The NCETM is holding a panel discussion about Teaching and Learning Proof on 9th June from 11:30 to 12:30, and some interesting debate has already started. Having read the comments below the event information, I thought, 'Mathematics is about searching for patterns and making generalisation of those patterns.' I also agree then that the proof idea is the next step, and that the problem-solving may be at the heart of mathematical thinking. Maybe somebody in each school could join in the discussion on the day, or have a go at posting a comment. Where does proof fit into your mind map of teaching mathematics? Which topics do you use as a vehicle for teaching proof?
I wanted to follow this thread about proof, so my next step was to put the word 'proof' into the search box aht the top right hand side in the NCETM portal to see what was there. The search was really useful:
- there was information about an ATM book on developing mathematical skills;
- in the NCETM Mathemapedia, there is a helpful entry on the nature of proof - What is a proof? - that gives us an insight about how to start in the classroom by asking students to explain and to answer the question 'Why?'
- also, have a look at Cut-Up Proofs as a practical suggestion about how to get started in the classroom.
This is the great thing about this portal: once you start looking for what you need, there is some very thought-provoking material which inspires you to have a go. I can see the Cut-Up Proofs idea being very useful for all ages and levels of learners as a way of developing systematic and logical thinking.
There are a few other things going on that are also worth a mention this month. The Mathematics-specific Pedagogy section has now been written, and you can find it in the Self-evaluation section of the portal. If you select KS3 and then have a look at Selecting Teaching Strategies and click Example, there are some really good ideas about different ways of teaching mathematics. For example, there are examples of the use of open questions to challenge and support students' thinking:
324÷4 can become 'Use the digits 0, 1, 2, 3, 4, 5. Make three-digit numbers that have no remainder when divided by 4.'
In the previous portal tour I mentioned NCETM Grants - they are definitely worth appyling for if you have a professional development idea that you woudl like to explore and develop. You can contact your local NCETM Regional Coordinator if you need to discuss your idea and how to progress it through the grants scheme.
The Regional Pages on the NCETM portal have a good collection of interesting information that can be useful wherever you are based. Go to the East of England page and look up their website of the week: at the time of writing, it is Gresham College. To find more events in your region, use the Events Calendar at the top right hand side of the page.
Last but not least...always check out the Communities, and join in the discussion both to help and learn from others in a similar situation. Again, I keep plugging the Geogebra thread, as I think this free resource has a lot to offer teachers in developing teaching strategies, and for learners in developing their understanding of mathematical concepts. Have you tried this free resource in the classroom yet? If not, after reading this, maybe you will be inspired to have a go!