From the BBC:
“Computers ‘do not improve’ pupil results, says OECD” http://www.bbc.co.uk/news/business-34174796
“Schools have yet to take advantage of the potential of technology in the classroom to tackle the digital divide and give every student the skills they need in today’s connected world, according to the first OECD PISA assessment of digital skills.” http://www.oecd.org/education/new-approach-needed-to-deliver-on-technologys-potential-in-schools.htm
In short, it’s not about plonking students in front of a machine, it’s about being able to use the machine effectively and appropriately. Obvious?
To say that long division is difficult is an understatement. The teachers who have the onerous task of teaching it know how to do it but the problem then is recognising all those tiny facets that are so internalised as to be invisible. Of course a teacher needs to know how to do it but they also need to know how NOT to do it. This is where problems are identified and children learn faster. Too often children are just taught a routine and some learners just don’t ‘get it’. This is a big routine!
So what understanding is going on (or not) under the surface? Here’s one:
After lots of short division we need to understand that it is unnecessary to ask how many 27s in 3. A two digit number is never going to go into a single digit. And what if it doesn’t go into the first two digits? Why do some children write a zero? No need for a place holder. (Concept: Place value)
Why do we have to subtract? The concept that a remainder is the result of a subtraction is unspoken in short division. The difference is often seen rather than calculated. (Concept: Remainder)
So there it is. What now? Bring down the 5? Why? We have to unlearn the putting the remainder in front of the 5 like we would in short division, possibly because when the remainder is double digit it would be crowded. However, too often there is an incantation of ‘bring down the 5’ because it’s the next step to be remembered rather than for a reason of maths. (Concept: Place value)
And so the process repeats either by rote or by understanding.
But look at the next part. How many 27s in 217? Has the learner practised situations like this as a one off? (Concept: Estimation)
I thought 7 but there are issues about whether another 27 can be found, shades of chunking. Is it OK if it’s a bit more than 217 rather than way under? In the end it was 8. If I take my eye off the ball to work this out without an understanding of the process I might end up re-entering the algorithm at the wrong point. (Concept: Multiplication, Inverse, Division as whole shares)
So there we are, 128 remainder 1. No good? 128 1/27? You want a decimal? (Concept: Equivalent fractions)
Where did that .0 come from? We didn’t have unnecessary zeros at the start so why now? (Concept: Decimals)
How many 27s in 10? Am I allowed a zero here or do I just stick another one on to make it 100?
And so it goes on. When to stop? Do we know anything about rounding to a certain number of decimal places? (Concept: Rounding)
The whole process is a minefield of potential misconception not to mention differences of process from the already learned short algorithm.
This will not be well learned by a rhythmic repetition of different stages but by understanding of concepts from earlier learning not all of which gets a mention in the National Curriculum in earlier years.
Every morning, and I mean EVERY morning, I wake up to an email from Computing At School full of news about events, new resources and comment. There are clearly some lucky young people out there on the receiving end of all this. I mention it lest you think my mission is to be negative. It’s not. I simply want to remind folk to keep their eye on the ball and to describe what I think the ball looks like.
You see, despite areas of excellence and schools that are doing their best for now and hoping to develop year on year (so please folks don’t criticise until you can’t see progress) there are some who are still doing little or, in some classes, nothing.
I want to explore some possible reasons for inertia and the risk they pose to what should be a groundbreaking curriculum development that is Computing. Not surprisingly it’s a cocktail of interacting factors that no doubt vary from situation to situation.
Let’s start with Ofsted. Download a recent report for a primary school and find me a reference to Computing. You’ll find plenty of references to mathematics and literacy but Computing? If I had a small bet on every report since, say, October 2014 I think I might make some money. Perhaps this absence is a factor of the amount of time in school available to inspectors or maybe it has something to do with the availability of inspectors with the necessary expertise. In any event what messages does it send about the subject’s importance? Computing is statutory, right? Well so was ICT and look what happened to that!
Imagine you’re in a school that has annual SATS results that are always around the norm after months of effort and booster lessons etc. English and mathematics again. Where are your efforts focussed? I’m sure there will be a lot of schools that meet my description that have a really broad curriculum all the same but SATS are the things that end up in the local paper, and the in-tray of the local school improvement team. It probably looks as if I’m having a go at a perceived rather shallow approach to education in some schools. I’m really not. I was a teacher for 30 years and I appreciate the things that weigh heavily.
