I have so much I want to blog about but instead I’ve been waylaid by an update from Ofqual about the GCSE research programme ( 20th March Update ).
Before I “go off on one” I have a little update to my last post where I summarised the accreditation process ( HERE ) and also outlined the fact that I’ve written to Nick Gibb asking him to confirm that he has received adequate reassurances about his concerns. My update is that I haven’t had a response but my local MP (Nadhim Zahawi) has asked that I keep him updated if I do and I quote: “I understand why you are so concerned about this issue” – he has also said that he will chase for me if I don’t get a response too.
Anyway …. When I started teaching, I approached the pedagogy of Maths with my own education in mind (how naïve was I?) and very quickly it dawned on me that this wasn’t necessarily the best way to approach it. Teaching is soooooo much more than subject knowledge …FACT! (Should I put the disclaimer there that it is a FACT only in my opinion? Nah!)
As someone that was allegedly “quite good” in Maths I know that as a teacher I have to stop and think about a whole range of things when planning to teach a topic. Let me say that this isn’t an exhaustive list but is meant to provide you with an overview as I haven’t even mentioned how I also consider what real-life links or links with other areas of Maths (I am NOT saying that it’s “the” way to plan a lesson – it is just one way and I am using it to illustrate a later point!) I go through a sort of process in my mind – I think about:
- What is the requisite knowledge that the students need to move onto the topic I’m about to teach? If they struggle I may need to remind them or even go off-piste until they’ve grasped this required stuff. Remember I haven’t taught any of my groups before this year so am still getting to understand what they do and don’t know.
- What “it” is that I exactly want them to learn and to what extent I want/can push them on?
- How can I can present that information and structure the explanation?
- What questions/activities I think they need to be able to do to construct that knowledge?
- What questions/activities they can do to develop what we’re doing further? Sometimes in a different context.
- How I can assess whether they’ve “got it”? What do I do if they aren’t yet confident that they understand the work and also where I can take the learning to deepen it?
Do I put this level of thought into every lesson? No of course not but when I’m teaching something I haven’t done before or when I’ve come across a new idea linked to a topic I have to rethink my plans for a lesson. If I don’t do this I am doing my students an injustice. I’m just a normal teacher, a normal person (some of you may disagree with my definition of “normal”!?) but I make mistakes sometimes in the way that I teach a subject; the difference is that when it all goes pear shaped I’ve only ballsed up one lesson and not an entire cohort of students. After all I get another opportunity in the next lesson to rectify my failings and I’m even honest with my students and we have a “take2” lesson where we try a different approach to a topic.
Underlying all of that planning, and probably the one of the most important things which I haven’t mentioned during this process is trying to second-guess where they are likely to stumble and what I can do to overcome this. It’s not just about the stumbling though – it’s also about foreseeing the misconceptions and where they stem from. Most of this body of knowledge comes from TEACHING experience and seeing students making mistakes – of course you can read about lots of misconceptions but there is nothing like seeing it in practice and exploring why they happen with a student in front of you as they can materialize in the most mysterious ways … ways that’s an able mathematician might never imagine.
So … what’s my point? I’ve been trying to type this all flipping day and have come back to it 3 or 4 times … The fact of the matter is that there is no denying there is considerable differences in the level of difficulty/demand (call it what you want) between the three exam boards and yes I get that this would be reflected in the grade boundaries (lots of people don’t get that) but this really shouldn’t be the case. I accept that each board can have different approaches to problem solving but the level of difficulty is so different that it makes a mockery of the accreditation process. We should not have gotten to the point where a research programme has had to be instigated – let’s look at each of the research strands and what the Ofqual update has to say:
“The first strand is assessing the relative mathematical demand of questions in the boards’ sample assessment materials against those from current GCSE maths papers and from 12 international jurisdictions. Around 40 PhD maths students have been looking at pairs of questions and been answering for each pair: “Which question is the most mathematically difficult to answer fully?” “
Seriously! Shouldn’t this have been done as part of the accreditation process to ensure that they would fulfil the aims that the DFE set out in their programme of study? I do hope that the research findings and all the data are made public because I have major concerns about this on so many levels – at a basic level I hope that the 12 jurisdictions they have chosen exclude any countries where the “high stake” testing takes place at 18 and not 16 like our GCSE’s. I am more concerned that PhD students are being used as they will approach this from the angle of being “able” in Maths.
“Strand two has involved the large-scale testing of the boards’ sample assessment materials on current Year 11 pupils. Some 4,000 students drawn from across the country each sat one full question paper under exam conditions during the three weeks to 13 March. The exam board whose paper each student sat was drawn at random – each board has produced foundation and higher tier papers so the school could nominate at the outset which tier each student sat, but other than that it was random. “
Such a small number of students – 4 exam boards with 6 papers each (except WJEC that has 4) equates to approximately 140 (ish) students doing each paper. The statistical variations that can come out of such a small sample make this so unreliable.
“We had decided to change tack in strand three as a pilot of our original approach had suggested we were unlikely to obtain meaningful data. Consistent with the revised approach, we asked around 50 Year 11 pupils to answer a range of problem solving questions in early March. The next step is to ask a number of teachers to identify which of the questions have allowed the students to demonstrate their problem solving skills to the greatest extent. “
This is the first bit of good stuff I’ve seen …. They are actually going to talk to teachers but oh how it makes me sad that its just 50 students (put this in context in your own mind … there are between 525 to 550 THOUSAND students in a cohort) What a massive responsibility! Again I hope the raw data is made available.
“So that’s the work we had planned, but we’ve decided to take one further small step. We will be presenting 5 maths experts with around 30 problem solving questions drawn from across the four exam boards’ sample papers and asking them to judge where differences and similarities between the questions exist and on what basis. Combinations of questions will be repeatedly presented in groups of three to the experts. We will be asking them to pair two questions together based on similarities and leaving one separate. They’ll then be asked for a reason for their decision. This will be repeated until the reasons being given for the differences/similarities dry up. Coming out of this exercise will be a number of different scales that the questions will then be scored on with the scores providing information on any systematic differences across the questions.”
Looking back to the Autumn when all the exam boards were accredited you could have asked any secondary Maths teachers worth their salt what they thought and they would all have said something that said we have a “Goldlocks” situation … so “well done Ofqual” for taking “one step further” but this should have been done at the outset… and by the way … these “Maths experts” …. Surely they should be teaching experts?
“We” (I mean Maths teachers) are having to deliver some of the biggest changes in our GCSE ever seen. We have some amazing teachers in this country, but there is a danger that through all of this some of us are now finding it all a tad offensive that the role of those that are actually going to deliver the end product have the smallest part to play in its evolution. It just adds to the feeling that those in power actually think that we aren’t good enough .. most of us actually support these changes but in the right way and not just shoehorned in.
AND THERE IS MY POINT!!! Got there in the end … it is all well and good asking “Maths experts” but for pity sake we are the experts. Improving Maths education is not just about the curriculum/exams in the same way that teaching Maths is not just about subject knowledge … in fact it is less about subject knowledge than you might think. It is not your academics or PhD students that have to deliver these changes, and of course like me with my lesson planning (before I knew any better) they are approaching it from the angle of being good at Maths.
On that note … good night and have a great last week before Easter and if you’re looking for a quiz for Friday … TRY THIS ONE -> Mrs Ms Easter Quiz 2015