In 2021, Matt Evans, Ben White, and I co-authored “The Next Big Thing in School Improvement“, a book that explores perennial policy challenges that arise when we try and fail to overcome the two fundamental problems of schooling:

1. The Invisibility of Learning: Learning is a largely unseen process, elusive to complete measurement and understanding by teachers.
2. Lockstep Problem: Students in a typical classroom possess a wide array of knowledge and skills, yet the curriculum expects them to progress in unison.

Much of my career has been spent cautioning about those who claim to have quantifiable solutions for measuring learning and other hard-to-measure psychological constructs. But let’s suppose, for a moment, the existence of a technology that could provide real-time insights into each student’s learning achievements and capabilities. As a teacher, what actions would you take with this wealth of information?

Addressing the first fundamental issue of schooling, the invisibility of learning, only serves to highlight the second issue: the lockstep problem. In a typical classroom, the disparity in student abilities, knowledge, and motivations is so vast that even precise knowledge of each individual’s needs among thirty students doesn’t equate to the ability to meet all those needs effectively.

Astonishing claims about learning inequalities

Or perhaps it’s not as insurmountable as we thought. Earlier this year, a group of US academics published a paper with a provocative title, suggesting the lockstep problem might be more manageable than previously believed. Despite my initial reluctance to block out a couple of hours to read into its complex statistical estimation methods and implications, any paper titled “An Astonishing Regularity in Student Learning Rates” was too compelling to ignore.

We’re well aware that students vary significantly in their academic attainment, and understanding the reasons behind this variation is crucial as it leads to vastly different policy approaches. For example, how much do students differ in their ability to learn new material? Is the variance in learning rates a significant factor in overall attainment differences, as opposed to variations in study time or prior knowledge? The paper’s title is striking; if students indeed learn at similar rates, then equalising their starting points through interventions like catch-up classes and summer schools could theoretically lead to uniform learning progress during regular classes, thereby addressing the second fundamental schooling problem.

The paper makes its remarkable claim across multiple datasets where students engage in skill and competency practice in various subjects, primarily those amenable to short-answer questions. The ‘learning rate’ is measured by improvements in accuracy on these practice questions. Admittedly, this method has its limitations, notably the lack of data on time spent practising, but let’s set that aside for the moment, as the datasets still offer valuable insights.

My reflections on the study somewhat deviate from the authors’ conclusions. Firstly, there were differences in learning rates among students, but they appeared marginal because overall improvements in accuracy on practice problems were relatively small. A ‘fast’ learner, at the 75th percentile, learns about 50% faster than a ‘slow’ learner at the 25th percentile. A minor improvement in my test score, from 70% to 76%, compared to your increase from 70% to 74%, might seem trivial. However, these incremental gains in understanding accumulate and become advantageous in subsequent lessons. This difference is akin to investing money: small variations in returns can lead to significant wealth disparities over time. 

Secondly, the study measured learning rate variations in a model accounting for initial knowledge levels. If students with more efficient learning abilities generally possess higher initial knowledge, then it’s less surprising to find minimal variation in learning rates after adjusting for prior attainment.

My third takeaway is the overwhelming importance of prior knowledge, a finding that becomes somewhat obvious once you consider that the study’s ‘initial knowledge level’ includes understanding of the readings, videos, or classes related to the practice topic. This may seem like stating the obvious, but the paper actually neatly illustrates the lockstep problem in a way I haven’t seen before. It is really hard and time-consuming for those with an initially weak understanding to catch up with those who have an initially strong understanding of a topic.

Inequalities in time to mastery

Consider a scenario where we’re teaching a competency, such as understanding fractions or the use of semi-colons, with the goal of students achieving 80% accuracy before progressing. After our explicit teaching and checking for understanding, we find variation in comprehension – quiz scores range from 55% to 75%. It seems manageable; you plan to provide a few more practice questions before moving on. But, how many questions will each student need to reach mastery? According to the study, high achievers might attain mastery after just 3 or 4 additional attempts, whereas lower achievers might require over 13 attempts. However, the typical class setting doesn’t allow the time for the 13 attempts (not least because most don’t need it), leading to a situation where we advance to the next topic before some students have fully grasped the current one. This issue is particularly pronounced in subjects with hierarchical knowledge structures, where prior attainment is crucial, which is why such enormous gulfs in ability to learn and progress emerge.