Teacher expertise is another important factor. Unsurprisingly our primary schools are not full of Computer Science graduates who have chosen teaching. Courses are offered and meetings arranged but why is take up sometimes so low? Believe it or not teachers really are busy. Don’t imagine that by simply creating another imperative time magically appears. It’s something that few people who haven’t worked in schools can understand. Teacher, surrogate parent, referee, advocate, therapist… Somehow time needs setting aside without taking teachers from where their head teacher needs them most; in the classroom with the children.
The volume of the training task is considerable too. It can’t be done on a single one-day course any more than you can run a course that supplies experience. Imagine trying to learn a foreign language on a one-day course. The idea is absurd. In the same way a completely new subject needs a lot of time and time is something many schools and teachers don’t have.
This has scarcely been a carefully managed piece of research, generalisable across all schools but I started to write it when the factors I have mentioned became too obvious for me to ignore. The content is based on observation and conversations with people who are at the sharp end. Let’s not allow an exciting curriculum development to become marginalised by default.
But let’s end on a positive. It can be done because it is being done in a lot of places and it’s a great subject. I’ve just had an email from someone in a primary school. It says, “I think I need to make my lessons more boring. They’re having way too much fun.”
I went to the BETT exhibition recently and noticed a change. It seemed to be far more about product than education. Each presentation seemed to be about how it could transform your class or school and solve all your problems and was aimed at all the things that are at the front of a teacher’s mind nowadays. It’s education but not as I know it. Still, I no longer have to do it so what’s my problem?
I have a granddaughter who has just started school and is full of enthusiasm for learning. Her little brother will be joining her soon so I want the best for them. That might include tools and systems but most of all it is about teachers who can use them innovatively. Instead we have lists of ‘stuff’ to be done. It’s called the National Curriculum. There seems to be no thought about how topics connect nor what prior learning is necessary. Children who can already read are unlearning the ability to use context to decipher words as they struggle to read nonsense words phonetically. Now I see on Andrew Marr’s programme this morning that the key indicator of success in maths is the ability to learn multiplication facts to 12 x 12.
Why this has surfaced again when it is already in the NC I can’t understand. Now, I like the idea of being proficient in basic multiplication. I’m not suggesting abandoning learning and getting out the crayons and the wendy house.It means you don’t have to take your eye off a problem while you grapple for a relevant fact but I get the strong impression that it is seen too often as an end in itself. And why 12? I could have sworn our system was decimal. I used to use multiplying by 12 as a way of learning how to multiply double digit numbers mentally as x 10 and x2 were already internalised. Perhaps we could continue to 16 x 16; it might have some benefit with things hexadecimal.
There seems nowadays no need to function mathematically, merely to compute. It is ‘the basics’ it is ‘traditional’. This despite the fact that inspector and government reports going back 150 years lament poor standards. Children will still get what they always got. Ask any adult who endured ‘traditional’ maths how they liked it. You won’t get many takers and few people become good at something they don’t like. Those of us at school in the 50s and 60s were the generation for whom it was OK to be no good at maths. And yet that is what we are told is the way forward.
What a shame that a subject so important and so exciting keeps being reduced to lists of facts while innovating with Computing. Bob Harrison tweeted “Surely now children are taught about algorithms and to code they could write a programme (sic) for 12 times table and a spelling/grammar check?” Yes, but they wouldn’t be allowed to use it in maths lessons!
The WordPress.com stats helper monkeys prepared a 2014 annual report for this blog.
Here’s an excerpt:
A San Francisco cable car holds 60 people. This blog was viewed about 1,200 times in 2014. If it were a cable car, it would take about 20 trips to carry that many people.
There seems to be something of a trend in open letters recently and when I realised that my granddaughter, who I’m sure was only born a few months ago, is starting school in September I felt I had to write one of my own. Nothing focuses the mind like personal circumstances.
Soon you will be starting school so I thought I’d write down my hopes for you.
Despite Mummy and Daddy, like many parents, learning that there is no such thing as parental choice you are off to school with all your options open. My first wish is that in fourteen years you leave with them intact.
