Verbalising mathematics

One thing that I think is very important to develop in students is their ability to describe mathematics, both verbally and in written form. I think that the ability to describe their thinking in a mathematically correct and concise way is a skill that can significantly improve the transition from GCSE to A Level in addition to the transition from A Level to University.
I recently stumbled on this activity on the Mathsbox website.

I used this activity as a starter for a lesson with my Set 1 Year 8s. I gave them 10 minutes to work in pairs and write as much as they could, using the terminology we had been learning, to describe the figure in front of them. We then discussed as a class the various things they had come up with. I was really impressed with the language that my class were using, and it also allowed me to tackle some misconceptions with labelling angles, angles on a straight line etc. The key words at the bottom of the page were great for differentiation as some of the students didn’t even notice they were there and managed fine, but I could point them out to the pupils who were struggling.

I can’t recommend Mathsbox enough. I persuaded my school to buy their very reasonable subscription this year and they have some great activities for use as starters. Follow them on Twitter here. They also seem to have an open house for half an hour tomorrow (Sunday 30th November 2014) where you can try out their resources and activities!


Exams and tests

I’ve just been marking some Year 7 end of term tests and I wanted to get people’s views on tests split up in to tiers.

I did two tests from different tiers with my class, and inevitably the levels reported by the tests don’t vary wildly.

To me, the whole purpose of summative testing is to get robust data. Why then do we not use as a matter of course one test that covers all possible levels, make it a bit longer and have everyone in a cohort sit the same exam paper. This approach would at the very least get rid of the “which paper will my students be able to get a C on more easily” debate at GCSE level. I also think that doing this throughout will lead to more robust data which is actually useful.

I’ve heard some arguments for having different tiers, such as students having lots of questions they can’t do being bad for self esteem.

What does everyone think? Do you have a preference?


The Perils of Grading Work

Last night, just as I was going to bed I was notified through Twitter of Manan’s (@shahlock) latest blog post where he looks at the grading (by another person) of some work that had been sent to him.

As he rightly points out commenting on just the written grading is fraught with problems as you do not have any idea of what has been said in class in relation to the work. I agree completely with everything Manan has said about this particular piece of work.

The assessor has been very thorough; looking at every line and not just skipping to the final solution. This is of course a good thing and should be applauded, as should the detailed feedback given. However, my initial thought on looking at this assessment and its grading was that it had been marked by someone slavishly (is that a word?!) following a mark scheme with less knowledge of mathematics than the person taking the assessment. On reflection, this is perhaps a bit harsh, maybe the focus of this assessment is exposition and explaining mathematical reasoning – this would explain some of the comments given for problem number 7.
I don’t feel that this explanation really holds for the other marks lost though. The “order of operations” one probably bothers me the most. Working out \(3(-7+9) – 5 \) by using the distributive property gives the same answer as calculating \(3(2) – 5\). Frankly who cares how this is worked out as long as the correct answer is given; it is a short calculation that doesn’t really require working out what is inside the brackets first! Similarly the marks lost on question 6 just don’t make sense…

I passionately believe that mathematics should be seen as a creative discipline (as well as a scientific one). This sort of grading completely goes against this belief and is only going to serve to diminish confidence and turn pupils off mathematics. We should be celebrating different ways of working things out and I think you can encourage and strive for correct written communication without being pedantic!

Please let me (and Manan) know what you think….