Our attention, confirmed by a baseline study that we conducted in 25 primary and 15 secondary schools, has been drawn to the needs that exist in especially the earlier grades. Our study revealed very low levels of performance in computation, right up to Grade 7 and even Grade 10.

Analysis of the data revealed several specific challenges in the mathematics programmes currently delivered in schools.

Low levels of quantity awareness,

Insufficient understanding of larger numbers as composites of smaller numbers,

Premature introduction of formalised formats of exposition for computation,

Ineffective teaching and learning of fractions,

Concept of variable and algebraic notation.

We believe these challenges constitute opportunities for constructive intervention and the details are listed below. Read More

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 constrain 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 multi digit 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.

Ineffective teaching and learning of fractions. With the persistent struggle experienced by learners with the fraction concept, it is strongly suggested that this may partly be due to unsuccessful programmes of teaching and learning. In the above mentioned baseline study only 17% of Grade 7 learners produced the correct answer for , while 34% gave the answer (adding the numerators, and adding the denominators). This indicates that learners do not understand as one fifth and as one tenth. And even at the high school level, only 4% of grade 8 learners gave the correct answer for the question “What is biggest, or ?”

Learners who do not understand fractions as quantities expressed in units smaller than one, e.g. 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.
Further, without proper understanding of fractions, learners can not understand decimals…which is simply a different notation for fractions. For example, 0,367 means and without understanding this learners can not have a sense of what 0,367 means or how computations with such numbers can be done. Neither can they understand percentages, since 37% (for example) is just a special notation for 37 hundredths, which can also be expressed as 0,37 or .

If learners have a proper understanding of fractions and computations with fractions, they do not need the special methods for calculating with percentages which are currently taught and consume much classroom time unnecessarily.

Concept of variable and algebraic notation. Few learners exhibited any understanding of the concept of variable (meaning of x, y), specifically the meaning of brackets, which is at the core of basic algebra and poor mastery of algebraic notation.