While the National Curriculum means you will not be cut adrift on the whims of individuals it does contain some weird things so I’m hoping you get a string of teachers who know how to skirt around the worst of them. I really don’t think you need to learn Roman numerals or to multiply up to 12 x 12. When we have time I’ll explain about decimalisation.
While we’re on the subject of maths I hope you come to love it and that you can say that you’re good at maths and not the maths test. I hope you have teachers who understand that arithmetic is a means and not an end and that understanding beats memorising hands down.
You’ll find that you are pretty much stuck before 1066 in history until you are 11. Where someone so young gets the experience on which to hang concepts like ‘1,500 years ago’ beats me but we can do the good stuff when you come to visit!
I wish you teachers who understand that assessment does not equate to a test and that no one ever says, “We can’t do that because your next school do it.” I also hope that they are familiar with Bloom’s Revised Taxonomy and that creativity is at the very top of it.
You’ve always been uninhibited with technology, both your camera and Grandma’s iPad, and long may it continue. I hope you enjoy coding but are also taught that there are other vital facets to technology industries like design and graphics. Daddy will tell you that learning real maths is more important than programming and since he’s better qualified in Computer Science than I am I won’t argue with that. I hope for a school that recognises the importance of new literacies like critical use of the Internet and how this contributes just as much to your safety as online stranger danger and privacy.
Don’t worry about SATs either. The only people for whom there are consequences are your unfortunate teachers. Other subjects are just as important. If you have a super confident school that recognises that the National Curriculum is only a minimum you will be doing the National Curriculum + too.
A lot has to go right as you pick your way through the dogma fuelled education system but, between us, we’ll manage.
I spent three days at BETT this year and, as usual, came away overflowing with ideas.
The breadth of things to see and do is staggering and it was only when I sat down on the train on my way home on Friday that it really hit me.
I spent some time looking at things as diverse as a combination learning platform, communication tool, school website and office staff and governors environment and a couple of startups. One was a series of cross platform maths apps and the other an innovative reading machine that, amongst other things tracked page turns so that it was always reading to you from the right page. It reads real books too!
The best way to meet people is to speak to them so I dida couple of ‘Ask The Expert’ slots for Naace and a Learn Live seminar.
However, everyone’s favourite attendee was…
Any views expressed here are my own but based on my experience. However I’ve seen enough good practice to know that success is often a product of the teacher’s personality as well as sound pedagogy. In short, there is no single right way. Good practice is dynamic and varied.
In the UK we seem to be expected to teach mathematics like we speak to foreigners when we’re on holiday. If it doesn’t work at first say it slower and more loudly. Rather than pressing on with new and innovative ways of working we look back to imagined golden ages. Was it the 1980s? We had the Cockcroft Report examining the problems of learning and teaching in maths.
Further back? “… a large proportion of entrants (to trade courses) have forgotten how to deal with simple vulgar and decimal fractions, have very hazy ideas on some easy arithmetical processes, and retain no trace of knowledge of algebra, graphs or geometry, if, in fact, they ever did possess any.” A Mathematical Association Report of 1954
Further still? “…accuracy in the manipulation of figures does not reach the same standard which was reached twenty years ago. Some employers express surprise and concern at the inability of young persons to perform simple numerical operations involved in business. … It is sometimes alleged … that the teacher no longer prosecutes his attack on this subject with the energy or purposefulness for which his predecessors are given credit.” A Board of Education Report of 1925.
Even further? “In arithmetic, I regret to say worse results than ever before have been obtained – this is partly attributable, no doubt, to my having so framed my sums as to require rather more intelligence than before: the failures are almost invariably traceable to radically imperfect teaching.” From reports by HM Inspectors 1876. So, dumbing down in the 19th century!
So it’s time for something new and we have a brand new age in terms of technology to help us.
The new National Curriculum for England tells us, “In both primary and secondary schools, teachers should use their judgement about when ICT tools should be used.” A strange statement. Are we to imagine that no judgement is called for when choosing other resources or that teachers will otherwise make random choices?
Ofsted make their own actually quite exciting statements about what outstanding practice looks like: “Problem solving and investigative approaches are central to learning for all pupils.” They also talk about independence, perseverance and learning from mistakes. So have we got the wrong message about an emphasis on content?
So why embrace technology? First I ought to say that technology is not a magic bullet. It is a teacher that makes the difference; the technology is the tool that, if used well, makes the good teacher even more effective.
