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Memory and the Internet

29/1/2015

 
Still checking through my old post archive and I found this. Thought it was worth reposting because a) it's reminded me what a good programme "The Digital Human" is (I will have to check when it's on again) and b) it seems even more relevant in the light of imminent GCSE curriculum changes. With a bit of digging, I've found out that I wrote this post in October 2012 - not sure which Katy Perry song I was referring to, but they all sound the same anyway!
Stuck in traffic on the way home today, and bored of listening to Katy Perry's latest offering on pretty much repeat on most of the local radio stations, I made a very exciting discovery on Radio 4. I caught the last fifteen minutes of the program Digital Human, which explores how the world around us has evolved in the Digital Age. The programme I caught the end of was on memory, and looked at the idea that our memory is getting worse because we now have information permanently at our fingertips through smartphones and the Internet. It's well worth a listen, but a couple of things on there gave me a lot of food for thought.

Transactional Memory
Now, I knew absolutely nothing about this until listening to this programme. Transactional memory refers to the fact that we know people (or increasingly, things) who have specialist knowledge about certain topics, and therefore we don't need to memorise the knowledge ourselves. 

A couple of examples mentioned were a husband who knew everything about sport (and therefore his wife could just ask 
him anything she wanted to know at any point, without needing to memorise as the information was readily available), and a dad who knew all the addresses, birthdays and anniversaries for his family - rather relevant to me, as every year around Christmas time, I inevitably call my mother for a list of addresses to send cards to. 

The programme made the point that we have just swapped these specialist people for "things", such as our smartphones or computers, and rather than memorising the information, we are instead using our memory to remember where to find the information when needed.

This rang very true with me (and not just because of the Christmas card thing). I thought of all the times in the past I used to phone my dad when my computer blew up or something malfunctioned, but now my first port of call is Google (usually on another device if I've majorly virused something). If I've forgotten a minor point from S1 to teach my A Level class, I turn to the Internet first, rather than ask one of my comparatively many friends who work with statistics on a daily basis.

Jack, the fifteen year old, and his breakthrough Science Fair project
To finish off the programme, an interview was conducted with a fifteen-year-old living in Maryland, who had designed a rather complex early warning system for various types of cancer. Judging by his vocabulary and verbosity, the lad was obviously quite bright - however, I was amazed when he explained the complexity of his ideas (and confess to not understanding them fully!). He explained that he had taken some personal research he had done on the Internet, connected it with his school Biology work, done a bit of additional reading, then invented this fascinating bit of equipment that's cheaper and more effective than the current warning systems. 

He discussed the fact that, without the Internet, his discovery would not have been possible, because he wouldn't have 
had so many scientific journals and research documents readily available at his fingertips. Crucially, the interviewer said something right at the end of Jack's slot that really stuck with me: being smart used to be about knowing lots of facts, because information wasn't so easily accessible, but that being smart now means being able to access, filter and synthesise the vast amounts of information available to us. Which got me thinking on the third point...

How does our education system relate to this?
This is something I've thought about a lot before, and I've read quotes from mathematicians saying stuff along the same lines: if your job involves mathematics on a professional level, you don't try to memorise loads of formulae, as you can just look them up as and when you need to. Another point the programme made was on the function of memory - it is designed that we should forget things after they have stopped being useful. One researcher talked about the brain being a "behaviour machine", not a "memory machine", which adapts to the situations we find ourselves in as we go through life and alters memory accordingly.

Which all boils down to one thing, really. Why, with all this technology at our fingertips, and continually evolving ways to access information as and when we need it, do we still have an exam system in Mathematics that focuses so strongly on memorising facts (which inevitably disappear from the heads of Year 11s very soon after they finish their exams), and not techniques for finding, synthesising and finding applications for existing information, which is surely a much more important skill to have to survive in the Digital Age?
Hmm... got a bit ranty at the end there, didn't I?

The programme is still available via the BBC using the link above. Gotta love blasts from the past!

If it ain't broke... Red Pen Green Pen

29/1/2015

 
In the grand site update, I've been looking through all my blog posts on my old site and trying to work out what's worth reposting. I found this gem from about three years ago...
"On the back of some fantastic A-Level CPD from Alan Jervis, I trialled "Red Pen, Green Pen Marking" with my Year 12s last year. I've now adopted this for all of my marking with all my groups, and it's working quite nicely. Well, except for the times I accidentally use the wrong colour and swear profusely. Occupational hazard of those funky BIC four-colour pens I suppose.

