Tag Archives: Gifted and talented

Count On Us Challenge: Congratulations to Kender School!

Kender School in Lewisham are the winners of the Mayor’s Fund for London’s Count On Us Challenge.

Val from the Maths Zone takes on Johnny Ball
Val takes on Johnny Ball!

Very well done to them and very well done to all of the schools who took part. The grand final took place yesterday at City Hall with 13 schools who had won their way through heats and semi finals to compete at solving 24®Game puzzle cards. Each card has four numbers; you can add, subtract, multiply or divide in any combination, but you must use all four numbers to make 24. Continue reading Count On Us Challenge: Congratulations to Kender School!

The MathsZone Course Boxes

We’ve been very busy at The MathsZone. Feedback from schools suggested they really love our gifted and talented courses Illuminate and Wondermaths, but they already have some of the materials that come with them. So, we’ve done a major re-design. Still the same fantastic courses for your gifted and talented students at key stage 2 (Wondermaths) or key stage 3 (Illuminate), but now in a neat plastic storage box, which will go on your book shelves. Each one has a comprehensive teacher guide detailing the structure and purpose of all of the sessions, with commentary and solutions (where appropriate!). For the students we have organised the materials into a beautiful student workbook. Now your students can keep all of their work in a really attractive book which they keep at the end of the course. Game cards, dice and counters are included for the activities.

There are fewer puzzles directly referenced in the course, so the price is lower, but of course you can buy all of the puzzles separately to extend the activities. Illuminate comes with a CD Rom with all of the course materials and additional materials for projection. Wondermaths has an associated web site with the materials available. When you are ready to run the course for a second time, you can get extra sets of 10 copies of the workbooks. The key objective for the teacher is to get up and running with the minimum of fuss, so you can focus on supporting your students explore their mathematics.

The aim of both course is to give students the opportunity to explore mathematics. Wondermaths has games, to compare strategies, puzzles to develop sustained thinking and investigational maths top explore maths language and move towards explanation and proof. Illuminate aims to develop the ideas of pure mathematics for those who are limited by the algorithmic nature of school exam courses. Students will develop and compare proofs, while exploring the nature of proof itself. Their is a comprehensive section on group theory, fully accessible to ordinary school students. Games strategies are developed and compared and the course ends with a project in fractal geometry. These are really course in the mathematics that mathematicians would recognise.

Illuminate: Gifted and Talented at Key Stage 3 School Reviews

This is a shameless commercial post because I am really excited that schools who have bought our Illuminate Gifted and Talented Course for key stage 3 have posted on-line reviews on the National STEM centre web site. Obviously I would only be saying this if they like it, but they really like it a lot and that is really exciting.

See here: http://www.stemdirectories.org.uk/scheme/wondermaths-gifted-and-talented-maths/#comments

Our aim was to produce a course in mathematics, so that school students had the opportunity to see what Maths is really all about. It is full of puzzles and games and tricky things to think about. But it takes them to the next level by unpicking fundamental ideas notably proof and isomorphism and giving students an incite. Maths gives a way of definitively saying how we know what we know. We use Pythagoras Theorem to unpick the idea of proof. From the essential structuring idea that sets up the proof to the language needed to be clear and the sequencing of the statements to construct the complete argument. It is thrilling that schools are reporting that students are able and interested to work on this. It is hard, but interesting things are, but students are game to carry on. Then we compare cyclic and Klein groups with isometries and modulo arithmetic. I cannot think there is anything more wonderful for the beginning mathematician to see that we can show that two complete areas of operation, so apparently dissimilar as arithmetic of clocks and transformational geometry have exactly the same underlying structure and hence, if we know something about one, we necessarily know the same thing about the other. That, to me is what maths is really all about. The mechanical processes that students learn for their GCSE and A Levels give no insight into this amazing world.

So, well done to those schools for being brave enough to work this way and really well done to the students who are becoming serious young mathematicians. Clearly we would be delighted for you to try it too. Just ask for some trial materials of the Illuminate course.

Also, come to ATM sessions and meet Danny Brown. Danny is the head of maths at the Greenwich Free School and he is getting his kids working on deep mathematical ideas all the time. Danny has presented regularly to ATM London Branch and has a web site of the amazing stuff he does. I persuaded Danny to get this out in book form and the first volume, on Number, is nearly ready, so look out for that.

What is this maths that we are teaching?

