# Adding Up Mastery Learning in Math

In 1984, Benjamin Bloom (of the famous Bloom’s taxonomy), published a paper titled “The search for methods of group instruction as effective as one to one” . In it, he and his research team split students into three groups – conventional learning where tests were done for summative purposes only, mastery learning where tests were given for formative purposes, and tutoring where students were either one on one or in small groups of 2/3 and where tests were given for formative assessment purposes as in mastery learning. In conventional learning and mastery learning, the pedagogy was otherwise unaltered and the class size of 30 was the same. What were the results?

70% of the mastery learning students achieved the results of the top 20% of the conventional students. They scored over one standard deviation above the average conventional class student. They were also much more likely to be on task during class. Bloom called this the **one sigma effect** – “the average mastery learning student is above 84% of the students under conventional instruction, even with the same teacher teaching both the mastery learning and the conventional classes”. This finding was replicated across grades and subject areas.

Mathematics is probably still the subject most committed to conventional learning. The constant testing done for summative purposes (i.e. the marks being collected for grading) is still a ubiquitous practice. While there may be some formative use of the tests, their prime function is to assess “good” and “bad” students. But Bloom’s and others research is very consistent. We need to use testing for formative purposes the vast majority of the time, and use summative assessment only to demonstrate the mastery learning of the students.

Today, Bloom’s research has taken us to a new place. In the same study, he and his associates demonstrated that tutoring had a 2 sigma effect – that 98% of students tutored did better than the conventional classroom. What he therefore found was that almost all students can do very well under the right conditions – the significant variation in learning that we find in schools is not aptitude related but environment related. This finding was discovered too by Salman Khan as he began working with classes of students in public schools. Watch this video beginning at 28 minutes to see his astonishing discovery that successful students are as much a product of testing date as they are of true capacity.

What does that mean in mathematics teaching as we consider the concept of personalized learning? This is the attempt to, so to speak, replicate the impact of tutoring but within a class setting. One implicit way in which “personalized learning” has been attempted is through the reduction in class size since the 1950s from above 30 to a class to about half that today. But can we create a tutoring effect, a 2 sigma effect, within mathematics classes of variable class size? In a recent EdSurge interview with Ed Meyer, Meyer said that personalized learning included some non-negotiables:

- Competency-based grading
- We need technological help

He also demonstrated significant skepticism about personalized learning being concrete in the classroom and identified significant current limitations of technology. He finishes the interview with this statement which seems a useful place to continue the conversations in your own classrooms and schools: “I think that we should all resolve to be a little bit annoying when it’s possible, and to ask people to clarify their priors to define personalized learning in very concrete terms. What does this mean on the ground level? What does a good classroom look like? What if I walked into your school? Get on that level as fast as possible, as annoyingly as possible. That’s my resolution.”