Three positive outcomes of failure in Maths

Welcome to the June 2017 Transum Newsletter. This month’s puzzle is about the Numlove family. Can you work out how many children are in the family from the following two clues?

  • Each boy has the same number of brothers as sisters.
  • Each girl has twice as many brothers as sisters.

While you think about that here are details of some of the more significant new additions to the Transum website last month.

Writing Expressions

Writing Expressions is designed to provide practice forming simple algebraic expressions for situations described in words. The words come as short audio clips which pupils can play over and over again by clicking a button on the web page. There are three different versions of each question which are independently chosen at random each time the page loads.

Area of a Trapezium is exactly what it says in the title. Level 1 requires finding the areas of the trapezia by using the standard formula. Level 2 requires the application of the trapezium area formula in different ways. There are some nice problem-solving questions here.

Venn Totals completes the Transum collection of Sets activities. It is a multi-level exercise in which you read or enter the total number of elements in regions of two- and three-set Venn diagrams.

Many other activities on the website have been updated during last month with better interfaces or more detailed answers. Talking of answers someone is needed to find the solution to the level 5 Tantrum Puzzle as I am stumped! A screenshot of the solution would be very much appreciated.

The book I am been reading at the moment is “Black Box Thinking: Why Most People Never Learn from Their Mistakes – But Some Do”. The author, Matthew Syed, argues that the most important determinant of success in any field is an acknowledgment of failure and a willingness to engage with it. This theme resonated with me as a teacher of Mathematics and made me think of ways we could better use learners’ failures or mistakes to help them improve.

One example mentioned in the book was about the analysis of a large data set. It was the story of mathematician Abraham Wald who was presented with the following question.

You don’t want your planes to get shot down by enemy fighters, so you armour them. But armour makes the plane heavier, and heavier planes are less manoeuvrable and use more fuel. Armouring the planes too much is a problem; armouring the planes too little is a problem. Somewhere in between there’s an optimum. Wald and his team had to figure out where that optimum is.

The military came to Wald with some data they thought might be useful. When American planes came back from engagements over Europe they were covered in bullet holes. But the damage wasn’t uniformly distributed across the aircraft. There were more bullet holes in the fuselage and not so many in the engines.

Here was an opportunity for efficiency; you can get the same protection with less armour if you concentrate the armour on the places with the greatest need, where the planes are getting hit the most. That would seem to make sense but Wald thought differently.

He reasoned that the armour should go not where the bullet holes are. It goes where the bullet holes aren’t: on the engines.

Wald’s insight was simply to ask: where are the missing holes? The ones that would have been all over the engine casing if the damage had been spread equally all over the plane? Wald was pretty sure he knew. The missing bullet holes were on the missing planes. The reason planes were coming back with fewer hits to the engine is that planes that got hit in the engine weren’t coming back.

Wald’s interpretation of the data with a little out-of-the-box thinking and a lot of common sense provided the solution that the engineers could put into practice.

What a wonderful ‘large data set’ story. Now if only I could get hold of the bullet hole coordinates to create a data analysis activity for the Transum website … !

On the topic of failure, did you know that Steve Ballmer, former chief executive officer of Microsoft and 22nd richest person in the world, was told he was failing at Maths when he was at school? You can hear him talking about it on the podcast version of this newsletter.

The last word on failure is the strategy of trial and improvement. It is valid mathematical technique that might be used in the Where’s Wallaby activity but refined as learners develop and use Iteration for solving equations. Learn from your mistakes!

Now here’s a success story from National Numeracy. They launched a new mobile game called Star Dash Studios, a free game that brings maths to life. The character in the game is a runner on a movie set who has to solve puzzles and carry out tasks for the producer – all of which relate to using numeracy in real life situations.

It has been about 6 months since their launch event with Countdown’s Rachel Riley and they are so pleased they have had almost 20,000 downloads to date. If you would like to download it for your mobile device the link is https://www.nationalnumeracy.org.uk/star-dash-studios

Finally here is the answer to this month’s puzzle.

Let the number of girls in the family be n.

The number of boys must be n + 1 to satisfy clue number one.

Clue number two produces the following equation n+1 = 2(n – 1)

So n+1 = 2n – 2 or n = 3

Therefore there are 7 children in the Numlove family.

Did you get it?

That’s all for this month

John

P.S. I will do algebra, I’ll do trigonometry and I’ll even do statistics but geometry and graphing is where I draw the line!