If you’ve been using Maths-Whizz for the last couple of months you will have noticed instructional videos popping up to explain features of our online tutor to parents, teachers and students.

The short and sweet videos are hosted by members of the Whizz team from our Paddington, London offices.

Over the next few days I’ll give you a grounding in Maths-Whizz by introducing key videos along with explanatory text and links to more tutorials. Call it Maths-Whizz 101.

If you’re a Maths-Whizz parent or teacher these will help you get the most out of our award-winning service. If you’re not yet sure what Maths-Whizz can do for your student, they might help show why we have had such success bringing Happiness in Numbers.

To get the ball rolling, we’ll begin with our introduction to the Maths-Whizz Tutor:

Title: How the Maths-Whizz Tutor works
Presenter: Richard Marett, CEO
For: Parents, Teachers, and Students
Time: 3:42

Notes:
Every student completes an initial assessment on starting Maths-Whizz. The results of the assessment give a picture of the child’s unique strengths and weaknesses (confidence in fractions but difficulty with division, for instance). This is the child’s ‘maths age’ profile.

The Maths-Whizz Tutor then delivers interactive animated maths lessons according to the student’s maths age profile, paying particular attention to weaker subjects, whilst consolidating stronger subjects. The lesson plan thus created is designed to give the student a more rounded maths age profile.

Once a student logs into his customized ‘bedroom’ (or ‘console’) area and begins the Tutor he will receive an animated maths lesson that first explains the maths concepts and then tests his understanding with interactive questions.

There are three outcomes that help define the Tutor’s method:

• If the child does well in the animated exercise he immediately receives a set of ‘exam-style’ questions that cover the same subject, but in a more formal, non-interactive fashion. This ensures the child’s cognitive connection between the engaging animations in the animated exercise and the more formal, pencil and paper context, of the classroom.
• If the student fails the animated exercise he immediately receives another, easier, animated exercise designed to boost his confidence and reinforce the maths skills that underpin those he just failed to demonstrate. If the student then passes this exercise he will have another chance to tackle the original, failed, exercise.

  This is a kind of automatic intervention that acts when the student will benefit most from targeted attention on a weak subject area.

• If the student has only modest success with the exercise (neither an outright pass or a complete fail) the Whizz Tutor assumes that he understands the concepts but probably needs another try. It will move onto another subject and return to the original exercise later.

  The randomised nature of almost every Maths-Whizz exercise ensures that the student won’t earn a pass the second time around merely by memorising the answers.

Students can only make progress when they pass both an animated exercise and its corresponding exam-style test. This, and the tutoring techniques described above, mean that students in the Maths-Whizz tutor improve their maths age in a particular topic only when they have shown that they really know the subject at hand.

The Maths-Whizz Tutor coaxes students towards understanding and improved confidence, but it is the students who make the progress. Students can log in without parental or teacher input, meaning that you don’t have to know what your child needs to learn – the Maths-Whizz Tutor does that for you.

Further Viewing
If you’re impatient to know more about getting the most out of Maths-Whizz, then check out the full list of videos, below. If you’re a parent or a teacher, a home-educator or a private tutor, or if you’re just curious, there’s a video for you.

Video tutorials in our little Maths-Whizz University:

Videos for Parents

• Overview for Maths-Whizz Parents
• The Student Assessment
• Understanding Maths Age
• Tips on Parental Involvement
• Motivating Your Children
• Combatting Holiday Learning Loss

Videos for Teachers

• Teacher Account Login
• Uploading Students
• Editing Student Details
• Completing Assessments in School Time
• Managing Student Motivation
• Recommended Usage – Tips For Teachers
• Tutoring for Schools – reports overview
• Reports for Teachers
• Reports for Head-Teachers
• Combatting Holiday Learning Loss

* NB: The Maths-Whizz University is something I just made up

The Mead School, in Tunbridge Wells, is a long-time Maths-Whizz Tutoring Plus user, and Independent Schools Association member.

The Mead School's high-achieving Maths-Whizzers!

Isobel Feaver, Mead’s literacy co-ordinator, year 5 teacher and all-round whizz herself is a champion of online maths tutoring; The Mead School has seen great successes on her watch.

Isobel describes how Maths-Whizz is making a difference at The Mead School:

By working on Maths Whizz both at home and at school every single child is developing and pushing forward their own ability in Maths in addition to all the fantastic Mathematics teaching that they receive at school.

Isobel used our Maths-Whizz Tutoring for Schools report tool to record each pupil’s weekly usage for the last three months. She then identified the child in each class who had improved the most (see pic).

As Isobel said: “Every Mead child deserves a pat on the back for all their hard work this term.”

