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

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.

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!

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]
 

The Gresham College is a venerable London institution devoted to providing free lectures and events for the public, in the best of traditions.

The venerable Gresham College

In the clip below, Barrow shows the maths behind bank numbers and what’s known as the ‘Luhn Test’.

View Barrow’s introduction to the lecture, and clips about the mathematical patterns behind everything – post codes, six degrees of separation, mobile phone IMEI numbers and all sorts of other things.

Even if you feel this another example of educational researchers preaching to the choir, it is worth having a look at the ScienceDaily report and the research site itself.

The researchers established that the lessons worked best when the teachers combined different didactic approaches, when they used different media and when they clearly explained the connection between all of the methods. As the students learn in pairs or in groups using both pen and paper and the digital environment, their learning experiences in the ICT environment are neither isolated nor individual.

This is a useful reminder that there may often be no single method that works best, but that a variety of media, a variety of methods and an engaged teacher to join the dots might be the ideal setup.

I’d be inclined to think that this study also undermines the debates in the US over ‘Reform‘ versus ‘Traditional‘ mathematics. It’s horses for courses, we’re inclined to tell our Maths-Whizz customers, and if different methods benefit different children all we can do is offer as much variety of learning as possible (such as pencil and paper methods, speed games, problem solving and mental methods – all included in Maths-Whizz), tied together in an intuitive fashion.

We’d like to think we have managed this with Maths-Whizz, but we also know full well that engaged parents or teachers are crucial to making any educational service succeed.

As the researchers noted, the teacher [or parent?] is the glue that holds different learning styles and media together:

During computer work, the teacher plays an important role in encouraging reflection. He or she must connect the computer work to the problem as well as to the ‘pen and paper’ maths. The learning arrangement with the different didactic approaches and media appears to demand a lot from the teachers.

The teacher is no less important in the new media age than she was in the days of blackboard and chalk. All we hope to do is give her the best (award-winning) tools to help her do her job.

We’ve had a torrent of spiced-ham-based electronic communications (otherwise known as ‘spam‘) on the blog of late.

Deleting them all is giving the Whizzers repetitive strain injury, so we’ve installed a clever little device called ‘reCAPTCHA‘ to ensure all our comments come from bona-fide humans.

If you want to comment on the blog on any subject from maths to Monty Python - and we thoroughly encourage you to do so – type the two words shown in the reCAPTCHA image and submit your comment as normal.

By typing the reCAPTCHA words you’ll even help to digitize the printed pages from which those words are taken. You can find out more on the reCAPTCHA page, above.

“Boo”, I hear you say. But what better opportunity to look back at the methods that made the central American Mayans (in whose wild forests the Professor’s Summer Adventure is set) such pioneers of maths?

This page gives a nice introduction to ‘Mayan Math’. The Mayan mathematics system was way ahead of its time, and certainly more advanced than the arcane maths system Europeans inherited from Rome. Mayan maths was ahead of its time in part because (as the Mayan Math page describes):

[It] was able to represent very large numbers by using only 3 symbols: a dot, a bar, and a symbol for zero…

Like our numbering system, [the Mayans] used place values to expand this system to allow the expression of very large values. Their system has two significant differences from the system we use: 1) the place values are arranged vertically, and 2) they use a base 20, or vigesimal, system.

Base 20, you say? That’s a lot of fingers! Of course, they could have been counting on their toes, too. Base 10 is the system we use today, but there have been other mathematical systems designed around different base numbers.

Using the Mayan system, you only carry when you get to 20 (not 10) and the place values look quite different. Instead of Units, Tens, Hundreds, Thousands, etc (multiplying by 10 each time) we multiply by 20 each time to give Units, Twenties, Four Hundreds, Eight Thousands, etc. Confused? The number ’562,677′ would be written ’3.10.6.13.17′.

Using this system for expressing numbers has two advantages:

1) large numbers can be easily expressed, so long time periods can be recorded;

2) simple arithmetic can be easily accomplished, even without the need for literacy among the population. In the marketplace sticks and pebbles, small bones and cacao beans, or other items readily at hand can be used to express the numbers in the same way that they are expressed on the monuments or in the books of the upper classes. Simple additions can be performed by simply combining 2 or more sets of symbols (within their same set).

Fascinating stuff, but if all this is a little much on a Tuesday morning, you get started with your Mayan Maths by learning the Mayan numbers to twenty, using the chart below:

 

Rather than offer endless examples of trains setting off from stations, apples in baskets, bars of chocolate and slices of pizza, teachers might well be encouraged to have their students think of problems less in practical terms and more in terms of non-specific abstractions.

The study in question, conducted by researchers at Ohio State University, presented university students with a set of mathematical rules, expressed either with abstract symbols or with concrete examples (tennis balls, and so forth):

“Then the students were tested on a different situation — what they were told was a children’s game — that used the same math.

“The students who learned the math abstractly did well with figuring out the rules of the game. Those who had learned through examples using measuring cups or tennis balls performed little better than might be expected if they were simply guessing. Students who were presented the abstract symbols after the concrete examples did better than those who learned only through cups or balls, but not as well as those who learned only the abstract symbols.”

The implication here is that abstract examples are transferable; students who study concrete examples are less able to ascertain the underlying principles, or apply those principles to other problems.

The article goes on to say that this issue is as relevant for younger brains as those of university age, and that this has implications for how elementary, or primary, maths is taught:

“…researchers suggested that their findings might also be true for math education in elementary through high school, the subject of decades of debates about the best teaching methods.

“The researchers said they had experimental evidence showing a similar effect with 11-year-old children. The findings run counter to what Dr. Kaminski said was a “pervasive assumption” among math educators that concrete examples help more children better understand math.”

Whilst not all researchers in this field might agree with the implications for primary education, the principle seems sound. After all, it is quicker to write an equation than it is to count out apples or cut up loaves of bread.

But, and here’s the caveat from this corner, it is natural to analogise in education. In other words, we readily use specific examples from life to extrapolate to the general. In some disciplines (like economics or history) particular examples can be less instructive when looking at the general issue. But it is just as true that 2 and a half apples are equivalent to 5 half-apples as it is true that 12 quarter-loaves are equivalent to 3 whole loaves.

Teasing out the principles behind equivalent numbers may not be as straightforward when you’re thinking about bread and fruit, but at least you have a jumping-off point, a handle for the young mind to grasp. We explore the world at first using all our senses – touch, vision, hearing, smell and even taste – and many students (and adults) continue to understand the world in terms of physical analogies. As an educational researcher commented in the NY Times piece: “Some children need manipulatives to learn math basics… but only as a starting point.”

Indeed, it would be absurd for an accountant to have to count out pound coins and pennies whenever she audited a company – she has to be able to abstract and apply general mathematical rules to specific problems. Taking aside facetious thoughts that some banking experts might have failed basic counting and adding up, it seems only right that educational methods help train young brains to think abstractly.

Ancient Greek mathematicians famously had difficulty thinking of numbers larger than ten thousand (known, then, as a ‘myriad’) and solved the problem by just multiplying myriads. It is thought the base 10 number system has arisen because, in short, we have ten fingers and thumbs. Both these examples hint that we have historically started with concrete examples and moved to the abstract as science and mathematics have matured. Science often works by collecting testable, real-world examples and building those into a framework that extends from the specific to the more general. If maths is said to be the science of patterns, this method can apply to numbers as well as it can to biology or physics.

This process of moving from concrete to abstract is reflected in the Maths-Whizz curriculum. We begin, at Foundation (roughly age 5 equivalent), by giving examples of ducks getting on and off buses, with eggs in baskets and buckets of water. Moving into Key Stage 2 our students have greater understanding of the number system and confidence with numerals and symbols. We can start to present worded problems, pencil-and-paper style problems, and basic algebra.

Finally, at Key Stage 3 we encourage students to create their own equations from given scenarios and extend given equations into new scenarios. The topics added at year 7 – Probability; Equations Formulae and Identities; Integers, Powers and Roots; Sequences, Functions and Graphs - reflect this new emphasis.

Even if we represent those scenarios visually – goats and fences one such example – Maths-Whizz students must always be able to give more formal, abstract answers. Our exam-style tests that follow each of our animated exercises are valuable tools for consolidating and reinforcing maths, even maths learned with jumping dogs and flying cakes…

Launch the updater again and when asked to select your current Maths-Whizz installation, browse to ‘c:Program FilesMaths-Whizz’, assuming you originally installed the product to this location (this is the default location). Double click this folder then click ‘ok’. You will now see the correct path in the input box. Click through to complete the upgrade.