Anyway, the idea is to mark the stuff you like in green, and the stuff you don't in red. I tend to tick correct answers and write additional comments like "Good, you've shown full working out" alongside in green, and circle any errors in red. I'm trying to avoid correcting them fully, especially if the error is something like the classic 1 x 1 = 2 mistake or something similar. Instead, I'm giving a bit of lesson time to reading homework feedback and doing corrections if necessary, with an opportunity for those who got it completely right to attempt an extension question or two.

Incidentally, the course I went on, "Maths - Improving Exam Results at KS5", is still running with Dragonfly. Worth checking out; thoroughly enjoyable!
Most of the old posts just got deleted - as they say, every day's a school day and I'm doing things a lot differently now to how I was three years ago. However, Red Pen Green Pen has stuck with me. Our school's marking policy now uses What Went Well/Even Better If, so all my WWWs are written in green and EBIs in red. It's really useful for me to see straight away if I've had to give a lot of improvement feedback (lots of red!) as that's an indication I need to do a bit more work on that topic, and the students seem to respond to it pretty well.
There has, however, been one groundbreaking change to my RPGP marking policy. I've upgraded from the blue BIC four-colour jobbies to a far superior pen (marking is slightly more enjoyable with nice stationery). For other nutters like me, I recommend these little beauts. My local Wilkos sells them for 69p each, and no, I didn't go in at the weekend and buy 10 of them...

Also, apparently Dragonfly are no longer running that course. Who knew?

Rally Coach

29/1/2015

 
During my NQT year, I worked at a school that was big on cooperative learning and using Kagan structures. I confess, I was never a huge fan - all the jazzy names got a bit complicated and all seemed to have the words "Round" or "Robin" in them. Interestingly, that fad seems to have fallen by the wayside now - I've not heard anyone talk about it for a while, in UK schools at least.

However...I love Rally Coach. I've not touched many of the other cooperative learning strategies for a good few years, but I still use this one. It's a fantastic way to jazz up those "do 10 questions to remind you about last lesson" starters. 

Students work in pairs. They choose who is A and who is B, and are given a set of problems to do. For any pesky groups of 3, two As and one B works fine.
Rally Coach example | NorledgeMaths
A template for Rally Coach problems (Image: http://commons.wikimedia.org/wiki/File:Tennis_racket_and_ball.JPG, GNU Creative Commons license, author unknown)
Student A tackles their first problem, while B watches and either praises if the question is done correctly or coaches if A gets stuck. Once A has done their first problem, students switch roles and B does their first question while A praises/coaches as necessary. Students continue to alternate in this way through the problems until they have finished. 

Depending on how organised I am, I either put the problems on the board, or create a worksheet. I much prefer the latter as it has two major benefits:
  1. I've found that giving one worksheet between two means that students actually do the activity properly, rather than just rushing to answer their set of questions - as they are sharing the same sheet, they can't do the problems simultaneously (although I have seen one pair of students try and fail hilariously).
  2. Students can tear the worksheet in half at the end of the activity and keep their problems; particularly useful if they have corrected or written on each other's work!
However, we all have photocopying bills and a finite amount of time. The activity works adequately on a board or even with problems from a textbook.
Rally Coach worksheet example | NorledgeMaths
Example worksheet for a Rally Coach activity
The emphasis is on peer coaching and using independent learning skills (e.g. prior knowledge or notes from previous lessons). It takes a bit of training to get them doing this properly, but it's worth doing. The first few times I run a rally coach with a new class, I get them asking me straight away rather than each other - I just refuse to answer until they get the message! Once we've done it a few times, I tell students to put deliberate mistakes in if they think their partner isn't fully engaged and listening to what they're saying.

Growing squares

29/1/2015

 
This investigation is great for getting pupils to “spot” square number patterns – it’s particularly useful as a little starter a couple of weeks after completing the topic to remind them of the sequence of square numbers. Pupils could also make the patterns from multi-link cubes and then demonstrate how the top and bottom patterns can be turned into squares.

I’ve also used this as a time-filler activity with half a class of Year 10s and asked them to come up with the nth term rule for the top and bottom patterns (n² and (n – 1)² respectively), then combine this to get the nth term rule for the complete pattern (gives 2n² - 2n + 1 when expanded and simplified). They then used this to predict and check the next pattern in the sequence.
Growing Squares investigation | NorledgeMaths
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Square differences

28/1/2015

 
Pupils explore which numbers can be written as the difference of two square numbers; a nice way to practise calculating with square numbers, but also encourages them to pattern-spot at the same time.

All the odd numbers can be written as the sum of two consecutive square numbers. Some pupils notice this very quickly, but some will need to try numbers for themselves first. It helps to ask pupils to look for patterns in answers they already have, then ask them to think about whether this pattern could apply to other numbers. It’s a little trickier for pupils to work out the other group – the multiples of 4.

