Educators have known for millennia that one-on-one instruction – tutoring that works with students at their own time and pace – is the best way for people to learn. It is what Alexander the Great had with his teacher, Aristotle. If Alexander was having trouble with a concept, I can imagine Aristotle slowing down for him. If Alexander had a knack for understanding military tactics, I am sure Aristotle would have sped up his instruction or gone deeper. By having this one-on-one attention, the student never feels stuck or bored. This isn’t just something that happened in the deep past. Today, top athletes and musicians, for instance, continue to learn through one-on-one coaching.
In the eighteenth century, we began to have the utopian idea of offering mass public education to everyone. We didn’t have the resources to give every student a personal tutor, so instead we batched them together in groups of thirty or so, and we applied standardized processes to them – usually in the form of lectures and periodic assessments (Khan, 2024).
While not perfect, that system dramatically improved the overall level of education in the societies that invested in it, increasing literacy rates globally and education rates overall (Khan, 2024). Still, the approach isn’t optimal for the majority of students. For instance, traditional fixed-pace classes force students to move on to a more advanced topic even if they haven’t really mastered the more basic ones. This forms gaps in their knowledge that accumulate over time.
Today, we see the implications of these gaps in every classroom and across every learning domain. A 2024 report in The Scotsman revealed a worrying statistic: only 40.1% of fourth-year pupils in Scotland passed National 5 Mathematics (The Scotsman, 2024). By the age of 15, many students have accumulated so many gaps in their understanding that they can no longer pass a core maths qualification. As a tutor, these results do not surprise me. I work with so many bright and capable students who can tackle the more advanced concepts at National 5 level, yet still struggle with the fundamentals such as percentages, multiplication and long division, skills they should have mastered by the age of 12 or 13.
Benjamin Bloom’s 2 Sigma Problem
In 1984, the renowned educational psychologist Benjamin Bloom attempted to quantify the effect of breaking out of this factory model of education through better personalization and one-on-one tutoring. As a researcher at the University of Chicago, Bloom compared the outcomes of conventional learning with those of students who studied with a good tutor.
What, exactly, was a good tutor? According to Bloom, a good tutor was one who practised the principles of what he called mastery learning. Mastery learning entails always giving students the opportunity and incentive to address any gaps in their knowledge or skills. Bloom argued that a tutor practising mastery learning should not move onto a new subject until the student had demonstrated 90% competency in the current one.
In conventional learning – still the norm in most schools – teachers educate students at a fixed pace and give them a quiz or test every few weeks. Even if students get 65 percent on a test, the class typically moves in lockstep to the next topic, usually without first addressing the 35 percent gap identified on the last exam. This process continues for years, with students accumulating gaps along the way – and then we act surprised when they struggle with basic grammar or algebra.
No matter how innately bright or hardworking someone is, how can they have a chance of mastering algebra if they have major gaps in decimals, fractions, or exponents? In mastery learning, students have the time to identify and address those gaps. Having the space to develop a strong foundation allows students to learn faster later too. In fairness to the traditional school system, without support, it’s difficult to pull this off with one teacher and thirty students, each with different gaps and learning paces.
In 1968, Bloom published a paper titled Learning for Mastery, which compared academic success between the conventional factory model of education and mastery learning. Bloom’s research focused on senior high school classes in the United States, typically with around 30 students. At the start of the year, he administered a basic IQ test. When he plotted the results, he unsurprisingly found the students’ IQs formed a bell curve: a few at the extremes, with most clustering in the middle.
Bloom returned to the class a year later and plotted the students’ final exam results. Once again, the distribution of academic achievement closely mirrored the original IQ distribution. He saw this as a clear indication of a deeper issue within the American education system. As outlined earlier, Bloom attributed this outcome to the fixed-pace model of conventional classrooms, where thirty students progress through the curriculum at the same speed regardless of individual understanding. In such a system, students at the lower end of the bell curve may grasp only 30% of the material before the class moves on, while those at the higher end may retain as much as 80%. The results of his findings are illustrated below (Guskey, 2022).
Bloom argued that if educators were effective, the distribution of achievement could – and should – look very different from the typical bell curve.
To test this hypothesis, Bloom selected individual students from various points on the IQ bell curve and gave them private tutoring instead of placing them in the standard classroom. He instructed the tutors to apply mastery learning techniques. At the end of the year, Bloom compared their final test results with their starting IQ distributions. The difference was striking (Guskey, 2022)
In his paper, Bloom wrote that students who received mastery-based tutoring showed a two-standard-deviation improvement. In layman’s terms, a student who began in the 50th percentile – average in both IQ and academic performance – rose to the 98th percentile using mastery learning. That’s the difference between a straight C student and one who qualifies for Harvard. Remarkably, these results have been reliably and repeatedly confirmed by researchers since Bloom’s original study in 1968 (Cohen, Kulik & Kulik, 1982).
Even more staggering was that the students weren’t spending more time learning than their peers. The total learning time was the same. But thanks to the one-on-one tutoring and constant feedback loop, students progressed much faster.
Harry’s Tutoring Academy
The work of Benjamin Bloom has profoundly influenced the way we structure every child’s experience at Harry’s Tutoring Academy. Mastery learning is the strategy we adopt for every student who comes through our doors. We work in small groups of just 1 to 4 students, constantly assessing progress, and only move forward when a student has demonstrated 90% mastery of a topic.
Bloom was pessimistic about the likelihood of his findings being widely adopted, pointing out that existing education systems were not built to scale this kind of instruction. As a result, he believed the two-standard-deviation improvement would remain out of reach for most students. But at our tutoring academy, our mission is to replicate Bloom’s results. We aim to move students from the middle of the pack to the top percentile. We want to maximise every student’s academic potential and give them the exam results that open doors to their best possible future.
Bibliography
Khan, S. (2024) Brave New Words: How AI Will Revolutionize Education (and Why That’s a Good Thing). London: John Murray.
Guskey, T.R. (2022) Implementing Mastery Learning. 3rd edn. Thousand Oaks, CA: Corwin.
Cohen, P.A., Kulik, J.A. and Kulik, C.C. (1982) ‘Educational outcomes of tutoring: A meta-analysis of findings’, American Educational Research Journal, 19(2), pp. 237–248.
Smith, J. (2024) ‘Maths pass rates drop to record low’, The Scotsman, 10 May