The process of learning




Look at this summary from the Grade 6 Maths SA CAPS curriculum for the Term 1 curriculum and its seemingly random order of topics and compare it with a thread design which shows how each concept builds on the concepts before it and are used to make understanding in the concepts ahead.


Now it is easy to see how a backlog can develop! A problem with an early concept can have a ‘knock-on’ effect, making it impossible for a learner to understand the successive concepts that build on that ‘problem’ concept. This creates a gap between the learner’s expected understanding for the grade they are in and their real understanding which has got ‘stuck’ years back.



Here is an example of a Grade 9 learner’s results on a diagnostic test of key concepts in fractions presented on a thread design.

Notice that the learner is proficient on both the Grade 3 fraction concepts. The learner is proficient on Grade 6 level except for the concepts of Rounding Decimals and Subtracting Decimals. However, the learner is not proficient at Grade 9 level in any of these concepts even though the learner is actually in Grade 9.

These results show learning backlogs at a concept level. You can see that the learner has backlogs on every concept shown: three years of a backlog on 8 concepts and an even greater number of years behind on the other 9 concepts.




  1. Big Ideas and Understandings as the Foundation for Elementary and Middle School Mathematics – by Randall Charles