Bloom’s 2 Sigma Problem

Thursday, December 1st, 2011

Bloom’s 2 Sigma Problem is an odd name for educational psychologist Benjamin Bloom’s discovery, first reported in 1984, that one-to-one tutoring isn’t just a little bit better than conventional classroom teaching:

Bloom found that the average student tutored one-to-one using mastery learning techniques performed two standard deviations better than students who learn via conventional instructional methods — that is, “the average tutored student was above 98% of the students in the control class”. Additionally, the variation of the students’ achievement changed: “about 90% of the tutored students… attained the level of summative achievement reached by only the highest 20%” of the control class.

The two-sigma part refers to average performance of ordinary students going up by two standard deviations when they received one-to-one tutoring and worked on material until they mastered it, and the problem part refers to the fact that such tutoring doesn’t come cheap.

My first reaction is surprise at the degree of the effect, but it should be obvious that advancing 30 students in lock-step means that many will be bored, a few will be in the sweet spot, and many will fall further and further behind, as the material builds on previous material they never learned.

So, my conclusion would be that conventional classroom teaching is largely a waste of time — but that’s not where educational experts place their emphasis:

Although much recent attention has focused on gaps in the achievement of different groups of students, the problem has been with us for decades. This paper presents the problem as one of reducing variation in students’ achievement, and reviews the work of renowned educator Benjamin Bloom on this problem. Bloom argued that to reduce variation in students’ achievement and to have all students learn well, we must increase variation in instructional approaches and learning time.

I suppose they see it as Bloom’s Paradox.

In his original paper, Bloom notes that a full-size classroom can get one-sigma results by switching to mastery learning, where students are tested not just for a final grade on a unit but to uncover where they need to do further corrective work, so they keep at it until they get it right.

It is odd, when you think about it, that we give students As, Bs, and Cs, and then advance them all to the next course, when they really should study the material until they earn a solid A before moving on — unless the goal of education isn’t conveying information but ranking students.


  1. Roger Sweeny says:

    Why, yes, a major goal of the educational system is ranking students. However, another goal is “exposing students.”

    When I complain that most of the courses young people are required to take will never be used and will be almost completely forgotten within a year, I am sometimes told that, while this is true, young people need to be exposed to all these courses to find out what they are interested in. One could then argue that it really doesn’t matter if they forget most of what they were exposed to in high school. The ones who are interested in a particular subject will take more courses and get good at it. They will forget what they don’t use and are not interested in. The latter is unfortunate but not really important. (If it is important, just about every high school in America stands condemned.)

    A necessary implication of this model is that requiring students to master a course before they advance would take much longer than the present system for most people. Not only would peer groups be broken up (a no-no in present day public schooling) but lots of kids would have to be retained well past current compulsory attendance age in order to get full exposure.

  2. Isegoria says:

    Our current (US) educational system does not expose students to much breadth of subject matter — at least not until college — and it wouldn’t have to reduce its breadth at all under the mastery system described. In fact, it wouldn’t necessarily require breaking up peer groups, either.

    The key is moving away from a final grade at the end of the semester and moving toward lots of “final” grades along the way, with make-up work any time you don’t earn an “A” on a test. Then you retake the test to demonstrate that you have learned the material.

    The amount of material you’d be expected to master to graduate would be smaller than the amount of material you’re currently expected to be exposed to.

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