Specific mathematical learning
The acquisition and application of facts, concepts, strategies and procedures is fundamental to the development of students’ knowledge, skills and understanding in Mathematics and needs to be reflected in teaching and learning programs. Facts, concepts, strategies and procedures are interrelated and interdependent and should be taught simultaneously.
1. Facts
Examples of teaching strategies that support students in the acquisition and application of facts include:
- providing frequent opportunities for practice so that students can recall facts quickly and efficiently
- providing opportunities for generalisation. For example, after practising addition facts to 10, students are asked to generate examples related to their everyday lives. After practising 4 + 2 = 6, a student might give the example ‘I had 4 dollars and got 2 dollars pocket money, now I have 6 dollars.’
- teaching related facts together. For example, students learn that +1 facts are equivalent to the next number in the counting sequence when counting by ones.
2. Concepts
Examples of teaching strategies that support students in the acquisition and application of concepts include:
- explicitly relating new knowledge to students’ background knowledge within and between strands and across KLAs (eg in Stage 1, counting forward by 2 from 2 relates to the pattern 2, 4, 6, 8 …)
- providing examples of the application of concepts to assist students to recognise the contexts in which the concepts are useful (eg in Stage 1, using concrete materials to model how the fraction ½ relates to division)
- relating teaching and learning to a ‘big idea’
- using learning experiences relevant to the students’ lives (eg in Stage 1, students gather data about favourite foods/TV shows and record the data using tally marks)
- explicitly teaching mathematics-specific language for the particular concept or unit of work
- drawing attention to the key features of a concept to assist generalisation (eg a rectangle has the following features: four straight sides, four corners, four right angles)
- explaining the meaning of mathematical symbols so that they are learned with understanding (eg the ‘=’ sign means ‘is equal to’ not ‘find the answer’, therefore the use of the sign in 8 + 2 = 10 and 8 + 2 = 6 + 4 is appropriate)
- highlighting similarities between related facts and procedures to support conceptual understanding (eg understanding that 5 × 3 and 3 × 5 are equivalent reduces the number of number facts a student needs to remember)
- providing examples and non-examples of concepts
- using a variety of visual representations for concepts (eg representing three-dimensional objects using concrete materials, dot paper, computer animation and nets)
- teaching concepts from concrete to semi-concrete to symbolic.
3. Strategies
Examples of teaching strategies that support students in the acquisition and application of mathematical strategies include:
- modelling strategies using explicit and planned language
- guiding students’ practice during the acquisition phase of learning
- providing feedback on students’ use of strategies
- identifying the strategy a student is currently using and guiding the student in the use of more efficient strategies. For example, when adding 2 and 8, a student is currently counting on from the first number to find the total (ie the student counts ‘2 … 3, 4, 5, 6, 7, 8, 9, 10. The total is 10.’). The student is guided to identify and count on from the larger number to find the total (ie the student counts ‘8 … 9, 10. The total is 10.’)
- teaching when it is, and when it is not, appropriate to apply a strategy. For example, in Stage 1, counting back from a number when subtracting is an appropriate strategy when the number being subtracted is small (ie appropriate for 19 – 2 but not for 18 – 15).
4. Procedures
Examples of teaching strategies that support students in the acquisition and application of procedures include:
- modelling procedures using explicit and planned language
- guiding students’ practice during the acquisition phase of learning
- providing ongoing practice in the use of particular procedures to build fluency
- monitoring students’ selection and use of procedures
- promoting the use of particular procedures, where appropriate, using a variety of examples. For example, in Stage 1, representing the same data using column graphs and picture graphs involves collating information and representing data using one-to-one correspondence.
