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Fibonacci Numbers

What comes next in this sequence:

1, 1, 2, 3, 5, 8, 13, 21, 34, …

The answer is 55. Each new number in the sequence is the sum of the two previous numbers. Children often find this a difficult one to solve, because the usual methods they are commonly taught to spot patterns in sequences don’t work – try looking at the differences between each term and you’ll see why. Look at the ratios between each term (divide the second term by the first, the third by the second, etc.) and you will see more of a pattern emerging – the number you are closing in on is known as the Golden Ratio, 1.618…

We’re not a great believer in reinventing the wheel here in the DoodleMaths office, so if you’d like to know more about Fibonacci numbers, their properties and their connections to nature, visit this great site here.

Features of DoodleMaths v2.0

The latest version of DoodleMaths went live in the App Store this morning and I’m pleased to say, so far so good! We’ve packed it full of new features and moved things around a bit. Here’s what you’ll notice:

1) You’ll be prompted to create an parent account. This enables you to back up your child’s work program on-line; sync work programs between devices (including Android from next month); track progress from the parent dashboard at parents.doodlemaths.com

2) We’ve hidden the Topic Index. Some cheeky monkeys have been racking up doodlestars by working on the same topic repeatedly. Whilst it gets them stars, it doesn’t help them progress mathematically, which is what we’re all about. It’s still available, in the parent’s section.

3) You can retrieve your PIN number. A long-standing glitch, this has been replaced by a retreivable password (go to parents.doodlemaths.com to retrieve or reset).

4) Your child’s DoodleMaths Age may have changed slightly (and likely downwards). We’re sorry about this. We have added new content and aligned ourselves with the new (harder) national curriculum that was introduced in September. More is expected of children at a younger age now, and this is reflected in the app.

5) You can message your child from the parent’s dashboard. This feature has proved popular with schools users, so we’ve integrated it into the home user version too.

6) You can log in as a schools user.

This latest update has paved the way for future updates, too. Here’s what’s coming:

1) Next month will see the release of our long-awaited Android version

2) Along with this release will be a full graphic overhaul of the app. Improved layout, usability and question diagrams.

3) More detailed reporting and a reassessment feature will be viewable in the parent’s dashboard (and also the teacher dashboard).

4) Teachers will also be able to set work remotely for individuals or the whole class from the teacher dashboard.

5) We are introducing a new game for children to be able to practice specific times tables.

6) We will be introducing a subscription pricing model. If you’ve already paid for your lifetime membership, this will always be valid, but new home-users will be charged £3.99 per month to reflect our high ongoing engagement levels and align ourselves more with our web-based competitors.

All our development is in line within ongoing customer feedback. We’d love to hear your thoughts!

Can children have too much choice in education?

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Sometimes, trends and issues in education can be equivalent to the Emperor’s New Clothes. Things go on as they always have done, and it’s kind of ok because they’re just kids, right? It took Jamie Oliver to point out that a Turkey Twizzler is not the optimum nourishment for tomorrow’s generation of leaders.

There’s a trend in education today that children should have choice about what they learn. This is nowhere more apparent than in the majority of supposedly educational apps and learning systems, which allow children an enormous degree of control over the content they follow.

Arguably, giving children a degree of choice can create autonomous, engaged learners, and we should all strive for this, without question.

But.

Not to be too obvious, or to stretch the nutrition analogy too far, but: have you ever offered a child the choice between a portion of chips or a portion of broccoli?

At some stage we have to accept that we are the grown ups in this scenario, and they are the kids. By definition, they don’t always know what’s good for them. And, to get back to the subject of education (finally!), children will rarely autonomously choose to tackle a topic they find difficult, especially if they have confidence issues surrounding that subject. Prevarication breeds prevarication for kids and grown-ups alike, especially when you’re avoiding doing something that makes you feel stupid because you don’t understand it properly.

Here’s a different analogy. If a child has tonsillitis, as a doctor you don’t give them a choice of treatment, because they’re not the experts. And in the same way, if a child is struggling with decimals, we as teachers must provide for them the path that will most help them understand this topic.

That’s where a really good teacher or tutor comes in. They can encourage the child on one hand, pitching questions at the correct level, and determinedly revisiting areas of difficulty from different angles till grasped. Thus their expertise can turn a problem area into a positive as the child gains confidence from a difficulty overcome.

As teachers ourselves, at DoodleMaths we developed the app’s algorithms to identify each child’s individual level, pitch questions at that level, and continue to revisit areas of difficulty until overcome. Just like a good tutor. The quality of the algorithms means that not only is the work at the correct level for each individual – not too easy (we know that praise for a task too easily accomplished does not ring true), not so challenging that they’re put off – but it is also engaging and encouraging, so the child is stimulated to keep going and overcome any difficulty.

It might be politically incorrect, but as we teach our children we have to be prescriptive and we cannot pass this responsibility on to the child.

So we at DoodleMaths do prescribe what children learn, question by question. Because we believe that as long as they’re taught properly, individually, as if by a good tutor, we will indeed create autonomous confident learners who WILL succeed at maths.

When too much praise is counterproductive

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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.

Prime Numbers

Prime numbers are the building blocks of maths. Prime numbers cannot be broken down (they have no factors), and so every number can be written as a product of prime numbers (for example, 210 = 2 x 3 x 5 x 7). The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19… They have fascinated mathematicians over the centuries because they do not follow any particular pattern, and thus it is impossible to predict the next one from the previous. They have many practical uses, most notably in cyber-security, but also in nature (for example, locusts only reappear to mate every 11, 13, or 17 years – always a prime number). Try these quick prime number questions, which recently appeared in our newsletter:
1) What is the only even prime number?