The implications of the paper, which used data from these hierarchical knowledge domain subjects (e.g. maths, languages, English grammar, and physics) is that ensuring students possess the necessary prior knowledge is essential for their success. However, in our current educational system, where classes progress through topics in a set sequence regardless of individual comprehension levels, ensuring mastery before moving on isn’t always feasible. This reality might be acceptable in cumulative subjects like the humanities, but it can be disastrous in more hierarchical subjects. For those unfamiliar with these concepts, I recommend Mark McCourt’s book ‘Teaching for Mastery’, which provides a comprehensive overview of the argument and supporting evidence.

The mastery approach aligns with what many teachers identify as effective instruction: pre-instructional diagnostics, quality teaching, and formative assessments to track progress. At its core, however, the mastery model acknowledges that some students will grasp and assimilate new concepts more readily than others. Embracing the philosophy that students should only progress once they fully understand a concept, the approach incorporates corrective instruction for those who need additional support.

Implementing mastery

If mastery is so crucial, why isn’t it more widely implemented? With finite time and resources, achieving mastery in schools is challenging. Matt Swain, a Leader at Kite Academy Trust, explains how their schools have introduced daily maths catch-up sessions at the end of each lesson. Students who haven’t mastered the day’s material receive additional instruction, sometimes at the expense of other activities like assembly or time outside. Even then, they acknowledge that this is insufficient for some students. Other schools might opt for individual or small group catch-up tuition, but this approach is costly. In secondary education, we often resort to assigning different curriculum pathways based on attainment levels. Internationally, some systems require students who fail to meet standards to stay after school for extra study or to repeat a grade.

None of these methods seem entirely satisfactory, partly because they conflict with our ideals of educational equality, where every child is entitled to the same learning opportunities in a fixed amount of time. Mastery provides the necessary environment for success in mathematics and other hierarchical subjects, but often at the expense of other enjoyable activities (or less curriculum coverage).

It’s perhaps time to more critically consider the sacrifices we expect students to make for mastery, especially as technology increasingly facilitates its implementation. Previously, individualised tuition or personalised curriculum pathways to address gaps in understanding were prohibitively expensive. However, this is likely to change in the next decade with advancements in independent learning platforms. If a student like Samuel is three years behind in maths, should we provide him with a tailored learning experience to achieve mastery at his level? Should we mandate extra hours of maths each week in hopes of him catching up with his peers? And if so, at the expense of other subjects or his free time? While this approach might enhance Samuel’s mathematical understanding, we must also consider its emotional and social impact on him.

Unmasking inequalities

What would happen if we fully embraced a system where students study (hierarchical) subjects at levels that correspond to their current understanding, adopting a ‘stage not age’ approach? The implications of this shift hinge on the extent of inequalities in both achievement levels and learning rates. In mathematics, there’s often mention of a seven-year gap in attainment between the highest and lowest performers¹. Can we accept a policy that boosts the attainment of lower achievers in mathematics, even if it means they may never engage with the same curriculum content as their higher-achieving peers? And what if this same policy enables the more successful students in maths to advance even more rapidly?

The paper’s title alludes to an ideal scenario where we somehow eliminate pre-existing knowledge gaps and then expect students to learn at comparable rates in class, effectively resolving the lockstep issue. I wish this world could exist, but it is simply inconsistent with the myriad of cognitive, environmental, and behavioural factors (beyond prior knowledge) that contribute to some students falling behind.

Emerging technology platforms may begin to change the dynamics of the fundamental problems in schooling. They may loosen the lockstep, enabling students to sit in class together studying quite different curricula. They may make the learning of individual students a little more visible. Yet, what they promise as solutions may instead reveal a different set of challenges and compromises that we must learn to navigate.

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1. Rob Coe reminded me that the source of the 7-year gap in maths statistic is the Cockcroft Report from 1982 (para 342). It would be nice to have a modern data source!
   Dylan Wiliam has shared two useful references for the dispersion of attainment (in years) within an age band:
   Wiliam, D. (1992) Special needs and the distribution of attainment in the National Curriculum, British Journal of Educational Psychology, 62, 397-403.
   Hodgen, J. et al. (2009) Secondary students’ understanding of mathematics 30 years on, BERA conference paper.