Teaching considerations

When developing teaching and learning programs for students working at the figurative counting stage, teachers need to consider:

Strategy development

Students working at the figurative stage of counting are unable to draw from a wide range of strategies to solve number problems. Therefore there is a need to model effective strategies. At this stage the main focus for teaching should be on developing skills in counting - on and counting-back to solve number problems. This will also be a major indicator when assessing students’ abilities.

Teachers need to ensure that students are given opportunities to practise the strategy of counting-on and counting-back in small-group, pair and individual activities. Be aware that students who demonstrate the ability to use counting-on-and-back may revert to the strategy of counting from one when they are presented with difficult tasks or more complex numbers.

Language development

As students develop additional problem-solving strategies, teachers need to explicitly teach the mathematical language needed to explain ideas and solutions. Vocalising the procedures used enables students to clarify their thinking and reinforces concepts. It also creates opportunities to listen to the thinking of peers and learn from the strategies used by others. Listening to a range of student problem solving approaches, questioning how, when and why strategies work can be used to address misunderstandings and help form generalisations.

Numeral identification

Students need to be exposed to as many representations of an amount as possible as this awareness is vital to understanding the flexibility that exists within mathematics and numbers. Students should be able to use a vast array of concrete and visual representations of amounts, varying colour, shape, size, object and orientation. Numerals and number words need to be presented and discussed using a range of font types, colours and contexts. Discussions about the similarities and differences between representations should be regularly included in learning opportunities.

For students working with figurative strategies it is important to explore numbers beyond 20 with the same richness they experienced at the emergent and perceptual stages. Teachers should provide regular learning experiences where students are supported to recognise ten as a unit.