How do we report and measure attainment in Maths? And Why?

An interesting discussion in the Maths office this week has led to some musings.  When the English education system moved away from Levels, my school took the new GCSE (9-1) grades and “translated” the old Teacher Assessed Levels (TALs) into new Teacher Assessed Numbers (TANs) as shown here on the school website:

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As I teacher I am required to provide a TAN on each student I teach at various points in the year. As I was doing this earlier this week I started thinking about what these are used for.  Here I am not talking about the actual process of assessment. I am just thinking about why we collect that information and what we do with it. It seems to me that there are 3 key recipients of this information each with their own agenda.

1, The Students.  This is a form of feedback, albeit a very blunt, summative piece of feedback that basically tells the student how good they are at Maths (in my case) summed up in a single score. The student may be aware of their previous score(s) so they may also get a measure of their progress.  They may also discuss it with their peers so get a sense of their relative position in their year group.  But mainly, it is a single measure that tells them where they are at today.  Students used to have a good understanding of what Level 4, 5, 6, etc. meant.  In fact I still hear of Year 8s and even 7s asking what level they are. It wasn’t that long ago.  Inevitably they will take time to get used to a new scoring system. In our case it is linked to 9-1 GCSE grades. But the key difference of course is that these TANs are their teacher’s opinion (based on summative end of unit assessments) on how they are doing, rather than the external impersonal authority of the exam board.

Due to the simplicity of the summative score this feedback doesn’t actually tell the student how to improve other than “work more” or maybe even “work less” depending on that student’s disposition and level of ambition towards that subject.

2, The Parents.  All parents want to know how their child is doing at school. Through parents’ evenings and other contacts, we can provide much more nuanced information on this progress.  But I believe most parents like the clarity of some sort of score. The score needs to be understood in context, e.g. in our case it looks like a GCSE grade but it is not any sort of prediction, well not until KS4 anyway.  The question for me is what do parents then do with this information? Obviously a full range of responses exist here from nothing at all, to deciding to get a tutor in and putting additional pressure on the student to work harder in whatever way they see fit. Even though the parents may do nothing, the mere fact that the TAN is shared with the parents is likely to have some impact on the students’ engagement with school, positive or negative.

3, The school leadership. By having a regular school-wide, “score” for each student per subject the school can do all sorts of analysis of the attainment and progress of their student base.  What the school then do with this information is myriad: e.g. decide on classes/sets, plan intervention including deployment of support staff, provide support to teachers, evaluate teachers as well as track overall school improvement.  The data may be shared with Ofsted although my understanding is that this is not statutory.  These are pretty wide-ranging but basically boil down to helping the school focus their efforts and resources in the right place.

It strikes me that these are 3 quite different and potentially conflicting sets of objectives. For example the school may wish to collect data that is useful for analysing whole school performance but is not relevant or motivating to individual students. (A Twitter conversation here with @LaSalleEd highlights how their MathsAge system shares specific content objectives with the student, but calculates an overall score solely for school use)

The dynamic between students and parents varies as children get older.  I believe there is a case for parents of primary children having information that their children don’t see, but as pupils approach GCSE they need a realistic view of what they are aiming for which can prove an incentive to work hard.

Lots of questions, not many answers, I’m afraid. I would like to understand more about what other schools do. I understand many have adapted the old levels system by basically changing the scale but didn’t see a need to make a broader change to reporting.

Please leave comments below or get in touch on Twitter, @mhorley.  Thanks!

 

Exterior Angles of a Polygon and other shapes

I find some students like to memorise this, or at least the first two or three rows and then remember that we keep adding 180 for extra size.

Reason being – an extra triangle.

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I feel that using exterior angles is more satisfying.  I find myself walking around an imaginary hexagon in my classroom with arm out stretched.

Here is a very nice Geogebra visualisation of this:

And here’s an activity which reinforces this idea.  Use a pencil as an arrow.  Does it always rotate through 360?  Does it always turn the same direction?  Use algebra, maybe?irreghex_42603_mdimages

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Mathematical Timeline

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I made this years ago, but just realised it is not on this blog.

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It contains snippets of bits of maths from 500BC up to the present day to adorn your classroom or corridor. The focus is on interesting, but accessible maths rather than historical completeness! Mostly inspired by the excellent Alex’s Adventures in Numberland (Alex Bellos) as well as Number Freak (Derrick Niederman)

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Best printed A3 in colour. Here is the whole thing as a pdf, and here as a word doc