It is with envy that some mathematics educators in England look to our colleagues in the Netherlands where the Freudenthal institute has generated a rich, coherent research debate which has been widely implemented in schools. Realistic Mathematics Education offered the antidote to the formalism of the New Maths based on Hans Freudethal’s view that mathematics was not pre-formed. He said; “… the global structure of mathematics to be taught should be understood: it is not a rigid skeleton, but it rises and perishes with the mathematics that develops in the learning process. Is it not the same with the adult mathematician’s mathematics?” So it is very sad to hear that the Commission for Examinations in the Netherlands is considering banning graphing calculators from public examinations. What is it that a calculator does that could be damaging to mathematics developing in the learning process? A machine can do only what a machine can do. If mathematicians continue to fulfill an important role, then clearly they must be able to things that machines cannot do. In his 2001 novel, Uncle Petros and Goldbach’s Conjecture, Doxiadis’ eponymous mathematician dismisses any process a machine could do as ‘shopping maths’. That of course includes anything a computer algebra system (CAS) could do.

So, learners of Freudenthal’s mathematics should have access to the tools to do the shopping maths, to free up the thinking space to engage with real mathematics; solving problems, generating conjectures, developing proof. These are the art of mathematics, not the mechanical grind. Godfrey Hardy acted as the foil to Ramanujan’s genius, but in the ‘apology’ he makes clear how well he understood that Ramajan’s ability for finding extraordinary new relationships that only he could see, was the real mathematical gift. Getting it into a publishable state was the routine work for afterwards.

The excellent Project Euler takes as it’s premise that mathematicians will have access to a high level programming language (Python, which naturally has a powerful CAS) to engage with problems in number theory. The wonderfully named https://brilliant.org/ designed for potential International Maths Olympiad candidates has a whole section of problem solving requiring programming (and hence CAS) available.

Having a machine capable of high level mathematics available in a public examination in mathematics forces examiners to take a considered view of what the maths is that they are examining. It prevents them from asking students to replicate what machines can do and focuses their thinking on the maths that matters. The maths that Hans Freudenthal was so keen to preserve in the Netherlands, against the onslaught of formalism.

This sad situation was brought to my attention through the English translation of a response by Erik Korthof to an advert for the new HP Prime graphing calculator. He suggests that the absence of graphing calculators in the past allowed the construction of ‘proper exams’. The task of mathematics education should not be to make the lives of examiners easy. Clearly, asking a student to complete a mechanical task that would be simply done by a machine is very simple. To construct a question knowing that the student has access to such a machine is hard. Specifically so, because the question must demand genuine mathematical thinking and that puts great demands on examiners. In the UK, the most progressive mathematics education project (MEI) for A Level students (age 18) have just had their first cohort complete an examination module with a CAS calculator available. The result is thoughtful, highly mathematical questions of exactly the type University maths courses are excited to see. The link will take you to their answer to Erik Korthof’s question: “Is secondary education served with a Computer Algebra System?”. Clearly they answer a resounding yes and MEI are major players in the future of maths education in England.

As I’ve said elsewhere the existence of tools like HP Prime which allow access to powerful mathematical visualization and calculation tools in the classroom liberates students from the mechanical processes that prevent them thinking deeply about the mathematics. Certainly there will be many lessons where the calculators are put firmly away and students will learn and practice these mechanical processes, like drawing graphs and manipulating algebra, not only because they need to see how they work, but also to give them a better feel for the outcomes. Happily teachers are sophisticated enough to manage this. They can also find secure ways to use exam modes to ensure devices adhere to local regulations. Schools are expert in this. These logistical issues should not be used as an excuse for not allowing students the tools that professionals have access to and reducing what is called maths in schools to a collection of mechanical processes. Especially not from the birthplace of RME and the beautiful, powerful view of mathematics presented to the world by Hans Freudenthal.

So, why do we put kids in sets?

I am not unique in wishing to question the omnipresence of putting kids into different groups according to the teacher’s perception of their potential to achieve. Jo Boaler has been shouting this loudly for some time now (see The Elephant in the Classroom) and Anne Watson makes the case forcefully (see Raising Achievement …). So, how can it be that even primary school teachers feel unable to to teach a class of 7 year olds the same number skills at the same time – because there is such a great gap in their likelihood to succeed? Continue reading So, why do we put kids in sets?

Gifted and Talented at Maths

About four years ago, I was asked if I could run a course for year 6 students from inner city London primary schools, who had been identified as ‘gifted and talented‘ in maths. Now, I’m troubled by this idea in general. What measures schools might use to identify gifted and talented is very hard to tell. My idea of a good mathematician is almost never the person who correctly answers all the arithmetic questions. However, the truth of the matter was that they were ordinary kids in ordinary schools. Continue reading Gifted and Talented at Maths