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What mathematical ideas were emphasised?
In this section we report the mathematical ideas and methods which were emphasised in lessons, so that from these students would form views about what mathematics is, and what they were expected to do. In some lessons there was nothing explicitly emphasised - neither a mathematical content idea nor an aspect of thinking or being mathematical.
| Key mathematical ideas | Mathematical methods |
|---|---|
| Purpose of definition v. description | Construct theories from the results of your activity |
| Algebra as the way to express mathematical generalities | Predict and test |
| Infinity is a limit | Experimental v. theoretical |
| Equivalence | Not guessing |
| What the equals signs in formulae mean | Importance of deductive reasoning |
| Inverses | Identify significant features of the work done? |
| Representation | Exemplification |
| How particular numbers can be categorised and why | Linking from visualisation to reproduction on paper |
| When to be accurate, when to estimate | Decide between different methods |
| Use non-integers | Rigour, being precise in what is said |
| Look for similarities | Break down a problem into understandable chunks |
| Maths is everywhere - look around for it | Maths learning takes time - e.g. historical acceptance of negative numbers |
Pages in this section:
- How did teachers help students
- How did teachers use questions
- How was discussion managed
- How were ideas shared
- How were right answers dealt with
- How were wrong answers dealt with
- Lesson structures
- Lesson structures details
- Observations about lesson comparison
- Public writing in lessons
- Questions and prompts
- Strategies to support independent learning
- Task types used
- What habits have been established
- What ideas were emphasised
- What questions were answered quickly
- What was said about what is important
- What were lessons like
- What were lessons like details
- What writing were students asked to do
