Tag Archives: Geometry

Guest Post: Reflecting on ICT In Maths Through The Lens of SAMR

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This post was written by Mr Ben Hilliam and was originally posted on his blog here.

Throughout this year I have been using Microsoft OneNote with my students at St Andrew’s College. Sam McNeill has a fair account of how I have been using it here with my year 9 one to one computing class, and I have been constantly reflecting on how I can continue this journey.

Using the SAMR model, I have currently been operating in the Substitution and Augmentation stage, where technology replaces some traditional aspects of teaching, such as “Chalk and Talk”, but with some added advantage. In my case, having examples, notes and work always live and accessible to students through Microsoft OneNote and also recording my lessons as I deliver them and link them back to my class OneNote. This is a very teacher orientated model and I would like to see students more empowered through their use of technology.

In the last topic I covered with my year 9s, Geometry, I took OneNote to a new level, setting up my students with their own editable OneNotes within the class OneNote:

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Here you can see the topic tabs up the top and the lesson pages down the side. You might also notice some tabs to the right of the topic tabs with names on them. These belong to my students. In their OneNote, they can only see their own OneNotes and edit them, whereas I can see them all as tabs and also edit them with the purpose of giving feedback.

Here is a sample of some student work:

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In this case the student is investigating circle geometry, with a triangle whose hypotenuse is also the diameter of a circle. Incidentally the program used for drawing the circle, triangle and measuring the angles is Geometer’s Sketchpad. While there is nothing revolutionary about the learning happening here, the thing I really like about it is the efficiency. When this task is done without digital technology could easily take up a whole lesson, but this task took no more than 10 minutes. With Geometer’s Sketchpad, the student was able to investigate the properties of the triangle by fixing a triangle’s diameter into a circle, then vary the two shorter sides while measuring all the angles.

He was able to quickly copy and paste some questions and a sample of their drawing. This gave the student a framework to explore a rich aspect of geometric reasoning. I like that in this case, time can be given to this rich task, where many mathematics teachers would simply draw the example, say the rule and get the students to copy it down.

When I reflect on where this task sits in the SAMR model, I feel that to an extent it is still mostly Augmentation. But there are aspects of modification. The ability to investigate a geometric rule using Geometer’s Sketchpad has modified the way I teach the topic in so much as it is a much more containable and manageable task within the confines of a 50 minute period. However, the way the student articulates themselves by pasting and commenting in OneNote is augmenting what they would do with pen and paper (and scissors and ruler and compass).

It will be interesting to see how my students perform in their next Geometry assessment. But I feel they have had more time to grapple with why these rules work rather than just apply them to a situation.

In terms of moving towards Redefinition on the SAMR model in this context, at the moment I am not sure how I would go about that. Perhaps I could get groups of students to explain different Geometric rules then the class can share their results using OneNote.

Maths! Cameras! Tessellations!

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I love it when I get tip-offs from teachers about something they have seen or heard from another class, as this shows our staff are increasingly sharing what is happening inside their classrooms which is excellent.

Recently I was told to check out what Mr Hayden Shaw, Year 7 teacher and Head of Preparatory Sport, was doing with his Maths class. It was suggested there were enthusiastic students hunting around the College for examples of tessellations and then taking photos of them. I have to admit that I didn’t remember my own primary school maths, and the nature of what exactly a tessellation was eluded me.

A quick catch up with Mr Shaw reminded me of exactly what a tessellation is:

an arrangement of shapes closely fitted together, especially of polygons in a repeated pattern without gaps or overlapping.

It transpires that towards the end of a unit on Geometry, Mr Shaw grouped his class based on who had a smartphone with a camera in it. There were eight students with one, and so in groups of three they set out to explore the campus hunting for tessellations. These are just some of the examples they came across:

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The idea behind this fantastic kinaesthetic learning activity came after Mr Shaw read a report on one of his students from Socially Speaking (an organisation that provides services for children with social, sensory or communication difficulties). The report suggested that some students would benefit from taking photos of their homework and then talking about it, rather than physically writing it down every time.

From this came the “tessellation hunt” activity, with students required to snap a photograph of a tessellation they located on the St Andrew’s College grounds and text it to Mr Shaw back in the classroom. When the students returned, he then displayed them all to the students via the classroom interactive projector.

I asked how comfortable he was having students take out their cellphones and use them for learning activities and he related a story that reinforces the College’s approach to Digital Citizenship. There had been an issue with some students taking photos of others in the playground without permission and so discussions took place in the classes reinforcing that phones were:

  • Only for ringing / texting a parent.
  • Permission was required from the teacher before they could do this.
  • If a student took it out twice without permission it was confiscated.

This eliminated the inappropriate use straight away. Once students understood the boundaries, teachers were then able to get them using their phones to support their learning such as this example, knowing that the students would be responsible.

The students in the class loved the opportunity to get out of the classroom and see the practical examples of tessellation in their school environment.