The Term So Far…

It seems amazing that we are already more (now much more than when I started writing this!) than half a term into teaching the new specifications of the A-level. When we planned this half term I was concerned that we had put far too much content in and that we would never get anywhere near completing it all. Remarkably this has not been the case and we finished exactly on schedule.

The way that we have set the scheme of work up has had massive benefits, this has been particularly evident in the linking of topics that were previously kept apart by being almost arbitrarily in different modules. We have found this is useful with the relationships between indices, surds, exponentials and logarithms. This week we have seen this again in teaching binomial expansion and the binomial distribution consecutively.

I am also much more confident that I know how students are coping with the course due to the changes we have made to our assessment structures. For each unit students have completed the online Integral assessment, for which they are provided feedback. This is an automated process where we copy the data from Integral into a spreadsheet which creates a sheet for each student, detailing which questions they have got correct and which they need to redo. Corrections are made on the back of this sheet so that we have a record that they are doing this.Eg1

We have also set students the chapter assessments from Integral, which unfortunately don’t mark themselves! These are marked and entered into another spreadsheet, which again provides individualised feedback for the students. This shows students their performance in relation to the rest of the class for each question, so that they can focus their efforts on areas that they need to. It also allows us to see any areas that need revisiting with the whole group.Eg2

Where there are significant issues arising from the assessment we are able to run intervention sessions either during form periods (fortunately as Head of Department I do not have a form group) or after school.

Another interesting aspect that we have incorporated into the scheme of work is reading and comprehension tasks. At the end of half term one, as a holiday task, we asked students to read an article from New Scientist and to answer questions based on this. Our aims with our development of our practice in the new course have always been to develop students as mathematicians, not just to allow them to answer the questions in the examination. The article in question looked at prime numbers, particularly into the question of whether there was a pattern in the way they appeared. Students were challenged to answer 6 questions, starting with information taken from the article, then progressing to independent research on the topic. Unfortunately none of the students managed the sixth…

  • Define “twin prime”.
  • Using the sieve method, which is the largest prime number that needs to be used such that all of the non-primes < 100 are sieved out?
  • When does sieve theory struggle?
  • Showing your calculations, write down a list of the first 6 Germain Primes (29 is the 7th).
  • Write a paragraph of no more than 200 words about either Goldbach’s Conjecture, Germain Primes or the Riemann Hypothesis.
  • Solve the Riemann Hypothesis, donating half of your winnings to Mr Hampton and Mr Davies.

The next challenge is to find a suitable article to set for reading over Christmas!

 

 

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Scheme of work and developing a teaching plan

This post is contributed by Simon Clay who is part of the Teacher Support team at MEI.

Given that the changes to A level mathematics are significant, an overhaul of teaching schemes for the new two-year long qualification is not a trivial task.  During 2016-17 a number of members of staff at MEI developed a Scheme of Work for the new A levels with the aim of trying to produce something useful for as wide a range of audience as possible.  This result is this freely available SoW, accessible via the MEI website.

Some of the thinking behind the design of the SoW units was as follows:

– It aimed to break down the new A level content into manageable units.

– It needed to function as a starting point for discussions in departments and therefore needed to be editable.

– It needed to take seriously the changes in emphasis of the new A levels, including the three overarching themes – Mathematical argument, language and proof; Mathematical problem solving; Mathematical modelling.

– It needed to incorporate useful features such as ideas as to how the use of technology can permeate the teaching of A level mathematics, questions which promote mathematical thinking, etc.

– It needed to be both adaptable and useable in the classroom.

– It needed to exemplify, and give free access to, some high quality teaching resources which can be ‘picked up and used’ in any classroom.

Since its launch in March, we have been pleased with the way the SoW has been received.  A common request, however, was for the provision of a plan for how the units could be linked together in a cohesive way to ensure the content is covered in the time available.  We have therefore worked on producing a series of schedules which show how the units of the first year (or AS content) can be arranged depending on considerations or constraints a department may have e.g. two teachers sharing a group, one of whom teaches pure and mechanics while the other teaches pure and statistics.  (We have so far only tackled Year 1 content but Year 2 will follow in due course!)

The reason for a post in this blog is because Schedule E is as a result of the thinking and work done by Bruce and the team at TGA Redditch.  It has been my privilege to take part in the discussions in which this SoW Schedule has been developed.

Below is an image of Schedule E taken from mei.org.uk/2017-sow and beneath this I describe the key features:

Image of 'Schedule E'

– The team wanted to begin the course with an emphasis on problem-solving and proof in order to set the culture of working in this way from lesson 1.  This means lesson 1 will contain no mathematics beyond GCSE and will instead focus on reasoning, language and proof.  Lesson 2 will look at indices but with an emphasis on reasoning and proof rather than subject content coverage.

– There was a strong desire to get the students working with and becoming familiar with the large data set (LDS) right from the start of the course.  Thus by the end of the first teaching week students will know about the LDS and have done some initial exploratory work using it.

– The team identified some units, namely ‘Problem-solving’ and ‘Graphs and transformations’ as being recurring themes which can be addressed in a number of different units throughout the course rather than taught as discrete topics.

– The team wanted to use a teaching model where the class is shared between two members of staff but essentially runs as a single series of lessons.  This will clearly involve a high level of collaboration between them but they are keen to dovetail their teaching so that the student experience is as coherent and seamless as possible.

– They wanted the applied units to be taught alongside the relevant pure unit so it is clear what mathematics is being applied.  It is hoped that this will also help with fitting in the content in the time available.

– They wanted technology to be used by teachers and students whenever possible and so in the first few weeks there are planned opportunities for this, in particular when analysing the LDS and exploring graphs of exponential functions .

– The school has made a central decision that all students need to be prepared and entered for AS level examinations at the end of Year 12. This means that although at points it would be nice to extend and cover Year 2 topics straightaway these will need to wait.

And now there are only a few weeks until the schedule can be implemented!