Mathematical modelling can reduce failure in maths in schools
COMMENT
Are South African learners set up for failure in maths? According to the latest International Mathematics and Science Study, conducted in 2019, which assessed general mathematical and scientific knowledge, particularly reasoning and problem-solving skills of learners worldwide, only 37% of grade 5 and 9 learners in South Africa acquired basic maths knowledge.
South Africa’s average maths achievement was lower than other developing countries, such as Bulgaria, Oman and Poland. This poor achievement average not only puts the prospects of thousands of our children at risk but also threatens our country’s growth and development.
This led me to ponder about just how learners are taught the subject at school level.
A 2017 meta-analysis on effective education interventions in sub-Saharan Africa revealed that teaching methods have a powerful effect on learner achievement. The report was conducted by Katharine Conn, a senior research scientist and a former evaluation consultant for The World Bank’s education research group, co-ordinating impact evaluations in education and public health for Innovations for Poverty Action in Africa.
One wonders, therefore, just how maths content is taught in South Africa, whether it is done in an abstract way that learners do not understand or in a manner that they can apply to their specific contexts
For maths to be meaningful and applicable in the real world, it is critical to expose learners to mathematical modelling as part and parcel of teaching strategy. Mathematical modelling is a way of explaining real-life problems in mathematical language, using formulas to comprehend and find innovative solutions to issues and validated in real life afterwards. Many teachers tend to avoid teaching maths in a manner that connects learning to real-life problems or situations. This is one of the most challenging exercises in teaching.
Sadly, the problem has persisted, despite many scholars backing teaching maths in a meaningful and practical way. In research conducted in Singapore in 2013, Tan and Ang found that independent mathematical modelling experiences with reflection activities shape knowledge of essential aspects of maths.
In Germany, a 2015 study by Maike Hagena revealed that fostering measurement sense improves mathematical modelling performance. Research in 2018 in Argentina by Villarreal and co-researchers established that digital technologies, such as the internet; spreadsheets; mathematical software and programming languages significantly affect the process of finding mathematical solutions and validation. According to them, there is a correlation between problem-posing and the use of digital technologies.
However, the difficulty in solving real-life problems becomes bigger if one considers the disparity between the simulated maths word problems taught in the classroom and the actual mathematical modelling conditions learners face daily. As such, mathematical modelling is central to grasping our world and empowering designers to create technology for tomorrow.
With mathematical modelling, we can find solutions to our energy crisis, address climate change and deal with poverty. For example, to apply mathematical modelling to unemployment, we use a few common steps:
- Start with the issue of unemployment by talking to the people involved.
- Clarify the need. For instance, people want to be able to get jobs, buy land and look after the health of their families.
- Encode these as mathematical equations, particularly the cost of a qualification, prices of properties and average expenses for a household.
- Take data from universities’ information brochures, house agencies and medical institutions etc to determine an estimated monthly income accurately.
- Use these as initial conditions to solve the equations for 12 months (using a calculator) to give an annual income.
- Conclude and update the envisaged income.
- Present and explain the results in a way that most can comprehend.
Teachers should consider mathematical modelling in its cultural context to fully appreciate its richness. As mathematical modelling is a vehicle to link maths to contextual problems, it is an indispensable way to approach the teaching and learning of maths. For this reason, many countries, such as the Netherlands, Belgium, Germany, France and the US, include mathematical modelling in their school curricula.
It is also worth noting that, in South Africa, the further education and training maths curriculum statement lists mathematical modelling and the inclusion of contextual problems as one of its specific aims.
This, therefore, asks the question of why mathematical modelling is not fully implemented in the classroom in South Africa and why it is not integrated into the teachers’ assessment practices, as prescribed in the maths curriculum.
First, one should apportion part of the blame to traditional teaching methods that teachers adopt at the expense of constructive approaches to actively engage learners in solving real-life problems.
Second, applications in many classrooms occur mainly in the context of dressed-up word problems. Mathematical modelling could also be complex for learners and teachers due to the gap between curriculum aims and school practices, beliefs about mathematical thinking and insufficient teacher training.
Last, one could attribute this discrepancy to some teachers’ negative attitude towards mathematical modelling. Teachers may lack confidence, be unmotivated to use mathematical modelling or not value and enjoy mathematical modelling as a vehicle to introduce contextual problems into maths content. Thus, a positive attitude shift towards mathematical modelling could enhance its application in the classroom.
While it might be challenging to shift attitudes, it is worth noting that, as far back in 1991, Paul Ernest, a professor of mathematics education and philosopher, raised the point that a shift in teaching depends fundamentally on the teachers’ system of beliefs, and in particular, on teachers’ conception of the nature of maths and mental models of teaching and learning maths.
Teachers’ attitudes are often deeply rooted, hard to change and relatively permanent. However, in-service training opportunities on teaching and assessing mathematical modelling can lay a foundation for a change in attitudes. A re-emphasis on conceptual understanding of maths will contribute to its meaningfulness. Assessments that include mathematical modelling will also ensure that the topic is taught and learned in the classroom.
Mathematical modelling counteracts maths failure at school level. Maths would be a less complex subject if teachers implemented mathematical modelling in South African classrooms like in many other countries.
If teachers exposed learners to mathematical modelling, South African learners’ problem-solving skills and conceptual understanding of maths would be applicable in the workplace.
Learners exposed to meaningful maths will understand and apply maths to their living worlds. Those who comprehend mathematical modelling can help to solve South Africa’s problems, including the energy crisis, climate change and poverty.
Professor Erica Spangenberg is deputy head of department in the Department of Science and Technology Education, University of Johannesburg. She writes in her personal capacity.