This post is about equation practice, but I guess it could be applied to other topics.
Also there are loads of posts out there about this and nothing I'm saying is particularly groundbreaking or even really new.
"I do, We do, You do", occasionally "I do, We do, We do, You do" is a familiar technique. It comes up in TLAC 2.0, we've all heard it suggested to us and yet some people aren't confident on how to implement it.
So what do I do?
I do:
Problem on the board. Everyone can see it. When it comes to solving equations there is value in using a mnemonic to remember the steps. On their own, the steps don't really have any meaning but they still need to be done in the right order else you don't get the answers. Our department uses a slightly bastardised version of DESCUS because it's more explicit than FIFA ("fiddle" is usefully vague but too vague for lots of our students) and there were lots of grumps about the "(Y)units" in EVERY. I don't think it matters what you go for as long as you keep it consistent.
I work through the question, narrating and writing my workings on the board as I go:
"Okay, 'a cyclist travels 30 m in 36 s, calculate their average speed. Give your answer to two significant figures'" I read the whole question aloud. We all know students start thinking as soon as they get half way through reading the question, so I like to at least try to emphasise the importance of getting to the end before starting. (Whether it has any effect, I have no idea.)
"What numbers do we have, that is: what data have we got? Okay, we've got distance which is 30 m, and we've got time which is 36 s. I want my distance in metres, do I need to convert any units? No we have metres already. What about my time, I want time in seconds, have I got time in seconds? Yes, brilliant" I'd probably highlight or underline the data while I'm going so it's clear where these numbers have come from.
"So, I'm looking for how fast the vehicle is travelling so I'm looking for speed, so my next step is to find my equation. What was our equation for speed? Speed equals distance divided by time. Right, now I can substitute my numbers into my equation, what was my distance? It was 30 m and my time was 36 s Do I need to rearrange anything? No, okay, now I can calculate my answer, so I get my calculator". At this point, I'll make a show of putting the values into my calculator, but because I've been talking for a while, I'll expect students to put it in their calculators too. The first few times we do this I'll be explicit about my expectations "I get my calculator, you're gonna do this with me, get your calculators, 30 divided by 36 is... what did you get, [pause] Erika?" But eventually it becomes automatic. I will cold call on a student to get them to check my answer against theirs.
"Okay, 0.08333333. Are we finished? No we need to put our units, what are our units for speed in science? m/s. Okay final step, let's check we've used the requested number of significant figures? It asked for 2, did we use two? No, okay what was our rule about zeros to the left? They're not significant, so what's our answer 0.083. Brilliant. So a cyclist travels 30 m in 36 s, calculate their average speed. Give your answer to two significant figures, their average speed is 0.083 m/s."
NB: for KS3 I'd skip the bit about sig figs - they haven't learned about them yet so.
We do Lite (or I do; You Help):
Again, the problem goes on the board, and again I narrate the process and show my workings, only this time, I stop when I get to a number:
"What numbers do we have, what data have we got? Okay, we've got distance which is [pause] Yousef? 100m thank you Yousef. We've got a distance of 100m , and we've got time which is [pause] Samiya? 9.81 s, thank you Samiya, we've got a time of 9.81 s. I want my distance in metres, do I need to convert any units? [Pause] Abdullah? No, fantastic thank you Abdullah. Okay, so what was our next step, it was to find our equation, what is our equation, it's speed = distance divided by time, what was my distance [pause] Emi?" I think you get where this is going, I don't think I need to repeat the whole spiel! Before, I would say the numbers, this time they tell me. I am still writing my workings on the board, I'm still highliting or underlining as before, but this time they're giving me the values.
(All of the student responses in this exercise would possibly be best done with choral response, but I haven't "trained" my classes to respond chorally so it would be a mess. Instead I cold call.)
We do Regular (or You do; I help):
Again, the problem goes on the board. This time, however, I ask for the step and then the number.
"What's our first step [pause] Rahima? Data, thank you Rahima. Okay, what data have we got? [pause] Saira? Distance thank you Saira, and what is our distance [pause] Fatima? 15000 m, thank you Fatima. What other data have we got [pause] Dean? Time, thank you Dean, and what is our time [pause] Mo C? 3600 s, thank you Mo C. Do I need to convert any units [pause] Maryam? No, thank you Maryam. Okay, what was our next step [pause] Brendan? "Equation", thank you Brendan, what is our equation [pause] Fiona? Speed = distance divided by time, thank you Fiona." You catch my drift.
Before, I'd walk them all the way to the number, this time they tell me what step we're taking and the numbers.
You do:
This is not independent yet. The problem goes on the board. I ask for the each step at a time. They give me the answer on their MWBs. (Think slow practical but for equation practice).
"On your MWBs, show me what data have we got? 3,2,1 show me. Okay, on your MWBs show me what was our next step 3, 2, 1 show me. Our equation, brilliant. Okay, so, on your MWBs show me what was out equation 3, 2, 1 show me. Fantastic: speed = distance divided by time. On your MWBs show me our data substituted into our equation 5, 4, 3, 2, 1. Great stuff. Mo B, check you've got your numbers the right way round." And so on and so forth.
By doing it step by step, it forces them to still think about the process, but it also means that I can see very quickly and easily where a student has tripped up. Some people like to get them to write their workings but I find that's still too much to look at and absorb quickly.
I will only move onto the next step once I'm satisfied the students have "got it". If I've got students who are looking at me like I've grown antennae, I probably can't move on just yet. If I've got three or more students who are tripping up, probably can't move on yet. I will generally give me students way more questions than they can reasonably answer in the time I'm going to allot, so I am free, if necessary, to do what were meant to be questions 1 or 2 or even 3 of their independent tasks as worked examples.
Does every lesson look like this? No. In fact, I probably wouldn't use all these steps to introduce speed calculations because it's a concept they're familiar with and the equation isn't tricky. Mole calculations on the other hand, I probably would do all the steps. Acceleration, again more likely to follow all the steps. Sometimes the class grasps what I'm teaching with ease so I'll skip a step. Sometimes it's something historically students haven't found challenging so again, I'll skip a step (I can always go back if I need to). Some classes (my year 10s, my year 8s) are well drilled on how to hand out whiteboards and pens, others (looking at you, year 9) struggle no matter how many times we practice so I am less likely to do the You Do this way. (Yes it might be useful to help them practice how I want the boards handed out but sometimes it's period 6 in Friday and I don't want the battle right now.)
Why is any of this important? If you set the kids off on their independent tasks too early, they get stuck. They can't do it. They lose motivation. They don't get to practice what they know because they don't really know it yet. On the other hand, if you don't let them go off on their own, again they don't get the practice.
Lemov, Doug (2019), Teach Like a Champion 2.0, Second Edition, USA: Jossey-Bass
Willingham, Daniel T. (2009). Why Don't Students Like School?, First Edition, San Francisco: Jossey-Bass