Archives For teaching math

I meet children every day who have lost their enthusiasm for maths. Why is this? When we start to learn maths we are all keen! It is new, relevant and important. So what causes us to lose interest?

I believe the answer is simple: the children who are disaffected are almost universally the ones who are falling behind in class. Note class, not school. I meet plenty of bright children who are fed up with maths – despite being in the ‘top group’, they are still struggling with what is being taught and are perhaps towards the bottom end of the class. I love maths, but I too became unmotivated for a time at university when I fell towards the bottom of my class.

Why is this? Because the enjoyment of maths comes from simply being able to do it. We all know the feeling: when we get a question right, we experience a small buzz of satisfaction, of contentment. The buzz is magnified if we know there was an element of challenge, too. It’s quite a pleasant feeling, and explains why Sudoku has become the most popular puzzle of all time.

Not many buzzes...

Not many buzzes…

So let’s consider our class of 14 year-olds who are learning, say, equations. The teacher explains how to solve an equation and asks the class a few questions. The brighter, more vocal students respond correctly in front of their peers (big buzz!) The class start the exercise. The top half of the class may then solve 20-odd equations in the lesson (lots of little buzzes, a sense of achievement and understanding.) The bottom few may solve a handful, perhaps with the help of the teacher. No buzzes. Not much sense of achievement. And perhaps disappointment, if the teacher asks them to complete the exercise for homework.

Lots of buzzes!

Lots of buzzes!

Working in our tuition centre, we have learnt that the simple way to rekindle enthusiasm for maths is to allow children to experience the buzz again. This may mean we have to take them back a level for a while, but we typically aim for a child to be completing 100+ computations in a tuition session with a success rate of about 75%. Lots of buzzes! And lots of progress, too. DoodleMaths, used daily for 10-15 minutes, should result in a child completing 200+ computations per week with a success rate of 80-90% (higher, because there is no teacher to encourage or offer a quick explanation.) Again, lots of buzzes! But this only works because the child is working at precisely the right level for them.

I have come across some ludicrous examples of attempts to motivate students in maths through gimmickry. It probably made a good news story, but the teacher featured on BBC News a few years ago who would ask his students to text him the answer clearly had no idea about motivating children in maths. More recently, I came across a dreadful app (mentioning no names) which rewards each correct answer with a game of “Whack-a-Monkey”. The developers obviously started with the premise that maths is dull and best broken up with something silly. They failed to grasp that the buzz of the correct answer is reward enough in the short term. My children rejected the game immediately – they became fed up because their enjoyment of the maths was being delayed by a trivial game.

If you ask a child why they don’t like maths, they will typically say it’s because “it’s boring” or “it’s no fun”. But before you start asking them to text you the answer, try this: ask them “If you were better at maths, would you like it more?” The answer is always an emphatic “Yes”. The key to getting children more motivated at maths is to get them working at the right level for themselves and to experience the buzz of correct answers again. Kids only learn maths if they are answering questions, and lots of buzzes = lots of progress + plenty of motivation.

We have a fantastic local village primary school right on our doorstep, and we are fortunate enough that they have taken a great deal of interest in what we are producing. So when it came to testing our product to try and see what kind of improvement it might offer a child with sustained use, it seemed natural to pair with them.

We asked the Headteacher, Mr Stone, to identify students that he felt would benefit from using DoodleMaths for 15 minutes per day over the course of a four week period. A group of six Year 6 students were quickly found and seemed delighted to be given the opportunity to use iPads at school.

Unfortunately for them, the first thing we did with them was administer a written test. To genuinely measure their level of improvement over the four week period we clearly had to use an assessment that was independent of DoodleMaths. We chose to use the Hodder Access Mathematics Tests: these have been standardised over a huge sample size and as well as returning a National Curriculum level, they also return a child’s maths age, much as DoodleMaths’ assessment does.

The children sat the Test A on Friday 28th September at 10.15am. The average Hodder maths age for the sample of six students was 8 years 7.7 months, which equates to a National Curriculum level of 2.9 according to the Hodder handbook.

On Monday 1st October the children did their DoodleMaths assessment. The average DoodleMaths age for the children was 8 years 5.4 months. On Tuesday, they finally started using the iPads for learning.
We are now almost two weeks into the trial. The children are working with so much energy and enthusiasm, they are a credit to themselves and their school. What I am most surprised about is that at the end of the session when they are allowed on games and personalise their pet character, they tend to opt to do another 7/8-a-day. They are enjoying maths now that it is personalised to their needs and ability.

We will be doing Hodder Test B on Friday 26th October with the children, and will post the results that afternoon.

We’re not the only ones who favour a little-and-often approach to teaching maths. In fact, part of the inspiration for DoodleMaths was the “a day” series of books written by A.L. Griffiths in the 1970’s.

I credit this series of books (along with some excellent teachers) with helping to give me a solid grounding in maths when attending Cherry Orchard Junior School, Birmingham, the same decade. These books formed part of the school day: between registration and assembly, every day, we would collect our book and work through the next set of questions. Users of DoodleMaths will see the parallels, I’m sure.

