As we describe the Rules of False Position, it is critically important to realize that the Egyptians and the Babylonians did not know algebra, indeed it did not exist at that time, nor did they have the notion of an equation; hence, they could not make obvious simplifications and they did not work with a general rule (Papakonstantinou and Tapia, 2013:504).
Given the preceding quotation, it is disheartening that in the year 2013, such an ignoramus statement could be made by Joanna M. Papakonstantinou and Richard A. Tapia, two well-placed mathematicians. And if I may quote their brief biographies in The American Mathematical Monthly (vol. 120, no. 6, June-July 2013) in which the statement is made, "Joanna M. Papakonstantinou received her B.A., M.A., and M.A.T., as well as her Ph.D., from Rice University, under the direction of the second author. After completing her postdoctoral work at Rice University in the Computational and Applied Mathematics Department, she joined PROS Revenue Management as a Senior Associate where she served as a science expert in the Center of Excellence. Currently, she works as the Senior Science Consultant at Advanous. She remains involved in research in the field of optimization, writes curriculum and teaches, and actively participates in outreach activities" (Papakonstantinou and Tapia, 2013:517). "Richard A. Tapia, 2011 recipient of the National Medal of Science [the top award the United States government offers its researchers given to him by President Barack Obama--author's note], holds the rank of University Professor in the Rice Department of Computational and Applied Mathematics. He is also the Director of the Rice University Center for Excellence and Equity in Education. Due to Tapia's efforts, Rice has received national recognition for its educational outreach programs and has become a national leader in producing women and underrepresented minority Ph.D. recipients in the mathematical sciences" (Papakonstantinou and Tapia, 2013:517). Even more disheartening is that the editor of the journal, Scott T. Chapman, another well-placed mathematician at Sam Houston State University, the three anonymous referees, and the authors' colleague, Michael Trosset, who the authors credited "for suggestions that greatly improved the paper" (Papakonstantinou and Tapia, 2013:516), ignored the pernicious statement.
It is quite obvious that all of these mathematicians have not read Cheikh Anta Diop's famous work, Civilization or Barbarism (1981/1991), and serious works on African Mathematics in which it is clearly demonstrated that ancient Egypt, in fact, is the origin of Algebra. Algebraic mathematical series, simple equations, quadratic equations, balance of quantities (pesou) were all invented in Egypt. Even the Rules of False Position, which is the main focus of Papakonstantinou and Tapia's paper, were invented by the ancient Egyptians. Add to these the many arithmetic and geometric techniques that were invented in ancient Egypt and other parts of Africa.
Indeed, that Africa was the center of mathematics history for tens of thousands of years is hardly a matter of dispute. From the civilizations across the continent emerged contributions which would enrich both ancient and modern understanding of nature through mathematics. Yet, today, scholars and other professionals working in the field of mathematics education in Africa have identified a plethora of problematic issues in the endeavor. These issues include attitudes, curriculum development, educational change, instruction, academic achievement, standardized and other tests, performance factors, native speakers, etc. (for more on this, see Bangura, 2012). In this paper, I argue that a major reason for these problems is that the mother tongue has been greatly neglected in the teaching of mathematics in Africa. Indeed, as Mamokgethi Setati (1998, 2002, 2003, 2005a, 2005b, 2008) has demonstrated numerously in the case of South Africa, even though teachers and learners who employ African languages in mathematics education position themselves in relation to mathematics and, concomitantly, epistemological access, and use those languages as instruments of solidarity, English is the dominant language in the classroom, its ascendancy privileged by procedural mathematics discourse. This situation must be changed if Africa is to benefit from the tremendous opportunities mathematics offers.
