Learning Stuff About Stuff

I have been using my mobile phone to record video feedbacks for homeworks this session. I post them as unlisted videos on Youtube and give the link to the pupils.

I expect all my pupils to attempt corrections once I have given them feedback on their formal homeworks, so I need the feedback to be good quality.  I have used two models:  individual feedback based on the pupil's own homework, and general feedback for the whole class.  The latter is obviously quicker, and is probably sufficient if the same errors are cropping up in most of the homeworks.

Here's why I'm using videos for feedback:

Verbal feedback is much richer than a few scribbled words and symbols in a jotter;I find it easier to give verbal feedback than to try and express myself in writing in a pupil's jotter;I do not have time to give verbal feedback to all pupils during class time. I do have time to record a wee video as I mark each piece of homework*;Video feedbacks are available to pupils as they are at…

Today my S2 class spent a lesson doing some mathematical thinking.  The prompt for this was an Nrich task, More and More Buckets. They are a high level set class, and this particular problem would not have been appropriate for all classes, but there are Nrich tasks to suit all ages and levels of prior learning.

This S2 class is used to the idea of "doing some mathematical thinking".  The pupils appear to understand that I am interested in the process rather than any particular conclusion they may reach.  They work on the task in groups of 3-4. Here are a few examples of the artefacts of their thinking:

This group were trying to find a formula.  They laid out possibilities in an organised list, and spotted some interesting patterns.

This group took a more qualitative approach - they did very well to analyse the problem sufficiently to reach this simple summary.


This group decided that it was helpful to think about the numbers that were missing each time, and this layout (whic…

The S3 class mentioned in the last post is a group which I am aiming to lead towards National 5 maths by the end of S4, but this is a wildly ambitious target.  Based on previous cohorts, I could reasonably expect only about half of the class to get there. This is one of those "could go either way" classes.  There are plenty of pupils in the class who are regularly getting into trouble around the school, but there are also many who are conscientious and hard working across the school.  Given that the class is behaving excellently and making good progress, I'm writing this post as a reminder to myself for the future.

Here are the strategies I have consciously employed with the class:

Consistent use of AiFL techniques in class - lollipops, think-pair-share, celebrating wrong answers  etc etcExplicit discussion about growth vs fixed mindsets (Carol Dweck's work).Zero tolerance of disruptive behaviour, backed up with generous praise, particularly for those who mend their w…

No, I haven't got a video of pets wearing hats.

This "awww" moment came this afternoon as my S3 class were queuing up outside my classroom.  I had asked a general "how has your day been today?" and had a few responses from others, then one of the girls said "good now we're at maths!" with a big smile on her face.  "Yes" said her friend.  "We were saying at lunchtime how much we are enjoying maths now you are teaching us." "Yes" said the first girl. "You make it so easy.." She saw the expression on my face freeze, and hastily added "no, not easy - but we have learned so much with you." "Yes, I've learned so much maths this year." I mumbled something about it having been their hard work that had made the difference.

What a delightful moment!

A two part question to determine if you "think like a mathematician," from Prof. Eugene Luks, Bucknell University, circa 1979.

Part I: You're in a room that is empty except for a functioning stove and a tea kettle with tepid water in it sitting on the floor. How do you make hot water for tea?

Answer to Part I: Put tea kettle on stove, turn on burner, heat until water boils.

Part II: Next, you're in another room that is empty except for a functioning stove and a tea kettle with tepid water in it sitting on a table. How do you make hot water for tea?

Non-mathematician's answer to Part II: Put tea kettle on stove, turn on burner, heat until water boils.
Mathematician's answer to Part II: Put the tea kettle on the floor.

I recently bought a class set of overlapping decimal dart cards for the department - this pdf link is essentially the same resource.

I used them today with a class of 14 yr olds, all of whom have been working with decimals for at least two years, but none of whom were able to correctly order this list of decimals at the beginning of the lesson:

0.26
0.102
0.2
0.8
0.13
0.7
0.34

I did not tell them the correct order - just that none had got it right.

I handed out the decimal cards and started by asking them to hold up the one that would go exactly half way between 0 and 1 on the numberline I had on the board. 100% success.

I then asked them to show me whereabouts on the line 0.1, 0.01 and 0.001 would go.

We discussed this for a while, corrected some misconceptions, and moved on with the idea under our belts that 0.1 is small, 0.01 is tiny and 0.001 is incredibly tiny!

I then asked them to hold up the decimals that represented 4 tenths, 7 hundredths, 3 thousandths etc. All got there after a bit of di…

I shared these two versions with a class recently. I'm sure you can guess which model better matches their perception of what is supposed to be going on in the classroom.

Model 1

"Mr Jones know loads of maths. His job is to transmit some of the stuff he knows to me, so I can use it in my life, my further studies and the exam at the end of S4."

Model 2

"Mr Jones has a version of maths in his head, that he has created over the years, in response to teaching, reading, activities he has undertaken etc. I also have a version of maths in my head, which I have been building since I was born. Mr Jones's job is to provide me with experiences and feedback that will help me to construct a bigger, better version of maths in my head."

Working after school with a pupil...

Me: How many of these [10cm lengths] would you need to make a 30cm length?
Pupil: 3
Me: Ah okay, so back to the problem, how many would you need for 300cm?
Pupil: [with a "got it now!" tone of voice] would it be 30?
Me: [with a slightly questioning tone of voice] What makes you say that?
Pupil [utterly deflated] I don't know, I don't think I understand.
Me: Really? You sounded quite confident before. 
... we spiralled around and back to the same problem, and the pupil eventually went with 30 and told me how they had got it.

Me: before, when I asked why you thought it was 30, with a tone of voice that maybe seemed like I disagreed, you went to pieces a bit didn't you, even though you really thought you knew why it was 30. I wonder why that happened.
Pupil: [pause as tears well up in eyes] I think it's because when my Mum helps with me with my maths she gets frustrated with me if I don't get it straight away - like she thinks I…