A slice of pizza is not a triangle! Exploring mathematical precision from the start.

We’ve been running our training session on Language of Maths in a few schools recently which includes the use of Frayer Models which have been discussed in previous blog posts.

When discussing language such as triangles and squares it is very common for the following things to happen:

  • Pupils to be provided with only REGULAR examples of shapes (e.g. a triangle with 3 equal sides and orientated so that the horizontal base is on the bottom, pentagon with 5 equal sides etc.).
  • Pupils to be provided with imprecise examples of shapes – in the triangle example, this might be showing them the musical instrument called a triangle or a slice of pizza… neither of which have the properties of a triangle.
  • Only naming rectangles where one pair of parallel sides is longer/shorter than the other pair.  A square is also a rectangle… just a special type of rectangle where all the sides are equal in length.  This means that a square is always a rectangle but a rectangle isn’t always a square.
  • Only sharing examples of the objects but not non-examples.  Using non-examples that are similar to the language/item you are trying to explore but not exactly the same can support pupils understanding.  By knowing what something is not, you can make better sense of what it is.

If pupils develop an imprecise understanding early on, this may cause problems in the future!

Take a look at this video with Doug Clements who explores this in more detail and then try to think about your own practice.   Click on the image of the video to be taken to the site where you can watch it.

Screen Shot 2019-12-11 at 12.52.38.pngWhat ideas related to understanding of shapes and their attributes are you supporting your pupils to make sense of through the activities you provide for them? 
Is there anything that you could improve on or that needs to change?

A thorough and correct understanding from the beginning is crucial if pupils are to have greater success with geometry later in their school careers but also to develop their spatial awareness which is vital in our everyday lives.

Take a look at these other two short videos of young pupils exploring shapes as well as making sense of examples and non-examples. Click on the image of the video to be taken to the site where you can watch it.

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Job Opportunity

For any PSAs in the Highland area, please see the advert on My Job Scotland for 3 PSAs fixed term until the end of March. Closing date is tomorrow – sorry for short notice, I hadn’t realised the job advert had been put out already.

This will be an exciting opportunity to work alongside the Highland Literacy and Numeracy Development Officers to provide additional literacy and numeracy support to pupils to help close the poverty related attainment gap.

Follow the link for more details: https://bit.ly/2Y5MnTs

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Upcoming CPD – November and December

29th November:
Mastery in Mathematics

Free CPD event run by La Salle Education and hosted by Inverness High School.  Follow link and book your place online if you are interested in attending: https://completemaths.com/cpd/mastery

3rd to 5th December:
Multiplication, Division, Language and Bar Models!

We still have a few spaces left on our training sessions next week.  The same day will run on three consecutive days – times and locations below.

The day is for probationers however the remaining spaces are open to anyone who wishes to attend.  Feedback from non-probationers who attended the first event earlier in the year found it very useful.  We deliver similar training in schools and so would hope that teachers would find it valuable regardless of their prior teaching experience.

The day will largely be focussing on multiplication and division taking a journey from Early Level to the end of Second Level and a little beyond.  We will also be exploring language and pre-teaching vocabulary as well as the use of bar models.  It should be an informative and action-packed day!!!

Sessions will be as follows:

Tuesday 3rd December: Inverness Royal Academy CPD Suits (enter through sports hall) 9.30am – 3.30pm

Wednesday 4th December: Alness Academy 9.30am – 3.30pm

Thursday 5th December: Inverness High School 9.30am – 3.30pm

If you wish to attend please sign up on the Highland CPD site.

11th December:
Teachmeet UHI

Teachers from Highland and Moray are being invited to attend the Teachmeet at UHI on Wednesday 11th December from 5pm – 7pm.  The session will be aimed at secondary maths teachers or primary teachers with an interest in maths in the upper stages.

Sign up using the Google Form, entry is on a first come first serve basis.

I’ll hopefully see some familiar faces there.

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Cuisenaire Rods Extravaganza!

