I think this has some real promise; it’s a rather good idea.
Rather than providing levels as a measure of assessment in mathematics development, use a ‘MathsAge,’ similar to ‘reading age.’ There are some niceties around clarity of communication with parents while still being able to track progress, but really I like that this creates an equivalence between mathematics and English. I live in hope that it could start to diminish the ease and comfort too many take in saying ‘I was never good at maths.’ It’s a toxic culture that people in our society feel too comfortable admitting this, in a way they would never admit to being unable to read. (Watch this space for future magic and wizardry from Bruno Reddy in tackling this problem.)
In this sense, however, it also has some real risks that should be considered.
I know little to nothing about how reading age is calculated, outside the fact that the normal distribution almost certainly feeds into it somewhere; how can you lay claim to a 14-year-old reading at the age of a 16-year-old unless you’re making some comparisons about the average reading ability of 14 and 16-year-olds! Yet something about reading age suggests that it should be absolute, rather than norm referenced. It shouldn’t be the case that ‘Reading age 14’ means ‘Half of all pupils aged 14 can read up to this level,’ that feels hugely counter-intuitive. Rather, surely it should be that ‘All 14 year olds, saving those with real cognitive impediments, should be expected to read up to this degree of ability by age 14.’
Is this how reading age works??
Beyond this, the general sense I get is that reading is a relatively limited activity; at least as far as ‘reading age’ goes. One could argue I suppose that being able to read content and bring to bear all manner of references and interpretations, divining meaning from complex ideas, intended by the author or otherwise, that others might miss, and being able to synthesise from all this novel thoughts of your own… are also all a part of what we might call ‘reading.’ But… in the sense of ‘reading age,’ I get the feeling that this isn’t quite what is meant.
Thinking about the idea of MathsAge then: in the LaSalle post Mark mentions MathsAge is mapped onto what everyone would need to know in order to achieve a Grade 9 in the new exams. Now I think we start to run into some problems…
The Grades will be awarded roughly in line with a normal distribution; at least, this will certainly be what the awarding bodies strive for. The degree to which a person ‘understands’ a mathematical idea at any one of the 11 stages hinted at in the post, by which I mean the different ways in which they can conceptualise it, relate it to other mathematical ideas, apply it directly with accuracy, spot that it could be useful in solving a problem when no direct mention of it is made, and so forth, will vary enormously from one pupil to another even if they can all demonstrate at least some limited use of the idea.
In short, there is extraordinary inherent complexity in mathematics which is not equivalently present in reading, and so is it right to create a measure that draws such a direct parallel? Does it make sense to say that all pupils who couldn’t achieve a Grade 9 are operating below a MathsAge of 16? Is this what is even intended by MathsAge, or am I misreading it?
What might MathsAge apply to?
Reading is a tiny but essential subset of English study. I wonder if it isn’t more appropriate to apply the idea of a MathsAge to a similarly tiny but essential subset of mathematics study? Examples might include real procedural fundamentals likes times tables, negative numbers, fractions, forming and simplifying expressions etc. An alternative approach might be one that I take, which is to suggest that there are certain fundamental procedures and question types that I feel I can expect every child to ‘master.’ They do extend up to the Grade 9 – or current A* – level. Here’s an example from trigonometry where I would expect every pupil to be able to learn how to respond correctly to 100% of these questions:
As another example, assuming pupils have already learned sufficiently well how to add and subtract negatives, how to rearrange equations, how to work with brackets, and have some idea about what a quadratic equation is and what it means to solve it, I would expect that every pupil would be able to solve a quadratic equation equation by completing the square by replicating and practising the process that I modelled for them. But, even if every child did master this – and everything else up to this point – I would not necessarily expect every child to therefore achieve a Grade 9 in the exams, nor be able to tackle some of the more complex Grade 7-9 differentiating questions that will no doubt be created by the awarding bodies.
An additional measure?
So… could MathsAge be a measure of this sort, without being a direct measure of final summative achievement in the style of the old levels, the current lettered grades, or the future numbered grades? An additional measure, rather than a replacement? In the same way, reading age is an additional measure to English GCSE grade, not a replacement, and a high reading age does not guarantee a high English GCSE score – though I expect there is strong correlation.
All this said! Mark also notes that wide range of people with far greater experience than me, including some who work for awarding bodies, have all been involved in this process. I can imagine that these issues have already arisen and been dealt with then; so really this is a long-winded way of saying I would just like to know more about how…
I was just about to hit ‘publish’ when I managed to get in touch with an English teacher who suggested that, surprisingly, my bell curve graphic at the start actually does broadly represent how reading age work – so a reading age of 14 is a comparison of the average reading ability of all 14 year olds, whereby many would fall below it, rather than a floor target.
Coincidentally I also recently learnt that Bodil Isaksen has been pioneering the idea of ‘calculation age,’ as opposed to MathsAge, which sounds very similar to my first suggestion above of using something like a MathsAge to represent only things like fundamental procedural calculations – times tables, fractions, negatives etc. I’m now hoping she might chip into the conversation by blogging in more detail about the work she’s doing with this.