Anne then began an initially bizarre session with number grids but then got us to consider the thought process she had gone through to decide on how to present each part of the lesson to us. Here are some of my thoughts:
- began by determining the terms involved: domino, cover etc.
- allowed us to choose our own shape: gives students a sense of personal engagement as well as meaning each student may be working on slightly different questions; deliberately disallowed the simple bar to avoid laziness!
- initially gave us the 100 multiplication grid then made it easier
- chose 7 addition grid next as it avoided any erroneous multiplication patterns that may have been found from even number grids
- the progression to a 8 addition grid provided an incentive to generalise, which was then forced when we were presented with a problem of an n addition grid
- we were tasked with writing our own questions similar to the ones that Anne had posed to us: this could be used to write a homework, using the pupils own ideas, or potentially a match up of shapes and co-ordinate sets
Van Hiele Levels of Geometrical Thought
Starting from the very basic thought process, Van Hiele define the levels as:
- Visualising: seeing whole things
- Analysing: describing, noticing same / different
- Abstraction: distinctinons, relationships between tasks
- Informal deduction: generalising, identufying properties
- Rigour: formal deduction, properties as new objects
Full definitions of the Van Hiele levels.
This way of thinking is not restricted only to top set with other groups just using arithmetic!
Adolescents are very concerned with identity (writing name on objects), belonging, being heard (but don't always know how to get your attention), being in charge (even of giving advice to the person next to them), being supported, feeling powerful (feeling that their idea was really important), negotiating authority (maths is the authority in the classroom), arguing in ways that makes adults listen.
"There are very few things in maths that can't be checked if the right tools are given."
Finding tasks can have either one or multiple answers, and maybe even define a class of these answers. A closed question can still open up your thinking!
Aside on powerpoints ... might be useful to have dots on a page where things will turn up.
Controlling parameters in examples helps students to see patterns and generalise, ie. introduce sequences as:
2, 4, 6
2, 5, 8
2, 6, 10
Rather than just choosing random examples, like the mish-mash that seems to be found in textbooks.
Gradient exercise: might have to know p-q-r-s question to do earlier questions even if it hasn't been explicitly written down, kind of like catching a ball and parabolas.
Lesson Planning
There is no research that shows that starter, main and plenary is the best way to structure a lesson. A plenary doesn't need to be at the end, as it is coordinating the whole class discussion and summarising ideas.
Lots of stuff about Japanese styles of teaching was discussed, the notes on it can be found at https://weblearn.ox.ac.uk/portal/hierarchy/socsci/education/pgce/maths/page/resources
at some point in the very near future!
The day concluded with a PDP lecture on Adolescents which was infinitely more engaging than the last!