We couldn’t agree more!

Einstein explains Relativity to his gran in order to understand it better...

This sentiment attributed to Albert Einstein is no less true of Relativity than it is of primary maths. And it is the thinking behind some sound advice reported in a recent article in Education Week sent my way by Whizz US’s Kate Vincent:

Teach in order to learn.

This is what’s known as the ‘protégé effect‘ (or, more prosaically, ‘peer-mediated learning’ and ‘reciprocal teaching’). Learning a subject in order to explain it to someone else forces the learner to remember and understand the material better.

Education Week reports on findings from studies in which children are required to ‘teach’ computer avatars that question the students, make mistakes, and so forth. Such students, compared to those who were learning only for themselves, spent more time studying the material and checking their work and “…As a result, the student-teachers performed better than learners…”

This effect is explained in common-sense terms by David Schwartz, director of a California-based learning research centre:

When you are looking at something yourself, you can fool yourself into thinking you know everything, but when you have to communicate it to someone else, you realize that you’re really not being precise enough.

Now, of course, you can take the teach-in-order-to-learn approach only so far. We’re not suggesting Whizzers do what a recent nominee for the 2010 teaching awards did by sitting the same Maths GCSE as her students.

But we are suggesting – if you’re the parent of a Maths-Whizzer – that you ask your child to tell you what he or she has learned, to explain the subject to you.

This isn’t simply a matter of saying “What did you learn today?” but, rather, asking your child to take the role of teacher, with you as student. Ask your Maths-Whizzer questions; make mistakes a novice maths student might make.

This is not an approach for the parent in a hurry. But a little bit of role-reversal might encourage your child to think more deeply about what he or she is learning, in order to be able to show their knowledge convincingly when you chat over the dinner table.

It is in both these respects that BETT has chosen to shortlist us for their 2011 BETT Awards:

BETT Awards 2011

BETT, as any fule kno, is “the world’s largest technology in education show.” The awards fall on the first night of the four-day show. Any fan of ed. tech. who has been to the awards or the show in recent years will attest to the scale, snazziness, and the impressive number of Madonna-style headsets worn by shiny-faced presenters in front of tennis-court-sized interactive whiteboards.

In the time since Whizz started attending – first as guests, and for the last five years as stand-holders – we’ve seen the event get glossier and more corporate. We don’t yet have Madonna-style headsets (The God of Whizz wouldn’t be seen dead, etc.) but we always have interested packs of teachers, parents, and students stopping by, some just to say hi, and many more to find out what makes us tick.

This interest goes both ways, and that’s why we come every year. We love to find out what we’re doing right, and what we can improve on. So if you want to bend our ears about Maths-Whizz, or tell us what you love, or just put faces to names in the Whizz team, then make sure you’re at BETT 2011 at London’s Olympia, 12-15th January.

Who knows, we may even have a shiny award to show you!

You can read up about our 2010 BETT Show and our previous triumphant BETT Award showing.

UPDATE (22/10/10): Bett Awards official shortlist now available to view online.

The name's Bond, Number Bond (Image:Wikipedia)

Parents and students often ask us if we do number bonds, at Maths-Whizz, as though they are mathematical methods exclusive to the initiated few. Nothing could be further from the truth.

Number bonds are, in short, pairs of numbers that combine to make a third. Number bonds help show that every whole number larger than one is made up of other whole numbers. 1 & 4, 2 & 3 both make five. They are the number bonds of five.

Number bonds are vital for mental arithmetic. When you ‘partition’, or ‘decompose’ a number you get number bonds..

For instance, knowing that can be 15 can be partitioned to 10 and 5 helps you perform calculations with 15. You can calculate with the ’10′ part, and then with the ’5′ part, and combine their answers. 5 and 10 are number bonds of 15.

Knowing and remembering the number bonds of 100 makes it easier to handle money, or give change. If I know that 70 and 30 are number bonds of 100, then I know instantly how much change to expect from a pound when I buy a 70p packet of sweets.

Number bonds can help you add. Knowing that 5 and 2 are number bonds of 7 makes adding 7 to five much faster. Add five to five to get 10, and then add the remaining two to get 12! And this is just scratching the surface.

In Maths-Whizz we don’t refer to ‘number bonds’, but we do talk about partitioning numbers, about finding pairs of numbers, about mental methods that require an understanding of number bonds, and so forth.

Dozens of our lessons rely on knowledge of number bonds, and at least ten specifically test rapid recall of number pairs, and missing numbers. We even test more advanced students on splitting a whole number into two decimals.

