Monday, 19 September 2016

Maths, Automaticity & iOS Devices...

Using iOS devices such as iPads for 'skill+drill' is something we generally discourage in school, where we would rather these technologies are used for creating and collaborating, along with the many other skills that are described in the UWCSEA profile.

You see, skill+drill Apps don't need a teacher, what they do need is a device, time, and perseverance; so what this is, is an excellent productive activity children can easily engage in at home. This kind of practise builds the kind of 'automaticity' (instant recall without hesitation) that is fundamental to confidence in numeracy. Knowing mathematics facts frees up the mind to solve more complex math problems.  If a child has to struggle to solve 8 + 3, they have no mental energy (or desire) left to grapple with the types of problems that will increase their capacity as a mathematician.

In my experience spanning over twenty years, I find that teachers commonly (and traditionally) facilitate this through a relentless torrent of photocopied worksheets, something I myself have relied on over the years. However since the advent of the integration of digital technologies, I really struggle to understand how having kids complete a photocopied Maths worksheet can ever be seen as better than the kinds of differentiated, adaptive, multimodal practise offered by Maths apps, and Maths sites like Khan Academy. If teachers ceased to set these tedious sheet as homework, they could free up the time to plan better lessons, no need to 'mark', instead use the time to analyse the data—where are they struggling? Where are the gaps? Where should they go next? What group of kids do you need to conference with tomorrow?

Automaticity is the ability to do things without occupying the mind with the low-level details required, allowing it to become an automatic response pattern or habit. It is usually the result of learning, repetition, and practise.

So while I generally discourage skill+drill in school, I can see its value at home. Below I have included the collection of Maths Apps we use (sometimes) at school that I believe are particularly powerful for this kind of learning, learning through practise. 

This is a small selection, no doubt a Google search would turn up many more, although I doubt they will be very different to these.

Top Tip: Ask your child to take a screenshot of their score after first attempt, then compare their progress after a week or so.


These kinds of Apps are basically teaching mathematics in old ways using new technology, albeit amplified

Chocolate covered broccoli...
These Apps are essentially worksheets on steroids, so while your kids may be more engaged in the short term, don't expect this to last. These tools are essentially 'chocolate-covered broccoli'. That’s what designers of educational games call digital products that drape dull academic instruction in the superficially appealing disguise of a game, using the trappings of games “as a sugar coating” for what would otherwise be unappetising content—in short don't treat these games as a replacement for 'proper' games like Minecraft, but by all means treat them as replacements for worksheets.

What these Apps do offer that worksheets don't are features like, interactivity, capacity, range, speed and automatic, accurate, reliable responses at the speed of light.  These unique features make a contribution to the teaching and learning process, in that they motivate and interest children by interaction, allowing them to change the work in progress and facilitate a variety of paces of working.

We sometimes think of being good at mathematics as an innate ability. You either have "it" or you don't. But what these Apps can encourage, is what we call a 'growth mindset' it's not about ability it's about attitude. You master mathematics if you are willing to try.  Success is a function of persistence and doggedness and the willingness to work hard for 30 minutes to make sense of something that some people would give up on after 30 seconds.

Drill & Practise

"Of particular interest is the effect of drill and practise – and despite the moans by many adults, students need much drill and practise. However, it does not need to be dull and boring, but can be, and indeed should be, engaging and informative. Drill is a euphemism for practise: repeated learning of the material until it is mastered – this is the key ingredient in mastery learning, [...] and of deliberative practice. It does not have to be deadly, and a key skill for many teachers is to make deliberative practise engaging and worthwhile. Luik (2007) classified 145 attributes of drills using computers into six categories: motivating the learner, learner control, presentation of information, characteristics of questions, characteristics of replying, and feedback. The key attributes that led to the highest effect included learner control, not losing sight of the learning goal, and the immediate announcement of correctness or otherwise of the answer to the drill." (Hattie, 2013)

Many computer games are basically invested with high levels of drill and practise and many students can be thrilled and motivated to engage in these often repetitive tasks to attain higher levels of skill and thus make more progress through the game. Computer games include much engaging drill and practice with increasing levels of challenge that usually is mastered by overlearning or undertaking high degrees of drill and practice. So often, the evidence has shown positive effects from using computers to engage in deliberative practice, particularly for those students struggling to first learn the concept." (p 224)

Hattie J (2013). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.