Abracadabra: Your number is 7 Sort of or is it?

“Science is magic that works.”
Kurt Vonnegut

In 1956 George A Miller’s paper “The Magical Number Seven Plus Or Minus 2 Some Limits On Our Capacity For Processing Information” was published in Psychological Review. This paper would go on to be one of the most cited psychology papers. The article starts with Miller talking about being persecuted by a number.

My problem is that I have been persecuted by an integer. For seven years this number has followed me around, has intruded in my most private data, and has assaulted me from the pages of our most public journals. This number assumes a variety of disguises, being sometimes a little larger and sometimes a little smaller than usual, but never changing so much as to be unrecognizable. The persistence with which this number plagues me is far more than a random accident. There is, to quote a famous senator, a design behind it, some pattern governing its appearances. Either there really is something unusual about the number or else I am suffering from delusions of persecution.

George A. Miller

This paper has to do with the similarity in a person’s performance on one-dimensional judgment tasks and memory span. In one-dimensional judgment tasks, individuals are asked to discriminate between items that differ only by one characteristic. The frequency or loudness of a tone or the saltiness of a solution. While there are some variations in different types of items individuals can distinguish about seven (plus or minus) different objects correctly. Memory span is the maximum number of things a person can recite back correctly immediately after being exposed (hearing, feeling, or seeing) to them. Again, the memory span is about seven. The similarity of these two items led to the obvious question, are they related? Was there something magical about the number seven, especially as Miller says since we see seven everywhere.

What about the magical number seven? What about the seven wonders of the world, the seven seas, the seven deadly sins, the seven daughters of Atlas in the Pleiades, the seven ages of man, the seven levels of hell, the seven primary colors, the seven notes of the musical scale, and the seven days of the week? What about the seven-point rating scale, the seven categories for absolute judgment, the seven objects in the span of attention, and the seven digits in the span of immediate memory? For the present, I propose to withhold judgment. Perhaps there is something deep and profound behind all these sevens, something just calling out for us to discover it. But I suspect that it is only a pernicious, Pythagorean coincidence.

George A. Miller

You may ask “why do we even care”? I first heard about the magic number in a teaching workshop years ago. Where it was being used to define the number of things you could present in a lecture. However, from a practical point of view, we care about memory span because it is a component of short-term memory and working memory. In education to “learn something,” the information needs to move into long-term memory. Information can’t reach long-term memory without passing through short-term memory. Working memory interacts with both short-term and long-term memory since working memory is the place where we do things with information; compute, analyze, and modify information.

The process of conversion to long-term from short-term memory requires reinforcement of the neural pathways, which is accomplished by repetition or reloading of the information into short-term memory. Repetition and reloading of information is where the capacity limit becomes essential. If we are teaching and we keep bumping information out or filling the short-term memory than the new information cannot be reloaded and reinforced.

In Miller’s law capacity is 7 + or -2 or 5 to 9 chunks. So, if we use this as part of a lesson plan do we teach five or seven or nine new things? I would argue the answer should be the lowest number since that gives the best chance for all the students to learn. Some people say we should teach seven or nine because that lets us identify the “best” students. I think this is incorrect because it fails to acknowledge one of the fundamental differences between short-term and long-term memory. Short-term memory has a capacity limit while long-term memory does not. So as long as there’s sufficient reinforcement every student in the class can learn (transfer to long-term memory) all the information regardless of what their memory span is.

Now I’m going to drop the other shoe the magic number seven was published 62 years ago it was a review of the research as it stood at that time. In 2010 Cowan published a new review titled “The magic mystery four: how is working memory capacity limited and why.” In this paper, Cowan goes on to show how research since Miller’s work has demonstrated chunking and multivariable decision-making shows a wide range of capacity limits that seem to be dependent on the type of information. However, working memory does seem to have restrictions, and moreover, these limits can be used to predict mistakes and failures in information processing. This limit on working memory is 3 – 5 or 4 + or -1.

I like this number a lot better, why? Not because of any research. The reason is that of course design. If I use the argument from earlier, I would “teach” three new concepts at a time. It’s that number “three” that makes me like the research better. Instead of saying I’m pursued and persecuted by a number, perhaps I will say three has been my companion.

Man with the number three
Man with the number three.

A story has three parts, the beginning, middle, and the end. When I write a proposal, I include three goals. The three primary colors in the RGB spectrum. I know these are just coincidences there’s no real meaning behind it. I also suspect if I’m aware of it and willing to think logically when the need is there, there is no actual harm in my companionable number three, for the time being at least I have some research to back me up.

How much do “magic” numbers influence course design? How much should they change course design? In the teaching is an art or science debate I’m on the science side, so I like research. What are you? The critical thing about Miller’s review is that he eventually concluded that the capacities of memory span and one-dimensional judgment were, in fact, nothing more than a coincidence, memory span is still essential to course design.


Thanks for listening to my musings

The teaching cyborg

2 thoughts on “Abracadabra: Your number is 7 Sort of or is it?

  1. Pingback: Tell Me a Story – The Teaching Cyborg

  2. Pingback: Common Core Math Does it Work? – The Teaching Cyborg

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