This month’s problem can be solved by pre-schoolers in seconds, but it can take maths professors much longer:

1235 = 0
2678 = 3
3668 = 4
9000 = 4
8000 = 5
3218 = 2
6777 = 1
8888 = 8
1568 = ?

The solution: count the number of enclosed spaces within each digit.

1, 2, 3, 5, and 7 have no enclosed spaces

6, 9 and 0 have one enclosed space

8 has two.

4 has 1 or 0 depending on what font you are reading this in – so I left this digit out.

Summer’s here and it’s time for you to come up with the punchline.

“Where do maths teachers go on holiday?”

Post your punchline below. If yours is our favourite, a bag of Doodle-goodies will be winging it’s way to you!

‘Practice makes perfect!’ It must be one of the most irritating things that was said to me as a child. But, in my view, never has an idiom been so true.

I know of a CEO who has a golf lesson every fortnight with a top coach. He pays almost £200 per hour. He hasn’t improved his handicap at all over the last year. Why? Because between his lessons, he couldn’t find time to practice.

The same with the numerous kids who have piano lessons every week. The ones who move through the grades aren’t the ones who have the best teachers. It’s not necessarily even the most gifted. It’s the ones who put in their daily practice.

Our experience as teachers and educators has taught us that the quality of practice in maths is far more important to the learning process than the quality of explanation. However elegantly explained, a concept will not be remembered unless it is practised sufficiently. Kids learn through doing.

We define good quality practice as being regular (ideally daily), engaging (touchscreens helps here!) and at the level most appropriate for the individual. The latter is vital – most children, when faced with a choice of tasks, will choose not what is most appropriate for them, but what will give them the highest reward for the minimum effort.

When it comes to the core basics of maths, regular practice is the absolute key to improvement. We can tinker with the Framework and the National Curriculum; we can try to employ the best graduates as teachers. But the simplest way to raise standards in maths would be to give children more opportunities to practice. In the UK’s quest to understand why Shanghai leads the way on the PISA tables, this has been one of the key findings: children in Shanghai spend more hours doing maths on a weekly basis than their counterparts in the UK.

A final warning: as with anything, if you don’t practice at all, you actually get worse at maths. Children regress more in maths than any other subject over the summer break – mainly because opportunities to practice are not so obviously available in everyday life as with reading and writing. Seeking out those opportunities, be it puzzle books, sudoko or DoodleMaths, is a great way to reverse this drop.

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.