Mathematics NQTs Dave Hewitt

Overview Within school Outside school: local support Outside school: national support Outside school: support from Loughborough Professional development: the Knowledge Quartet

Within school You will have support built-in during your NQT year – make good use of it; Talk with your department colleagues, share lessons which went well and be prepared to talk about things which did not go well. Seek advice; Does your department have part of its department meetings talking about teaching different topics or sharing ideas for teaching? If not, ask if this is possible; Take time to explore the resources which the department has, such as worksheets, ideas for lessons, practical resources, e- resources; Sometimes you can get support from someone who teaches a different subject, possibly another NQT. What is important is that you find someone who you feel comfortable talking about your lessons and sharing strategies about working with children.

Outside school: local support Across the country there are a number of Maths Hubs which co-ordinate CPD sessions. Do you know your local Maths Hub? Are you receiving automatic s informing you of courses which are available? Go to:

Maths Hubs Cornwall and West DevonCornwall and West Devon Jurassic Boolean GLOW Central Salop and HerefordshireSalop and Herefordshire North Mids and Peaks North West One North West Two North West Three Great North Archimedes NE Yorkshire Ridings White Rose Yorkshire and the HumberYorkshire and the Humber South Yorkshire East Midlands West East Midlands East East Midlands South Enigma Cambridge Matrix Essex and HertsMatrix Essex and Herts Norfolk and Suffolk Bucks, Berks and OxonBucks, Berks and Oxon Kent and Medway Surrey Plus Solent Sussex London North East London Central and NWLondon Central and NW London Central and WestLondon Central and West London South West London Thames London South East

Outside school: branches of professional associations There are local branches of each of the following associations: Association of Teachers of Mathematics (ATM) Mathematical Association (MA) Institute of Mathematics and its Applications (IMA)

Outside school: branches of professional associations ATM:

Outside school: branches of professional associations MA:

Outside school: branches of professional associations IMA: l

Outside school: National support You can get a lot of ideas and support from many different places. Join one of the main professional associations so that you receive their journal(s) with lots of ideas and reflections upon teaching mathematics. It will keep you up to date with ideas and events. ATM: MA: Both associations also have YouTube channels

Outside school: national support Both ATM and MA have many publications which are excellent sources of ideas. Go to their websites and consider purchasing some, or ask your department to buy some.

Outside school: national support Consider going to the ATM annual Easter conference. It has the best mathematics professional development you will get. Ask your school if they will fund you.

Outside school: national support Register on the National Centre for Excellence in the Teaching of Mathematics (NCETM) website. It is free and has lots of professional development support and resources

Outside school: national support There are many websites full of ideas, some better than others! Be selective! I can recommend the following for ideas which can be different to what is usually found: NRICH: RISP (for A level): MEDIAN: Underground mathematics (for A level): Dan Meyer:

Outside school: national support Explore the National STEM Centre. This has an extensive archive of texts and resources from the past. There are many excellent resources there, full of ideas. Remember that many of the ideas around now are just re-workings of what has already been published in the past! Register (it is free) to get access to the resources:

Outside school: national support There is excellent support for Further Mathematics A level and also A level Mathematics from the Further Mathematics Support Programme (FMSP). They have got a channel on YouTube where they have videos which go through solutions to a number of examination questions. (Go to YouTube and search for “FMSP Revision Videos”).

Outside school: national support Another organisation is Mathematics in Education and Industry (MEI) who also manage the government funded Further Mathematics Support Programme (FMSP). MEI run a number of courses and also have an annual conference. They also have a YouTube channel.

Outside school: support from Loughborough NQT day contact In 2016 we offered financial support for two NQTs to go to the ATM annual confernce Remember that we have our own collection of ideas and resources which are on our shared Google Drive!

Professional Development: reflecting upon your practice The Knowledge Quartet (Rowland et al., 2005): Foundation Transformation Connection Contingency Rowland, T., Huckstep, P. and Thwaites, A. (2005). Elementary teachers' mathematics subject knowledge: the knowledge quartet and the case of Naomi. Journal for Mathematics Teacher Education 8, pp

The Knowledge Quartet: Foundation Knowledge in preparation for your role as a teacher For example, what you learnt during your PGCE year, including: –“One example is never enough” –Developing understanding of mathematics and not just memorising procedures –Relational and instrumental learning (Skemp, 1976) –Asking questions vs telling –Being aware of misconceptions –Offering visual support for what is being said Beliefs about: –The nature of mathematics –The purpose of mathematics –How students can learn mathematics well Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching 77, pp

The Knowledge Quartet: Transformation Transforming the content of the syllabus into an approach which makes that content accessible for students. For example: Finding ideas/approaches from textbooks, colleagues, internet, etc.; Careful choice of examples; Forms of questioning.

The Knowledge Quartet: Connection Making links between different topics within mathematics so that mathematics feels connected and not just a series of isolated topics. This was found particularly significant in what was common amongst ‘effective’ numeracy teachers (Askew et al., 1997). Sequencing of topics (which topic should follow on from which other topic and why?); Using one topic as a context for work in another topic (e.g. practising co-ordinates when working on area by giving shapes by their co- ordinates rather than just drawing them); Stressing common notions which exist within a number of topics (e.g. linearity with topics such as percentages, ratios, scale factors, equivalent fractions, etc.). Askew, M., Rhodes, V., Brown, M., Wiliam, D. and Johnson, D. (1997). Effective teachers of numeracy: Report of a study carried out for the Teacher Training Agency, London, King's College.

The Knowledge Quartet: Contingency “Thinking on one’s feet”. Dealing with the unexpected or the things which cannot be pre-planned. For example: Responding to students’ ideas and comments; Willingness to deviate from the lesson plan if that is considered appropriate; Sensitivity to the notion that individual students construct their own knowledge (von Glasersfeld, 1987); What beliefs or frameworks inform your decisions “in the moment” during a lesson? von Glasersfeld, E. (1987). Learning as a Constructive Activity. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics, New Jersey USA: Lawrence Erlbaum Associates, pp

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