Beginning to Order

One of the first things I am considering when putting together my scheme of work is the order in which we will teach. It feels like I have performed this task repeatedly in the last few years. My first scheme of work included modular examinations in January, then those were removed so I shuffled C1 and C2 into a single ‘core’ unit. When I moved schools to my current position I wrote a new scheme of work, within which a teacher took control of a single module, meaning that each group had three teachers. Last year I had a slightly smaller job of transferring my existing scheme of work into a new format so that it was on the correct templates.

Should we teach the topics broadly in the order MEI have placed them in their scheme of work (albeit with the statistics and mechanics spread throughout) or re-arrange so that similar content is taught together. In the past, when teaching C1 and C2 as a single ‘core’ unit I have rearranged the content so that, for example, all of the differentiation is together. This has already been assumed in the scheme of work, but should integration be taught immediately after. Perhaps it would be even better to teach them at the same time? This would hopefully create a much better understanding of the inverse nature of differentiation and integration – students could differentiate a curve, then integrate to get back to it, using a point on the original to find c.

A different strategy would be to separate similar content, allowing more structured interleaving. As students come back to a topic, they revise the original content and then build on it. This has obvious benefits of seeing things more than once, but is likely to lead to too much time being spent going back over previously learned content and falling behind as a result. As time is already tight we cannot afford too much slippage.

On Friday I will be meeting Simon and my head of department to start to build up the scheme of work, beginning with this process of ordering topics. I have loosely grouped topics – we now need to come up with an answer to the questions posed above. I am ready with the topics on cards to move around, string to make links between the topics and a blank timeline…

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Teaching Structure

Today I met with Simon and my head of department, Pete, again to continue our discussion with how to move forward towards the first teaching in September. The main talking point was what we need in place before we can really start creating a scheme of work.

One thing that has been confirmed since our initial discussion is that the school will want us to enter students for the AS examinations at the end of year 12. This will be school policy for all subjects and, as such, is non-negotiable.

The next decision we will need to make as a department is how we are going to divide up the teaching between two or three colleagues. We are very lucky in that all of our members of staff are confident to teach A-level and keen to do so, but any significant changes to the way we currently operate is likely to mean that at least one person will miss out next year. This of course assumes stability, something that at the moment seems likely but that we can never rely on.

In our current structure each module is taught by a different teacher, so that each class has three teachers. This means that each teacher is responsible equally for the attainment of students across the course. It also means that the content is neatly parcelled out, and there are not too many tricky decisions over when to teach content, although with the core modules some thought has been needed so that, for example, differentiation is reached in C1 before C2.

In my previous role at a different school I abolished the distinction between the two core modules and taught it as one block. Where one topic was included in both modules it was taught at the same time, allowing more time to be focussed exploring ideas around the area as a whole. This led to a better flow, with topics seeming less disjointed. The teaching was split between two colleagues, but taught in a linear fashion with them handing over at the end of each lesson. The applied unit was split across the year, dovetailing with the core content at appropriate times. It would make sense if we were to adopt this model to have each of the two teachers leading one of the applied sections.

A further model would be to have one teacher cover all of the core material and one covering the applied. This is probably my least preferred option given the new split in the applied material between statistics and mechanics. I have heard of this model being used successfully in other schools (although obviously with only one applied option being taught), but have also heard of complaints from the applied teacher about being seen as less of a priority than the “main” teacher covering core.

My instinct at the moment is that the two teachers sharing equally will be the most workable solution, so I will start building on this principle. The next thing to start thinking about will be the order in which to cover the content.

 

Overarching Themes: Problem Solving

Today I attended an MEI CPD event on the “Principles of the New A-Level.” I came away with a lot of ideas and things to think about further as I continue to work towards starting teaching the new syllabus in September. One of the new “Overarching Themes” in the specification for A-level maths is problem solving and it was this that my thoughts have kept returning to this evening. What is problem solving in mathematics, and specifically what is it that makes on question a problem solving task?Rectangle.png

Take the picture here (one of the tasks we worked on at the session). What might students be asked to do? As an example we might ask “find the area of the rectangle”. In the previous specification students were likely to be guided to a solution, with parts of a question asking them to find relevant, intermediate, pieces of information such as the equation of the line that joins A and D. The idea of removing this and having to think really appeals to me as a mathematician but scares me as a teacher.

What interested me most about this was my own response to then thinking about how I would approach the question. I initially decided that I should work out the coordinates of the points A, B and D, then work out the lengths of segments AD and AB and multiply them together to find the area of the rectangle. As I started working through the problem it quickly dawned on me that having worked out A, B and D it was much more efficient to work out the area of the triangle made by them, and then double it, rather than using Pythagoras theorem twice. While my initial strategy would have led to a correct solution, my adaptation of it led to an easier process. However, if I had not been able to think of a strategy at all I would not have been able to start the problem.

Another aspect of the new schemes is the use of technology. Some of these problem solving tasks are better explored with dynamic software. We looked at a geometric method for showing that sin (a + b) = sin a cos b + cos a sin b. This looked at drawing a rectangle and dividing the area up in different ways. One area students may struggle to grasp is that this is true for all values of a and b. By creating a dynamic model we are able to illustrate that it holds for different values and we can then generalise.

