Now that we have literally thousands of users, we at Whizz can begin to see the exercises which are more of a struggle than others, and frankly there are exercises we must  improve to ensure  that the children do really understand the learning objective all the time. A  Certain of our tests get failed much more than others which could be about the test or the animation which preceded it as we know, for example, that many children struggle with telling the time on an analog clock. Mine did, how about yours?

Occasionally we find that we have been too hard on our users. In one of our exercises for 7 year olds, we didn’t realise (until the consistently high failure rate convinced us!) that we were expecting them to be familiar with 3x, 4x and 5x number facts when at that age level, the curriculum requires only 2x and 10x knowledge. Hopefully now, many fewer of our children will have to face repeating one of the 7 year old animated exercises over and over again.

Many of the other most highly failed animated exercises are Rapid Recall ones. They are usually fun to do and frankly if they get failed a lot, it’s no bad thing if the child has to do them again. In a few cases, we are going to review the times we allow for the answer to be given. But we don’t want that time to be long enough to use a calculator or to go and find Dad! We’ve got some other ideas up our sleeve for this issue but it would be great to hear some suggestions from our users. So please do let us know what you think.

With tests we know we have to find a balance between going slightly beyond how we have taught the learning objective- without going beyond, you can’t always test whether the point of the exercise has been understood- and taking too big a step. We know we haven’t always got that balance right and are fine tuning where necessary. There’s no sense in having a test which only a tiny minority can pass first time, and condemning children to excessive repeats of the same animation.

In the Parent Dashboard we have through Exercise Preview given parents the possibility of allowing their child to skip repeating an animation but it’s a nuclear option which we would rather never had to be used!

Care to comment on any of these issues? We would love to hear your thoughts!

A test administered by researchers for Channel 4′s Dispatches programme found that:

Only four out of 10 teachers could work out that 2.1 per cent of 400 is 8.4. Only a third knew that 1.4 divided by 0.1 is 14, and less than 50 per cent could work out that a half divided by a quarter is 2.

As The Telegraph points out, ‘The material covered in the Dispatches test is contained in the primary national curriculum…’. And this chimes, rather sadly, with our long-held assertion that most adults have a maths age of 10 or 11. This is late Key Stage 2 – primary – maths, never mind GCSE.

In itself that might be worrying, but that we only ask a C-grade maths GCSE of new Primary school teachers implies that pedagogy and method is more important than knowledge and the confidence that comes from skill.

The God of Maths is a firm believer in the idea that you don’t have to know everything to teach excellently. Just as a good manager should always hope that he promotes his subordinates’ skills above his, a teacher should hope that his charges eventually over-take him. He just has to light the fire.

Despite this, something you cannot fake or rationalise away is a basic confidence and competence in a subject, and if significant numbers of primary teachers really are failing questions like these below, we ought to worry:

• 1.4 ÷ 0.1
• 2.1% of 400
• ABCDE is a pentagon. Name all its diagonals
• 7/16 + 3/4
• The mean height of a group of 4 people is 2 metres. One more person joins the group and then the mean height is 1.9 metres. What is the height of the new person?

Students logging into our online math tutor this weekend until Tuesday will get a seasonal treat with a rolling pumpkin head, cobwebbed corners, and rolls of thunder beyond the window.

Whizzers can get a fright with some of our witch-themed measures lessons, ghoulish multiplication questions, and goblin-infested graphing problems. It’s all in Maths-Whizz, with over 1200 more animated games to teach (nearly) every maths objective under the clouded moon this weekend.

Have a happy Hallowe’en, and may your treat for 2009 be all the tasty math skills you need!

In the meantime, check out this ghostly maths lesson from a truly inspired teacher:

(via Seattle PI Big Blog)

often scared of basic numeracy and should be required to study English and maths at A-level

…according to a report by the moderate conservative Politeia think-tank.

The report, titled ‘Teachers Matter’ focuses on entry standards for teachers. An author, David Burghes, of the University of Plymouth, said:

One of the issues that bedevils our teaching profession, and particularly my subject of mathematics, is that of the inadequate subject knowledge of teachers.

But Nansi Ellis, head of education policy at the Association of Teachers and Lecturers, countered:

As well as knowing their subject, teachers need to understand the different ways children learn and develop.

Instead of hysterical reports of so-called under-educated teachers we should have a proper debate about the skills and knowledge teachers need to be good at teaching children.

The report goes on to argue that central control and management of teachers is damaging the profession, but the department for Children, Schools and Families strongly criticised the comments.

