Reflecting!

Like many of you I have just had another IBDP class go through. I have read a few posts in different places from teachers reflecting on the exams, the current syllabi and the frustrations of always wanting to do our best for students. I wanted to write something on this for a few reasons. Firstly, I have my own thoughts and perspective to add here. Secondly I wanted to respond to some things I have read and thirdly because I am actually really grateful that people share their views about this stuff online and get a lot out of reading and exchanging with teachers. I hope I offer something in return.

Square Pegs and Round Holes

In our department we offer Analysis and applications both at HL and SL, between three classes. We have one mixed Analysis HL/SL class, one mixed Applications HL/SL class and the third class, mine, is Applications SL only. Some SL apps students opt to be in the mixed class that goes a bit faster through the SL syllabus and leaves quite a lot of preparation time at the end. Most opt for a steadier pace in the SL only class. It works, just about, but we do review every year depending on numbers and choices. This, as I am sure is true in all schools, presents perennial challenges. Changing the way we structure tends to just change the challenges. Whichever way we cut it, because of the nature of the IBDP and the nature of teaching itself, it always feels a little like we are trying to put a square peg in a round hole. (As a mathematics teacher, the lack of specifics in this saying has always made me smile!). There is never enough time. If you gave me more I would use it and then tell you it still wasn't enough. It is frustrating. I want to do so much more, I want to go into greater depth, I want to be more thorough and help students to truly understand these deeply relevant ideas and work with them fluently. There is never enough time. The challenge is optimisation, but it is not always satisfying.

We are naturally a bit lost

Since the new syllabus was first assessed in the midst of the pandemic, it is hard to know where we stand. Education and the pandemic is a whole other debate and there are clearly pros and cons to the way things went. Probably the most important thing to say is that it has been complicated and stressful for all concerned and I am glad I didn’t have to make any of the big decisions. The end result of all the mitigations put in place and grade distributions and so on is that we don’t quite know where we stand with grade boundaries. This is unsettling, but inevitable. Hopefully over the next couple of years (and through the next syllabus change) we will feel better about this.

Maths Studies

I fell completely for the maths studies course. Although I had an international upbringing, until 2004 I had only known about teaching in the UK, where post 16 mathematics was not compulsory. Maths studies was my first experience and I loved it. I thought the course was fabulous for most of the students who took it. It was big enough to be challenging (7s were hard) and small enough to allow plenty of scope for diving into the meaning and role of mathematics. I started writing resources, websites, workshops etc and thought it was brilliant. I should add that I feel similarly about the new applications course, but for different reasons. Like many of you, I still miss maths studies.

Applications, realities and goals

I do really love the new course too, but, as I said, for different reasons. I love pure and applied mathematics alike, and I can really see the merit in this meaningful and technology fuelled focus on applications of mathematics. I am so glad I get to talk about probabilities in more depth and the hypothesis tests that work across the natural and human sciences. I enjoy the contexts for modelling and most of the syllabus items. I am giving the rest a chance too. It feels like a relevant move forward in the nature of mathematics courses that are on offer. There is clearly much more to write about this, but I wanted to balance my affection for maths studies with the way I feel about the new applications course. 

It's also important to add that, like many, I find it has become more difficult to teach and learn for a few reasons. The syllabus is considerably bigger and although there is built in exploration time, it does leave less time to really dwell on and think about the important concepts. Also, there is no doubt that the contexts for questions that are required to fit the philosophy of the course are wordier and harder to get at. Often the mathematics that is ultimately required is relatively straightforward, but recognising what mathematics to do is challenging.

This is the goal of this course though and I think it is a good one. It is also the reality in front of us. I accept there are challenges. I face them too and it does mean that many of our students find this a good deal harder. This can be frustrating.

