# REVISITING THE MATHEMATICS OF OUR ANCESTORS

Joshua Abah Abah

► To cite this version:

Joshua Abah Abah. REVISITING THE MATHEMATICS OF OUR ANCESTORS. Joshua Abah ABAH. Joshua Abah ABAH, 2020, Joshua Abah ABAH, 978-978-58675-0. 10.5281/zenodo.4706229. [https://hal.science/hal-03203710](https://hal.science/hal-03203710)

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Submitted on 21 Apr 2021

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## About The Book

Long before the advent of publishing, the people of Nigeria are known to openly display their rich cultures and traditions. Embedded in this expressive culture are tangible evidence of mathematical elements in the form of geometric shapes, numbers, counting systems and exotic patterns. Ancient Nigerian peoples and cultures devised numbering systems, counted objects, constructed homes, and designed works of art based on mathematical principles that are presently taught in schools under different names. Still, many indigenous perspectives in mathematics are fading into oblivion, further mystifying the subject. This book uses the scoping review framework to showcase early revolutionary reactions to the suppression of information on the development of indigenous mathematics in Nigeria. It traces ample scholarly evidence of Nigerians' skills in the use of numbers and other elements of mathematics long before the arrival of the White Men. This work is intended to serve as a bridge to our noble mathematical past as preserved by great thinkers from diverse fields, locations and cultures. It sought to beam the searchlight on what we are missing as modern academic societies when we turn our back on rich instructional aids hidden in the cultural practices of our people.

## About The Author

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Joshua Abah ABAH is a researcher in the Department of Mathematics Education, Federal University of Agriculture, Makurdi, Nigeria. His research interests are Technology of Mathematics Education, Ethnomathematics, Statistical Computing, and Instructional Design. He is happily married to Christy and the marriage is blessed with two children, Prime and Hephzibah.

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ISBN:

REVISITING THE MATHEMATICS OF OUR ANCESTORS

# REVISITING THE MATHEMATICS OF OUR ANCESTORS

A Scoping Review of Early Scholarly Works on the Mathematical Systems of Nigerian Peoples and Cultures

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Joshua Abah ABAH

Joshua Abah ABAH
REVISITING THE
MATHEMATICS OF OUR
ANCESTORS

*A Scoping Review of Early Scholarly Works on the Mathematical Systems of Nigerian Peoples and Cultures*

Joshua Abah ABAH

<figure><img src="image_4.png" /></figure>

Network for Grassroots Science and Mathematics Education

(The VillageMath Network)

https://ngsme.villagemath.net
<figure><img src="image_5.png" /></figure>

REVISITING THE MATHEMATICS
OF OUR ANCESTORS

A SCOPING REVIEW OF EARLY SCHOLARLY
WORKS ON THE MATHEMATICAL SYSTEMS OF
NIGERIAN PEOPLES AND CULTURES

Joshua Abah ABAH
Copyright © 2020 Joshua Abah ABAH

Network for Grassroots Science and Mathematics Education

(The VillageMath Network)

Department of Mathematics Education

Federal University of Agriculture, Makurdi, NIGERIA
# PREFACE

This book bears a catchy name. But the title is apt in drawing attention to the benefits accruable from *Ethnomathematics* as a paradigm in Mathematics Education. Ethnomathematics requires a dynamic interpretation because it describes concepts that are themselves neither rigid nor singular, namely “ethno” and “mathematics”. The term “ethno” describes all of the ingredients that make up the cultural identity of a group: language, codes, values, jargon, beliefs, food and dress, habits, and physical traits. Mathematics expresses a broad view of mathematics which includes ciphering, arithmetic, classifying, ordering, inferring and modeling. Many educators may be unfamiliar with the term, yet a basic understating of it allows teachers to expand their mathematical perceptions and more effectively instruct their students.

Teachers and the public in general do not commonly say that Mathematics and culture are connected. When teachers do acknowledge a connection, often they engage their students in multicultural activities merely as a curiosity. Such activities usually refer to a culture's past and to cultures that are very remote from that of the children in the class. This situation occurs because teachers may not understand how culture relates to children and their learning. An important component of Mathematics education today should be to reaffirm, and in some instances to restore, the cultural dignity of children.
Although multicultural Mathematics activities are important, they should not be our final goal. As students experience multicultural mathematical activities that reflect the knowledge and behaviours of people from diverse cultural environments, they not only may learn to value the Mathematics but, just as important, may develop a greater respect for those who are different from themselves.

