By the time I was ready to apply to be a head of department, I had a new tool at my disposal.
Mymaths (mymaths.co.uk) provided online interactive lessons on every secondary mathematics topic to tie into the UK National Curriculum. Although the accompanying homeworks were not yet in place at that stage there were already booster packs which could be used as homeworks. These gave me detailed information on the progress of each students and, in doing so, empowered me to require that each students work through the curriculum at their own pace. The quality of the interactive lessons was much higher than previous online tools due both to the high level of mathematical and pedagogical insight of the designers and also to the interactive visual tools they had incorporated.
I had a very clear vision that I wanted use this technology, combined with individual examples of key topics incorporated into lesson starters, to take a great deal of the strain of teaching the National Curriculum, leaving the teachers at my school with substantially more freedom to decide how best to use significant portions of lesson time.
The 'synthesis of paradigms' strategy was probably most evident in students homework, where I set them an online homework each week which was automatically marked and therefore had more energy to spend on the detailed marking of personal investigations, also set as homeworks. In this second type of homework students were required to think for themselves, independently interpreting and analysing pure and applied mathematical situations.
Classes probably didn't look so different as you might expect. We did some applied tasks and some rich investigations. Some lessons the students worked primarily with high quality texts. Students were explicitly taught to explain their thinking to each other (see or example the previous section of this blog on how the Chinese do it) and their skills in listening to, explaining to and supporting each other were explicitly cherished. We were dealing with many challenges at the time, such as mixed ability classes (due to the school being small and working towards closure) and having many students with challenging behaviour and specific learning difficulties and it was my perception that the framework I had allowed us more time to focus on using teaching methodologies which responded the needs of our students rather than on our need to deliver a National Curriculum which contained more material than many classes could cover.
By focusing on teaching rather than on the content to be covered a substantial proportion of the time, in our different ways we covered many elements of that National Curriculum in powerfully connected contexts. Thus they were relatively easy for students to understand during starter questions and during those online homeworks. Those individual questions and the computer based teaching wouldn't have worked without the rich earth of experience in which they were taking root.
This structure for organising teaching and learning also allowed me and other staff to focus on some of the more challenging pedagogical strategies which are often neglected in the pursuit of curriculum content coverage. In experimenting in this way I found that I experienced substantial personal growth as a teacher and my student clearly benefitted from this.
I felt I was delivering on Barcelona. The two sides of maths education were empowering each other:
Personal investigation of the world is much more effective if the personal investigation has mastered the use of many key tools and the universal vocabulary which will help them analyse and interpret what they see.
It is easier to learn and more deeply understand can personally make connections in a curriculum if you have spent time considering the situations where the maths it involves is generated and you have experienced the need for that maths.
Verification of my claim for the success of this strategy is limited. Our results were very good despite the considerable challenges we faced but there were only four externally examined year groups and they were small. But I think I can validate my claim in the theory of education and in the intuition of experienced teachers. Much of the content based curriculum was being discovered in context and then taught in abstract. Students needed core techniques in order to be able to think mathematically and mathematise situation. To me it just all made perfect sense. And I think that, as we move from Web2.0 and 3.0 to Web4.0 it will make easy and fluent sense to many others too. I'll continue to work on this validation in my future posts in this section.
I wrote up my efforts to synthesise the paradigms of teaching when the school where I was working closed in 2008 and these can be found here, under my previous name (Rebecca Teasdale). Sadly there is a £3 charge to access this article. http://www.atm.org.uk/journal/archive/mt210.html
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