When the clocks went forward in March and we arrived in British Summer Time, I made an abortive attempt to change the time on my car’s clock. I knew, from having eventually changed it six months ago, that this is a process entirely within my grasp and yet, after about 10 minutes of frustrated fumbling, I’d only succeeded in moving the time forward by 20 minutes. I gave up and resigned myself to having a clock that is 20 minutes fast for the foreseeable future. 

This has resulted in a few moments of confusion and panic over the past few weeks. Things came to head when I rushed to get my daughter to her music lesson last week. There’d been a fair bit of bitterness, recrimination and stress, only to find we had actually arrived ridiculously early. Sod it, I said, it’s time to get the manual out. Perhaps unwisely, considering how high feelings were running, my daughter scornfully pointed out that this was exactly what I’d eventually done six months ago. Quietly seething, I looked up the instructions and changed the clock to the correct time.

This is, I think, the problem with problem solving in a nutshell. The ability to solve problems is an evolutionary adaptation; very young children rapidly learn how to solve the various problems they encounter. They look about themselves to establish what means they have available and then apply these means to achieving their end, whatever that may be. In this way, they learn to roll over, fit blocks together, and get adults to do stuff for them. Most of the problems we solve are ones we need to solve again and again. As such, the most efficient way to solve problems is to remember the solution and apply what we did before. With sufficient repetition, we store the solutions to solved problems in long-term memory, which means when we face the same problem again we don’t even have to think about the solution. How efficient is that?

Problem-solving search is the name cognitive scientists have given to our biologically primary ability to solve problems. The two main strategies involved in problem-solving search are schema acquisition (remembering successful solutions, then recognising similarities between novel and previously solved problems) and means-end analysis (working backward form the goal until a workable solution is found). Most of the problems we face in life are ones we have already solved, or are close enough that we can generalise solutions from closely related problems. Schema acquisition is the key to expert performance within a domain, allowing experts to think about other, possibly more interesting things as they go about their business. But, when novices face a problem for which they don’t have a conveniently stored solution, they have to think.

In this paper, John Sweller explains why problem solving is an inefficient way to build up the schemas required for expert performance. The attention and processing required to engage in means-end analysis results in less capacity to store solutions in long-term memory in a way we can be easily accessed in the future. In order to build up useful schema, Sweller says “a problem solver must learn to recognize a problem state as belonging to a particular category of problem states that require particular moves.” This takes attention which, if it is being used to search for solutions, will not be available to recognise patterns.

Back to the clock in my car. Because I’ve successfully solved the problem of how to rest the clock, I’ve stored the solution in long-term memory, so why do I struggle to retrieve the solution every six months? This is the difference between familiarity and recall – although I’m familiar with the solution (that is to say, I recognise it when I look it up) I can’t bring it to mind when I want it. My car clock schema isn’t well enough developed for the precise solution to be stored, ready for recall. If I were to regularly practise changing the time then I’d quickly strengthen my schema and would, in due course, permanently store the solution. But I don’t; I only try to change the time twice a year. And because each attempt involves means-end analysis, all my working memory is involved in trying to solve the problem rather than trying to remember the solution.

This is exactly what happens in lessons. If students spend lesson time trying to solve problems – whether that’s writing an essay, choreographing a gymnastic routine, or using a computer program – they’ll be applying the only means a novice has available: means-end analysis. Even if they successfully solve the problem, the likelihood is they won’t remember the solution. But, if students spend lesson time having the patterns of problems explicitly modelled and then practise retrieving solutions, they’re likely to build up the schema necessary to solve future problems.