Archives For Maths

 

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With the announcement of this year’s Pupil Premium Awards finalists this week, it’s been wonderful to see all the different ways this funding can have a real impact on a student’s life. We’d like to say a big well done to all the schools who have been shortlisted! You can see the list here.

Inspired by the creativity of teachers, we wanted to share with you how some schools have put Pupil Premium to work:

  • Buying PE kit and a pair of trainers for a student to enable her to take part in after-school sports clubs
  • Free breakfast club to make sure children would start the day with healthy, full stomachs
  • Lending a bike to a student who was always late to enable him to get into school on time

 

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We’d love to hear your stories and ideas on how Pupil Premium can be used to make a difference in a pupil’s life in the comments below!

P.S. Did you know that Pupil Premium funding can be used to buy DoodleMaths licenses for your school?

PISA tests are occasionally in the news and well known amongst teachers. They rank the 65 OECD countries according to results in standardised maths, science and reading tests. Here in the UK, we ranked significantly higher in reading than in maths (23rd in reading, 26th in maths). Incidentally, our ranking in both is dropping*, described even by government as “at best, stagnating, at worst, declining.”

Why do we consistently perform better in reading than in maths? I think the answer lies in emphasis we put on reading (as opposed to maths) from a very early age. We read to our children at night from a very early age. Throughout primary school, children work through personalised reading schemes and bring a book home every night. And in adulthood, it is much easier to be bad at maths than bad at reading (in fact, we even have a national standard excuse for it – “I was always rubbish at maths” is almost a catchphrase, but something one would never say about reading).

The Biff, Chip and Kipper series of books is used by over 80% of UK schools

The Biff, Chip and Kipper series of books is used by over 80% of UK schools

The National Literacy Trust states that if a child does their 10 minutes of reading daily, they are 13x more likely to reach their expected reading age by the time they leave primary school. Schools invest in personalised, carefully-graded reading schemes like The Oxford Reading Tree (aka Biff, Chip and Kipper) and work hard to make sure children read them regularly. But if reading is resourced and encouraged so strongly, how does maths fair in comparison?

In fact, no such ’13x’ stat exists for numeracy. Very rare is the school that sends home 10 minutes of maths daily. In fact, maths homework generally consists of a weekly one-size-fits-all worksheet or on-line game which, to be frank, does little if anything to raise standards. Of course for a teacher to produce personalised homework for each individual would be almost impossible, which is where adaptive learning in the form of DoodleMaths comes in.

If 10 minutes a day can make such a significant difference in reading, just think what a difference it could make in maths!

*There is a perception that it is the Far East that dominate the top of PISA rankings – or that it is language differences that cause these changes. But English-speaking economically equivalent countries such as Australia, New Zealand and Canada all perform significantly higher than the UK. There is also little to support the myth that educational systems take generations to change: Ireland ranked 32nd and 21st in maths and reading respectively in 2008, but had improved these to 20th and 6th by 2012. Why do we exchange maths teachers with Shanghai (where cultural differences such as the one-child policy do skew results) when perhaps the answers are closer to home? For more on our PISA ranking, click here

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There’s always a buzz word, and it the world of education technology at the moment it is probably adaptive. But what does this mean, and how does an adaptive product differ from a product that personalises?

pəːs(ə)n(ə)lʌɪz/
verb: personalise
design or produce (something) to meet someone’s individual requirements.

We personalise things ourselves by making them individual to us. Most products in edtech that claim to be personalised do so through allowing choice: as well as choosing motivational features such as avatars (fairly standard these days) you may also make choices about the work that you do. Alternatively, tasks might be selected by a teacher or a parent, either in the app or website itself or remotely through a dashboard.

əˈdapt
verb: adapt
1. make (something) suitable for a new use or purpose; modify.
2. become adjusted to new conditions.

For an edtech product to adapt to a new purpose or new conditions, first it is necessary to assess or measure what those conditions are. Learning systems that are adaptive will incorporate three elements:

  1. data collection on existing progress
    b. analysis of data, leading to
    c. adaptations in the child’s work program.

Easiest here to use DoodleMaths as an example:

  1. aside from the initial assessment, the following data is collected for every child for every question answered: time taken, attempts taken, and date stamp.
    b. this is then analysed to gain an understanding of both the child’s progress and also the population as a whole (as a basis for comparison)
    c. the work program is adapted in three ways: level (on a general basis, are the questions too difficult, too hard, or just right for the child?); strengths and weaknesses (e.g. what are they finding difficult? Do we need to remediate here? – if yes, add it into the work program); pace of learning (e.g. if they found the last topic easy, let’s crack on, but if it’s tricky, let’s stick with it until they’ve mastered it).

