## Show that questions

On the recent episode of “Wrong, but useful” Will Davies (@notonlyahatrack) asked the hosts Dave (@reflectivemaths) and Colin (@icecolbeveridge) and guests Samuel (@samuel_hansen) and Peter (@peterrowlett) to discuss ‘why do students hate show that questions?’

I was was a little surprised by the question, as my students love them. They get excited by them because they know where they’re headed and if they make a silly mistake it means they haven’t got the right answer and know to check through to find the mistake (often with my year 13s it’s something really silly because they’ve rushed, such as a plus sign becoming a minus sign or a daft arithmetical error such as 2×3=5!) (nb that’s an exclamation mark, not a factorial sign).

The discussion on the podcast was interesting, but it was accepted by all four members of “the panel” that students do hate them. It really got me thinking, are my students weird? Is it something to do with the way I teach them? I know my students tend to love the subjects I love and, as mentioned here, have often picked up my preferences for methods. Have I drilled my students in such a way that I’ve made them love these questions? Perhaps I have, but I think that’s a good thing. They are the questions where you can be sure to eliminate silly errors, so if you have the mathematical ability, you should have the marks.

I was fascinated by the discussion though, Dave suggested that the hatred could be built from the myth that maths has a right or wrong answer. This is a myth that I find irksome. It’s a total fallacy and yet people who lack knowledge about maths assume this to be the case. We’ve all had those comments “ha, marking? You’ve got it easy, just tick or cross right?!” These negative perceptions of maths are often passed on by parents, and sometimes by teachers of other subjects! I think this could be due to their own experiences of the subject. This is something that needs to change, Maths is about a LOT more than right or wrong, as maths teachers we need to work on this. I’ve touched on this before here.

During the discussion Dave also suggested that, as we are interested in the mathematics more than the correct answer, perhaps we should have maths tests where the correct answers actually have no marks attached, where all the marks are attached to working. This is something that I find intriguing. It can be infuriating to have to give full marks to an answer with no working (it could be a guess!) but give another pupil only half the marks despite perfect working because they copied a number wrong from one line to the next. I would, however, worry about how the marks are awarded. As we know, there can be many equally correct ways to get to the right answer, and all would need to be able to get the same marks, otherwise we wouldn’t be testing mathematical ability, rather we’d be testing the ability to guess what’s on the markschemes!

Do you have a view about Dave’s proposal? Do your students like those show that questions? I’d love to hear your views/experiences.

You’re right, none of us did challenge it! I’ve had a few students recently not know what’s legit and what’s not (“you can just sub it in and show it works, right?”) but I’ve not encountered any hostility – certainly nothing like as much as ‘Explain why…’ questions get.

Funny you should mention that. Last week one of my Y13s was doing an M3 question and the first part was “Verify cos(theta)=3/4” for 1 Mark. He spent ages proving it, then checked the markscheme and it just wanted him to put it in!

I would love for my pupils to love these questions, they tend to look at them, roll their eyes and sigh, all while I’m reiterating that these are just normal questions, but with a hint and the answer all rolled into one.

Dave’s idea of all working, no answer maths is similar to what happens at university with project work. We set open-ended questions and see where students will take them. Though I got the impression Dave was thinking of smaller-scale questions. I like the idea.

I’m amused that you chose minus signs going missing and 2×3=5 as your typical errors, as this is exactly the examples I’ve mentioned to my students as we’re inverting matrices, which is straightforward but prone to silly mistakes. I’m saying this to calm the frustrations of students who think that because they got the answer wrong, they will lose all the marks.

If the learning outcome a question is assessing is ‘student can apply technique X’, and the student uses the X method perfectly but makes a daft arithmetic error, why would I give them zero? They’ve shown what I wanted them to show. Small penalty for the daft error, sure, but not zero!

By the way, you have “four members if “the panel”” – ‘if’ should be ‘of’. Also, I spotted a “silky errors” and a “tto”.

Peter.

Dave’s idea of all working, no answer maths is similar to what happens at university with project work. We set open-ended questions and see where students will take them. Though I got the impression Dave was thinking of smaller-scale questions. I like the idea.

I’m amused that you chose minus signs going missing and 2×3=5 as your typical errors, as this is exactly the examples I’ve mentioned to my students as we’re inverting matrices, which is straightforward but prone to silly mistakes. I’m saying this to calm the frustrations of students who think that because they got the answer wrong, they will lose all the marks.

If the learning outcome a question is assessing is ‘student can apply technique X’, and the student uses the X method perfectly but makes a daft arithmetic error, why would I give them zero? They’ve shown what I wanted them to show. Small penalty for the daft error, sure, but not zero!

By the way, you have “four members if “the panel”” – ‘if’ should be ‘of’. Also, I spotted a “silky errors” and a “tto”.

Peter.

Thanks for the comments folks. Interesting stuff, especially the ideas on matrices. Will ammend my typos!