Linguists have for a long time been concerned with the context of teaching any subject/text, be it qualitative or quantitative. Students of linguistics can readily find examples where the meaning of an utterance changes with its contextual framework. The following are examples: (a) General Motors had no success selling the Chevy Nova in Mexico because Nova (no va) means "no go" in Spanish; (b) the "I'm a Pepper" advertisement that was successful in the United States had to be changed in England when Dr. Pepper's management realized that pepper is a slang word for prostitution to the English; (c) the "Pepsi, the choice of a new generation" advertisement translated into Taiwanese got many Taiwanese angry after they flocked to buy Pepsi only to realize that their dead ancestors were not coming back to life. The extent of the problem became more widely known when computer programmers were faced with the vexing task of translating texts. A famous example was an attempt to translate "The spirit is strong but the body is weak" into Russian. The resulting phrase was "The Vodka is stale and the meat is rotten." Yet still, linguists also know that any subject, even mathematics that has become extremely abstract, can be taught effectively in any language once the appropriate tools are made available.
While a great deal of works exists on the nexus between linguistics and mathematics in general, only a small number can be found on the nexus between African languages and mathematics in particular, and these latter works are not linguistics-theoretically grounded. Thus, this essay begins by identifying the objects of study of linguistics and mathematics and delineates which ones they study in common. Next, because the object of study of linguistics is language, the nine design features of language are employed to examine each of the objects as it pertains to African languages and mathematics. The nine design features are (1) mode of communication, (2) semanticity, (3) pragmatic function, (4) interchangeability, (5) cultural transmission, (6) arbitrariness, (7) discreteness, (8) displacement, and (9) productivity.
Since to offer examples for each of these features from each of the more than 2,100 African languages would require at least a book-length manuscript, a small number of examples from a small number of languages across the continent are presented for the sake of brevity. After that, the discussion turns to the role for mathematicians in fulfilling the African Renaissance--defined by Dani Wadada Nabudere as the initiative to recapture the basic elements of African humanism (ubuntu, eternal life, and immanent moral justice) as the path to a new humanistic universalism. He quotes Chancellor Williams as stating that this initiative "is the spiritual and moral element, actualized in good will among men (and women), which Africa itself has preserved and can give to the world" (Nabudere, 2003:4). The proposition in this section is that just as mathematicians had played a major role in the development of African societies during antiquity (see Bangura, 2012), they are sorely needed now to work with experts in other disciplines to help fulfill the African Renaissance. In the end, conclusions are drawn and recommendations are offered.
Thus, the observations made in this paper are not directed at the discovery of any method or pedagogical panacea. They are presented in complete modesty in the belief that what matters most is not the method but the teacher. May the observations serve then, at best, as a starting point for that self-examination. Since teaching about the nexus between African languages and mathematics is one to which many of us are deeply committed, it is the hope that this paper will not only inspire colleagues to give serious consideration to its suggestions and perplexities, but also strive to suggest better solutions than those proposed.
Objects of Study of Linguistics and Mathematics
Before identifying the objects of study of linguistics and mathematics and delineating which ones they study in common, it makes sense to begin with brief definitions of the two fields, with the caveat that, as many linguists and mathematicians have pointed out, providing concise and meaningful definitions of these fields on which everyone can agree is virtually impossible. Nonetheless, to avoid providing working definitions of the fields will cause more havoc than it solves. Linguistics, according to Francis Dinneen (1995), can be generally defined as the scientific study of language. Mathematics, following Keith Devlin (2003), can be generally defined as the systematic study of change, quantity, relation, space, structure, and other topics dealing with entity, form, and pattern. Consequently, these italicized aspects of the definitions constitute the objects of study for the two disciplines, whether they are dealing with numbers, other fields, hypothetical abstractions, or other things.
With this backdrop of what linguistics and mathematics are and their objects of study, the question to be probed here then should be about those objects the two fields study in common. The answer must show that the two disciplines are parallel and must interact where they happen to coincide, especially since there is even a sub-discipline in linguistics called mathematical linguistics.
The most common answer one usually finds in many textbooks and articles is that mathematics is a universal language among the numerous different languages spoken all around the world and...