It’s highly unlikely that proofs of these will be applicable when first introducing square numbers to a group. However, the activity could be revisited in the context of lessons on proof or expanding quadratics.

Square Differences investigation | NorledgeMaths
Square Differences solutions | NorledgeMaths
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Happy numbers

28/1/2015

 
This is one of my absolute favourite investigations to use when teaching square numbers. It can fit quite nicely into 15/20 minutes as a simple activity, or extend to a whole lesson with the class working together.

To find out if a number is happy:

  1. Pick any two-digit number (e.g. 23).
  2. Square and add the digits (4 + 9 = 13).
  3. Repeat (1 + 9 = 10).
  4. And again (1 + 0 = 1).

A number is happy if it eventually gets to 1. There are 20 happy numbers between 1 and 100; asking pupils to find two or three happy numbers works well as a quick activity, possibly towards the end of a lesson introducing square numbers.

However, the most interesting part is what happens with numbers that aren’t happy. Every number that isn’t happy eventually “spirals” into a repeating loop:

4 → 16 → 37 → 58 → 89 → 145 → 42 → 20 → 4

By extending the time allowed, pupils quickly discover this loop for themselves. Some then realise that they can rule out reverse digits (e.g. if 42 isn’t happy, then 24 won’t be either). It’s quite powerful to ask pupils to work in pairs or groups, as this allows lots of opportunity for planning and discussion.

I’ve previously used the board to map this “spiral” out for pupils, asking them to come up and add any numbers that they can. I also spent one very rainy Sunday afternoon transferring this map to a PowerPoint slide with colour coding (cause I'm a loser)... I think it looks very satisfying!
Happy Numbers | NorledgeMaths
Happy Numbers spiral | NorledgeMaths
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The Cross Method for factorising quadratics

28/1/2015

 
Factorising quadratics is one of those topics that, for some reason, students just don't seem to get. I always teach factorising straight after expanding; it seems that students understand the basic principle of "working backwards", and can even factorise fairly simple quadratics (all positives, of course) pretty quickly and simply. However, I've never quite managed to work my way around more difficult quadratics with a > 1 with much success; the students seem to understand what they are trying to do, but really struggle with putting it into practice.

Anyway, last week I went on a training course for the new 9-1 GCSE from Edexcel. All interesting stuff about the exam changes, but my biggest takeaway was this: the "Cross Method" for factorising quadratics with a > 1. I was keen to give it a go with Year 10, so after doing some simple quadratics with a = 1 (mostly OK, apart from the usual wrangles with negative numbers and having to unteach negative add negative is positive), we tried a few with a > 1.

I started with my usual "reverse grid method and reason it out" approach; blank stares and confusion. I then showed them the same question using the "Cross Method". Cue shouts of "oh that's easy!" and "why did you even show us that first way?!". 
Cross Method for factorising quadratics | NorledgeMaths
Things I like about this method:
  1. It's an easy way into the problem; it turns a complicated quadratic into a little number puzzle.
  2. It helps students to structure and record their trials. It's useful for both them and me to be able to see what numbers they have tried.
  3. It works for all quadratics. I probably wouldn't encourage this for simple quadratics with a = 1, but it would work!
  4. It really does help with issues with negative numbers, as students have to do the calculation at the side, which makes them think more carefully about their working.

I think I'll be using this a lot more in future! It's not a substitute for understanding, but once the understanding is in place, it provides structure and organisation for the trial and error method.

Exciting times ahead...

28/1/2015

 
So, it's been all go on the Interwebs for me lately! Over the last few months, I've mostly been wasting my evenings on the following:
  1. Tidying up and revamping a lot of the resources I'd made for my students on the original site. Everything I've got is now housed over at the Students section of Miss Norledge Maths. It's not complete by any stretch of the imagination. My main goal was to produce most resources for the first few stages of the Elementary curriculum (as of this year, we're following the Mastery Pathway at Key Stage 3, and I really wanted things available to support independent learning for my classes). I also did a few bits and pieces for Year 11, as they sat the IGCSE in December and wanted some revision resources.
  2. Doing some more YouTube vidoes. I'm still missing a load of topics, but I really wanted to get started properly on...
  3. Creating this section of the site - the area for resources! This is going to be my main project for a while, as it's looking really empty at the moment. I'm planning to collect lots of links to useful resources by topic, as well as adding and sharing my own resources. Check out Resources by Topic for anything available at the moment, and keep popping back as updates will be happening daily!

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