Failure to acquire key concepts early on in primary school, and at appropriate stages thereof, can constrain effective learning of mathematics over several grades.
- Learners with low awareness of quantity may not be able to make sense of computation when first having to engage with it in the second term of grade 1, and may then suspend personal agency in engaging with numbers and may adopt and become entrenched into a receptive and rote approach to learning mathematics. Analaysis of written work done by learners indicated a high incidence of learners adopting such an approach.
- Learners who do not understand the positional notation for numbers larger than 10 early in Grade 2, cannot make sense of computation with multidigit numbers which is introduced from Grade 2 onwards, and may resort to digitisation: acting on the digits without regard for the numbers represented by different digits. Digitisation may become a habit persisting into the higher grades, strongly undermining learner performance in computation.
- Learners who do not understand fractions as quantities expressed in units smaller than one, e.g. 5⁄8 as 5 eighths, and who do not have a sound concept of equivalent fractions as different ways of expressing the same quantity as a fraction, can not make sense of computation with fractions. Such learners are prone to a systematic error like 1⁄5 + 1⁄10 = 2⁄15, which was committed by 41% of Grade 5 learners, 45% of Grade 6 learners and 34% of Grade 7 learners in the baseline assessment study.