Teaching Procedural Knowledge

School Science is stuffed full of declarative knowledge, which comes in lots of different forms and has to be applied in lots of different ways. I think this makes it hard to teach well. I’ve written about the basic approach I share with the trainee teachers at the University of Southampton in a couple of earlier posts.

However, the calculations and other procedural knowledge seem to also present a stumbling block. I’m a bit surprised by that because I think it’s a lot more straightforward to teach these parts of the curriculum. On the other hand, when faced with a calculation you can’t really do, there’s no pretending that you’re half-right. I’ve seen a few trainees really mess this up, making a hash of things the first time then, faced with a class unable to tackle independent practice, have another go, only to dig a deeper and deeper hole for themselves.

I think we all experienced the “I do; you do” approach in our own maths classes at school. That often works for high achieving children trying to do something that’s not hugely challenging for them, but it’s not enough when achievement levels are lower, or challenge is higher. “I do, we do, you do” is more like it but I think there’s still a bit more to it than that so what follows is the model I want my @SotonEd trainee teachers to start from. Here’s the overview.

  • What does ‘good’ look like?
  • What are all the steps needed?
  • Check and/or teach each step
    • Example/problem pairs
    • Modelling
  • Combine steps
  • Are there any exemplars?
  • Independent practice (faded scaffolding)
  • Assessment

What does good look like?

This is about the level of challenge you are aiming for. Do you want the children to be able to balance this:

Mg + O2 –>  MgO          or this?          Al + HCl –> AlCl3 + H2

If you don’t think about this, you’ll probably teach to the first example, and then most children will get shut down when their independent practice gets to the second example.

What are all the steps needed?

@chemDrK wrote a terrific description of the steps involved in working out the formula for magnesium sulphate (read the whole post but scroll down a fair bit for MgSO4 ). It’s this level of detailed analysis that’s needed. Trainee teachers have a terrible time getting past the curse of knowledge and really breaking a procedure down into its smallest steps.

Check and/or teach each step:

Since we seem to be on chemistry, and balancing equations is a good example of procedural knowledge, let’s stick with that. If children can’t confidently distinguish between Co and CO, and don’t know what CO and CO2 represent then they’re not likely to get anywhere with balancing C + O2 –> CObecause there will just be too many things to think about.

So before teaching balancing equations there needs to be some careful checking that children can ‘read’ chemical formulae correctly. Usually, as their teacher, you’ll have a fair idea of what they ought to already know. If you think they already know it then checking shouldn’t take long but you must still check! If they don’t know it, you can fix things before confusion sets in; if they do know it then they’ve activated the relevant schema and should be able to use that prior knowledge more easily. I’d tend to use mini-whiteboard questions for this.

Once the checking is done and any missing knowledge is dealt with, it’s time to teach the new procedure, step-by-step. Example-problem pairs are an excellent way to do this. @mrbartonmaths explains these in How I Wish I’d Taught Maths (Chapter 6) but the heart of it is two near-identical questions, the first completed by the teacher as an example, the second completed by the children to match.

exampleproblem

Example-problem pairs are just a specific example of modelling. If you look at this (by now I hope well-known) presentation of a good method for balancing chemical equations, it might not fit into an example-problem pair format but I do, we do, you do, can still be applied. The key is to make the first supported examples as similar to your modelling as possible. The other thing about modelling is you must always follow the same procedure, and you must always set out all your working neatly, in full. Again, and again, I see trainee teachers rushing through a calculation, skipping steps and jotting messily on the board. You might be able to get away with doing it like that occasionally but you’re just teaching bad habits. Slow down; do it properly!

Sometimes the whole procedure needs breaking down into smaller pieces. For example, with Punnett squares, it’s well worth doing how to set out the parental genotypes as a separate step, getting them to successful independent practice, and only then doing the diagram completion step. I also think it’s worth isolating the conversion from completed Punnett square to an “Each offspring has a 25% chance of having white fur” style answer. Again, the curse of knowledge features heavily here. You’ve either known how to do Punnett squares for years, or you’ve spent an hour earlier in the week swotting up. You know how the whole thing works. The terms homozygous and heterozygous, and the relationship between genotype and phenotype all make sense to you. The only difficulty you have with expressing the outcome as a probability is making sure you use correct language – you know the square doesn’t show exactly four baby mice. None of this is necessarily true for children learning this procedure. Break it down!