2) What is the first prime number with consecutive digits?

3) Apart from 2, prime numbers always end in the same four digits – what are they?

4) A prime quadruplet is four prime numbers as close together as they can be within a decade. The first such example is 11, 13, 17, 19. What is the next example?

5) A palindromic prime reads the same forwards as backwards. The first three digit palindromic prime is 101. What is the next?

Scroll down for the answers!

 

 

 

 

1) The only even prime number is 2. As you may well have worked out, all other even numbers have 2 as a factor.

2) The first prime number with consecutive digits is 23. This is one reason amongst many that some people believe that 23 is special (in fact, there’s even a group called the 23rdians who believe it has mystical powers). In maths, and particularly prime numbers, it has some unusual properties, for example,

11,111,111,111,111,111,111,111 (there are 23 number 1’s here) is a prime number

10^23 – 23 = 99,999,999,999,999,999,999,977 which is the largest 23 digit prime

And in science, to create human life, each parent has to contribute 23 chromosomes, and the Earth is currently tilted at 23 degrees…

3) Since primes have to be odd (apart from 2) and cannot be a multiple of 5, they must always end in 1, 3, 7 or 9.

4) 101, 103, 107, 109 is the next one. Incidentally, if you cross decades, prime quintuplets and sextuplets also exist. Incredibly, 43777, 43781, 43783, 43787, 43789, 43793 are all prime.

5) The next is 131. Their search can rapidly be narrowed by a process of elimination. For example, we can immediately discount palindromic numbers in the 200’s since they will also end in 2 and thus be even. And we can discount 4-digit, 6-digit, 8-digit palindromes (etc.) because these can all be shown to be multiples of 11. So the next few are: 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, for example.

The 30 Second Rule

“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?

*http://doodlemaths.wordpress.com/2014/07/23/dealing-with-study-tantrums/

Communication channels with teachers: Dos and Don’ts

We’re almost three weeks into the school year – does anybody else feel like time is flying? We sure do! Hopefully by now the children have eased into learning mode, new knowledge is being effectively built up, and all is well in the world.

Until the time comes for a parents’ evening.

On paper, it should be easy – after all, both you and your child’s teacher have the same goal in mind, which is helping your child to succeed. But sometimes misunderstandings happen, and it can sometimes be the case that the teacher has a different plan on getting to that goal than you might. (And if your action plans happen to coincide, GREAT! You’re in for an amazing year.)

Whatever the case, it’s important to establish a good dialogue with teachers, so, as parents as well as educators, here are our Dos and Don’ts for those first face-to-face meetings:

DO ask the teacher questions. Sometimes (especially for new teachers) it can be difficult to articulate everything they wanted to say. In cases such as these, having a few concrete queries can help the conversation flow.

DO talk about things that concern you. If you read an article in the Daily Mail about how the curriculum is getting more demanding and you worry about your children being overloaded, tell the teacher. It’s likely that they’ve considered this already in depth with their colleagues and will be able to allay your concerns.

DON’T make assumptions that last year’s action plan is still on. Teachers change schools. Budgets get revised. The Ofsted report said the school was a couple of points short of being “Outstanding” so now everyone must Work Harder! and restore honour. None of this means that your kids will get worse tutoring, or that the teachers won’t try to make that very neat idea from last year happen in some shape or form. Keep an open mind to change – after all, the end goal remains the same.

DO ask about the best way to help your kids from home. We all want what’s best for our children, and the teachers come only second to you in knowing their individual strengths and weaknesses. Maybe your daughter needs to work more on her spelling. Maybe she’s on top of her class and doesn’t need to do anything in that area. It’s always a question work asking.

DON’T ask the same question again and again. If the teacher already gave an answer you didn’t like, repeating the enquiry won’t change it. If they don’t have an answer immediately, assume it’s because they’re working on a solution and they want to be sure on it on their end before they bring it up with you. Again, keep the end goal in mind.

DO arrange for a follow-up, if there is no time to discuss everything. In business, a major factor contributing to goal-keeping is having regular check-ins between team members. The same logic applies to school. If the teacher can’t discuss everything with you at the moment, exchange numbers and arrange for a good time to call. (And call exactly when agreed upon. And set up an agenda beforehand. If you say you need five minutes to discuss your son’s latest test, then make sure the conversation lasts four and a half. This allows you to cut the frills and see the point of the matter.)

DON’T demand a point-by-point discussion of the school budget. Even if you’re on the governing committee and the teacher in question is in charge of finance, a parent-teacher conference is not the place to have this talk. If the teacher brings up the plans for buying iPads, then by all means, ask them about details – they have likely anticipated the questions and prepared in advance. (Or, alternatively, if you think it’s a neat idea to buy the children iPads, and if there’s time, you may bring it up on the condition you and the teacher agree on a follow-up conversation. They would likely need to do their research first.) But don’t put anyone on the spot – it hardly sets the grounds for a happy relationship.

And finally…

DO celebrate the children’s (all of the children’s) successes. While we’re all anxious to solve any issues that may arise, focusing on the negative can take away from the joy of the positives. Take the time to congratulate the teacher on a school project they supervised, or to say how much your kids enjoyed their summer learning project. If the teacher brings up plans to innovate at the school which you like, say so, and if you can spare it, volunteer to help out. (Even if they don’t need extra hands. The gesture counts.)

 

What are your dos and don’ts about communicating? Are there any tips you’d like to share?

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