The Learner Focused Learning Blog

April 25, 2024

Solving the 2 Sigma Problem Once and For All: It's about People, Pedagogy, and Technology

April 25, 2024

Learner Focused Learning

Fergus McShane

The two sigma problem is nothing new. First introduced in 1984 by educational researcher Benjamin Bloom (yes, the Bloom's Taxonomy Bloom), it evidences with theory the experience of many teachers - that the more individualised the learning pathway, the more success students find as they progress through it.

Despite the fact that Bloom's research paper is celebrating it's 40th birthday this year, the insights within it remain surprisingly (or, perhaps, unsurprisingly) relevant. The research, particularly the way in which Bloom frames the different modes of instruction, offers a useful perspective from which to view the stubbornly persistent challenges we face in state education in the UK today.

Introduction to Bloom's Two Sigma Problem

Bloom's Two Sigma Problem emerged from an investigation comparing the effectiveness of different teaching approaches. His research revealed a significant finding: students who received one-to-one tutoring outperformed their peers taught through conventional classroom methods by two standard deviations.

This difference highlights the potential of individualised instruction to enhance learning outcomes dramatically, suggesting that if we could effectively individualise each students' learning journey at scale, we could elevate the average student's academic achievement to the achievement levels that the top 20% of students in a traditional classroom attain.

The research underscores the limitations of a one-size-fits-all approach to education, especially given the diverse array of learners in any classroom, each with their own backgrounds, abilities, and challenges. It's not a new idea; every teacher has seen this in the classroom, but the way in which Bloom's analysis clearly defines, evidences, and gives language to the phenomenon is useful.

In particular, the focus of the Two Sigma Problem is on how the student experiences and is impacted by what the teacher does. It doesn't advocate for teachers doing x, y, or z, but simply that whatever the student is doing should be individualised to the appropriate level of that challenge for that student; in other words it advocates for an individualised learning pathway.

We see the echoes of this concept across the landscape of education. From scaffolding and small group interventions, to differentiation and quality first teaching, we continue to design new frameworks to achieve that goal of an individualised learning experience.

We know summative exam achievement isn't the be-all-and-end-all of education, but the picture painted here is clear.

Implications of the Two Sigma Problem

What does it mean then for a learning pathway to be "individualised"? Bloom's research noted the highest academic achievement among the 1:1 tutorial group, but noted a one sigma improvement in academic achievement through the mastery learning approach. This suggests that individualisation exists on a spectrum, making Vygotsky's concept of the Zone of Proximal Development (ZPD) a useful heuristic.

The ZPD heuristically comes down to a simple rule - to maximise learning, a given learning challenge should be difficult enough to challenge the learner to think or do in a new way, but not so difficult that the challenge is insurmountable. When read together, Vygotsky's Zone of Proximal Development and Bloom's Two Sigma Problem tells us that accurately challenging pupils according to their zone of proximal development* is fundamental to the learning process but also that, by necessity, each of these "Zones of Proximal Development" are unique to the individual and, therefore, optimal learning occurs when instruction is individualised to a level of challenge in their zone of proximal development.

*See also: cognitive overload.

Achieving individualised learning, however, has never been a challenge of pedagogy; Aristotle was using 1:1 instruction methods in ancient Greece. Instead it is a challenge of resources - money for sure but more importantly the time that it buys. Bloom's model of instruction in which he achieved the highest academic outcomes, 1:1 tutoring, is not scalable for many of the wealthiest of private schools let alone the state sector. The question is not then "How do we individualise learning" but rather, "how do we build a system of individualised learning that is scalable with the resources we have available that best approximates the efficacy of 1:1 instruction?"

Solving the Two Sigma Problem

A successful solution to that question, in our experience, appears to be built upon the consideration of the three key foundations:

  • People - How do we bring people together in a culture that works towards leaving no learner behind; that maximises every learner's success no matter their needs?
  • Pedagogy - What pedagogies do we need to deploy in order to support the individualised approach? How do we look beyond knowledge to the development of the whole individual?
  • Technology - How do we leverage the power of technology, specifically its ability to extend our capacity for action, to fill the resource gaps in the individualised model?

Tomes have been written on the first two areas, especially the development of pedagogical approaches (such as mastery learning) that challenge the model of the traditional classroom with its uniform pacing and generalised instruction. The approaches we need to the development of individualised pedagogy and the people to deliver it in the traditional classroom model exist and are deployable, but are at the very edge of what's possible with the limited resources available. In schools with high levels of comorbid challenges, those edges seem to get very close very quickly. What's exciting about bringing the Two Sigma Problem into the 21st century, however, is access to that which Bloom didn't have access to when he wrote his research paper: technology. Cheap, scalable, and increasingly limitless technology. Technology that, with the right application, creates the most precious resource of all in a school: time. Time to do the thing only educators can do - understand young people and help them succeed.

The advent of machine learning algorithms, big data, cheap compute, and now generative AI has opened up new avenues to explore in the realms of pedagogy and people too. How we deploy these technologies, not just in our curricula but in the running of our schools and our education systems, may allow new and exciting modes of classroom and school operation as we expand the boundaries of what teachers, leaders, and schools can do with the time they have available to them to support students.

Addressing the Two Sigma Problem in contemporary education, and building a model of education that leaves no learner behind, requires these innovative solutions across the realms of people, pedagogy, and technology. The innovative solutions that transcend traditional classroom setups and instructional methods, that give staff the time to critique the way things have "always been done" and imagine new ways of operating instead. By leveraging technology, in addition to the essential components of people and pedagogy, educators can more effectively cater to the diverse needs of their students, shifting from a primary focus on content delivery to better understanding and building relationships with students and facilitating their individual learning journeys.

At Learning 3D, our goal is to help schools to develop the people and culture; the pedagogies; and the technologies that allows us as educators to move from the "factory" model of education to one in which every learner maximises their success through an individual learning pathway; crucially without losing the rigor, aspiration, and community element of traditional models. In short, a model of education where no child is left behind.

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