Combine Steps:

If you’ve split into more than one step, you do have to blend the steps together. It’s just the same process of modelling it first. Emphasise when you start and finish each step. On the other hand, you don’t need to narrate your way through each step. The children know how to do the step. Let them follow without the distraction of having to ignore you talking.

The first step is to put the alleles from each parent into the Punnet square… [silent working]… Now that the square is ready we need to complete it… [silent working]… Finally we need to look at the question again, which says [read it] so our answer is… [write it out].

Are there any exemplars?

Exemplars is another idea taken from Ruth Walker. Although procedural knowledge can be used to tackle a near-infinite range of questions, sometimes there are particularly good illustrations that are an expected part of school science. This is much more of a thing with declarative knowledge but, for example, you’d want all children to have encountered naming the salts formed from sulfuric, hydrochloric, and nitric acid, but not necessarily from citric, ethanoic, carbonic, sufurous, oxalic, phosphoric, and titanic (yes, I know, if you’re not a chemist, there is a titanic acid – that’s mega! Only just learned that today). For Punnett squares, mouse fur colour, dog coat type, pea flower colour, stem length, and smooth or wrinkled seeds, are probably exemplars. For calculations, there aren’t normally any exemplars but certainly most children should have done v=fλ with visible light and domestic radio wavelengths.

Independent Practice (faded scaffolding)

When I started teaching, and certainly when I was at school, we were well-served by textbooks with loads of questions. I particularly remember a thin blue chemistry book from which we had to do five questions every week for homework, and one for A-Level physics calculations that I used to set work from until the dissonance between not having a single diagram in the whole book, and A-Level papers having one for every question, became too great. For a while, the move to rush out GCSE-spec-specific texts meant we lost all that, but I digress. The point is that resources for Shed Loads of Practice (SLOP) are back in fashion, and need to be used. The #CogSciSci website is one starting point but science departments ought to have this at least semi-organised for you.

I’ve already said that “I do; you do” doesn’t really cut it. Here are ways to bridge the gap from modelling to independent practice beyond the example-problem pair idea:

Faded worked examples

As well as making intuitive sense there’s been some decent research on this. Here is an example from Joseph Allen but it’s not hard to create these if you already have an electronic version of the questions. The format can be very simple. You will find you need to explain what’s going on, the first few times children encounter these.

Worked examples when the questions get slightly trickier

Here is an example I use for practising unit conversions on the @SotonEd Subject Knowledge Enhancement course.

worked egs

Re-modelling

Sometimes you might want to increase the demand of the procedure and go back to modelling. Here are three example-problem pairs I use for teaching calculation of gradients. The first is like maths with no quantities on the axes, working through to the last with proper graph paper and non-linear parts that need to be ignored. After each one, students practice a few in that format.

Here are some final thoughts on independent practice.

Decide on the level of noise you want and stick to it. Personally I can’t see any reason not to go for total silence but it will depend on you and your setting. Just bear in mind that quiet conversation = significant numbers of children only applying 50% concentration = half the learning and/or takes twice as long.

You need to create a culture where there is an expectation to work hard but no expectation to ‘finish’ otherwise you get horrible dead time waiting for the last few. Ideally, all children will have done several questions, most will be nearing the end, and a few will have got on to something else. Sometimes this might be adding challenge (balancing S + HNO3 –> H2SO4 +  NO2 + H2O, or a bit of information and a dihybrid cross to try, or drawing the steepest and shallowest gradient on a set of data and finding the range of the gradient) but avoid setting something you then have to spend time explaining when supporting the strugglers is more important. Avoid that by having something from previous topics to do as a permanent standby for early finishers. This also takes pressure off to always find interesting extra challenge. The thing to avoid is just more of the same.

Assessment

Finally, you need to know whether it’s stuck. You can’t do this in the same lesson. If children have just calculated a dozen resistance values, you’re not going to find out anything by asking them to do one more as an exit ticket – just look at their books. However, asking them to do one in the next lesson, or in a week or two, will tell you something useful. Asking them to elaborate on the procedure is also useful – a good elaboration shows deeper understanding than just being able to do it, and therefore longer-term stickiness.

Best wishes

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