There are other ways a program can adapt, too, for example, confidence level (some children are disheartened getting lots wrong, others can cope) or learning style (some children will exhibit more success with questions delivered in particular styles).

In the future, it will even be possible to adapt according to misconceptions: if a child consistently believes that a negative multiplied by a negative is a negative, for example, a really smart system will be able to detect this, adapt, and deliver the correct lesson to address this misconception.

So personalised and adaptive mean very different things: personalising is done by the user, usually at the start of using a product; adapting is done on an ongoing basis by the product itself. You might say that an adaptive product is aspiring to make decisions on an individual basis in a way that a good tutor might. Most edtech products have some kind of personalisation feature, but very few are truly adaptive.

On the assumption that your five-year old has a grasp of addition, these are the most important numerical facts a child can learn at this age.

Children who are good at maths have committed a lot of what they know to heart. By this, I mean that important number facts have been learnt and committed to long-term memory. Note that it is widely accepted that there are two ways to commit something to long-term memory: either learn by understanding (perhaps you’d learn the events leading to the start of WW1 in this way) or rote learning (times-tables must be learnt this way in my view.)

I digress… back to the point in hand. The more number facts a child has committed to long-term memory, the more they free up their working memory to perform more complex calculations. A child who can recall the doubles of numbers below ten can then also learn the following without much more effort:

– Near doubles: if you know that 6+6=12, you can instantly work out that 6+7=13.

– Adjusted doubles: to work out 6+8, change it to 7+7 and use your doubles. Doubles, near doubles and adjusted doubles account for the majority of addition facts to 20.

– Double 10, 20, 30 etc. and 100, 200, 300 etc. This innately teaches children place value, and excites them because they are using big numbers! You’ll get them doubling 1000, 20,000 before you know it.

– 2x table: same as your doubles!

– Halving: the reverse of your doubles. But you have to learn them off by heart: if you choose to teach doubles by adding a number to itself, whilst this is sensible in the short term, in the long term many children learning how to halve will attempt some kind of subtraction. Better to get them to learn off-by-heart early on.

– If they can halve, they can quarter. Teach it by halving, and halving again.

– And you can even lead in to percentages, because 50% is one half.

– Partitioning: if they know their doubles confidently off-by-heart, they can double any number by partitioning. Double 24? Well, double 20, double 4, then put it back together.

Of course, the other by-product of doing this is it gets children into the habit of committing numerical facts to their long term memory from an early age. Because maths is never duller than when you are still continually counting on your fingers at 9 or 10 years of age…Image

DoodleMaths 111

The world of education is constantly changing, and over my 20 years in teaching there has been a general shift towards praising a child as a means to motivating them. This has been a hugely positive move in my view: at my Grammar School in the early 1980’s, most teachers ruled over the boys by fear and occasional casual violence; by the time I moved to a more forward-thinking comprehensive in the late 1980’s, I personally responded far better to the praise, encouragement and positive feedback offered on a routine basis.

So it’s interesting today to read of the study by The Sutton Trust suggesting that praise can in fact be counterproductive. Unlike Christine Blower, leader of the National Union of Teachers who dismisses this as faddy thinking, I think this is in fact an important piece of research and one that concurs with discussions I have had with some of my colleagues over the years.

Here’s the issue: children know for themselves whether or not they have done a good piece of work. Therefore they know when to expect praise, and when to expect criticism. They are anticipating it. Here’s where it can go wrong:

If a child is expecting praise and it is not received. Your child spends two evenings on their history project, but then it’s not marked for a month, or worse, ever. This is not common but does occur in teaching from time to time – and we all remember when it does.

If a child has done a poor piece of work but gets praised all the same. This is VERY COMMON, especially amongst low-achievers where a teacher might be grateful just to get any work at all from them. The issue is, the child is receiving praise on what they know is a poor piece of work. It has two results:

1) It lowers expectations
2) It makes all future praise meaningless. When the child does produce a great piece of work, where do you go?
3) It erases confidence. Children like to know where they stand.
4) It sets them up badly for the future – the “real world” it’s so often called.

So how should we deliver praise and criticism? The answer is to target our praise. In the same way that we should criticise specifics, it’s no use saying to a child, “that’s really good!” without explaining what is making it good. “It’s fantastic that you have set out your working exactly as expected” or “You’ve clearly learned how to accurately estimate angles” is specific and can also be balanced with areas to work on.

And if a piece of work is not good enough, it is fine to ask them to do it again. Not all of it, but the areas that need improving. My own son, who is 6 and in year 2, has made fabulous improvements in his drawing this term. He is fortunate to have a highly-skilled teacher who, in studying Matisse with the class, has encouraged them to draft, and then re-draft their drawings five times, often using peer feedback, to the point where they produce work that they are truly proud of.

