The Eight Zones
Development of the LAF
The Learning and Assessment Framework for Multiplicative Thinking (LAF) was developed on the basis of a detailed item analyses (Rasch Modelling) on data collected from approximately 3000 student responses to multiplicative assessment tasks administered at the beginning and end of the Scaffolding Numeracy in the Middle Years (SNMY) project.
The analysis dealt with predicting the probability of correct responses to test items as a function of student’s ability. The probability scale predicts the level a student is likely to be performing at 50 percent of the time. In terms of teaching implications this means that students need further consolidation of the concepts and strategies indicated at this level while being introduced to aspects of the next level.
More information about the SNMY research project and its methodology is available in the project background section of this site. Technical reports and other documents related to the research are available in the resource library.
How to use this resource
The LAF brings together, in a hierarchy, all the key ideas, strategies and representations of multiplication and division needed to work flexibly and confidently with whole numbers, fractions, decimals and percent across a wide range of contexts.
You can also download the LAF as a document showing all eight zones and teaching implications.
More information
Using the resources on this site, you can also:
- Compare across zones by downloading Learning and Assessment Framework as a table (PDF - 83Kb)
- Find out more about multiplicative thinking
- Read about how the LAF was developed through project background