Michael Seery has posted an interesting summary and discussion of this paper on grading practices, specifically showing working/reasoning. Go read both if you haven’t already, but here’s a TL;DR question: if a student gets the correct answer to a question, do they automatically get full marks or do they need to show their working/logic? Another way of looking at it is this: does the burden of proof lies with the student or the examiner?

Philosophically, students showing their working is something I want to encourage, as it is good for them (makes clear the sequence of logical steps taken, makes checking/reflecting on their work easier) and makes a marker’s life easier (important in the context of exams).

As a test case, consider a student who gets the correct answer using an incorrect method (e.g. two mistakes cancelling each other out, or a correct choice made for incorrect reasons). This will be obvious if they show their working, but not if they don’t. In this scenario above, penalising the student only when they show their (incorrect) working has the effect of discouraging students from showing their working in the first place, so it’s not something I want to do. On the other hand, taking marks off for incomplete or missing working does seem a bit harsh if the student has in fact used the correct method!

My question setting/marking philosophy

My broader philosophy is that we should be looking to award marks for working/logic shown, not looking to take marks off for what is not shown. The difference is subtle, but I think the former is a better attitude. A corollary of this is that as an examiner, if you want to see something in an answer you should allocate a mark for it when you’re deciding how much the question is worth.

On the burden of proof question, my personal opinion is that the examiner should write questions such that there is no problem with the burden of proof lying on the examiner if the answer is correct, but that showing working is still encouraged by shifting the burden of proof to the student if their answer is incorrect.

1. Avoid error-cancelling

I try to avoid situations where numerically correct answers can be obtained by an incorrect method. This generally entails just using numbers that are not as nice and/or ensuring that dilution factors/aliquot volumes/concentrations don’t coincide or cancel.

2. Eliminate trivial steps or award marks only for non-trivial steps

As an example, consider the following question:

25.00 mL of 0.1012 M hydrochloric acid is required to neutralise 20.00 mL of a sodium hydroxide solution. Calculate the molar concentration of the sodium hydroxide solution. (3 marks)

For which my ideal working might go something like this:

HCl(aq) + NaOH(aq) ? NaCl(aq) + H₂O(l)

n(HCl) = 25.00 mL x 0.1012 M = 2.530 mmol

n(NaOH) = 2.530 mmol

[NaOH] = 2.530 mmol / 20.00 mL = 0.1265 M

Conceptually the student has to take 3 logical steps (for 3 marks):

1. Calculate n(HCl)
2. Realise that n(NaOH) = n(HCl)
3. Calculate [NaOH].

But consider a student who writes the following (quite common in my experience):

n(HCl) = 25.00 mL x 0.1012 M = 2.530 mmol

[NaOH] = 2.530 mmol / 20.00 mL = 0.1265 M

They have clearly done steps 1 and 3, but how can you be sure about step 2? Does the burden of proof lie on the student or teacher here (i.e. do you award them 2 marks or 3 marks)?

I would alter this question in one of two ways to avoid this problem:

• Make the question out of only two marks and to award those marks for steps 1 and 3 (i.e. no marks awarded for taking the trivial step 2). This is not my preferred option, but it does keep the question easier.
• Keep the question out of 3 marks and make step 2 non-trivial

e.g. use H₂SO₄ instead of HCl so the mole ratio is no longer 1:1 and change the NaOH volume to 10.00 mL:

25.00 mL of 0.1012 M sulfuric acid is required to neutralise 10.00 mL of a sodium hydroxide solution. Calculate the molar concentration of the sodium hydroxide solution. (3 marks)

For which my ideal working might go something like this:

H₂SO₄(aq) + 2NaOH(aq) ? Na₂SO₄(aq) + 2H₂O(l)

n(H₂SO₄) = 25.00 mL x 0.1012 M = 2.530 mmol

n(NaOH) = 2 x 2.530 = 5.06 mmol

[NaOH] = 2.530 mmol / 10.00 mL = 0.506 M

Conceptually the student has to take 3 logical steps (for 3 marks):

1. calculate n(H₂SO₄)
2. realise that n(NaOH) = 2 x n(H₂SO₄)
3. calculate [NaOH].

This shifts the burden of proof off the student: if I (as an exam setter) want to find out if a student can do something, I make sure they have to do it in order to get the right answer. I favour this course of action, as it also means that students who blindly apply the dilution formula (C₁V₁=C₂V₂) will not get the right answer.

If a student gets the correct answer then they must have performed all required steps, so I am comfortable with the burden of proof being on the examiner in this case.

The problem with this philosophy is that it doesn’t encourage or require working at all. Here’s the kicker though…

3. Award carry-through errors only if working is clear

So if a student gets the correct answer but with little/no working, they are awarded full marks. What if they don’t get the correct answer? This is where the exam-based reinforcement of all the intrinsically good reasons for showing your working/logic happens…

Got the wrong answer but showed all your working? You’ll be awarded marks for any step for which you have the correct working (regardless of previous errors). So for the example above,  if you show correct working for steps 1 and 3 but you miss the 2:1 ratio in step 2 (or apply it the other way around), then you will still be awarded marks for correctly performing steps 1 and 3.

Got the wrong answer and didn’t show clear, logical working? You’re out of luck, buddy.

I don’t have a problem with shifting the burden of proof onto the student in this case, as they’ve already demonstrated that they haven’t done at least one of the required steps.

What do you think? Where do you decide the burden of proof lies? Are you comfortable with the burden of proof shifting depending on whether the final answer is correct or not?

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