A Rate of Learning


The inspiration for this post comes from this tweet by Heather Julian (Twitter @mathrules13) and re-tweeted by Jill B (Twitter @jillgrafton):mathrules13


I will take it as a given the readers are familiar at least one set of skill/attainment level descriptors going from “can recognise” to “can exploit”, and agree that different people have different levels of recall for different things. I will also take it as a given that readers are familiar with Maslow’s hierarchy of needs.

This post does not refer to any publications, scholarly or otherwise. It is merely one person’s thoughts, and it is intended merely to provoke discussion.

The Teaching-Learning Equation

There are a number of phrases associated with the acquisition of skills and knowledge from a source outside the learner, each phrase having its own level of acceptability in different contexts. Examples include “teaching”, and “delivery of learning”. My own sense is that such phrases can obscure the dynamics of the teacher-pupil situation. Given the context implied by Heather’s tweet, I propose a scenario where the teacher:

  • has full command of the subject
  • is totally self-confident
  • has excellent communications skills
  • has good empathy
  • has a good grasp of the pupil’s current knowledge base in the subject

(I can hear some of you thinking back to your own school days and thinking “I wish!”.) Also, to do justice to Heather’s question, I think that we need to focus on what is going on in the pupil’s mind (and here I am forced to rely on my own memories of school, as augmented by how some of my own students have demonstrated learning).

A Model of Learning

My own model of learning is constructivism. In the context of numeracy, a grasp of whole numbers is necessary before the idea of fractions can have any meaning, for example, and the rest of this post is written accordingly.

I find the words “truly remember” and “meet our standards” to be thought-provoking, as it raises questions about what level of memory is being envisaged, and whose standards are being applied during assessment. Using the “quadratic formula” as an example, memory may range from recalling “I know that phrase means something” to being able to write it down upon the instant (as well knowing what it is used for), and its consequent relationship to skill/attainment level descriptors.

Extending the words “truly remember” and “meet our standards” to what the learning experience means for the pupil can also be revealing. Again from personal experience at high school, I was in one cohort where everybody was expected to learn lines of poetry and recite them in class. I learned what I needed to in the preceding 48 hours, recited, and promptly forgot them one hour later. In terms of the teacher’s expectation that we should all enjoy poetry, it was for me a disaster: his standards were irrelevant to me at a personal level.

At the opposite extreme, and at the same school and at about the same time, I had a number of experiences that I found to be highly relevant. I have room here to describe only one of them. The subject was mathematics. The class had been working though material for a few days, and I was not quite sure of how all the bits and pieces fitted together. Towards the end, the teacher spoke a single sentence and everything suddenly fell into place. That learning has stayed with me for over 40 years, this in stark contrast to the poetry experience.


Teachers may have aspirations for their pupils. Sometimes those aspirations are selfish. At other times they are focused on the pupil. I have memories of both from my school days. It is for this reason that I posited the scenario above.

We are now into the complex area of the teacher’s motives, skills, knowledge and abilities and the interaction of these with the pupil’s motives, skills, knowledge and abilities. I argue that it is this complexity that rules out any simple answer or answers to Heather’s question, and that perhaps we should instead be asking ourselves “What can I do to help this pupil towards self-actualisation in as quick and as efficient way as possible?”.


It’s not an easy job!