Breadth versus depth

It's an age-old question, but I think it applies here about this course and also at the whole diploma level. I can think of some syllabus items I would let go, but know there are good reasons for them to be there and that others of you might choose different ones. That said, I think there are questions to ask about what fits well in the time available. The whole diploma program barely squeezes in. We can’t leave out content because that is not fair to students, so we end up short of time to look at depth, meaning and problem solving. This is what students need to tackle the kinds of problems we see in exams and to understand how and when mathematical ideas are relevant. 

I also recognise that syllabi are what universities will focus on so if we cut out content then we will devalue (in the view of some whose view is important) the qualification. Look what happened with Standard Level Vectors.

It is a complex puzzle with a lot of people to keep happy.

Missing topics

In my less than objective moments I have raged about the fact that some topics went entirely untested this year and last. I have seen others write about this too. Of course, this is common practice, in many cases because it is simply not possible to test everything in the time allowed. The thing is that with maths studies we could be sure that everything would be on the exam one way or another. I did a quick look back through my planning to calculate that I could have reclaimed 4 weeks of teaching if I had known some topics were not coming up. Arghhh! Then I remember (or am reminded) how often I talk about the wider value of education. The exam is supposed to be the symptom, the goal is education. So maybe there were no questions about amortisation on your exam, but at least you know something about how loans work (lets face it, most of us are more familiar with loans than savings and, haha, gift annuities!). I do say that. I do mean it. But if you have worked hard with students to help them understand ideas it is frustrating that they don't get the chance to show it. It is also a bit unfair right? I’d love the four weeks back, but I’d rather they just got a question on everything. I also know that not examining the whole syllabus is fairly commonplace. When you work with students who, like you, are struggling with that square peg it does make me wonder. We are all human.

Knowledge, problem solving and difficulty

This is the biggy for me. We all know that there is a difference between understanding how to carry out mathematical processes and problem solving that involves those same mathematical processes. It is reasonable to offer a guided time for how long it might take you to teach a topic, but near impossible to designate a similar allowance for how long it takes to develop the ability to solve problems in context using that topic. I see this across the maths courses. Essentially Sudoku puzzles involve the same mathematical skills, but the fiendish ones take a lot longer right?

Difficulty levels are worth thinking about. Two exam boards could offer the same syllabus but one could have an exam that was considerably more difficult. I don't suppose anyone is too interested in either extreme. So easy everyone does it with their eyes closed or so hard that everyone comes out crying. It does seem that there is wiggle room here that would help to alleviate some of the stresses and strains of our square peg problem

Exam review form

I am sure you all know but it is really important that we all give our feedback. Ask your IB coordinator for the link and then just be honest. I think it is great that we have this direct voice, and it says quite clearly that they could consider points in grade awards.

Thinking ahead

I think it is worth ending with some thoughts about how I feel my teaching of this course is developing in the face of the challenges mentioned above. No silver bullet I am afraid, but maybe something….

There is no doubt that the emphasis has shifted towards exposure to the kinds of problems that we see in exams. I think a sub topic like quadratic models is a good example to dwell on here. It is such a rich mathematical topic and in another context we could spend weeks on quadratics, their properties, equations, the algebra, their applications and their curiosities. As mathematics teachers we have probably all spent a lot of time with quadratics one way or another. We don't need to on this course. Very little in fact. For the most part students need to know how to find zeros, y-intercepts and turning points using their calculators - maybe one lesson. Then they need to see lots of examples in context where the focus is on what the zeros, intercepts and turning points mean. I have noticed my emphasis shift significantly in this direction and have tried to look for opportunities throughout the course to similar things. I have mixed feelings about it, but what I sacrifice in terms of pure mathematical structure I gain in understanding what the results mean in context. It's not everything but this kind of thing is helping me round the corners on our square peg.

In summary

As ever, this has been helpful to write. I hope that some people read it and find comfort in knowing that I share frustrations and problems. I hope also that I have shown an understanding of the different perspectives at play here and why some things are what they are. Fill in your forms and if we have suggestions for improvement we should make them!

If you got this far then thanks for reading!