Tuesday, 1 July 2014

The Realistic and Max Reward, Min Photocopying Version of Value-Adding Differentiation

Don't be fooled by the list of activities in the previous post about addition and subtraction, we don't do each activity once, then yield to the ever-present battle cry, "MOVE ON!" that comes from the time pressure in every school and curriculum on planet Earth. Those units spanned for roughly three weeks on addition and the same on subtraction, with an additional week focused on both and more in-depth worded problems, plus pre and post-testing at their commencement and conclusion. Although omniscient, that 'move on' cry can serve to corrupt even the most noble of math teachers. A practice that I believe very strongly in, and something that my former numeracy leading teacher supported and strongly advocated for, is that students need time for mastery. That may mean running the same activity three times in a row.

Don't shout me down yet, I don't mean the exact same, the highs would go nuts at you, or at least should. But as you have read during the list, much of the time, the extension students are actually doing a different activity or harder version of the task to start with. You increase the challenge of the task each session, generally this can mean that by the third session, the mids who have been moving well (and sometimes a low who's really put in or benefited from the extra time for mastery and instruction and has earned a promotion to group two) are tackling the same task but with the challenges that the highs took on during session one.

As Practice Perfect advocates: to develop a competitive advantage, be alert for the times, when participants learn something in an especially valuable type of practice, when it would be more productive to say, Good, lets keep practicing this until were truly great.

Practice the 20

  • Identify the 20 percent of things you could practice that will deliver 80 percent of the value.
  • Practice the highest-priority things more than everything else combined.
  • Keep practicing them: the value of practice begins at mastery!
  • Save time by planning better in advance.
  •  Engage participants by repeating productive drills with minor variations instead of constantly introducing new ones.

Your purpose adapts then to the rate of mastery demonstrated in practice, and you arent afraid to circle back and repeat a topic, possibly multiple times.

The trick, half the time, is to learn how to differentiate the same broad task. Most of the time, in number-based numeracy sessions, this is as simple as:
  • Changing the number of digits or adding decimals (in number plates, group threes uses a decimal point between the digits prior to starting the equation or estimation process, very advanced highs could use the number plate digits to create like or unlike fractions and then add or find the difference between these). 
  • Changing the starting place of the task (in races, group three starts from 50,600 using four digit draws or four dice rolls, while group one is starting at 132 and draws two-digits to take away using Popsicle sticks for renaming assistance).
  • "Create your own" (with a specific focus) sounds unrealistic at first, but think about your highs, they're the ones who'll be able lot do this with limited assistance after initial instruction and modelling, and it adds an extra element of independence and intellectual challenge to the task (look back at footy subtraction, where the highs created their own match scores with a focus on renaming over zeros).
And no, differentiation is very rarely about having five different tasks (that's the misconception that often means differentiation is put in the 'too hard' basket). It's also not about having a boring worksheet for the highs as opposed to an engaging, materials-based, real-world related task.

And yes, the strugglers will mostly be working towards the same objective for three lessons in a row. So what? That gives them time to consolidate the concept and not have to also grapple with the actual mechanics of how this new activity is done every lesson. The strugglers actually know what to do, and so have more mental capacity to exert on how to do it. Accordingly, they more often experience success and confidence at the start of math, as well as an opportunity for advancement and increasing challenge as they progress and they develop self-belief that they can do maths. Plus, you spend less time explaining how to roll this and how to set up that in your book, and that means more time modelling to the whole class at first, and then the groups who need it, the actual content, in this case estimating, lining up place values, renaming and solving.

It also means time to model higher concepts to extension students while the rest of the class is able to independently function on a task; I often think highs miss out on this modelling and group instruction on higher content. This is probably because it is just almost impossible to spend precious minutes modelling to or instructing groups of highs when every math lesson you witness your mids and strugglers in absolute mental chaos grappling with both how to do this new type of task and how to do the math in it. The inevitable thought comes to your overburdened teaching brain: "Why fix what doesn't seem broken?" as compliant highs nail your learning objectives and make you feel better about your lesson, whilst they really learn nothing from the task at all. The trick is, not to put yourself in that situation by constantly changing the goal posts on your strugglers and mids every day. 

I say all this with the caveat that this is how I extend my highs half of the time. The other half, once they've fully nailed the learning objective of the first session and would gain nothing more from the next two, or when there is very little way of making the task sufficiently challenging to justify their time to start with, involves a mixture of extension projects on the next level of learning or www.ixl.com tasks relating to the same.

What are your views on running the same task, with different adaptions and levels of challenge, for two or three math sessions in a row? What to do you to support your strugglers? What methods do you use to extend your high fliers? 

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