So, far from dismissing this study as “faddy and fashionable” and suggesting that “teachers know their students best” I’d like to see leaders such as Christine Blower actually engaging in the debate – the vast majority of teachers are more than happy to accept they’re not the finished article. There’s a lot to be learned from this!

For the original article, click here.

We’ve written similar articles to this in the past:
Maths: when giving help isn’t necessarily helpful
5 ways to raise your child’s self-esteem in maths
Why league tables have failed to raise standards
Choice vs Autonomy

For more about DoodleMaths, click here.

The 30 Second Rule

September 22, 2014 — Leave a comment

“If what you’re explaining takes more than 30 seconds, either you’re not explaining it clearly, or the concept is currently too difficult for the child..”

But what exactly does that mean? We mentioned the 30-second rule a few weeks back in our “Dealing with study tantrums” post but we didn’t really delve into the reasoning behind the rule and why it’s so important to consider the way in which we present ideas and concepts to children.

Before we continue, though, it’s worth noting that the 30-second rule applies best to short-answer questions on fundamental concepts (fractions, decimals, areas or metric units.) There are teaching strategies for problem-solving and mathematical reasoning, which require constructing a more lengthy argument, but that’s a topic for another day.

Our attention spans vary, not only from age to age, but also depending on the time of day, the type of activity we engage in, and our own disposition towards the subject at hand. It’s widely agreed that children’s attention spans are much shorter than those of adults, so it’s very important to keep explanations concise and to the point.

But how do we do that? Here are some suggestions if you find yourself past the 30 second mark:

#1. Ask yourself: Do I understand what I’m trying to explain?

Sometimes we need to check with ourselves whether this concept is clear to us or not. If it isn’t, it’s worth looking for a way to explain it to yourself, so that you can then explain it to your child.

#2. Consider your presentation – are you going overboard with the explanations? Or are you getting lost in an example?

Some people understand things better when the concept is contextualized (ex. linking fractions to baking a cake.) Some would rather have the concept presented to them straightforwardly. The best explanations are a combination of both, but it’s easy to go overboard on either side. If you rely on one, why not try out the other for a while?

#3. Break it down.

Consider what you are explaining. Can it be simplified into two or more steps? Or perhaps you need to go back to basics and build from there. If you have a problem with fractions, go back to illustrating basic ones using a pie chart, then build up from there.

#4. Take a break.

Studies would suggest that focusing too much on a single task diminishes our capacity for understanding. If you and your children are finding it hard to focus, why not take 3 minutes for a cup of tea and a biscuit before you review your explanation? The solution might well present itself.

What is the teaching rule you swear by?

Early in August, we took part in a #BETTchat on Twitter which posed a fascinating question: Is Education Technology too expensive to work?

Given our upcoming appearance on the ICT for Education conference in Newcastle, we thought it might be worth revisiting the topic.

As the chat quickly revealed, the cost of buying a bunch of apps for students to use in the classroom is the smallest item on the ICT budget of a school. (Indeed, the apps themselves range in price, but it’s rarely enough to break bank.) Nor is the cost of acquiring hardware necessarily the biggest barrier to implementing #EdTech, although not all schools can necessarily take part in volume purchase programmes like those on offer by Apple. Aside from capital expenditure, the two biggest items on the ICT budget of a school are maintenance and training costs.

While we agree that EdTech can be financially demanding, though, we strongly believe it’s a profitable long-term investment, for schools and teachers alike. These are our top reasons why:

  • Technology, especially interactive apps, can cater to a variety of learning styles.
  • Big data (like the performance of a student over time) can be harnessed to create individualised work programmes at minimum cost for the teacher, as it saves them time and effort.
  • Interactive apps increase student engagement and encourage them to take ownership of their learning.
  • Technology is an integral part of students’ lives – it makes sense to bring it into the classroom as well.
  • Teachers get the most out of their face-to-face interactions with students when the software helps them target and address the most important areas of weakness.
  • Teachers become more confident in the classroom.
  • Teachers also become more tech-savvy the more they use EdTech, so they are able to identify the kinds of apps that would be most effective in the classroom.
  • Student performance improves.

None of these changes can happen overnight – both students and teachers need time to learn how to use a piece of technology and integrate it in lessons. All of it requires time and patience, which can be difficult if a school needs to meet criteria or is preparing for nation-wide exams. But as educators we need to consider the long-term effects of our policies. Learning more about EdTech and giving teachers time to get comfortable with using it can well prove to be the winning factor for a school.