You can try one such number bond speed game on our maths addition page. Scroll down to Year 5, and click the right-hand lesson image.

Click to try a free number bonds speed game

Get busy number bonding!

Money makes the maths go down...

Money can make the maths go down, to coin a phrase.

Since Britain’s currency was decimalised many of us have had their first introductions to base ten maths and decimal concepts in money.

Most children are likely to have got a basic grasp of the notion of pennies and pounds, and how they relate, from an early age. And children are likely to have understood this long before they are required by national curricula to have understood tenths, hundredths, performing operations on decimal numbers, and the like.

If nothing else, this proves that if there is a need and a daily context in which to learn, we can acquire complex skills without really realising. But it also gives us a useful tool when tackling calculating with decimal places.

Take the question “3.6 divided by 12″.
It sounds pretty tough to the unconfident. After all, 12 is larger than 3.6, which means the answer will be smaller than one, a decimal value.

Now take the question “£3.60 split amongst twelve people”.
Does the question seem easier? Suddenly it’s about a dozen students going Dutch on an order of poppadoms (substitute scenario as appropriate!).

As soon as we add a pound sign in front of a decimal value in a calculation, it can seem easier to visualise, to handle.

0.01 is one hundredth, an abstract concept. Whereas £0.01 is a penny – it’s solid, and there’s a hundred of them in a pound – easy!

If you struggle with decimal calculations, it might just help to shove a pound sign in front of the numbers, turn 0.4 into £0.40 or 40p, etc. One of the commonest pitfalls of multiplying or dividing with decimals is the failure to show the answer in the right order of magnitude.

For instance, taking 3.6/12, we could make the question easier by writing it 36/12 – the answer is 3. But now what do we do to find the answer to 3.6/12? This can stump people, but using the context of money means that we know £3.6 is 36 10p coins, or 360 pennies.

If the answer to 36/12 is 3, that means three 10p coins, or 30p! And how do we write 30p in pounds? £0.30. Easy! We’ve just converted the whole-number answer to our simplified calculation back into the final decimal answer.

This Maths-Whizz tip comes courtesy of Hilary Koll and Steve Mills, the esteemed and award-winning maths boffins who designed all our Maths-Whizz lesson concepts, people to whom even the God of Whizz tugs his forelock.

Policy wonks have found that summer learning loss, an established side-effect of long school holidays, is particularly pronounced in some groups:

…children from the poorest backgrounds suffered most with ‘summer learning loss’ because they were the least likely to practise reading and writing during the six-week break.

The Education Guardian has reported on plans from think-tank The Institute for Public Policy Research (IPPR) to shorten the long summer holidays. This should interest parents from any wealth bracket – without the right attention even the most expensively educated can suffer.

Further to this, long term times might be causing ‘burn out’ in some students.

A co-author of the IPPR study, Sonia Sodha, calls for a five-term system, with two-week breaks between eight-week terms, and a month for summer hols.

Many parents remember their long summer holidays with fondness, even though the original purpose of the long break – to allow children to return to farms for the picking season – has almost entirely been forgotten, certainly in practice.

Margaret Morrissey of the National Confederation of Parent Teacher Associations argues that children may also need “…a chance to recharge their batteries”; but one could well argue that if the terms weren’t so long, children’s batteries wouldn’t need recharging in the first place.

(As of 2010) Former Children’s Minister Kevin Brennan said the IPPR report (which also includes recommendations on increasing the role of play in classes for 5 and 6 year-olds and suggestions that secondary and primary schools employ in-house counsellors or use counselling networks) matches commitments made in the coming ‘Children’s Plan’.

Keeping children constructively entertained over summer is an issue, whether or not the Children’s Plan includes shortening the summer holidays. The finding that unstructured holidays can lead to ‘learning loss’ is still relevant, and is something we recognise. In 2007, Whizz Education launched our Summer Adventure – featuring the Professor lost in the jungle. Students were charged with helping him escape, by solving maths puzzles and playing jungle-themed games.

(a maths puzzle from the 2007 Summer Adventure)

The Summer Adventure was a huge success – Maths-Whizz students at Mead School, Kent, had a great day helping the Professor escape from the jungle when Toni Burkett and Monique Kleinschmidt from Whizz visited with prizes for their top-performing students.

(Our 2007 Summer Adventure in use at the Mead School, Tunbrdge Wells)

Our Summer (and Christmas) adventures encourage students to continue learning with Maths-Whizz; students must finish lessons before they can try the themed games, and they get to learn about jungle creatures with our colourful worksheets.

