Self-evaluation Tools Results: Understanding Shape/Geometry

The NCETM has a series of tools for analysing how confident you feel about various areas of mathematics. Part of the MaST programme requires me to complete each area over time. I also have to complete the sections for a range of Key Stages – 1, 2 and 3 – to demonstrate a broad knowledge of the subject.

Here are my results for the Understanding Shape/Geometry sections. (1 is not confident and 4 is very confident)

Key Stage 1 – Understanding Shape

1. How confident are you that you understand the relationship between angle as a measure of turn?
2. How confident are you that you can give relevant examples to illustrate the meaning of reflection?
3. How confident are you that you can give relevant examples to illustrate the meaning of line or reflection symmetry?
4. How confident are you that you know common side, angle and symmetry properties of polygons?
5. How confident are you that you know common side, angle and symmetry properties of triangles?
6. How confident are you that you know common side, angle and symmetry properties of squares and rectangles?

I answered 4 for each of these, giving me an outcome of very confident. I chose 4 for each of the answers as, reading through the examples given, I use the techniques described and go deeper too, being a Key Stage 2 teacher.

Key Stage 2 – Understanding Shape

Again, I answered 4 for each of these questions, giving me an outcome of very confident. I chose 4 because of the ways I have used to teach shape over the years in Years 5 & 6. I use pull up nets to show how the 5 Platonic solids are made, regularly discuss the properties of shapes – especially the range of triangles – with my class. One minor concern was the use of ICT in the first 6 questions, but I consider my SMART Notebook slides to be using ICT and I rarely teach a maths lesson without one.

Key Stage 3 – Geometry

1. How confident are you that you are aware of a range of visualisation activities to help pupils to appreciate properties and transformations of shapes? (3)
2. How confident are you that you understand through practical activity and the use of ICT the meaning of translation? (4)
3. How confident are you that you understand through practical activity and the use of ICT the meaning of reflection? (4)
4. How confident are you that you understand through practical activity and the use of ICT the meaning of rotation? (4)
5. How confident are you that you understand through practical activity and the use of ICT the meaning of enlargement? (4)
6. How confident are you that you know the meanings of alternate angles, corresponding angles, supplementary angles, complementary angles? (3)
7. How confident are you that you can prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles, the sum of the angles in a triangle is 180° and the sum of the exterior angles of any polygon is 360°? (4)
8. How confident are you that you can prove that the opposite angles of a parallelogram are equal? (3)
9. How confident are you that you know the conditions for congruent triangles and can prove that the base angles of an isosceles triangle are equal? (3)
10. How confident are you that you know how to establish through geometrical reasoning the side, angle and diagonal properties of quadrilaterals? (3)
11. How confident are you that you know how to execute and prove the standard straight−edge and compass constructions? (3)
12. How confident are you that you know how to describe simple loci? (2)
13. How confident are you that you know how to explain and prove some circle theorems? (3)
14. How confident are you that you understand Pythagoras’ theorem and its application to solving mathematical problems? (4)
15. How confident are you that you can explain the conditions for similar triangles? (4)

This held some trepidation for me, as I haven’t ever really considered the Key Stage 3 curriculum before now for geometry while teaching. My answers are in brackets above and a mainly a mix of 3s and 4s with one 2. This gave me and outcome of confident. The 2 is for the question about simple loci – a choice made because I can’t remember having done any locus work in years! (The locus of a point is its path when it moves according to given rules or conditions. The plural is loci.) I think, having read the examples on the NCETM site, that I could certainly do the work for myself, but would probably struggle to teach it.

Where I chose 3, it is often because I felt I fully understood most of the content but there were areas where I may not have been able to give examples. In question 6, for instance, I would be fine with alternate angles, corresponding angles and complementary angles but may confuse supplementary angles.

Clearly from this, I need to develop my knowledge of some of the Key Stage 3 geometry material.