From this corner, it seems that questions about the qualifications of teachers will never go away. Commenters from both sides of the political divide will argue that life experience and teaching knowledge are more important than academic bona-fides, whilst others will argue that degree- or A-level knowledge is vital to ensure good teaching in that particular subject.

I’m inclined to hedge my bets on this one. I had excellent teachers whose passion was fuelled by their deep understanding of the subjects they taught, and I had dull teachers whose poor teaching seemed a direct result of their academic immersion.

In earlier years, I remember most the teachers who showed vigour and interest, but it was easy to spot teachers who were less confident in particular subjects. I’d like to think that the love of teaching must come first – a motivated and bright teacher can be taught fluency in a subject that isn’t her own, but a knowledgeable teacher isn’t necessarily willing to be motivated. I know that not all teachers want to tackle subjects they didn’t learn beyond GCSE – the teacher training process should identify those people and ensure they are pushed towards areas they are comfortable with.

A teacher who is dull, or even disparaging, about a subject can sometimes do more damage than good. Feel free to comment!

Slumdog maths?

And whilst I don’t really keep up to date with hip young swingers like Sophia Loren and Ben Kingsley (concerning myself instead with matters maths tutoring), I do like to keep a toe in the cultural waters, to so speak. To this end, I’ve found a blog that combines the silver screen and the squeaky whiteboard in the shape of ‘Maths teacher goes to the movies’.

The language isn’t always suitable for the youngest Whizzers, but the blog is witty and irreverent, combining movie review and maths analysis in regular posts. Here’s the teacher’s take on some bad maths teaching in new release Doubt:

Yes folks, what we have here is a clear transgression of Maths Teacher’s (hitherto secret) First Rule of Movie Mathematics: Thou Shalt Do The Math. Clearly Sister Amy has been at the communion wine when she should have been revising her knowledge of basic fractions, and a better movie would surely have seen the eagle-eyed Ms Streep getting all righteous on Ms Adam’s ass for her shortcomings in matters arithmetic. PSH could still have been around, going on about Godel’s Incompleteness Theorems, if he was keen to be seen as “trendy” – and you just know a dedicated actor like him would go off and study the subject for a good few months, just to get the part right.

Talk about a missed opportunity!

I’ll be checking in back in with the moviegoing maths teacher soon.

Joined-Up Teachers looks at the fact that there are many different types of maths teacher, and many of them, maybe even tens of millions (if you count all the adults in positions to influence students’ maths education).

Despite the universal application of Maths, there is little joined-up thinking in maths teaching:

In an ideal world, the instruction across these millions of teachers would be smoothly joined up, but we all know that this is far from the case. Many parents are at odds with the maths their children bring home from school (“that’s not how we did it in my day”).

Worse, there are many homes that are anti-maths. Negative messages from parents who tell children that they were always hopeless at maths themselves (and “it hasn’t done them any harm”) undermine much of what school teachers are trying to achieve.

Rob wonders how many primary teachers see their secondary counterparts in acton, or vice-versa. Similarly, how many teachers of difficult, low-achievement classes get to see how teachers of attentive, high-achieving students work, and vice-versa?

Eastaway implies that we must think of all these varied maths teachers, from lay to professional, as lying on a continuum, a ‘spectrum’. The home environment is as much a place of maths learning as is the university lecture hall, and everyone on that spectrum should think of him- or herself as a maths teacher.

Mathematics is joined up, and its practitioners need to join up too. By presenting a united face, the maths community has the best chance to engage those who feel disconnected from the subject. And by recognising that we are all on a spectrum, in our own ways we are all capable of being mathematicians and maths teachers.

[see also our post on Rob's recent book How Many Socks Make a Pair?]

Try Maths-Twister! In this video, a teacher demonstrates a useful classroom game to help students practise their number facts and mental arithmetic by playing a variation on the classic game ‘Twister’.

Read on for our take on the ‘Maths-Twister’ recipe, or watch the video on the BBC’s new ‘Backpage’ website where – as they put it - ”parents of primary school kids share their top video tips about helping with homework.”

Many of the homework hints give physical ways of learning subjects, which can be handy if you’re desperate to enjoy the sunshine. We recommend our home students use Maths-Whizz for between 60 and 90 minutes a week, which gives lots of time for exploring maths in the real world – give it a try!

(* number pairs that total a given amount)

Recipe:

• One Twister game set (you can make your own with a large cloth and smaller cloth circles
• Playing cards or number flash cards
• Velcro stickers or ribbon

Stick velcro sections to the backs of the playing cards (or number cards), and stick velcro to the Twister spots, ensuring that any card will stick to any spot.

Place the cards on the playing mat, ensuring there are enough number pairs to make the stated total and that the pairs are far enough apart to make this something of a challenge!

Rather than select a random number or colour for every turn, a child is given a random number every other turn. For instance, I give three children the numbers 2, 6, and 7 respectively – they each put a foot on a number. I then ask each child to find the corresponding number that will make ten – 8, 4 and 3, respectively.

Things get messier when the hands come into play! I choose another three random numbers and each child in turn places a hand on their respective numbers. On the next turn, they have to find the corresponding numbers to make ten, just as they did with their feet.

If we didn’t believe this fervently, we wouldn’t have embarked on producing Maths-Whizz in the first place. As it turns out, lots of parents and teachers (and even students!) agree with us. It now seems the UK independent think-tank Reform is equally enthusiastic about learning maths, but they have come at it from a different angle.

To quote from the much-publicised Reform report The Value of Mathematics (pdf)

 

The UK’s maths economy which powers the financial services sector and wider industry is in danger of atrophy as fewer students study mathematics and attainment falls… Scores of less than 20 per cent on the top [GCSE] paper regularly suffice to gain a grade C, despite a much reduced level of difficulty. Many students are turned off by the narrow teaching which results, and this has led to a generation of “lost mathematicians”. Individuals lacking mathematical skills stand to lose £136,000 in income over a lifetime, and so have cost an estimated £9 billion to the UK economy since 1990.

 

The last line is the kicker. For anyone who naively believes that higher education exists in some kind of parallel universe from the economy this finding should serve as a reminder to the contrary. It is, frankly, tiresome hearing about entrepreneurs and business leaders who claim they got where they are not in spite of lack of qualifications, but because of them. Such people believe knowledge and academic success is for the boffins, moneymaking for the businessmen, and it’s claptrap.

The Reform report puts the loss of skilled British mathematicians down to “…the diminution of the O-level/GCSE, which has gone from a key “staging post” to a “tick-box test”.” and the “narrow teaching” which comes from this, blaming a lack of emphasis on abstract thought and problem solving, and a drop in difficulty.

 

The Gordian knot of political control has been tightened in an attempt to reverse the misguided trend towards “progressive” teaching. The unintended consequences of politicisation and centralisation of the subject are demotivation of teachers, a diminution of the enjoyment in mathematics by pupils and an exclusion of universities and employers from education policy. Steps to increase accountability taken by the Government and a focus on examination results have created unhelpful pressures on institutions and exam boards, which have in turn led to declining examination standards.

 

The target of Reform’s report is the government, but one can also assume this shift in testing and teaching has reinforced the wider idea that maths is more about learning skills and methods than it is about rigorous thought and creativity. If maths is just a skill, then so is entering numbers on a calculator – so why bother understanding long division or the reason why the internal angles of a triangle add up to 180 degrees? As the report says: “The global maths economy is driven by high personal capability, initiative and logical thought.”

(anecdote: I once spent a rather frustrating quarter of an hour on the phone with an accountant parent who claimed her son didn’t need to learn long division, because the electronic calculator made the skill redundant. I hope she isn’t counting on her child taking maths at A-level or, indeed, becoming an accountant.)

The Reform report summary points to those ‘Masters of the Universe’ – top maths graduates who are the brains behind the city and the acme of the maths skills developed at and beyond GCSE. (Personally, I would rather those brains are put to better use than devising ‘collateralized debt obligations’ and other such wizardry behind the sub-prime crisis, but if the only place that values good maths skills is the city, that is where such rare minds will go.)

Returning to the better earnings of skilled mathematicians, we might assume that an investment in Maths-Whizz of a couple of hundred pounds over a year could be the stimulus for a child to take maths beyond GCSE and on to A-level or university and, thence, to a lifetime of higher earnings. Investments with that rate of return are few and far between, never mind the fact that learning and knowledge are good for their own sakes.

As The Reform report introduction closing paragraph says: “Radical measures have to be taken to move mathematics from “geek to chic”", something we noted here, two weeks ago. But we can leave the final word to an astute ten year-old Maths-Whizzer who, in our kids’ survey, said why she believed it was not good to be bad at maths:

You would not get a very good job if you were bad at maths

‘Nuff said.