We’ll be bringing back the Prof and his rainforest antics each Summer, with brand new features. If you’re wondering how to keep your child occupied this summer, make sure he or she logs onto Maths-Whizz, because the Professor isn’t going to escape from the Mayan jungle all by himself…

[UPDATE: Read a study of 39 investigations into Summer Learning Loss]

[Read more about summer learning loss - Wikipedia]
 

But as it’s all in a good cause – raising money for the charity Cardiac Risk in the Young (CRY) – I suggest you watch, enjoy, and check out the charity’s good work.

The video was made at Surrey’s Amesbury School, with the help of students, teachers, and parents.
Good show!

The number line can be a powerful beast, employed in addition and subtraction, and frequently in concepts of place value. The number line describes the world in the way instantly familiar to most of us, with smaller items on the left (if horizontal) or towards the bottom (vertical).

We could investigate the many ways culture and psychology define our experience of numbers, and why so many (but not all) of us perceive numbers increasing in those two directions, but that would be beyond the scope of this blog – even if the God of Whizz might enjoy the intellectual excursion…

Number lines in addition and subtraction

Instead, we can have a quick look at how to add and subtract using the number line. The line is a great way to visualise the ‘journey’ up and down through the numbers. Just like a ruler, the line can be any length, at any level of detail. Keep zooming in, and the increments on our number line show smaller and smaller amounts.

Number lines can be to scale (like a ruler) or not to scale, like a simple ordered list. In the example maths addition lesson above, we show how you can add a number with Tens and Units digits to a number with Hundreds by counting along the number line, starting with the larger number.

You need to understand the values of digits; for example, 63 is made up of six tens and three units (or 60 + 3). You also need to know that adding numbers means moving to the right along the number line, and subtracting means moving to the left. We make a large rightward ‘hop’ to add six tens and a smaller ‘hop’ to add three units.

For those of us who think in visual terms, it can be very helpful to think of addition and subtraction as movement along the number line. More complex examples show the benefits of this approach. Say we have to answer this question:

800 + 300 – 150 + 220 – 400 = ?

We can imagine starting on the line at 800. We jump forward 300, and we jump backward 150, and so on. If we plot our frog-like adventures we find we’ve gone backwards 550 and forwards 520. This puts us 30 behind where we started. 30 less than 800 is… 770!

Of course, this is a slow and round-about method when your mental maths improves, but visualisation of the process can help enormously. You can do all the forward jumps in one go, and then to all the backward jumps in one go; the answer is the same.

At Maths-Whizz we know that anything that helps reveal the underlying maths is good – because once you can get a mental grasp of the ideas, the numbers suddenly seem to make sense…

This only scratches the surface, of course, so do share any ideas you have about working with number lines on the Whizz Forum.

No, you’re not allowed to use a calculator, or or phone a friend…

Stuck? OK, it’s 2.

“What?” I hear you cry, “But that doesn’t make sense. We’ve divided something small by another small thing, that should make an even smaller thing, surely.”

And, of course, you’d be wrong. If you already knew the answer, or you’ve already seen this February’s Channel 4 documentary The Kids Don’t Count, then read on with a smug smile. If you were genuinely stuck by the question, let us demystify division for you.

First, division isn’t about making things smaller. Sure, that’s often what happens: when you divide 10 by 2 you get 5. But what does it mean to divide?

The division sentence A/B = C can be described in two ways:
- We’re taking A and splitting it into B groups of equal size
- We’re taking A and and finding out how many groups of size B it contains.

This sounds like splitting hairs, but the former is known as ‘partitioning’ division, the latter ‘quotative’ division. These aren’t terms that Maths-Whizzers need to know, but they can help show that division isn’t about making things smaller.

Let’s go back to our teaser. If you were stuck, then think of the question this way – “How many groups of one quarter are in one half?” You should know that there are two halves in a whole and four quarters in a whole, so there are two quarters in one half, which means the answer is 2!

Simple, no? Maybe not yet, but it will be.

What if we reverse the question: “What is one quarter divided by one half?”. Here the issue isn’t so straightforward. One half does not ‘fit’ completely into one quarter, but if we ask ourselves how much of that half can we squeeze into that quarter, we see the answer is one half. In other words, there’s half of a half in a quarter.

One quarter divided by one half equals one half!

Now we’re rolling!

You need a simple rule for dividing fractions, not simply an understanding of the principles. So remember this process below and forever look upon division of fractions with confidence.

Step 1. Turn the second fraction (the one you want to divide by) upside-down (this is now a reciprocal).
Step 2. Multiply the first fraction by that reciprocal
Step 3. Simplify the fraction (if required)

The Mathisfun page below goes into greater detail, explaining why this method works, so check it out to get all the info.

Sources: