Many psychologists accept variations on a model of the mind that consists of a limited ‘working’ or ‘short-term’ memory and an effectively limitless ‘long-term’ memory. This model is the basis of learning theories such as cognitive load theory.
The working memory is the mind’s sketchpad where we complete conscious and effortful thinking. However, once we have sufficiently practised something we can simply and easily retrieve the steps from long-term memory without really thinking about it. The classic example of this kind of ‘automatisation’ is driving to work and not being able to remember much about it.
The limitations of working memory have been used as a basis to argue against discovery and other implicit forms of learning. However, I am also of the view that these limitations have profound effects on the act of teaching.
How does working memory affect teaching?
Recently, I was teaching a Year 12 maths class. I displayed a question on the screen that asked for the coordinates of the maximum value of a restricted function. This wasn’t as straightforward as it might appear and so I worked quite hard to both solve the problem and simultaneously explain what I was doing. At the end of it, I stated an x-value and stopped.
I then flicked to my next slide that showed a solution to the same problem; a solution I had worked through in advance. The difference between this answer and the one I had just demonstrated was apparent: I needed more than just an x-value because the question had asked for coordinates. The students noticed the difference and this prompted a discussion of ‘silly’ mistakes. Finding an x-value and thinking you have finished the question is a classic silly mistake but such errors are badly named. Silly mistakes are nothing of the sort. Instead, they tend to indicate that a student hasn’t yet mastered the required method and so needs to devote so much processing power to solving the problem that key details slip out of working memory.
So why was I making such a mistake as a maths teacher? In the comfort of my office I probably wouldn’t have done so but in class I had the added cognitive demands of explaining what I was doing in real time.
Teaching is an extremely complex act. Teachers need to attend to the classroom on a number of levels. Some of these are about classroom management, others relate to basic administration, and that’s before we even start on the cognitive work of the subject itself, overlayed with monitoring student responses and levels of understanding. I can still remember being overwhelmed as a trainee teacher. It’s not simple.
Increasing working memory capacity
I’ve managed to forget to do pretty basic things in class like take an electronic register or pass a message to a student. I have taught a whole lesson with a marked set of work to return to the students, only to realise, once the last student has left, that the pile is still sat on my desk.
It would be great if I could increase my working memory capacity but, although many training programs have claimed to be able to do this, it doesn’t seem possible right now. General intelligence is related to working memory capacity and so another solution might be to replace me with a more intelligent teacher.
Cognitive aids
Short of somehow becoming brainier, there are a number of steps that teachers can take to mitigate the effects of limited working memory and they all involve cognitive aids that teachers can subcontract some of their thinking to. In my case, I plan my lessons around a PowerPoint and so I add my cognitive aids to this.
For instance, if there is an important point that I want to make then I add a little box to the relevant slide that says, “remember to mention domain” or whatever it is. Sometimes, I animate these reminders so they appear before I can move on to the next slide but without sitting on the original slide from the outset. Cognitive aids that the students can see are useful because the students will point these out to me if I miss them myself.
And that’s why, in the example above, I had produced a slide with the worked solution to the problem, even though I intended to model this solution myself. Having the solution available enabled students to spot the difference and sparked a discussion.
In reverse
The fact that we tend to automatise things that we practice a lot means that the working memory problem also acts in reverse. An experienced teacher might do something automatically and not think to make a note of this in her lesson plan. If a less experienced colleague then uses this plan he will need to do that thing consciously and yet there is no prompt for him to do so.
Much as I hate role play, I now believe that one of the most powerful things we can do in meetings is ask teachers to model, in real time, how they would teach a particular concept. The concept in focus must be tightly contained and may be decided upon by looking at assessment data: What do some students find tricky? What questions do Teacher A’s students do better on than Teacher B’s? You then pass Teacher A a board marker and ask him to show you what he did, while questioning him on why he did it that way. It is then possible to capture the little unwritten subtleties and place them explicitly into the plan as cognitive aids so that everyone may benefit.
Filling the pail 
What cognitive scientists call the “central” strategy to improve student problem solving is “memorization to automaticity.”
In the 2008 Report of the US National Mathematics Advisory Panel (NMAP), cognitive experts Geary, Renya, Siegler, Embertson, and Boykin write,
“[T]here are several ways to improve the functional capacity of working memory. The most central of these is the achievement of automaticity, that is, the fast, implicit, and automatic retrieval of a fact or a procedure from long-term memory (Geary et al. 2008).
Most instructors will likely agree that a student with a poor math background will tend to have difficulty in quantitative science courses. What may be surprising is how well students must memorize fundamentals to be adequately prepared for scientific problem solving. The NMAP authors add,
“[During calculations,] to obtain the maximal benefits of automaticity in support of complex problem solving, arithmetic facts and fundamental algorithms should be thoroughly mastered, and indeed, over-learned, rather than merely learned to a moderate degree of proficiency (Geary et al. 2008).
“Over-learned” means that facts and fundamental algorithms are memorized until they can be recalled fast, perfectly, and repeatedly. The rules for mathematics also apply when solving well-structured problems in the physical sciences (Anderson et al. 2000).
For additional detail, see http://arxiv.org/abs/1608.05006 and NMAP Chapter 4.
Greg,
Sounds like you need
Assuming Doctors and pilots are reasonably smart people who have adopted checklists because you want to concentrate on some things and not everything it makes sense to follow their lead.
A generic checklist at the start and end of each class would mean – all messages given out -tick , all marked work returned tick, etc.
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