Teaching Grade 12 Euclidean Geometry

Do you think, as maths teachers, we take mathematical ability for granted? When I was in Sub B (Grade 2) I was seated in the group that was good at maths.  My school was piloting a project called New Maths. Now that I’m older (and uglier), I understand that they were getting us to develop conceptual understanding before teaching us the methods of adding, subtracting, multiplying and dividing. I really enjoyed this and it made a lot of sense to me. But was that because I have a natural ability?

Leigh proposed that we use a similar approach to teaching Euclidean Geometry. She proposed that we introduce the pictures of the theorems and test them in investigations. After that we introduce numeric and abstract problems. It is only once we have done all of that, that we show how to prove the theorem.

I would not have thought this would be her recommended method. Actually, I suspect most teachers first introduce the formal proofs of the theorems, and then do problems using them. Maybe this method is a little like handing Tolstoy’s War and Peace to a Grade 1 and then use it to teach them how to read. Maybe that’s why we’re all so scared of this section, we start with the difficult part.

Two weeks is not enough time to go into depth with this work. The Grade 11 work is also examinable and Euclidean Geometry is meant to be 50 marks of the 150 mark paper 2. Anyone else feeling panicked? So, what are we going to do about this?

At this point in the year, it’s impossible to prepare them only in class. The learners will need to do some work at home. Here are some possible resources you could give to them:
Mindset resources for Grade 10 Euclidean Geometry
Mindset resources for Grade 11 Euclidean Geometry
Mindset resources for Grade 12 Euclidean Geometry
At the top of each of these pages, you’ll see a button that says ‘Download the Series Guide’. Each series guide contains a list of links to other websites which are appropriate for this section.

Let's take a look at Leigh's slides.

---

5 Point Teaching Strategy

• Make sure the necessary basics are in place so they do not hinder the learning.
• Explain the theorem in a visual and numeric fashion.
• Work numerically with the theorem.
• Move towards abstract problems.
• Now prove the theorem with rigour.

---

3 Pressure Points (or in this case, the lies we tell ourselves)

• You can either do geometry or you can not.
• There are no techniques you can teach your pupils to make the section more accessible.
• Geometry should be left to last as it is time consuming.

---

Tips and Tricks

• Learning Theorem statements does not help pupils to use the theorems effectively.
• The visual pictures of the theorems help them to identify the theorems in problems.
• Making sure the necessary background is in place to explain the theorem.
• Teach pupils’ ways to use the rigour of geometry to help solve a problem.
• Teaching them techniques from mathematical logic also helps to streamline their proofs and gives them direction.
• Use colour to draw out what you need.

---

The Geogebra links we looked at:
http://www.geogebratube.org/student/m87673
http://www.geogebratube.org/student/m46860

---

Do you have any resources you want to share with us and the world? If you submit them to us (complete with the secret code displayed on screen during the webinar), you could win a phone or a tablet. See http://digitalclassroom.co.za/digitalclassroom/webinars/webinar-competitions for more details.

Until next time, happy teaching!