Adult learners need to learn to interpret and solve particular kinds of number problems for their individual purposes. As their tutor, you have to be able to analyse the problems the learners need to solve and identify the demands and supports that such problems present to the learners.
This section provides a guide to mapping (analysing) the kinds of problems that adult learners need to be able to solve in relation to the learning progressions.
Mapping problems against the progressions
The learning progressions for numeracy reflect both number knowledge and strategies for solving number problems. The examples offered in this section and in Appendix A show how the demands of number problems can be mapped against these progressions. These examples show the approximate step (or difficulty level) that a learner would need to be working at in order to meet the demands of a particular task or problem.
To determine the challenges of the actual number problems that learners are expected to solve, you need to compare typical examples of these problems with the numeracy progressions and make decisions about each problem in relation to each progression. By comparing this information with what you know about the learners’ knowledge and strategies skills, you will be able to determine the priorities for teaching and learning.
The examples provided are models to help you work out how to analyse the problems the learners will need to solve. Not every problem needs to be analysed in such detail, but it would be worthwhile analysing problems that are fundamental to a course.
General process for all numeracy strands:
- Identify the strand or strands involved.
- Identify the progression or progressions involved.
- Identify the appropriate step in each applicable progression.
If the problem relates to the Make Sense of Number strand, ask yourself:
- Does the problem involve working out a calculation and/or knowing facts about numbers?
- If it involves a calculation, which of the three strategies progressions are applicable? If it involves knowing facts, which of the three knowledge progressions are applicable?
- Which step on the progression is the ‘best’ fit for the size of numbers in the problem?
Analysing problems in this way will help you to decide the nature and amount of scaffolding (guided support) you will need to provide for the learners. For example, if you know that a learner does not have the knowledge of place value required by the problem, then this is what you need to teach to enable the learner to solve the problem.
Identifying complex demands
Many everyday work, social, personal and community activities present a wide variety of demands that cross over the (artificial) boundaries between ‘numeracy’, ‘literacy’ and other realms of knowledge and expertise. In order to make teaching and learning manageable, it may be necessary to break down a task (for example, conducting a stocktake and ordering from a catalogue) into component parts and then identify the task demands in relation to the learning progressions. You can go on to decide whether to address the demands one at a time or to select parts that can be addressed together, depending on the most immediate needs of the learner.
To use the stocktaking example noted above, the demands of reading a catalogue to find and record items could include:
There will no doubt be other factors involved in the task, but by identifying the demands in relation to the progressions, you can combine this information with information about the learning needs of individual learners (see Knowing the learner) to make decisions about what to teach first