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Approaching Problem Solving: Procedural Knowledge

 

I am moving to a new exam specification next year for A-Level economics which has more extended writing questions where pupils problem-solve rather than shorter factual questions (which there were more of in the EdExcel spec).

Following on from an excellent chapter on novices not being mini-experts in ‘How Learning Happens’ I have just read David Didau’s ‘Making Kids Cleverer’ where he talks about this in depth.

Aside from the points about the need for pupils to have a deep schema of knowledge that they can easily recall enabling them to effectively problem solve, I found the notion of different types of knowledge especially useful.

Declarative Knowledge

What I found particularly useful is the distinction between declarative and procedural knowledge. Declarative knowledge would be the ‘things’ I want pupils to know. If I wan pupils to be able to eventually solve problems about when governments should intervene in a market by imposing an indirect tax the declarative knowledge they should know is:

·         the market mechanism with perfect competition with no market failure

·         causes of market failure

·         comparison of this and under perfect competition

·         how an indirect tax can correct this market failure

·         potential drawbacks of imposing this tax (government failure)

This does not include the tacit knowledge that experts use when solving a problem without realising it. This needs to be automated with a strong retrieval strength so they are not having to think about this when problem solving. So far, so obvious but the part I have been missing that intrigued me is how experts and novices then use this information to process solving a problem.

Expert v Novice Learners

He speaks about a novice looking at the superficial elements of a problem rather than the deep structure. So to the question ‘evaluate if the government should impose a ‘sugar tax’ on fizzy drink manufacturers’ they will focus on the detail of the issues of fizzy drinks rather than the deeper structure of negative externalities and government intervention that the question is really asking about.

To me, the exact way to solve this problem is clear, something he refers to as expert-induced blindness when I have forgotten the steps to take to solve this problem as a novice. Rather than consider the similarities between this problem and similar problems (which they clearly can’t do as they haven’t encountered many similar problems before) they look for potential solutions to problems, or a means-end analysis.

The key is schema acquisition or obtaining greater knowledge around the solution to problems rather than setting them endless problems. Or in other words, don’t give them the endless essay questions that I had been setting them where they devote their working memory purely to means-end analysis and not storing solutions.

So what the hell do I do?

Rather than ‘solving’ endless problems, what pupils need to understand is how to solve similar problems so they can use this knowledge when looking at new problems with similarities. A novice will need to understand the steps I take when solving a problem, the procedural knowledge.

I have been thinking about this today and I found this quite difficult to consider what I think about when approaching these problems. I suppose that is not that surprising when we consider that I am likely to do it automatically.

But with a bit of thought for solving this type of problem, what I think it:

1.       what is the difference between this situation and perfectly competitive markets?

2.       What is the outcome of this (what is the market failure?)

3.       Which economic agents does this affect?

4.       How would a tax correct this market failure?

5.       Will the costs of imposing the tax be high?

6.       Will the government be able to quantify the market failure to set the right rate of tax?

7.       Will politicians have other non-economic incentives that will influence what rate they set?

8.       Is demand for the product elastic or inelastic and how does this impact the effectiveness of the tax?

9.       Do the benefits outweigh the costs?

And that is the 9-step process that is going on in my head. You could categorise 5-7 as ‘government failure’ but I think it works better to explicitly state the exact thought process.

Teaching this procedural knowledge

The first step is to explicitly model the thought process going on in my head to address this problem. Then, as a novice learner what they will require is a worked example. I would provide a case study which we would read, and I would show my answers to the questions above.

The next step may be a partially completed answer, so they look at a different news story, I go through the first half of the questions and they attempt the last few themselves with feedback. This continues until they get to the point, they can complete this effectively.

There should then be practice of this to the point of fluency with opportunities for retrieval so that pupils are able to use this procedural knowledge to solve similar problems. This does not cover exactly how this should be converted into an essay.

I hope it will make it easier for pupils to understand how to effectively solve these types of problems. I am looking forward to trying it in September, if anyone has any views on this or if I have wilfully misunderstood any of this then please get in touch!

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