Here's a number: 579831. If I let you stare at it for 20 seconds, and bar you from taking notes, would you be able remember it correctly in half an hour? The chances are, with a little effort, most of us could. What about this number: 638592746109837? Under the same conditions, without a toolbox of memory techniques to hand, the vast majority of us would fail.
The reason for this failure is the limitation of our working memory. And for teachers intent on challenging their students with ever-harder tasks, these limitations are worth examining if we are truly to help young people learn.
Before we begin to explore the issue, we must accept the following: all thinking is hard and most of us try to avoid it. As psychologist Daniel Willingham explains in his book Why Don't Students Like School?, "People are naturally curious, but we are not naturally good thinkers; unless the cognitive conditions are right, we will avoid thinking."
In order to learn something we must think about it, so teachers have to be adept at creating that appropriate environment. One way we do this is by ensuring that a task is challenging: we push our students towards more difficult tasks in the belief that their learning will increase accordingly.
This is where working memory comes in. Unfortunately, the number of things we can pay attention to is extremely limited. In fact, it is thought that we can concentrate on only between four and nine items at any one time. If we are presented with more than this, we are likely to suffer from cognitive overload and find ourselves unable to grasp all the features of a problem or task. At this point, we stop learning.
A classic example of this is when students complete practical work in science lessons. Often, the demands simply of following the procedure can fill up the working memory, leaving little space to consider the science involved.
On the surface, this all seems very debilitating, putting limits on our performance. However, there is good news. Once we have internalised knowledge and organised it into coherent "chunks" by committing it to long-term memory, that knowledge is then available for us to manipulate. Each chunk acts as one item. For instance, the letter "b" would be a single chunk if it were in a list of random letters we wanted to remember. However, the word "brain" is also a single chunk rather than five different ones, because the concept of the brain has a meaning that we can draw on from our long-term memory.
So in the science lessons referred to above, the problem can be mitigated by practising the process in advance so that students are using procedures they are already familiar with, or by looking at the theory and the practical work separately.
This point is reinforced by the "worked example effect". The Australian psychologist John Sweller trained students to solve algebra problems in two different ways. The first group learned by working out how to solve the problems unaided. The second group were given worked examples (solutions showing each step) to study before solving problems themselves. Given that the first set presumably needed to think harder, you might expect them to learn more. Not so. It was the students who studied the worked examples who showed the greatest gains. The first group had become "overloaded".
So offering the right level of challenge is crucial. Too little and the students learn nothing; too much and you get the same result. What teachers need to do is to find the sweet spot between the two extremes - a point that Russian psychologist Lev Vygotsky called the zone of proximal development.
In trying to determine this point, we have to realise that people don't often solve problems or respond to tasks by thinking them through. It takes a lot less mental effort to pull a ready-made solution out of the long-term memory than it does to think one up from scratch. For example, when a child who has memorised her times tables recalls that "seven eights are 56", she is not working this problem out from first principles.
Our tendency to defer to our long-term memories can be a problem. We are so keen to do this that we often come up with inappropriate solutions to the problems that we face. We have all taught students who have answered a different - usually more straightforward - question than the one that was asked. If you find yourself writing "read the question" repeatedly on your students' work, there is a good chance that this is what is happening.
So finding the balance of challenge is difficult but it is not impossible. The first step is to recognise that these problems are occurring - we must be alert to when a student is recalling not thinking, for example, and should consider separating instructions from work and recalibrating how we view tools such as worked examples. You can also try these techniques:
One reason for cognitive overload can be that there are simply too many things to focus on. Strip your lessons back to the essentials, especially when students are new to a concept. Treat different aspects of a complex problem as separate entities before bringing them together. Avoid complicated contexts when introducing students to an idea - a chemistry question that begins with a paragraph of dense text about iridium production in some far-flung region before resolving into a relatively straightforward calculation is probably best left until later in the learning cycle.
Ensure background knowledge
In order to think well, students need chunks of learning that they can manipulate. Some of these chunks are fairly obvious, although not always highly regarded: times tables, vocabulary, spelling, the basic processes that become subsumed into the larger problem. By teaching subject-specific vocabulary, for example, you are clearing away some of the problems a student has to work through, thereby lessening the chance of cognitive overload.
Conflict is good
Students will always fall foul of common misconceptions and it is useful to tackle these head-on. You should not only point out when your students are incorrect but also set a few traps in the form of questions or tasks that they will get wrong if they have misunderstood. This is a powerful learning experience and will save them time in the long run.
Spot the signs
Finally, if you are ever in doubt as to whether the task is too hard, look for the warning signs: panic in the eyes, furious rereading of the task and that familiar phrase, "I just don't know where to start."
Of course, we all want our students to work hard. But we need to remember at the same time that working too hard simply restricts their learning.
Greg Ashman is a teacher at Ballarat Clarendon College in Victoria, Australia
Clark, R, Kirschner, P and Sweller, J (2012) "Putting students on the path to learning: the case for fully guided instruction", American Educator, Spring: 6-12.
Danziger, S, Levav, J and Avnaim-Pesso, L (2011) "Extraneous factors in judicial decisions", Proceedings of the National Academy of Sciences of the United States of America, 10817: 6889-92.
Sweller, J (1988) "Cognitive load during problem solving: effects on learning", Cognitive Science, 12: 257-85.
Willingham, D (2009) Why Don't Students Like School? A cognitive scientist answers questions about how the mind works and what it means for the classroom (Wiley).
Read a study about information overload in online courses.
Improve students' memories with this useful selection of strategies.
Extend young people's thinking with 50 brain-stretching exercises.