As a newly qualified teacher, really thinking about the pedagogy is so important to me and something I struggle with sometimes. Jo said the idea of exploring topics in depth came about from sharing a class with a non-maths specialist. She asked him to cover the topic of angles and he took two lessons to cover what Jo would have spent 6-8 lessons on. During my PGCE year, I felt pressure to move quickly through topics but felt sometimes I missed the opportunity to really check the students understanding.
When thinking about planning a topic Jo's key tips of things to think about are:
- topic progression
- primary curriculum
- assessment (prior knowledge assessment & end of topic assessment)
- misconceptions
- resources
- stretch and challenge
Here is a SATs question that tests students knowledge of opposite angles, angles in a quadrilateral and the notation of a right angle. I think I underestimate what is covered in KS2 so being aware of what they have seen is important. Equally important, however, is to not underestimate the forgetting that goes on over the summer between year 6 and year 7. A reason I was so surprised by what is covered is that a lot of my students don't come across like they have seen these things before.
By the end of KS2 some of the things that have been covered in relation to angles are as follows:
- Rotations (quarter, half, 3 quarter turns)
- Obtuse and Acute angles
- classify shapes
- angles in a quadrilateral add up to 360 degrees
- angles on a straight line add up to 180 degrees
- Opposite angles are equal
Jo then highlighted some common (and not so common) misconceptions that students have when dealing with angles.
1) The misunderstanding of what is meant by angles on a straight line add up to 180 degrees.
Students incorrectly believe that angle b is equal to 150 degrees as there are two angles and they are on a straightt line, therefore, believe they add up to 180 degrees. Jo talked about the importance of language in definitions and encouraged teachers to use definitions such as:
1) adjacent angles on a straight line add up to 180 degrees
2) angles at a point on one side of a straight line add up to 180 degrees
In conjunction with a really clear definition, showing examples and non-examples is really important so students know what fits the definition and what doesn't. I can see how that would really help reduce misconceptions.
There were a few heated comments about the how much emphasis should be on the fac that an angle is a measure of turn. I will admit it is not something I'd ever really thought about and whilst I do think it is important, it is so easy to get lost in that core meaning. I do feel a little sad that some educators couldn't phrase their questions or beliefs in a more considered manner when someone kindly gave up their time to share some amazing ideas.
Jo talked about introducing different notations early on in year 7 which I believe is really important. Students must be familiar with the different notations use to describe angles and triangles and straight lines and I think these help with other topics later on, like constructing triangles and vectors.
Now I initially had doubts at how Jo felt teaching angles could take so long (with no parallel lines either!!) so she helped us by breaking down what should be covered.
Straight Lines
- standard horizontal straight line with one angle labelled and the other missing
- vertical straight line with one angle labelled and the other missing
- Straight line with angles hidden within other shapes
- 3 angles on a straight line
- a straight line with angles on both sides
- multi-step straight line problems
Angles in a triangle
- measuring angles in a triangle
- demonstration that angles in a triangle add up 180 degrees
- basic two angles given, find the missing angles
- angles in a triangle combined with angles on a straight line questions
- substitution of algebra ( x=30, y = 40, z = ?)
- multiple triangles in one question
- triangles in a rectangle - using interior angles of a quadrilateral add up to 360 degrees
- equilateral and isosceles triangles rules to use
- Algebra - single letters
- Algebra - single letters (in isosceles triangles)
- Algebra - letters and numbers (need to rearrange and solve)
- writing reasons for each step of a problem
- Angle proofs in triangles
- Problem-solving questions
- GCSE questions that are accessible for year 7
There was so much wonderful information to take in and I can't possibly do justice was Jo was saying and she has made her slides available here. I really hope I have a chance to hear Jo speak again and it has really inspired me to do some similar planning for some other topics as it has given me so much to think about.
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