To give some context for this post, I’ll start by saying that I absolutely love Craig Barton’s podcasts. Whenever I listen to one I almost always have to re-visit given the ridiculous number of ideas and claims made. One thing’s for sure – Craig Barton deserves a bloomin’ medal for the work he’s done on these podcasts and his contribution to maths education in general. It’s crazy just how good these episodes are for PD – I always learn so much – but then I always leave with more questions than I know what to do with.
With that in mind, last night I re-listened to the podcast with Greg Ashman; like every other Craig Barton podcast it’s absolutely brilliant! Greg is highly knowledgeable about Cognitive Load Theory and I took a lot away from his responses. Since the start of my career, I’ve been a proponent of a balanced view of educational theory in that I happily use explicit instruction, but also think that there’s a good chunk of mathematical knowledge that can be internalised through structured investigation or inquiry (I rarely use open investigations or inquiries). More recently, proponents of Cognitive Load Theory (CLT) have begun to swing my thoughts towards the balance between explicit instruction and investigation, and if I’m honest, I’m starting to come round to changing elements of my practice to take more account of CLT.
I’ll also be additionally honest and say that I’m a bit worried by all of this. I’m worried that teachers aren’t questioning every element of CLT and ensuring, as far as possible given that we’re in the social science game, that they dig deep into CLT to fully understand how it might affect their practice. With this in mind I have a few questions about CLT, specifically based around the Greg Ashman’s responses. I could look it all up in the Literature – assuming it’s present – but that wouldn’t be taking advantage of the benefits of social media. So here are my major questions from this podcast – hopefully some awesome person will answer these without much effort and then I’ll be happy to move forward.
Working Memory and Discovery
Greg explains a piece of interesting research conducted by Sweller that students were given some problems in which they either had to multiply by 3, or add 29 (something like that anyway). Sweller cleverly put these problems together so as to ensure that the students were simply alternating from adding 29, to multiplying by 3, to adding 29, etc. He did this to determine whether they would discover this underlying structure to the problems, or whether their working memory would be filled up by the act of determining what to do. It turned out that the wide majority of students didn’t see the underlying structure, and their full attention was on the surface operations of the problems.
Questions:
- Did Sweller notify the students that there was an underlying structure to the problems? This would clearly have an effect on their mindset during the task and might shift the focus to a higher level of discovery for more students.
- What if Sweller had simply told the students to track their calculations by just writing them down – and said nothing else about discovering anything. Students wouldn’t have to hold extraneous information in their head, and this would not affect their processing of working memory. In this case, I assume that their attention during the task would be on solving the problems, and then after some time it would be simple to recognise the deeper structure. The whole premise behind CLT is to reduce the processing of working memory, and tracking your process in a written form does not conflict with that.
Explicit Instruction vs Pure Discovery
Greg explained a separate piece of research where science students were explicitly taught concepts, and in contrast, other students were given the opportunity to discover the same concepts. When it came to the assessment, those students who had discovered those principles performed no better than those students who had been explicitly instructed during the assessment task.
Point:
- I agree with that fact that, probabilistically speaking, more students in the explicit instruction group would have attained the knowledge required for this specific assessment. That clearly has implications for teaching knowledge that we all have to be aware of.
Question:
- When did the assessment happen? Straight after the learning experience, a few weeks later? I have always thought that when learning is attached to our emotions – in this case the pleasure of discovery – that we are more likely to retain that knowledge. Of course I agree that deliberate and spaced practice, retrieval cues, etc. will also improve long term memory, but memory seems more intricate than a basic knowledge of the Forgetting Curve. Indeed, a quick google search provides a large body of research on this (Example Link). Therefore, is it plausible to think that those who discovered these principles, whatever they were, are more likely to retrieve them at a later date?
One last point I’d like to make is that I’m pleased that Craig asked Greg about the continuum of direct instruction because most things in education aren’t binary. If I say that I prefer an explicit instruction approach, then that could mean a whole world of things. I could be on the “lecturing” end of that continuum, or the more liberal end of the continuum. Some people prefer to call the more liberal end dialogic instruction (Danny Brown introduced me to dialogic teaching in this blog), where there is constant dialogue between yourself as the authority in the classroom, and your students. In this case, if you’re introducing anything, such as the formula for the area of a trapezium, you lead and steer the construction via a mixture of explanations and student responses.
So if anyone can help with the questions above I’d massively appreciate it. I can’t help thinking it’s our professional duty as educators to maximise outcomes for our students (and I think to excite their curiosity and interest in mathematics). I therefore really want to fully understand the true implications of Cognitive Load Theory on my practice.
Teaching Mathematics 
Some of the studies that focus on single lesson ‘who learned it better?’ miss the point to me. In the science discovery study, did the explicit instruction learners also do no better than the discovery students? What was the usual mode of the class? If it was explicit and the students did that well in a novel discovery lesson, that’s interesting. What about longer term retention? What about attitudes/disposition towards science? Which group of students learned better how to do science? Pose questions?
For me, in practice, CLT is about trying to be able to understand what I am asking my learners to do. When I err teaching, frequently, it tends to be on the side of not providing enough support to do the challenging things I’ve asked. But I’ve found it’s easier to add support than it is to add challenge. Sometimes it’s a good opportunity to demonstrate my thinking, which to me is different than explicit instruction.
I think you got answers from Christian, and I’ll do my best to answer based on what I know. I like your questions because they go into individual studies, which I think is always productive for thinking about research.
Did Sweller notify the students that there was an underlying structure to the problems?
No, he did not. Your thought that this might help the discovery condition seems plausible to me. Still, I think that this wouldn’t help much for true novices. People are already pattern-seeking machines — I think a reminder to look for patterns might help a bit, but I’m not sure how much. Plus, that’s another reminder that the learner would have to pay attention to mentally, which would make it harder to look for patterns…
What if Sweller had simply told the students to track their calculations by just writing them down – and said nothing else about discovering anything.
In that case, though, what is the problem solving contributing to the learning? Wouldn’t it be more effective to just supply students with the list of steps and ask them to look for patterns in them? (“Timothy was trying to solve a problem and found the following…”)
There is an answer I have to this question, personally. Sometimes, discovery is fun and worthwhile. It gives students a taste of the excitement of doing math at the highest levels. It makes kids proud to figure things out.
The way I square CLT with this is that I say, ok, what am I going for right now? There are times when I want to teach in the most effective way possible. Other times, I think I’m OK losing some efficiency for the sake of a fun lesson or doing something that really teaches what the domain is like at the highest levels. Or because I want kids to be looking for patterns. Whatever. (If you’re eager for more thoughts along these lines, check out this post of mine.)
I have always thought that when learning is attached to our emotions – in this case the pleasure of discovery – that we are more likely to retain that knowledge.
For what it’s worth, this is not what I find. Or, rather, I find that kids remember what they spent their time thinking about. When kids look back on Friday’s lesson, will they remember the math? Or will they remember that they had a blast and had that great insight?
Again, I don’t think this is a case against making the classroom fun or enjoyable. But I think extreme emotions can be a distraction to lasting learning. What this means to me is that if I engineer a really thrilling experience for kids (every blue moon!) that I need to be especially careful to follow that up with something that will follow-up on the experience to make sure that learning is general, that it’s sticking, etc.
I frame things in terms of trade-offs, because I do think that this reflects how I think about my teaching. It’s important to have teaching tools for the different sorts of classroom experiences you want to create. If CLT has figured out some nice techniques and general guidelines for efficiently engineering learning in the classroom, it’s good to figure out how to incorporate them as much as possible in your teaching. It doesn’t mean they’re all that you ever do.
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