Puzzle

What comes next?

Scroll down for the answer:

It’s the top half of ABCDE, so the top half of F comes next.

After May’s frantic preparations for tests and exams, June and July seem a constant wave of sports days, residential trips, projects, activity days and school performances. Maths can seem to go by the wayside – and then it’s August. Children can quickly forget what they’ve learnt, and also get out of the habit of using the left (logical) side of the brain.

‘Brain Drain’ is very real but it affects some students more than others. If you’ve read Malcolm Gladwell’s very excellent book ‘Outliers’ you’ll already have an inkling as to why. Gladwell described studies into why wealthier children outperform those from poorer backgrounds during their early years of schooling. The studies found that all children, regardless of background, made similar improvement during term time. It was during the long summer break that differences occurred: children from wealthier backgrounds had better access to the kinds of activities that keep their brains active, be that summer camps, physical activity programs, formal tutoring or simply more conversation with adults. In short, summer brain drain affects all children, but is much more apparent amongst children from less-wealthy families. In these New York based studies, this was shown to be the most significant factor in the discrepancies in academic performance between children of differing backgrounds.

You’ll have to read the book.

How do I stop brain drain? Here are a few tips to offer parents:

  1. Reading: lots of local libraries run a ‘6-book challenge’ over the summer holidays.
  2. Puzzle books: rather than videos on long flights or in the car, try mini-sudoku, hangman, word-search or brain-training books (or apps).
  3. Physical exercise: this has a beneficial effect on the brain, and can also involve plenty of maths – timing laps on a bicycle, scoring in cricket or tennis. Making up new games can help develop children’s creativity.
  4. Encourage play with construction toys such as Lego and Meccano on those (not-so) occasional wet days.
  5. Keep a diary and write postcards.
  6. Do something formal but fun as part of your routine – this is what DoodleMaths was made for!
  7. For more ideas on how to build maths into the summer hols, visit our this previous post written by our guest blogger Katya last summer.

As a teacher, it often feels like September is all about getting children back up to where they were in May last year. A new year is a fresh start and those children who make a flying start to the Autumn term are often those who carry that confidence through the whole year, perhaps moving up a maths group or performing better than expected in early assessments.

As a parent, I know I want my kids to have a break from formal learning this summer, because learning through play is equally important to their development. But where I can introduce the opportunity to keep their brains active, I will, by recognising that some types of play are better at staving off the dreaded brain drain than others.

Want to read more? We also really like this article from mathsinsider.com about beating the summer maths slump.

When I first used a tablet, what struck me, apart from the intuitiveness of touch-screen, was its potential in educating children in the poorer corners of the Earth – children who have a desire to learn but no access to formal education. Here are five reasons why tablets could transform education in these parts:

  1. They have long battery lives, minimal power consumption and can be solar-charged
  2. Many apps can work on or offline
  3. They are intuitive (you don’t need prior knowledge of Windows, for example)
  4. Generally speaking, tablets are cheap
  5. Tablets are durable and low-maintenance

To illustrate their potential, The One Laptop per Child organisation conducted a fascinating experiment by dropping boxes of tablet computers into two remote villages in Ethiopia.&MaxW=640&imageVersion=default&AR-312269921 The Motorola Xooms, loaded with educational apps, were quickly adopted by the villages’ children even though they had no previous contact with any such technology. When the researchers visited months later, the kids in both villages were still heavily engaged in using and recharging the machines, and had been observed reciting the “alphabet song,” and even spelling words. One boy, exposed to literacy games with animal pictures, opened up a paint program and wrote the word “Lion.” Older children had even worked out how to hack the Android operating system to gain access to hidden software. The full article is available here.

There are some remarkable charities doing pioneering work in Africa with tablet computers. We have paired up with one of these, Livingstone Tanzania Trust, who are running a pilot project using Hudls pre-loaded with educational apps including DoodleMaths. We believe that DoodleMaths will provide the opportunity for motivated students to learn maths for themselves, but also provide a structure and framework around which the local teachers may be able to base lessons. Each Hudl will be offline for periods in excess of a month, meaning children will need to stick to using the same tablet each time. DoodleMaths can store the work programs of up to 100 students at a time in an offline situation. We’re excited to see how it pans out!
For more information about the work of Livingstone Tanzania Trust you can visit their website.

I understand the fuss: the question will certainly have thrown students because there’s no precedent question in any previous past paper. And the same goes for some of the other questions in that paper too. But that’s not to say it shouldn’t have been included.

It takes us right to the core issue about how we teach maths in the classroom in this day and age. The new National Curriculum for maths states its aims as:

“The national curriculum for mathematics aims to ensure that all pupils:

  • become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
  • reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
  • can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions”

The issue is, in the past we as maths teachers have focussed far too much on the first of these aims, concentrating on the fundamentals, focussing on repeated exercises and applying the same methodology for exam preparation by working through past exam papers. The new national curriculum wants us to spend much more time applying these fundamentals to solve problems and reason mathematically. And I suspect this was the thinking when the EdExcel team included the question in the exam paper this week.

