29 July 2015

Math Bytes

Units of Measure in the 21st Century

It's always been a source of great consternation to me, that mathematics benchmarks around the world still appear to be completely and utterly oblivious of the implications of the impact of digital technologies in the world of mathematics.

To see explicit evidence of this, you need to look no further than the Mathematics benchmarks that are currently used for the teaching of measure, which are still confined purely to units which, while still useful, are no longer the most common units of measure that are are significant in the lives of people who rely upon digital technologies in their daily lives, which means most of us, especially if you're reading this.

Why is it that in schools that are blessed with the ubiquitous provision of digital technologies, one-to-one laptops and iPads, the students never learn anything about how file sizes and the measurements of these file sizes work?

There are two main reasons for this as far as I understand:
  • Almost universal ignorance on the part of teachers, who are still completely oblivious of the difference between a megabyte and gigabyte
  • An assumption that a generation of digital natives just automatically get this stuff, trust me, they don't. 
  • A somewhat naive assumption that if there is a subject area that will remain unaffected by the influence of digital technologies it has to be mathematics. 

Teach Maths for your present, and their future not your past... 

Ask yourself, how can it make any sense in this day and age for students to be able to complete their mathematics education, competent in the calculations relating to kilograms and kilometres and millimetres and litres, but not have the slightest clue about the units of measure that are fundamental to the devices that they rely on every day?

The problem is caused by this lack of awareness are profound. I struggle to envisage students who find themselves in difficulties because they were confused about the difference between a metre and a kilometre, but I regularly encounter students and teachers who are flummoxed by their their inability to understand how big a megabyte is and why they can't email that 200MB video ‘rejected by server'.

Cries of frustration abound with rhetorical questions such as, 'WHY is taking so LONG to upload/download?'

Answer? Um, because it is a 1 GB file, and you're using a 2 Mbps connection... ?

Response: :o|

Fortunately, the solution is obvious; educate the teachers and they will educate the students, but unfortunately it looks like these things will not change until the ‘official, mandatory' benchmarks change. If anything this post is a desperate plea for just a bit of common sense; do we really need a mandatory benchmark to realise that in this day and age it is absolutely essential, that our teachers, and their students are as familiar with kilobytes and megabytes as they are with metres and kilometres?

One extremely rare example of digital measures in Maths - Khan Academy

Trust me, it's not that difficult, if anything it’s actually easier to understand than traditional units of measure. When teaching measurements of length students have two differentiate between tens and hundreds and thousands, but when dealing with units of measure for file size, it's much simpler, everything is 1000 times bigger than anything before. That's it.

Put your practice where your pedagogy is...

So, inspired by Khan Academy, I put my my practice where my pedagogy is, I ran a lesson with a grade 5 class, with the single goal of demonstrating how easy it is to enable students to get to grips with this fundamental unit of measure. Essential to this was simplicity, and I know of no technology that is simpler to use, and as transformative in application as an effectively used 'wiki' space, in this case we used a Google Site, but any kind of online fora will suffice, more on the power of online 'interthinking' here.

As with all of these kinds of lessons, most of the work goes into formulating a decent provocation, one that is not too narrow, otherwise all you get is 22 responses that are pretty much identical, as every student just imitates or duplicates the previous response. The prompt below shows how this can be avoided. In terms of 'doability' this task took me about 15 minutes to set up, and while I was able to complete the activity within one lesson, and one homework, to be honest it could have run for a week if I'd had the time.


It was immediately apparent how natural this online environment is for our students, and as can be seen in the clip below, far from this being a screen dominated task, it stimulated a great deal of (on task) discussion and collaboration.  Remember these kids wrestle (usually without any help from teachers or their outdated textbooks) with file size every day, so asking them to envisage scenarios that use these quandaries as problem solving situations is not that big a deal.

Interthinking - online and offline

It's important to note that, while the activity is screen centred, the learning is not confined to the screen, the students were just as animated (I reckon more so) than they would have been if this has been presented to them as a worksheet (which it could). But the transformative difference here is that moving it to a web based interactivity (not just an activity—see what I did there ;)?) facilitate the leverage of the transformative elements of SAMMS:

Access: They can easily search for clarification on specific elements they find confusing, such as units they want to consider that are not in the prompt (petabytes anyone?) particular vocabulary, or clarification about the amount of storage associated with particular contexts they wish to consider, eg the capacity of their smartphone, their games console, memory card, tablet etc.

Mutability: In response to feedback (from peers and their teacher), students can easily duplicate and revise their posts and post a second post (by effectively 'replying' to themselves) that shows clear evidence that relevant criticisms have been resolved.

Multimodality: Of course this entire medium is multimodal, if we had had another lesson, this activity could have been expanded to allow students to incorporate image, audio and video.

Socially Network & Situated: As it is online, we can facilitate a P2P homelearn (as opposed to homework) activity. Assign assessment buddies to feedback on each others posts at home, of course the teacher can now easily monitor the quality of these online interactions, and interject, support, clarify, redirect as necessary.

I've included some examples below that illustrate how powerful this task was, and how easy it is to set up. 

Note that a great deal of the conversation (on screen and next to it) centred on wider mathematical concepts that would be relevant to the teaching of any of the traditional units of measure, eg appropriate use of units, conversion of units, and that old favourite, explain your thinking... Now that's what I call a #winwin

Below you can find a PDF of the original discussion in it's entirety, bear in mind that this is not the actual discussion, which continued to develop following this capture.