Technology, in those circumstances:
- enhances learning;
- allows you to do something that can’t be done any other way;
- makes life easier (without damaging standards);
- connects with children’s lives outside school.
These bullet points are generic rather than relating solely to mathematics. It must also be remembered that technology needs to be planned and targeted rather than being a token use.
I also want my tech to help me use different strategies in my lessons. Paragraph 243 of the Cockcroft Report was good in 1981 and is still good today.
Mathematics teaching at all levels should include opportunities for:
- exposition by the teacher
- discussion between teacher and pupils and between pupils themselves
- appropriate practical work
- consolidation and practice of fundamental skills and routines
- problem solving, including the application of mathematics to everyday situations
- investigational work
My decisions on what technology to use will be informed by the above and my own personal beliefs based on experience.
- Learning on tiptoe (the learner is the best (s)he can be)
- Learn regularity not tricks
- Learn by heart and not by rote
- All activities must be connected to other learning and activities
- There should be a variety of approaches
- No one is completely unable to do every part of something (When a learner says “I can’t do…” there is often one facet that needs addressing that is blocking progress)
- There are some hidden basics in maths. These are items not covered in curricula but vital from an early stage to many areas that are. Examples:
– Area as covering surfaces
– The meaning of =
Lastly I’d think about how technology can help learners climb Bloom’s Revised Taxonomy.
Let’s look first at calculators, that most reviled of resources. First of all no sensible person would use a calculator to perform a calculation they could do more quickly another way. Children should be as good as they can at mental calculations, as good as they can at written calculations and able to estimate and approximate to be able to use a calculator effectively. Then they should know exactly when to use one of these alternatives.
- Tables card games. See #4 in https://icttalk.wordpress.com/2010/09/23/not-by-rote-but-by-heart-how-to-learn-multipl/
- Prepare a worksheet with sets of questions like:
1.6 x 10
3.8 x 10
7.2 x 10
23.5 x 10
2.45 x 10
8.32 x 10
9.01 x 10
17.74 x 10
The learner must answer each in turn, check it on the calculator and use the result to inform their answer to the next question. Sets of four are usually sufficient.
- Find how many different numbers less that, say, 30 you can make with four 4s and any symbols (This is the father of the 3+3×3-3+3 question that was on Facebook a while back)
Which of the reasons to use technology listed above did you spot in these ideas?
I’ve used them for modelling situations where doing it by hand takes far too long and detracts from the mathematics and the ability to experiment. Creating a chart and watching the effect as the data changes is fantastic. We all have a blind spot (I hope) and mine was cumulative frequency. I could never get my head round it until I created a chart and manipulated the data.
- Maximising area problem (see area and perimeter can be different in NC)
- Using graphs
Of the apps, programs and environments listed here others are available which are equally as good. The examples, while good, are meant to be generic rather than a claim to be the best.
Here are three very different environments.
The Khan Academy has had a bad rap in some quarters. It’s not designed to replace teachers but brings something else to the table. Students can practice, extend and watch the videos again and again and again and … It might have its place in a flipped classroom but this begs the question as to whether watching a video is necessarily always best as a solitary activity.
Geogebra is best described as a dynamic geometry environment but is rather more. It has a cut down version for younger users and works on just about every platform known to mankind. I confess to using it in a rather trivial fashion to model vertically opposite angles and what happens as one changes. It beats holding two slippery rulers across your chest!
Beluga Learning is an environment where users have to solve challenges as they move through it so it is neither a learn and practice activity nor a model.
I’ll tag on to this the sort of virtual tool that is available online, in IWB software and on tablets for example a protractor, base 10 materials and a virtual pinboard. I’m happy to debate the inclusion of the latter, apparently somewhat trivial resource.
Daunting for non-programmers but as Conrad Wolfram said, “If you really want to check you understand math then write a program to do it.” Scratch will bring computing and mathematics together as will the still free offering from EducationCity, Code Crunch. Go on, be subversive, make a calculator!
Expertise and collections
From the environment
There’s a lot of maths in the virtual world too. The recent freezing temperatures in the USA threw up lots of data in news feeds, real life maths features http://www.teachersmedia.co.uk/videos/interpret-and-construct-tables-food-scientist and my holiday pictures revealed a fantastic number square on the wall of the Sagrada Familia in Barcelona.
