This week I decided to capture data to explore Bloom’s 2 -Sigma Problem (Bloom, 1984), in which he demonstrated students who received 1-1 tuition with a mastery learning approach, outperform students in a class size of 30 by two standard deviations (2-sigma) in exam performance.
Thirty-five years later, with the advent of EdTech, AI and data-driven platforms, we can be on the cusp of solving the problem of how this level of mastery can be replicated on a larger scale. What if the cognitive distribution between human-technology assemblage, which lead to ammeter chess players using technology to beat grandmasters and more power machines (Beard, 2018), can also lead to more effective teaching?
I chose a student for this pilot, who I will refer to as student A and gave synchronous live teaching as we worked through topics on the Hegarty Maths site. The six topics listed in figure 2b together form a unit on Solving Equations. Student A was asked to watch the video for the topic, make notes before answering 12 questions on the site. The video solutions offer good models of worked examples to offer cognitive support (Rosenshine, 2012). At each stage, the student could ask for help if needed and go directly to the part of the video which demonstrates the concept which needs to be applied. Students receive two attempts to answer a question before it is given a red light and move on. I recorded the number of times I offered ‘corrective measures’ as suggested by Bloom as a means of direct support and intervention to a student-centred learning model; taking this approach and intervening only when student A was stuck, allowed me to get a more accurate picture of strengths and weaknesses. For topic 3, student A received an amber light and before continuing to the next topic, we decided to work through a few of the ‘building block’ topics suggested by Hegarty maths before re-attempting topic 3 again; these were not personalised to the needs of the student but based on the pre-requisites of the topic. The data visualisation diagram (fig 2a) represents no fixed structure and would offer a visual-map through the horizontal and vertical flights of the student’s journey through mastery learning of the topic.
Student A is yet to re-attempt topic 3. In addition to completing the six topics at mastery, student A would then be given a topic test, as per Bloom’s assessment of mastery learning. Based on my role as a teacher, I picked relevant sub-topics identified by Hegarty Maths for topic 3 and what I felt the student’s needs were based on the ‘corrective measures’ I had intervened in. In the future, AI should offer a far greater level of personalisation by not only ‘plugging the gaps’ with questions from default subtopics but personalise them with individualised questions to the student’s specific needs at the time. Hegarty Maths also collected additional information of student A, included time taken, how much of the video was watched, specific questions which were attempted a second or third time, all of which would be useful had I to take an asynchronous approach to mastery learning; such an approach may be more suited to teaching students in large numbers for whom personalised instruction and support would need to be differentiated accordingly. A barrier to mastery-learning, which teachers may face is teaching to the test or exams, under the added pressure of having to ‘deliver’ the curriculum with enough time for revision before the actual exam (Steve Griffiths, 2016).
Beard, A. (2018) Natural Born Learners: Our Incredible Capacity to Learn and How We Can Harness It. London: Weidenfeld & Nicholson.
Bloom, B. S. (1984) ‘The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring’, Educational Researcher, 13(6), pp. 4–16. doi: 10.2307/1175554.
Rosenshine, B. (2012) ‘Principles of instruction: research-based strategies that all teachers should know’, American Educator, 36(1), pp. 12–21.
Steve Griffiths (2016) Let’s teach for mastery — not test scores | Sal Khan. Available at: https://www.youtube.com/watch?v=-MTRxRO5SRA (Accessed: 21 February 2021).