Research Based Pedagogic Tasks RBPTs

This has been a long time coming, but I intend to restart sharing thinking about work I’ve been doing in projects around the world! I am part of a Sheffield Hallam, British Council project for the Indian Institute of Science Education and Research in Pune. The idea is to work with teachers of undergraduate science and maths to develop tasks requiring problem solving skills in settings of genuine benefit. The problem with maths, is that the problems are frequently unrealistic or too simplistic. One of our co-tutors wrote to ask my thoughts on this …

The issue is that teachers of mathematics are so fixed in their need to teach some specific mathematics that all they can ever do, is invent some ‘story’ that fits the mathematics they want to teach. In applied mathematics, the solution is led by the application. The mathematics is not fixed and will keep changing. So the vital issue is to start with a real problem that someone really wants to solve. You may have to accept that the mathematics that ends up being used is not necessarily what you wanted to teach.
Probably the best situation is for mathematicians to find a group of scientists who already have a genuine problem and work with them. The vast majority of the RBPTs created by participants at the workshops would have benefited from much better design and analysis of the data. Claims were being made e.g. of the relationship between certain diseases and certain things found in rivers. This needs good statistics. NOT finding a simple correlation and saying that therefore one is caused by the other. On the same subject, flow rates in water courses generate problems needing differential equations as for examples would traffic management problems.
I saw an RBPT on nano technology. The issue of orders of magnitude was very clear. For example we did an experiment with waterproof sand (yes, seriously). This is grains of sand covered in a polymer coating one nanometere thick. What is the relative size of the sand grain to the polymer? Making serious calculations at the nano level of sizes requires some complex handling of numbers. But again – the application must lead.
Finally Space technology requires sophisticated mechanics and calculus and of course India is a world leader. Differential equations are needed to model rocket speed/time trajectories and escape velocities, so a nice RBPT would be to design a satellite flight path to put it onto successful orbit.
So: (i) wean the mathematicians off starting with their bit of maths and onto finding an interesting problems and (ii) force them (!) to work with scientists who already have the problems and need some help with the maths.

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.

It is quite astonishing to see pupils in years 4 and 5 (aged 8 to 10) able to solve these puzzles almost instantaneously. Their teachers certainly can’t, my PGCE students with top maths degrees can’t. So how is it done?

I talked with Bob Sun, inventor of the 24®Game in Easton, Pennsylvania and he gave me a copy of a book by journalist Daniel Coyle called The Talent Code. Coyle examines a series of instances in which exceptional performance is found in different fields and looks at the elements that came together to produce it. A great coach is always included, so teachers, you know you are important! However, the coming together of real desire and serious hard work with lots and lots of practice are the principle elements. In the end, the final few percent are achieved through an intangible element that can be called ‘talent’. But, for sure these kids can beat there teachers because they have worked hard at it.

Now, playing the 24®game is not like memorising your times tables. It involves flexibility of mind. You generate a whole raft of relationships which make up parts of the 24, like looking for 8 and 3 or 6 and 4, or 23 and 1 made up of pairs or triples of the numbers available. So, you are juggling lots of combinations. The outcome is young people who see numbers and are aren’t interested in seeing if they can remember the answer, but recognise the need to fiddle with what they’ve got to unlock routes to the answer. You can’t get more like true mathematical thinking than that in a 9 year old!

So, the Count On Us Challenge provides the desire. Compete for your school, win the prize, get to walk across the top of Tower Bridge. It doesn’t matter, it was a great day out for everyone, but everyone involved was ready to compete because they cared and they’d worked hard at it. Net result, 100s of young people with much better and more flexible number skills than their teachers. That’s good!

All of the 24®Game sets are only available from The Maths Zone. There are class kits, tournament packs, the competition standard one and two digit sets, primer sets for early practice and tougher sets for advanced challenges. 

There will be a Count on Us Challenge next year. So, start practising now. The kids from Kender School are very good. Very good indeed. They will take some beating! (And please don’t think it is a school with any special advantage, not at all, it is a very straightforward urban primary in SE London. They work hard at it and their kids practise and my are they sharp with their number skills. Well done to them.