Short applications / programs / tools
I haven’t said a lot about practice here but there is a wealth of tablet apps that fill this space. The ICTMagic site has more than enough resources for even the most enthusiastic teacher and the Primary National Strategy programs are still alive and well. Try letting the children use them learning instead of using them for teaching.
Last but not least consider screencasting where learners make an electronic product to demonstrate an area of mathematics. You can build up a library for other learners to view over the years and the process can really enhance the learning process when the producer finds themselves having to explain something to another person.
And if you must teach Roman numerals…
Lastly, my own social bookmarking for mathematics.
Mark Twain said, “Travel is fatal to prejudice, bigotry, and narrow-mindedness…” which prompted me to do something I’d been meaning to do for ages, have a go at Google Maps and see if they could easily be used to demonstrate learning or tell a story. And then I found this! http://www.wetellstories.co.uk/stories/week1 Could something like this be made as easy as possible?
First of all I brainstormed a list of situations when maps might be useful in several curriculum areas. I came up with this:
All of these activities can be solo or collaborative.
- Lit trips. If you are studying a book that relies heavily on location, make a map that describes what happens in those places. – English
- Famous events. – History
- Local / national / world interest. – History, Geography, RE
- Story maps like the one from Penguin. Number your placemarks or join with a line. – English
- A virtual field trip (e.g. Pompeii. Take holiday snaps and send a postcard) – All
- Habitat maps – Science
- A foreign language guidebook. (e.g. Different shops) – MFL
- Build up information about another country – Geography, History
Sign in to a Google account and open Google Maps. Ironically this is the hardest part because there is now a new version and I wanted the older one because I could include images and movies. So you’ll see something like either
You need to create with classic My Maps. Give it a title and a description if you want one and decide whether it will be public or unlisted.
If you want to work solo you can safely ignore the bit on the right of the image below but if you want to work with others you need to click on the ‘Collaborate’ link which will show you that screen.
Zoom in on your first location and click the blue placemark at the top of the page, drag it into position and click to secure. A window opens and you can put a title and some text. Click ‘OK’ and you’re done!
The first entry in your story. Click ‘Saved’ and ‘Done’. (Mine’s rather brief!) Not very exciting? Add an image.
First, find your image online and copy the URL. Make sure your URL is that of the image rather than that of the page usually by right clicking on the image but don’t do it to the thumbnail in a Google search or you’ll end up with a hyperlink.
Click ‘Edit’ and choose the rich text option in the edit box. You will find an Office-like button to click and then paste the URL in the box that appears and click ‘OK’, ‘Save’ and ‘Done’.
Now to video.
Find your video online, YouTube is a good bet. Get the embed code as shown in the image above. prepare to edit your map again as you did for the still image but this time click on Edit HTML and paste the embed code. Bizarrely you will need to insert http: as shown for it to work.
Below is my map. It’s a rather humble one as it has just one place on it and with text, albeit rather brief, an image and a video it might be considered overkill but it shows what’s possible.
If you are not able to see the video your browser might be waiting for your permission to allow it.
Lastly you might want to save as a KML file to be able to open it in Google Earth.
Simply buying because everyone else is or buying in isolation in the hope that you’ll be able to find a use won’t do but answering the question, “What do you want to do with it?” be it hardware or software is never easy.
Four very good reasons for using ICT:
- Computing itself is vital for the 21st century and requires hardware.
- Using ICT with a good teacher raises standards.
- Using ICT brings school into line with children’s experience of the world outside.
- Sometimes using ICT allows you to do things that are otherwise impossible.
Now comes the question, what to buy?
Computer hardware falls into three main categories: desktop, laptop and tablet. Each has its uses and there is a degree of overlap but these simple pros and cons should help you choose.
Once you’ve decided that you move on to the level of spec you require. In the case of tablets which operating system (OS), Android, iPad or Windows, needs to be decided first. With the variety of, particularly Android, devices about you need to ask questions about priorities. Is it the range of apps you want or simply a genuinely portable note and data collection machine? In any event these are not laptop replacements.
In general for any hardware the best spec you can afford is the way to go but ask, can you afford sufficient units to be effective?
Next move? Have a look at some kit and try it out. Don’t buy blind.