To acquire requisite skills while maintaining cultural dignity and to be prepared for full participation in society require more than what is offered in the traditional mathematics curriculum. Much of today's curriculum is so disconnected from the child's reality that it is impossible for the child to be a full participant in such reality. The Mathematics in many classrooms has practically nothing to do with the world that the children are experiencing. Just as literacy has come to mean much more than reading and writing, Mathematics must also be thought of as more than, and indeed different from, counting, calculating, sorting, or comparing. Considering that today's children are living in a civilization that is dominated by mathematically-based technology and unprecedented means of communication, it is safe to assert that much of the content of current Mathematics programmes does little to help students learn the information and skills necessary to function successfully in this new world.

The goal of Mathematics Education should be to foster students' ability to successfully use modern technology to solve problems and communicate their thinking and answers as they
gain an awareness of the capabilities and limitations of
technological instruments. The school system can help students
realize their full mathematical potential by acknowledging the
importance of culture to the identity of the child and how culture
affects the way children think and learn. Children must be
taught to value diversity in the mathematics classroom and to
understand both the influence that culture has on Mathematics
and how this influence results in different ways in which
mathematics is used and communicated. Such an understanding
is gained through the study of ethnomathematics.

Ethnomathematics as a programme studies the cultural
aspects of Mathematics. It acknowledges that there are different
ways of doing Mathematics by considering the appropriation of
academic mathematical knowledge developed by different
sectors of the society as well as by considering different modes
in which different cultures negotiate their mathematical
practices. Ethnomathematics researchers investigate ways in
which different cultural groups comprehend, articulate and
apply ideas, procedures, and techniques identified as
mathematical practices. These mathematical practices refer to
forms of Mathematics that vary as they are embedded in cultural
activities. Ethnomathematics presents the mathematical
concepts of the school curriculum in a way in which these
concepts are related to the cultural backgrounds of students,
thereby enhancing their ability to make meaningful connections
and deepening their understanding of Mathematics.
Culture is a learned behaviour consisting of thoughts,
feelings and actions and is transferred in social interaction.
Within every culture, there exists indigenous knowledge which
encompasses the complex, intergenerational and cumulative
experiences and teachings of the indigenous peoples. However,
many contemporary educational researchers agree that there is
a discontinuity between the home or community culture of
students and the education they receive in mainstream schools.
The lack of relevance of school Mathematics to the learners'
everyday life and culture suggests that there is need to
incorporate into the mathematics curriculum such cultural
practices, ideas and beliefs that would connect the school to the
community in which it exists and functions. Educators,
academics and policy makers have called for more research
that addresses gaps in understanding of culture-based
Mathematics Education.

Culture-based Mathematics Education is teaching and
learning of Mathematics that takes into consideration the context
of the learners, blending academic and vocational
competencies. Contextualization is based on the proposition
that people learn more effectively when they are learning about
something that they are interested in, that they already know
something about, and that afford them the opportunity to use
what they already know to figure new things out. The use of
locally relevant contexts-situations and phenomena that have
local and personal meaning to students and teachers for whom a
curricular product is designed, provides access to educational
and social participation and opportunity at multiple levels of practice. In other words, Culture-based Mathematics Education, in addition to attending to academic goals, must take seriously the ways students' experiences are structured by policies, institutions and societal practices and work with students to confront them.

This work, *Revisiting the Mathematics of our Ancestors*, is a response to the call for more enlightenment on the pre-historic mathematical practices of the ancient peoples of Nigeria. The book intends to clarify that pre-colonial Nigeria is not at all “primitive” as many history books would want us to believe. The use of such terms as “primitive” would be considered as derogatory in the light of the remarkable scholarly evidence gathered in this work. The considerations in this book should ultimately provide a solid footing for researchers of Nigeria’s Ethnomathematics and encourage classroom practices that imbibe culture-based Mathematics Education.