We have produced a guide to help you run a number challenge tournament in your school or your area. You can use the 24®Game cards as they do in the Count On Us Challenge. If you want a more equally weighted tournament, we also have SuperTMatik, which is a card game from Portugal where they have a National (and World!) championship, but the problems are seeded so you can have pupil’s competing at different levels in the same game. Target Set 3 CMYKFinally there is Target Maths, where the numbers are combined to make a different target each time. Try this one (the target number is in the middle).

So, an in-school tournament to provide the desire, then plenty of opportunities to practice, practice and young people get really good. And then in secondary school what happens? They forget, because they stop practising. What does Andy Murray do before during and after every tournament? He practices hard. That’s why he is so good (and he may just have a bit of that extra few percent too!). It was humbling to see how good the kids from Kender (and indeed all of the other schools) are. Teachers can get all of their kids to that level with enough desire and a lot of practice. Good luck for next year!

 

 

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Financial Education: How does that work?

From September 2014 it will be compulsory for schools to teach financial education. This will be built in to the mathematics and the citizenship curricula. See this article from the Daily Telegraph. Notice the picture of school life that they choose to illustrate the article with. This is how students learn; in rows at individual desks, looking seriously bored! The trouble is that a good proportion of the materials available for ‘financial education’ in schools is perfect for this scenario. Standard worksheet based discussion and practice activities are the norm and work in the same way that makes PSHE such a disappointing subject, taught by non-specialists, with no exam, it is hard to see the purpose when you are in school.

What makes these important things come alive is getting students into the setting. They have to care about the issue in order to engage with the ideas. I have seen fantastic drugs education sessions where former users and dealers have come in and talked to teenagers about their experience and where they are now. It is edgy, but it is real and they certainly listen!

Finance is tricky. Kids in school rarely have any real need to save with interest and if they have a bank account, their main worry is losing their cash. Certainly, they cannot borrow beyond their means or need to budget in a life changing way. Some, certainly, have life experiences that may necessitate any or all of these, but they are a small albeit important minority.

We have been working in financial education for over a decade. As a development of the Number Partners project which I was director of for many years, we designed a series of large format board games designed to set up scenarios in which players have to make important financial decisions: how to invest a small amount of capital, to generate profits to reinvest. Managing money between cash and different bank accounts, to enable purchasing but retaining security. Budgetting for a holiday and managing exchange rates. Making the life transition from school to work, while meeting your life goals.

The power of a board game is that the social setting frames the decision making. You are playing with real people who you have to engage with, framed by the settings of the games. The games were trialled in very ordinary schools, in classrooms with groups of students and have been widely used in different settings since. The effect is impressive. Students talk to each other about their financial decision making, developing strategies to succeed in that setting. Naturally, winning strategies involve good financial decision making.

We set up a web site to showcase the games. So see what you think. All of the games have teacher guides with extra materials and school use ideas. Please get back to us with your questions and thoughts. But, when you plan to deliver financial education this September, get your students into a setting in which they care. Only then will they be able to make decisions in a way that matters to them.

Playing Maths Games Makes You Do Better at School!

OK, so I came to this by being responsible for public maths events for maths year 2000. We had 22 shopping centre events, at the end of January 2001, where we set up staffed table stands with maths activities. It was humbling to see ordinary shoppers give up on Sainsburys and spend the day doing maths puzzles and games. So, the I end up being a part time shop keeper selling maths games and puzzles. It is just great to keep being reminded that people love doing this stuff. Continue reading

Finding Good Maths Resources

The internet for teachers, blessing or curse? In the past, you would have a set of text books or work cards as your basic resource. The department would have bought a small library of additional books and materials from people like the ATM. If you needed a good idea, you would never have to look beyond the maths office or the maths cupboard (do you still have those?) Every department would have a pile of good physical manipulatives like centicubes and logic blocks, cuisenaire rods and probability kits. A set of large compasses and ruler for board work and a good collection of games and puzzles for activity days. There would be copies of those wonderful books by Brian Bolt (which are still available) for practical problem solving and a set of Points of Departure books for maths investigations. Always excellent, always to hand. Continue reading