We are going to have to make sure that we build enough of these sorts of tasks into our lessons so that students have experience of the thought processes required to answer them. This will obviously require time to allow students to develop their skills. Something that I am currently looking at to help free up time in the classroom is flipped learning, but that is a topic for another day.

I am off to try and make a geogebra applet that shows sin (a + b) = sin a cos b + cos a sin b!

[My first attempt at the geogebra is available here: https://www.geogebra.org/worksheet/edit/id/qtNKm2pa  Needs some work on the labelling!]

Initial Thoughts

Initial thoughts on the changes to A-Level Maths that are on the way for first teaching in September 2017

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From September 2017 new AS/A level Maths and Further Maths qualifications will be taught across England. This means that during the next 9 months mathematics departments will be need to think carefully about how they will implement the changes for their teachers and students.  Simon Clay (MEI TAM Coordinator) approached the mathematics teaching team at Tudor Grange Academy Redditch, to see if they were interested in working together to think through the issues which are raised by these forthcoming changes.  This blog will therefore document one department’s journey as they navigate preparing for the new A-levels through the eyes of the Curriculum Leader.

Over the last few years a number of teachers from the school have participated in professional development and other activities run by MEI, including the Teaching Advanced Mathematics (TAM) and Teaching Further Mathematics (TFM) courses. The school is part of the Tudor Grange Academy Trust and has 440 students on roll. Until recently it has been a high school, teaching students from years 9 to 13. This year it welcomed its first year 7 pupils. The maths department is made up of 6 teachers, all of whom teach some A-level maths.

 

Bruce’s thoughts:

In this initial blog I have recorded where we are as a department now and the initial thoughts I have for moving forward with the new A-level. This has been prompted by being approached by Simon Clay and MEI to work with them as we begin our journey towards first teaching in 2017.

As the Key Stage 5 coordinator for maths some key decisions need to be made over the next 6 months regarding the new A-level specifications. At this stage, with none of the specifications having been approved, I have not thought too hard about this. This is not a position I want to continue with as I am keen to start rebuilding our scheme of work while there is still time to do a good job with it.

We normally run two A-level classes in each year group plus a small further maths group and all members of the department teach at least one module. In our current scheme of work we have tried to include the use of activities which promote deeper thinking, such as those that are available through MEIs Integral website. However time pressures mean that these are rarely used. I see the change of course, coupled with the changes to structure, as an opportunity to totally rethink the way we are teaching and to promote this sort of activity further. This fits into the way the structure of the A-level is changing, with the new over-arching themes of problem solving and the increased use of technology – this is our opportunity to tear up what we have done before and start afresh.

 

AS levels, Specifications and Applied content

One possible barrier to a total rethink of the current scheme of work structure is that the school currently has a policy that students sitting the new specifications of A-level will all sit AS-level examinations at the end of year 12. If this policy continues it will impact on the amount of time we have available and the order in which we teach content.

This feeds into our need to think about which examination board we decide to use. We have offered Edexcel, which was the course that was offered when I joined the school last year. With the change to curriculum I thought it was unnecessary to make changes twice in quick succession. I have previous experience of teaching both AQA and MEI, but everybody else in the department has only ever used Edexcel. I have been reading specifications for all of the examination boards and have also attended an OCR Maths Network meeting. I am not in any rush to make a decision due to all of the content in A-level Maths being core, and again that specifications have not been finalised so we don’t know what the final examinations will look like yet.

Another consideration is how we split the teaching in the new courses. Historically we have run the A-level courses with a separate teacher for each of the modules. This has allowed everybody to build their own specialisms, but makes linking between content in the core modules more difficult. It does mean that we are in a position that we have somebody confident with all of the different areas required by decision to make all of the A-level content compulsory as we have offered mechanics and statistics in one or other of our courses previously. This is tempered by the huge change in the emphasis in the statistics module with the large data set.

 

In conclusion, the key questions that we need to address in the short term are:

– Do we continue to offer AS examinations for all students?

– Which examination specification should we use?

– How should we structure the course in light of the new linear format?

 

Bruce Hampton is the Curriculum Leader for Sixth Form Maths at Tudor Grange Academy Redditch. He has been teaching for 12 years, initially at a school in Birmingham, moving to Tudor Grange Academy Redditch in 2015. He completed the Teaching Further Maths course in 2014-15. He studied Mathematics at the University of Birmingham and has a Masters in Teaching and Learning from the University of Warwick. In his spare time he is a keen rugby fan and likes to get out on his bike.

 

Simon Clay is part of MEI’s Professional Development team where he is involved in a number of different aspects of MEI’s work including working with teachers on the Teaching Advanced Mathematics (TAM), Introduction to Mechanics and Head of Mathematics courses. Before joining MEI in 2012 he had taught Mathematics in schools and Sixth Form Colleges for 12 years, during which he had been a Head of Department for 5 years.