The Myth of Average

The Problem with Prize-giving

What is the purpose of prize-giving? We award prizes, certificates, trophies, or book vouchers to students who have been assessed by an educator against a rubric and then compared to a group who have done the same or similar assessment. Those that score highly in comparison to the rest are rewarded. This process, known as standardised assessment, is flawed. It is not only unscientific but also outright dangerous and damaging to children and students.

Understanding Ergodic Theory

Ergodic theory, used by physicists, is a set of mathematical principles that specify when you can use information about a group to draw conclusions about individual members of that group. The rules are straightforward:

1. You can use a group average on a standardised test if every member of the group is identical.
2. Every member of the group will remain the same in the future. Such a group is called an "ergodic" group.

Schools do not meet the criteria for being ergodic. If we had a group of frozen human clones who were identical and unchanging, then we could use standardised testing, find an average, and rank the performance. However, schools are learning spaces made up of unique individuals with a variety of combinations of intelligence, who learn at different speeds and develop at different rates.

The Fallacy of Average-Based Norms

Peter Molenaar, an acclaimed scientist, believed in the concept of "the average." He built his entire career relying heavily on average-based norms. However, towards the end of his career, in 2003, he had to teach a class on The Theory and Method of Mental Testing. It was based on the textbook "Statistical Theories of Mental Scores" by Frederick Lord and Melvin Novice (1968). The textbook suggests that the best way to find out an individual's ability is to test them repeatedly on the same work and average their scores. However, Lord and Novice agreed that this was not possible with humans, as humans learn from testing and their scores improve each time until they achieve mastery. Instead, they suggested testing many people just once.

Molenaar instantly recognised the flaw in the theory he had used throughout his career. It called into question the validity of many scientific tools used for admission tests, selection processes, special needs diagnostics, and more. Group distribution of measurement cannot be safely substituted for an individual's distribution of measurement. Essentially, you cannot understand an individual by ignoring their individuality.

The Dangers of Ignoring Individuality

Sadly, those who cannot think cannot learn. Education systems and schools know this truth, but it often falls on deaf ears, deemed as anarchy or too radical. "It's the way we've always done it," or "The department expects it like this," are common arguments. These same arguments were used during apartheid in South Africa, a painful reminder that we should have learnt from that experience.

The final argument against moving away from averages goes like this: "If you cannot use the average to model, evaluate, and select winners, then what can you use?”

Embracing Dynamics Over Statistics

Despite initial resistance, Molenaar approached Penn State University and was offered a tenure position. His work distinguished between statistics (working with static "frozen clones") and dynamics (the maths of changing, nonlinear, and dynamic values). This shift is crucial as we begin to understand brain development and the uniqueness of each individual. Teaching for 100% achievement for each child matters.

The Chubby Thighs Theory

A useful story that highlights individuality is the "Chubby Thighs Theory." In the 1960s, it became evident that the brain hardwires certain pathways at certain stages, a process called myelination. This theory led paediatricians to diagnose neural disorders if a baby’s stepping reflex did not appear or disappear at a certain time.

American psychologist Ester Thelen discovered that many of the fixed ages and stages of child development were highly variable, dependent on the individuality of the child. She proved that the reason some babies’ stepping reflex disappeared was because of "chubby thighs." Slow weight gainers moved their legs the most and for the longest period, while fast weight gainers lost their stepping reflex earlier because their muscles were not strong enough to lift their legs. What mattered was the amount of body fat relative to the development of muscle strength.

Breaking Free from the Myth

The world our children are growing up in is one of measurement based on a myth. We constantly judge ourselves against the average person. We judge our salary, buy an average car, and get married at the average age. Once we free children from the myth of average, they can discover their true worth.

The Question for Schools

Is our school based on average, or is it focused on growing unique individuals? We cannot have a prizegiving system based on average, as it rewards the wrong people.

"The individual is a high-dimensional system evolving over place and time." - Peter Molenaar, Pennsylvania State University

Gavin Keller