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03 October 2018 | Story UFS | Photo Stephen Collett
Using ethnomathematics to enhance understanding maths
An ethnomathematical approach helps to create a connection between mathematics in the classroom and the real world, said Prof Mogege Mosimege during his inaugural lecture.

The integration of ethnomathematical approaches and studies in the teaching and learning of mathematics is almost certainly bound to change how learners view and understand mathematics. It is the opinion of Prof Mogege Mosimege of the School of Natural Sciences and Technology Education in the Faculty of Education at the University of The Free State (UFS), where Prof Mosimege delivered his inaugural lecture.

His research interests include sociocultural contexts in mathematics education (ethnomathematics), mathematical modelling; indigenous knowledge systems and mathematics teacher education.

Classroom maths must connect real world 

He says an ethnomathematical approach does not only serve as a sound basis for a deeper conceptual understanding, but it also helps to create a connection between mathematics in the classroom and the real world.

Prof Mosimege says the foundation phase of the South African school mathematics curriculum indicates, amongst others, that there must be a critical awareness of how mathematical relationships are used in social, environmental, cultural and economic relations, and that there must be a deep conceptual understanding in order to make sense of mathematics.

"I want to argue the current curriculum does not give enough space for that," he says. "The minute you say deep conceptual understanding you must do things differently and not just teach formulae, but also teach why things work the way they do."

Prof Mosimege says the classroom activities teachers engage in must be able to push learners to that deep understanding phase.

He says even at the Further Education and Training Phase real-life problems should be incorporated into all mathematical sections whenever appropriate.

Teachers need to make maths real


"Contextual problems should include issues relating to health, social, economic, cultural, scientific, political and environmental issues whenever possible."

 If done this way teachers will make mathematics to become real. "It will perhaps not be as abstract as it is perceived, and will help our learners and students to understand why it is important to relate what they do to real life."

Prof Mosimege says his future work would be to look past the phase of focusing strictly on procedural aspects of mathematics and look further at an ethnomathematics bridge to mathematical modelling, which is his next area of research. He says the definitions of ethnomathematics suggest that mathematical concepts and processes would be more comfortable and better understood by the learner when they are related to sociocultural contexts as well as real-life situations.

"How can we use ethnomathematics to do problem-solving?" he asks. 

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Media: ANC can learn a lesson from Moshoeshoe
2006-05-20


27/05/2006 20:32 - (SA) 
ANC can learn a lesson from Moshoeshoe
ON 2004, the University of the Free State turned 100 years old. As part of its centenary celebrations, the idea of the Moshoeshoe Memorial Lecture was mooted as part of another idea: to promote the study of the meaning of Moshoeshoe.

This lecture comes at a critical point in South Africa's still-new democracy. There are indications that the value of public engagement that Moshoeshoe prized highly through his lipitso [community gatherings], and now also a prized feature in our democracy, may be under serious threat. It is for this reason that I would like to dedicate this lecture to all those in our country and elsewhere who daily or weekly, or however frequently, have had the courage to express their considered opinions on pressing matters facing our society. They may be columnists, editors, commentators, artists of all kinds, academics and writers of letters to the editor, non-violent protesters with their placards and cartoonists who put a mirror in front of our eyes.

There is a remarkable story of how Moshoeshoe dealt with Mzilikazi, the aggressor who attacked Thaba Bosiu and failed. So when Mzilikazi retreated from Thaba Bosiu with a bruised ego after failing to take over the mountain, Moshoeshoe, in an unexpected turn of events, sent him cattle to return home bruised but grateful for the generosity of a victorious target of his aggression. At least he would not starve along the way. It was a devastating act of magnanimity which signalled a phenomenal role change.

"If only you had asked," Moshoeshoe seemed to be saying, "I could have given you some cattle. Have them anyway."

It was impossible for Mzilikazi not to have felt ashamed. At the same time, he could still present himself to his people as one who was so feared that even in defeat he was given cattle. At any rate, he never returned.