Of course, technology has made a huge difference not just to how these questions are delivered, but also to how they are chosen. When a child selects 7/8/9/10-a-day on DoodleMaths, their set of questions are chosen according to the following criteria:

– to reinforce topics that have been recently learnt
– to reinforce topic areas that the individual needs further practice in
– to review prerequisites to up-coming new topics to be learnt
– to help identify other weak areas.

This means that no two children will ever receive the same set of questions, which makes sense, since no two children are the same.

As a footnote, if any reader knows where we could find a copy of 7 and 8 a day, we’d love to complete our collection!

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

I know of countless 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.

Maths is no different. We can tinker with the Framework and the National Strategy; 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 exercise the left side of their brain.

[To illustrate this, at our tuition centre last week we assessed a 14 year-old. She had previously attended our centre for 18 months up until she was 11. She performed worse in the standardised test last week than she did in the same test when she finished with us over three years ago. She knows her maths has got worse: behavioural problems in her class and a lack of confidence and motivation on her part have meant that she has barely practised her maths for years.]

A good teacher will be asking themselves, as they write a maths exercise, “What is the purpose of this question?”

There are, in my view, four types of maths question

  1. Questions that teach
  2. Questions that reinforce understanding
  3. Questions that test
  4. Questions that generate discussion

Questions that teach are rare. This is because they are difficult to write and traditionally, teachers have done the teaching. Examples of such questions can be found in my earlier blog about inductive learning: https://doodlemaths.wordpress.com/2011/11/01/inductive-learning/ .  Children like doing these types of questions. They also don’t mind getting them wrong.

Questions that reinforce are very common. These are easy to write and extremely important when it comes to long-term understanding. Children like doing these questions – as long as they are getting them right.

Questions that test are, for many teachers, favourite questions to write. They are more interesting to write and help a teacher assess the ability of a child. For this reason they are often overused – with damaging consequences: if introduced too early they can damage a child’s confidence. Some children thrive on these questions, but for others, these questions lead them to a dread of maths.

Questions that generate discussion are created by skilled teachers who have the ability to control the direction of the ensuing discussion to reach the desired learning outcome. All children like participating in these discussions as long as it is conducted appropriately.

Before the advent of ICT, the learning process was typically: teacher teaches; child does questions of type 2 and 3; teacher marks questions to gauge level of understanding.

Tutoring websites have tried to replicate this with: video/animation teaches; child does questions of type 2 and 3; website marks questions to gauge level of understanding.

So far, we have missed the huge teaching opportunity that technology has presented to us: to get children involved in the learning process from step one. It is easy to generate questions of type 1 on the iPad, and children love doing them – this is the way children should be learning.

 

You’re 15, in a maths lesson, and your class teacher announces that today you are going to learn about percentages.

You don’t understand percentages. You did for a week or two last year, and also the year before that. In fact, it is quite possible that you have understood percentages (for a week or two) every year since you were 10.

Maths in secondary school is taught in topics. Once you’ve learnt percentages, you will move onto equations, or probability, or some other topic that may even feel like a separate topic altogether. Maths has always been taught like this, so why the problem?

There are two problems: first, by the time you are 15, you don’t want to be learning percentages for the fifth time, knowing you’ll forget it in a couple of weeks; second, teaching in this way can often make maths seem like a series of discrete, rather than interconnecting range of topics.

Of course, the brightest students, to whom maths comes easily, will remember from year to year how to do each topic, will see links between topics for themselves, and will continue progressing towards an A or A*. But for the substantial majority of students whose only goal is a C, they forget what they have learnt pretty rapidly.

The solution is to give students the opportunity to review what they have learnt, as well as to learn the new stuff. I believe that for students aiming for a C at GCSE, over half of their classroom time should be devoted to reviewing what they already know (or, should I say, have been taught.) With maths, if you don’t use it, you soon lose it. As adults, with our secondary education well behind us, most of us are familiar with this.

The DoodleMaths blog has been quiet for a while since we’ve been preparing for release. Now we are up-and-running, we’re finding a great deal of interest in people simply wanting to find out their “DoodleMaths Age”.

This is not a new concept and there are websites such as Maths Whizz that already assess children in this way. Parents have long-had their child’s ability in the literacy-related disciplines of reading, comprehension and spelling described in this way. This is simply a way simplifying the mysterious-sounding national curriculum levels, sub-levels, attainment targets, strands etc. etc…

Your DoodleMaths Age is a comparison to the maths ability to an average child of that age. This means that in a typical sample, about half the children will come out with a DoodleMaths Age of above their chronological age, and half below. Two interesting points came out of the testing process:

  • The range of DoodleMaths ages from a typical group of Year 4 children (aged 8 to 9) was from 7.1 to 12.1. This indicates the typical range of abilities that face a primary school classroom teacher (not a surprise to teachers but perhaps to parents)
  • Of the (rather smaller) sample of adults who were willing to do the assessment, the average DoodleMaths Age was 10.4 (not a surprise to parents but perhaps to teachers!)

As well as giving parents an idea of their child’s ability, this also allows us to benchmark progress through the use of the app.

**You can download DoodleMaths for free from the Apple App Store if you want to work out your own DoodleMaths Age.