I am a huge fan of Cuisenaire Rods.  They are probably the most versatile concrete material I’ve come across and can be used to teach such a vast array of mathematical ideas in ways that pupils (and adults) can really make sense of.

I frequently come across schools who assure me they have no Cuisenaire Rods only to find deep trays of old faded wooden rods hidden away in a cupboard or in a draw that someone thought was just some wooden construction blocks for the P1s to play with… it is so much more than this!

If you haven’t ever come across or used Cuisenaire Rods, I can almost guarantee they will change your life (from the perspective of teaching maths anyway).

Here are a couple of older videos from the 60s with their extensive use being highlighted by Dr Caleb Gettagno.

This first one is one of three…  you can find the others on YouTube if you are so inclined (they are worth a watch)

And another here exploring them in a slightly different way:

If you want to read and learn more about Cuisenaire Rods, you can check out this free ATM open resource: Working with Rods and Why

Or you can follow this link for a series of books by Gettagno himself (all available for free online): https://issuu.com/eswi  (Scroll down to find the titles… some are related to subjects other than maths.)

So, what are you waiting for!  Go and have a look in that dusty old cupboard and dig out the Cuisenaire.  If it’s not there then see if you can encourage your school to purchase some – it is definitely worth it!

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Educational Research – Espresso Research by Cambridge Mathematics

I find educational research fascinating but it’s a bit like diving into the rabbit hole in Alice’s Adventures in Wonderland (written by Lewis Carroll, writer and mathematician who came up with the Carroll diagram).  It can be endlessly interesting but endlessly frustrating at the same time.

While driving up North today and listening to another of Mr Barton’s Podcasts, I was listening to an older episode with Lucy Rycroft-Smith and came across Espresso Research by Cambridge Mathematics.  How I haven’t come across this before I don’t know but now I can share it with you all!  In their own words, Espresso is… ‘a small but intense draught of filtered research on mathematics education, expressly designed with teachers in mind.’ 

Research related to a particular question is summarised in a handy two-page document but for those who wish to delve deeper (and this is where I can see more hours of my life disappearing), links are provided to all the referenced research.  Unless you are in an educational institute, it can sometimes be hard to access journal articles so these links are very handy!

I was looking something specific up when I arrived at my destination and suddenly found myself reading another four articles and I still haven’t looked at the one I had intended to find!

So for anyone else interested in keeping up to date with research that directly impacts our profession, I would definitely recommend you take a look: https://www.cambridgemaths.org/espresso/ 

Here’s a link to one of the issues I read today about Introducing early algebraic thinking:Screen Shot 2019-11-25 at 21.52.41.png

 

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Next steps… another video

Hopefully people enjoyed the video I put on looking at ‘Next steps’ for pupils.  Here is another one which explores a few different ideas.

 

As always, any feedback people have is more than welcome both in terms of what you liked and what you didn’t like.  For the latter, any suggestions on how this could be improved to make it better are always welcome.

Enjoy!

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Next Steps… Videos

As part of the new online training we’re piloting for the diagnostic assessments, we’ve included some ‘Next Steps…’ videos.  These possibly make more sense viewed alongside the pupil completing the assessment so you can put it into context better but my hope is that they are useful as stand alone videos as well.

Take a look at the video below which covers a range of ‘next steps’ for an older pupil who is experiencing some difficulties with grouping and place value, basic facts and addition and subtraction.  These difficulties are some of the most common difficulties I see in schools so will probably seem familiar to many of you and as such the video will hopefully give some insight as to how they might be addressed.  Depending on the particular idea being discussed, there are ideas here that would be relevant as low as P1 and P2 but also older pupils into secondary school who are experiencing difficulties.

It would be great to get any feedback about:

  • Whether the video was useful and you’d like to see more of this type of thing and specifically what was useful about it.
  • Whether there was anything you didn’t like.
  • What you thought about the length?  Too long, too short, just right… 
    If it was too long, what would you want to cut out?
    If it was too short, what else would you want included?
  • Whether it works as a stand alone video without the accompanying video of the pupil being assessed.
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