*In this article, Ruan Moolman argues that there is not one fixed paradigm or strategy for teaching Mathematics. To illustrate this, he briefly discusses three different approaches to Mathematics Education.*

It seems that with so many different views on teaching and learning mathematics, most mathematics education researchers and specialists will always disagree with each other on the best methods to foster learning amongst mathematics students.

From Piagetian to Vygotskian views, or one’s belief in Symbolic Interactionism or that of Anna Sfard’s perspective on how to develop students’ mathematical proficiency, it seems that such disagreements may lead to a hidden form of ‘competitive’ views on mathematical learning.

However, the main question will always remain: what is the best paradigm or framework that lecturers and teachers should follow when it comes to improving their students’ mathematical learning performance?

Instead of having one fixed view and shunning others’ perspectives, it may be best to rather consider how the different paradigms and methods of instruction can complement one another. Below I briefly discuss just some of the beliefs and methods that researchers, lecturers and educators have on mathematics education.

__Jo Boaler: Why Struggle Is Essential for the Brain — and Our Lives__

Jo Boaler is Professor of Mathematics Education at the Stanford Graduate School of Education. Having published a great number of articles and books on students’ learning mathematics, she is a well-known name in the Mathematics Education field. Some of her research has focused on enquiry-based learning, gender equity in mathematics, and the links between timed testing and math anxiety.

In October 2019, Boaler argues in an article for *Edsurge* that it is critical for students to struggle with mathematical problems to obtain mastery of the subject: “…as parents and teachers, we do just about everything we can to make sure that children don’t struggle. It turns out we are making a terrible mistake”, she writes.

Boaler believes that one needs to tell young learners that struggling in mathematics is needed and it is okay to make mistakes. “Students no longer give up on problems when they find them hard—they push through the struggle to the wonderful places on the other side. When students look at me with a puppy dog face and say, ‘This is hard’, I say ‘That is fantastic’. That feeling of ‘hard’ is the feeling of your brain developing, strengthening and growing”.

Boaler notes that students start doubting their mathematical abilities the moment they struggle or see that their peers can solve a problem with ease. She believes that students should realise the importance of struggling since this helps them in their understanding of a mathematical topic.

Maybe we as educators and researchers forget the importance of letting our students know that being stuck with a problem is beneficial to one’s learning, that it is not such a bad thing in finding a problem hard and working through it till you understand it better. Perhaps parents, students and at times educators as well, should ask themselves is it just okay to get the correct answer and merely memorise an algorithm, or is struggling much more important in developing a stronger mind?

One can read more on Jo Boaler’s views on struggling in mathematics at https://www.edsurge.com/news/2019-10-28-why-struggle-is-essential-for-the-brain-and-our-lives

__MindCubeMaths__

Many researchers and educators believe that the best way for learners to develop mathematical proficiency is by utilising ‘exploration’. When working with children at the primary school level, such ‘exploration’ is usually linked with concepts such as ‘fun’ and ‘interaction’, implicitly that learners need to ‘struggle’ with a mathematical problem or concept.

One learning programme that focusses on how to develop children’s understanding of mathematical concepts in a playful manner is that of MindCubeMaths.

The MindCubeMaths programme is designed in such a manner to assist teachers and parents in explaining mathematical concepts and calculations to learners from age 3 to 13 years. MindCubeMaths believes that learners must be also must also be able to discover and learn to understand mathematical concepts by themselves, and one such way is through play.

Jaco van Zyl, the owner of MindCubeMaths notes that the MindCubeMaths programme is ‘a practical interactive course that concentrates on life skills, memory and metacognitive development, self-confidence and mathematical understanding.’

More information on MindCubeMaths can be found at mindcubemaths.com.

__AMSAT – Motivating Critical Thinkers__

Several mathematics and applied mathematics lecturers are concerned that students entering the university lack the needed critical thinking (metacognitive) skills to succeed at university level.

Like MindCubeMaths that focusses on students’ metacognitive development, AMSAT, the Academy of Mathematics, Science and Technology, offers programmes for grade 12 learners and post-matric students, in developing the needed critical thinking skills for success in university mathematics.

AMSAT’s courses give students an advantage by making first-year mathematics less daunting, by preparing students for the demands of university mathematics, and by giving them the confidence and motivation to succeed in university mathematics and mathematics-related subjects.

Through years of observation of first- and second-year university students’ ability to solve mathematical problems, and research on how to improve students’ learning performance in mathematics, AMSAT’s academic director, Dr Ruan Moolman has developed a programme in which students are trained in specifically designed questioning techniques. These questioning techniques enable students to acquire the critical thinking skills needed to succeed in their mathematics studies.

For more information on how AMSAT assists students in preparing for university mathematics, visit www.amsat.academy.

### Ruan Moolman

UNIVERSITY OF CAPE TOWN