## Concrete Pictorial AbstractUsing concrete material as a first step before moving into visualising and extending ideas. ## Bar Model methodUsing double number line to teach concepts such as percentages, ration and proportion helps students to develop a better understanding. ## The two basics: basic knowledge and basic skills taking a spiral approachConceptual understanding and Procedure Skills mutually reinforce each other Keep a balanced view about the Two Basics and other aspects of maths learning (for example, high-order thinking skills). Teaching with Variation can help expand the Two Basics. Students need to experience variation for the new concepts to be learnt. Varying each task within a sequence of tasks will help learning. This can be divided in two types: Examples, non-standard examples and counterexamples play a crucial role in Variation. As with CPA, there is a role for multiple representations (see CPA). Marton, Runesson and Tsui (2004) formulate the functions of variation like this: **Contrast. “… In order to experience something, a person must experience something else to compare it with…”****Generalisation. “… In order to fully understand what “three” is, we must also experience varying appearances of three …”****Separation. “… In order to experience a certain aspect of something, and in order to separate this aspect from other aspects, it must vary while other aspects remain invariant.”****Fusion. “…if there are several critical aspects that the learner has to take into consideration at the same time, they must all be experienced simultaneously.”**
Teachers should try to accumulate a large number of examples of teaching different topics using variation. For more information visit Future Learn online course. |