Incidentally, this is something close to our heart at DoodleMaths. Our philosophy is that the learning of these fundamentals (which is largely best done by rote) needs to be taken out of the classroom where possible: we have the technology now to be able to deliver an adaptive, individualised study programs which teach children these fundamentals in a way that is personalised to them, their strengths and weaknesses, and the pace at which they learn. Crucially, this frees up teacher time up to do what only they can do in the classroom: teach children to reason mathematically, problem solve and develop their powers of mathematical modelling. Whilst tech can help with the fundamentals, it will never be able to do this.

I’ll get off my soap box now, since most visitors to this blog will be after the solution, I’m guessing. So here it is. I’m off for an orange sherbet.

“There are n sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow.

Hannah takes a sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet.

The probability that Hannah eats two orange sweets is 1/3. Show that n²-n-90=0″

EdExcel Higher Maths Paper, 4th June 2015

Here's the solution to EdExcel's famous orange sweet problem.

Here’s the solution to EdExcel’s famous orange sweet problem.

Whilst we’ve presented it poorly, we haven’t got the maths wrong! It makes more sense if we put some units into our equation:

30 students x 30 days = 3 months average improvement in their maths age.

Most trials don’t come with a promise or a guarantee. But based on the independent tests conducted in schools during the development of DoodleMaths, and the feedback from our existing users, our trial does.

Why does DoodleMaths improve results?

Most online/digital maths products are resource banks. On a pedagogic level, by simply replacing a worksheet with a game or online exercise, we are not doing anything radically different. In recent years, the ability to rapidly analyse big data, along with 3 kids insidethe advent of touchscreen technology and a better understanding of how children learn as individuals (and the development of algorithms alongside this) has led to the development of DoodleMaths: a learning system that mimics the actions of a good tutor. DoodleMaths identifies a child’s strengths, weaknesses and the pace at which they learn, and creates a work program to ensure they are always learning exactly what they need to learn in order to progress most rapidly.

How do I run my trial?

Sign up here.

  • We will process your application and set up your account with 30 free licences for DoodleMaths. Upload your students’ names and distribute their logins. They can log in to any device with the free DoodleMaths app installed.
  • Encourage students to do 10-15 minutes of DoodleMaths on a daily basis.
  • Measure their improvement in maths age. You can do this either by monitoring this through our own online teacher dashboard, or by using an independent assessment as we did in our trials (we used Hodder’s Access Mathematics Assessments).

Please let us know how you got on!

We can’t claim this as one of our own but it is one of my favourites:

What comes next in this sequence:

what comes next question

Some people get it straight away (including Bart Simpson, much to the frustration of his more academically-acclaimed sister Lisa who didn’t, when it was famously featured in The Simpsons). Here’s what comes next:

what comes next answerStill not got it?

Notice that all the figures have a vertical line of symmetry. Cover up the left hand side of each figure and you should see the pattern straight away.

Interestingly, my 7-year old got it before I did. It may have helped him that he still reverses most of his digits when he write them though – on this occasion it’s worked to his advantage!

Here’s the sequence in full:

what comes next whole series

DoodleMaths was created by teachers who really understand how kids learn. Now that exam season is upon us, what are the best tips we can offer for revision?

1. Revise actively. Don’t stare at books trying to remember formulae and methods. You’ll remember them far better by using them and applying them to questions.

2. Don’t be tempted to revise what you already know. Learning is most effective when you are learning at your threshold, that is, marginally beyond what you are confident with. So if you are aiming for a ‘B’ at GCSE then work at this level first, and don’t get bogged down in all that ‘A’ grade stuff. If you’re doing SATs, stick at the work that’s been recommended for you.

3. Revise with a buddy. We’re social beasts, and a maths problem shared is often a problem solved. You’ll need to be a positive influence on each other, and be a similar level in maths – it won’t work if one is getting much more from it than the other. If you’re under 12, your study buddy is one of your parents.

4. Invest in appropriate resources. There are a lot of resources out there, both digital and paper-based. Much of it is poor quality and sometimes out-of-date. Check it applies to the exam board and current examination year, as well as being suitable for your level. It should be designed by or alongside experienced teachers. Use what your teacher has given you.

5. Short bursts are best. Try 20 minutes on, 10 minutes off.

6. Be conscious of the time of day you are at your best. I’m a morning person, but Nicola (my co-founder) is an evening person. We’re similar levels at maths, but we’d make hopeless revision buddies!

Stay fresh, stay happy, try your best and relish the opportunity to show them what you can do!