Core Maths

Spring 2017 (February half-term)

A lot seems to have happened this past half-term:

  • Students have sat their internal January mock exams.
  • The majority of the content from the specification has now been taught.
  • Thoughts are starting to turn to next year.
  • I have plucked up the courage to look at last year’s exam papers!

If I take each thought in order… starting with the mock exams.

I guess typically at this stage of year 12 it is normal for students to sit a 1 ½ hour exam to demonstrate their understanding of material covered since September. As our students are doing a one-year course, time is much more precious – so our students had the joys of a 2 ½ hour mock paper!

It might be wise to explain the rationale behind such an excessively long paper (Mathematics in Context was by far the longest of ANY year 12 course):

Take a typical question on regression. We all know how a question will start:

  1. a) Work out the equation of the least squares regression line.

 

But the variation on how it might continue is unpredictable, with the following all being possible follow-up questions:

b) Plot the regression line on your scatter diagram.

c) Show clearly that your regression line goes through the mean point.

d) Use your regression line to:

i) Predict y when x is ***
ii) Predict y when x is ***
iii) Which prediction is likely to be more accurate? Give a reason for your answer.

 

e) Interpret the gradient of your regression line.

f) Interpret the y-intercept of your regression line.

It would be reasonable to predict two of the b) – f) follow up questions might come up – but which ones? So we chose them all!

It did highlight to students that they need to know their work in depth, and not simply be able to scratch the surface.

Outcomes ranged from Grades A to U (using a typical 80% = A, 70% = B, etc approach). The U grade students weren’t horrifically short of an E, reflecting that we are justified in expecting a 100% pass rate.

Two questions were answered disproportionally weakly than the others. This was really helpful – as the week following the mock exams we started after-school revision classes (which are supposed to be an opt-in, but all are expected to attend. Any absentees had parents contacted – and now I have 100% attendance!).

Simply having an extra hour with the class a week is making a huge difference in their progress… and this extra time will offset not teaching the students in June/July once their course has finished.

My teaching partner will also run revision classes. Whilst I will expect whole class attendance, she will choose 3 or 4 careful targeted students who are having particular difficulty with certain aspects of the course. This model went down well with both parents and students at parents evening.

By the time the February half-term arrived, we have probably covered 95% of the specification in terms of content descriptors. Students have really valued knowing this – we have tackled many unseen topics of late with an air of “you do have the maths background to have a go…” even if the particular topic hasn’t been met before.

It might be easiest to illustrate this with an example. Much to my husband’s horror, I have delivered a topic on “The Creative Arts”. I don’t have a creative bone in my body – and I have shared this with my class. Whilst I am not creative at heart, I can understand the Maths in the Creative Arts…

  • Architecture – Fibonacci and Recurrence Relationships (which had previously been met)
  • The Drums – programming a drum machine with beats in both arithmetic and geometric progressions (again a previously met topic)
  • The Piano – again Fibonacci – but we also looked at the frequency of the waves on each key of the Keyboard. This lead to some exponential graphs (which we last looked at when studying absorption of drugs into the bloodstream).
  • The Piano work also lead to some new work – reciprocal graphs (wavelength is inversely proportional to frequency)… students could really feel the difference between an exponential decay graph and a reciprocal graph.

We have some minor polishing off of new material to cover over the next few weeks. However, by Easter we will have completed all new material. The concern that “we can never get this covered in a year” hasn’t materialised… we have worked the class really hard this year – and they have responded so well.

Turning towards next year – it has been confirmed that if the course goes ahead, we will be moving to a two-year model. Unfortunately, so far we have only had 3 students showing interest in the course for next year. In a way, I am not surprised… Our current crop of students chose the course as a 4th AS-level. Next year our school are turning to a 3 A-level model… with a fourth choice being a rarity. The benefits of this course for other subjects and future Higher Education cannot be underestimated, so we need to get the message of the benefits of this course out more clearly to students. Thoughts of how to do this…

  • We could set aside a portion of one of their maths lessons in the comings week to discuss Core Maths (some students are clearly not aware of what it even is!), and the benefits of studying it!
  • A chunk of a year 11 assembly could be used to spread the message.
  • We are looking at options of putting in the course in an “optional time” slot of the Sixth Form timetable. Students might then see that “optional time” can be used to gain a level 3 qualification which might appeal to some.
  • I think that if we run this course over two years we can pretty well do away for the need of setting homework (currently our students have 5 x 50 mins lessons a week and about 5 x 20 mins homework a week). This has got to be an attractive proposal!

Obviously before next year comes around, there is the small matter of this May’s exams. I refuse to be a teacher who “teaches to the test” – and this is critical when studying Mathematics in Context… every exam paper will choose new contexts – so “teaching to the test” is impractical. However, I have now had a sneaky look at last years’ papers…

Thoughts: they are more direct than the mock paper we gave our cohort! Indeed some questions were much more direct. Our students need to know this for an ego boost – so over the next half-term I might do a drip-feed of some of the sections within some of the papers.

Looking through the papers, I did find myself thinking that “the way a student needs to think” is very different to a traditional GCSE or A-level paper. To really appreciate the different assessment style, I think I need to be in the role of the student – so I have entered myself for the exam this summer. To have a first-hand appreciation of seeing seen and unseen data sources – and tackle a paper which is much more of a comprehension paper should be a real eye-opener.