In South Africa, we know we have low numbers of learners doing mathematics and we know we have low achievements in mathematics among the majority of these learners. But we also have another challenge: the quality of our top maths achievements are also being called into question!
At the end of 2019, Professor Sue-Ellen Shay at UCT analysed the students’ results at the end of the first year maths courses at university. She compared these with the Grade 12 maths results with which the students entered university.
Professor Shay found that the learners who had achieved between 80% and 89% at the end of Grade 12, only achieved an average of 47% at the end of first-year maths. This is particularly disturbing as 50% is the requirement to pass Maths 1.
The cause of this problem is related to misconceptions of what learning actually is! A high mark in mathematics is no longer a measure of learning but it has become the goal of learning!
In the pursuit of that goal, learners take short-cuts. They buy books of past exam paper questions and they practise answering these questions. They don’t realise that they are not using their understanding to solve mathematical problems, they are only matching memorised procedures to recognisable question formats. They are only finding the pattern of producing a correct answer – it has nothing to do with any understanding of the concepts.
This method of doing maths only works while the question is presented in the same or similar format, and that is not what happens at university. We must be certain to distinguish between building understanding and showing understanding! The latter cannot happen without the former.
Unfortunately, shortcuts through the use of test preparation materials can mask the lack of understanding in the short term. There certainly is value in preparing for a big exam by familiarising oneself with the design and format of the paper beforehand but this should never be at the expense of learning and understanding the concepts first.
To be clear: learning does not happen through practising test questions!