Last time, when we looked at Daphne Koller's TED talk, we highlighted a pivotal 1984 result from famous education researcher Benjamin Bloom, the Two-Sigma "problem":
|The two-sigma challenge: the effect of mastery approaches (cf. here & here also) and individualised, interactive, high-feedback, highly responsive and flexible learning processes|
Wiki, in its article on the two-sigma issue, has an apt, pointed summary:
Considering the significant outcomes of these studies on student performance, educational researchers can make a number of implications and conjectures for follow-up studies. Among them:
- Labeling students as low achievers is less relevant, since altering one or two variables can have significant positive effects on the average learner.
- Technology may simulate tutoring affects without the high cost of providing a live tutor for each student.
- Social aspects present in one-to-one tutoring may imply a larger role for consideration of sociality in (or the social nature of) learning.
“The tutoring process demonstrates that most of the students do have the potential to reach this high level of learning. I believe an important task of research and instruction is to seek ways of accomplishing this under more practical and realistic conditions than the one-to-one tutoring, which is too costly for most societies to bear on a large scale. This is the ‘2 sigma’ problem.”I had three immediate reactions to Bloom’s statement. First, I am more determined than ever to be heavily involved in tutoring my children regardless of whether we go with a home school, private school or public school approach. Second, what does it say about our society that even the home cannot be a “safe bet” for one-to-one tutoring? Regardless of the reasons, I am troubled that an entire value system has been built that deems it “too costly” for us to bear. I wonder what the general attitude and level of education in our nation would be if families didn’t assume that education was something to be outsourced to an already overburdened and complicated public school system? Third, it struck me in the context of workplace mentoring. How often do I make myself available to be a mentor for junior software developers? How often am I seeking out other senior developers or managers to mentor me?
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.
Bloom proposes the impressive but possibly attainable goal of trying to make group instruction as effective as individual tutoring. Bloom identifies several alterable variables that have been shown to provide a partial "solution" to this two-sigma problem.
Note that this emphasis on the two-sigma problem does not contradict the importance of academic learning time [--> ALT, aka "Time on Task"] discussed earlier in this chapter. Indeed, the main reason these strategies have such impact is because they promote the effective use of academic learning time.Table 2.7 lists modifiable factors that Bloom found to be related to enhanced learning. Note that on Bloom's scale a score of 2.0 indicates the level of improvement that would occur under individualized tutoring. This is Bloom's "ideal" score, and other pedagogical strategies can be regarded as effective to the extent that they approach this ideal. For example, when teachers assign homework, there is an average effect size of .30 compared to similar classes in which there is no homework assigned. When teachers not only assign but also grade homework, there is an effect size of .80 compared to similar classes in which homework is not assigned.
Table 2.7. Selected Alterable Variables That Influence Student Achievement Effect Size Percentile* Strategy 2.00 98 Tutorial instruction 1.20 86 Reinforcement 1.00 84 Corrective feedback 1.00 84 Cues and explanations 1.00 84 Student classroom participation 1.00 84 Student time-on-task 1.00 84 Improved reading / study skills .80 79 Cooperative learning .80 79 Homework (graded) .60 73 Classroom morale .60 73 Initial cognitive prerequisites .50 69 Home environment intervention .40 66 Peer and cross-age remedial tutoring 30 62 Homework (assigned) .30 62 Higher order questions .30 62 New science and math curricula .30 62 Teacher expectancy .20 58 Peer group influence .20 58 Advance organizers .25 60 Socioeconomic status (Included for contrast - SES is not easily alterable by teachers.) *The percentile indicates the percentile at which the "average" student would typically score if he/she received this treatment instead of "traditional" instruction. (Ordinarily, the "average" student would score at the 50th percentile.)
(Adapted from Walberg, 1984)
Vockell (1994) has reversed Bloom's logic and has discussed the "minus two-sigma problem." He reasons that if teachers teach really incompetently, they will lower students' performance by an effect size of 2.0. (Having no teacher at all could be perceived as the opposite of having an individual tutor.) He suggests that various activities in which teachers sometimes engage hurt student performance to the extent that they approximate a truly do-nothing teacher.
[--> hint, hint on the importance of "cell groups" for discipleship and ministry training . . . similarly on organisation by "squads" led by competent and committed "NCO's" in getting capacity built through training and in getting effective work done . . . ]