I look at our situation in South Africa and find that the wisdom of Moshoeshoe's method produced one of the defining moments that led to South Africa's momentous transition to democracy. Part of Nelson Mandela's legacy is precisely this: what I have called counter-intuitive leadership and the immense possibilities it offers for re-imagining whole societies.

A number of events in the past 12 months have made me wonder whether we are faced with a new situation that may have arisen. An increasing number of highly intelligent, sensitive and highly committed South Africans across the class, racial and cultural spectrum confess to feeling uncertain and vulnerable as never before since 1994. When indomitable optimists confess to having a sense of things unhinging, the misery of anxiety spreads. It must have something to do with an accumulation of events that convey the sense of impending implosion. It is the sense that events are spiralling out of control and no one among the leadership of the country seems to have a handle on things.

I should mention the one event that has dominated the national scene continuously for many months now. It is, of course, the trying events around the recent trial and acquittal of Jacob Zuma. The aftermath continues to dominate the news and public discourse. What, really, have we learnt or are learning from it all? It is probably too early to tell. Yet the drama seems far from over, promising to keep us all without relief, and in a state of anguish. It seems poised to reveal more faultlines in our national life than answers and solutions.

We need a mechanism that will affirm the different positions of the contestants validating their honesty in a way that will give the public confidence that real solutions are possible. It is this kind of openness, which never comes easily, that leads to breakthrough solutions, of the kind Moshoeshoe's wisdom symbolises.

Who will take this courageous step? What is clear is that a complex democracy like South Africa's cannot survive a single authority. Only multiple authorities within a constitutional framework have a real chance. I want to press this matter further.

Could it be that part of the problem is that we are unable to deal with the notion of "opposition". We are horrified that any of us could become "the opposition". In reality, it is time we began to anticipate the arrival of a moment when there was no longer a single [overwhelmingly] dominant political force as is currently the case. Such is the course of change. The measure of the maturity of the current political environment will be in how it can create conditions that anticipate that moment rather than ones that seek to prevent it. This is the formidable challenge of a popular post-apartheid political movement.

Can it conceptually anticipate a future when it is no longer overwhelmingly in control, in the form in which it currently is and resist, counter-intuitively, the temptation to prevent such an eventuality? Successfully resisting such an option would enable its current vision and its ultimate legacy to our country to manifest itself in different articulations of itself, which then contend for social influence.

In this way, the vision never really dies, it simply evolves into higher, more complex forms of itself. If the resulting versions are what is called "the opposition" that should not be such a bad thing - unless we want to invent another name for it. The image of flying ants going off to start other similar settlements is not so inappropriate.

I do not wish to suggest that the nuptial flights of the alliance partners are about to occur: only that it is a mark of leadership foresight to anticipate them conceptually. Any political movement that has visions of itself as a perpetual entity should look at the compelling evidence of history. Few have survived those defining moments when they should have been more elastic, and that because they were not, did not live to see the next day.

I believe we may have reached a moment not fundamentally different from the sobering, yet uplifting and vision-making, nation-building realities that led to Kempton Park in the early 1990s. The difference between then and now is that the black majority is not facing white compatriots across the negotiating table. Rather, it is facing itself: perhaps really for the first time since 1994. It is not a time for repeating old platitudes. Could we apply to ourselves the same degree of inventiveness and rigorous negotiation we displayed up to the adoption or our Constitution?

Morena Moshoeshoe faced similarly formative challenges. He seems to have been a great listener. No problem was too insignificant that it could not be addressed. He seems to have networked actively across the spectrum of society. He seems to have kept a close eye on the world beyond Lesotho, forming strong friendships and alliances, weighing his options constantly. He seems to have had patience and forbearance. He had tons of data before him before he could propose the unexpected. He tells us across the years that moments of renewal demand no less.

  • This is an editied version of the inaugural Moshoeshoe Memorial Lecture presented by Univeristy of Cape Town vice-chancellor Professor Ndebele at the University of the Free State on Thursday. Perspectives on Leadership Challenges In South Africa

 

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