieving a master level on the assessments; how students do on the original assignments is not usually considered.

The other comment to make about Mastery Learning is that the model is not just about skills and procedures, even though most uses of ‘mastery’ refer to only that. Mastery Learning is an approach for any content. The financial resources make both Mastery Learning and ‘more than skills’ a challenge — they both cost more. Does your college have the commitment to the goals of Mastery Learning?

In my view, the main disadvantage of Mastery Learning is that it tends to deal mostly with individual situations, not social; group learning processes tend to be very difficult. I like to create a sense of community in my classes, and that would be very difficult in a Mastery Learning model. Of course, that is also true of the ‘lesser cousins’ that we see much of today — online homework, modules, emporium, etc; these are all ‘lesser cousins’ of Mastery Learning, as they share disadvantages without any of the benefits.

The best thing about Mastery Learning is the demand it places on us — we seek to have 95% of all students become masters; ethnicity would not be a correlation with success, nor would economic status. In Mastery Learning, all predictors of success are eliminated because all students (at least 95%) succeed at the master level. As you know from your test analysis work, the highest discrimination is possible when the difficulty is 40% to 60% — which is exactly where our courses are today. If we could do Mastery Learning in developmental mathematics, that outcome would be worth the disadvantages and costs. We tend to reinforce inequities, not overcome them … Mastery Learning can be a part of a solution.

Most of us will not have the institutional commitment to make Mastery Learning work for the 95% of our students. Look at the emerging models for developmental mathematics (New Life, Pathways, Mathways) for other ways to get our course difficulty out of the high discrimination zone (pass rates). In those models, pass rates in the 70% to 80% range are possible … and that would be a big step to eliminate the high discrimination we currently see.

Whatever your model, never take the Mastery Learning label lightly. It’s way more than a setting on a homework system.

Join Dev Math Revival on Facebook:

Learning math | Jack Rotman | July 6, 2012 9:39 am

2 Comments

By schremmer, July 6, 2012 @ 10:02 am

Mastery Learning sounds to me like farmers talking about what is the best way to fatten up cattle.

Distraught regards
–schremmer
By Jack Rotman, July 6, 2012 @ 10:21 am

Awkward metaphor, though I think I understand.
I am neither advocating Mastery Learning nor condemning it. From the outside, Mastery Learning can sound like a production process with an emphasis on numerical quality control. However, from the inside, Mastery Learning can create a space where all students succeed at a high level regardless of prior learning in math based on meaningful interaction between student and faculty. Mastery Learning has high validity and high costs; I don’t think many institutions can handle it. Instructors are not likely to be able to do Mastery Learning on their own.

Developmental Mathematics Revival!

Bringing a new vitality to college mathematics 2011 to 2019