Joshua Abah ABAH
2020
# TABLE OF CONTENT

<table><tr><td>Title Page</td><td>--</td><td>--</td><td>--</td><td>--</td><td>--</td><td>--</td><td>i</td></tr><tr><td>Copyright Page</td><td>--</td><td>--</td><td>--</td><td>--</td><td>--</td><td>--</td><td>iii</td></tr><tr><td>Preface</td><td>--</td><td>--</td><td>--</td><td>--</td><td>--</td><td>--</td><td>iv</td></tr></table>

## CHAPTER ONE

<table><tr><td>Ethnomathematics in a Digital World</td><td>--</td><td>--</td><td>1</td></tr><tr><td>Introduction</td><td>--</td><td>--</td><td>1</td></tr><tr><td>Digitizing our Cultural Heritage</td><td>--</td><td>--</td><td>4</td></tr></table>

## CHAPTER TWO

<table><tr><td>Overview of Scoping Review</td><td>--</td><td>--</td><td>13</td></tr><tr><td>Introduction</td><td>--</td><td>--</td><td>13</td></tr><tr><td>Typology of Literature Review</td><td>--</td><td>--</td><td>15</td></tr><tr><td>What is Scoping Review?</td><td>--</td><td>--</td><td>25</td></tr><tr><td>Process of Scoping Review</td><td>--</td><td>--</td><td>32</td></tr><tr><td>Format of Scoping Review</td><td>--</td><td>--</td><td>37</td></tr></table>

## CHAPTER THREE

<table><tr><td>Methodology</td><td>--</td><td>--</td><td>42</td></tr><tr><td>Introduction</td><td>--</td><td>--</td><td>42</td></tr><tr><td>Title</td><td>--</td><td>--</td><td>42</td></tr><tr><td>Review Question</td><td>--</td><td>--</td><td>42</td></tr><tr><td>Review Objective</td><td>--</td><td>--</td><td>43</td></tr><tr><td>Review Protocol</td><td>--</td><td>--</td><td>43</td></tr></table>

## CHAPTER FOUR

<table><tr><td>1800-1919</td><td>--</td><td>--</td><td>48</td></tr><tr><td>1886: Notes on the Numeral System of the Yoruba Nation (Adolphus Mann)</td><td>--</td><td>--</td><td>48</td></tr></table>
## CHAPTER FIVE

<table><tr><td>1920 - 1969</td><td>53</td></tr><tr><td>1920: Duodecimal Base of Numeration (N.W. Thomas)</td><td>53</td></tr><tr><td>1962: Yoruba Numerals (Robert G. Armstrong)</td><td>59</td></tr></table>

## CHAPTER SIX

<table><tr><td>1970 - 1979</td><td>63</td></tr><tr><td>1970: Mathematics of the Yoruba People and of thier Neighbors in Sourthern Nigeria (Claudia Zaslavsky)</td><td>63</td></tr><tr><td>1973: Africa Counts: Number and Pattern in African Cultures (Claudia Zaslavsky)</td><td>78</td></tr><tr><td>1975: The Geometry of African Art: Catalog of Benin Patterns (Donald W. Crowe)</td><td>84</td></tr><tr><td>1978: Change in Mathematics Education since the late 1950's - Ideas and Realization (R. Ogbonna Ohuche)</td><td>101</td></tr></table>

## CHAPTER SEVEN

<table><tr><td>1980 - 1989</td><td>103</td></tr><tr><td>1984: The Sorry State of Mathematics Education in Nigeria (Peter N. Lassa)</td><td>103</td></tr><tr><td>1984: Integrating Traditional Games and Play Activities into Primary Science Education Programmes (Eunice A. Okeke)</td><td>104</td></tr><tr><td>1988: Historical and Ethnomathematical Algorithms for Classroom use (Lawrence Shirley)</td><td>110</td></tr><tr><td>1989: Mathematics in Rural Societies (Sam O. Ale)</td><td>112</td></tr></table>

## CHAPTER EIGHT

<table><tr><td>1990 - 1999</td><td>119</td></tr><tr><td>1995: The Combinatorics of Mancala-type Games: Ayo, Tchoukaillon, and 1/[(Duane M. Broline and Daniel E. Loeb)]</td><td>119</td></tr><tr><td>1997: The African Heritage of Benjamin Banneker (Ron Englash)</td><td>124</td></tr></table>
CHAPTER NINE

2000 And Afterwards -- -- -- -- -- -- -- -- 130

2001: Science and an African Logic (Helen Verran) -- -- 130

CHAPTER TEN

Conclusion -- -- -- -- -- -- -- -- -- -- -- 134

References -- -- -- -- -- -- -- -- -- -- -- 137
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