Teaching considerations

Strategy development

As students develop a wider range of arithmetical strategies, teachers need to model and explain the appropriate use of these methods in problem-solving. Students need to be provided with opportunities to explore student-invented strategies and other methods, recognising when particular strategies are most efficient and situations when they are not. This will support students in becoming competent in selecting and using the most efficient strategy.

Teachers need to ensure that students are given opportunities to practise their strategies. Be aware that students may revert to counting-on-and-back 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 methods 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

Whilst using the arithmetical strategies associated with counting-on-and- back, students may be working at various levels within 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 using counting-on-and-back strategies it is important to explore numbers up to and beyond 100 with the same richness they experienced at the emergent, perceptual and figurative stages.