Dedicated to the promotion of excellence in mathematics and physical science education.
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.
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.
A baseline study conducted by the Ukuqonda Institute in April-June 2019, conducted in 30 primary and 15 secondary schools, revealed very low levels of performance in computation, right up to Grade 7 and even Grade 10. Analysis of the data revealed a number of specific challenges in the mathematics programmes currently delivered in schools. The major challenges observed in terms of learners’ constitute opportunities for constructive intervention and are listed below.
Low levels of quantity awareness at school entry and higher levels, and little provision for the development of quantity awareness in the preschool and Foundation Phase curriculum. Low levels of quantity awareness constrains learners’ capacity to make sense of numbers and of computation.
Insufficient understanding of larger numbers as composites of smaller numbers (e.g. 37 is thirty and seven) and hence of the positional notation for multidigit numbers. This is sometimes described as “learners not understanding place value”,and the baseline data indicated this as a major cause of poor performance in computation in Grades 3 to 7. This weakness in learners’ knowledge often results in learners resorting to operating on the digits without regard for the quantities (numbers) represented by the digits, a phenomenon we refer to as “digitisation”. This problem is deep-rooted and it is associated with the tendency, observed for many learners, to interpret numbers by counting (drawing stripes, even for large numbers) instead of by decomposition into smaller parts.
Premature introduction of formalised formats of exposition for computation, with insufficient opportunity for learners to apply their minds to computational tasks by themselves and to represent their own thoughts, prior to being required to utilise standardized formats of exposition. This problem stems from the flawed belief held by most teachers that learners can only do what they are shown to do, hence that teaching mathematics should essentially consist of demonstration followed by repetitive practise. Teachers need to experience learners’ potential to act in mathematically meaningful ways when engaging with questions that make sense to them, without being told/shown what to do.