11 - Fractal Complexity in Mamokgethi Setati’s Work on the Nexus between African Languages and Mathematics
CODESRIA Bulletin,
No. 03-04 (2013): CODESRIA Bulletin, Nos 3 & 4, 2013
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- Adeleke, Tunde. 2009. The Case against Afrocentrism. Jackson, MS: University Press of Mississippi.
- Awoonor, Kofi Nyidevu. 1990. Ghana: A Political History. Accra, Ghana: Sedco Publishing Ltd. and Woeli Publishing Services.
- Ayittey, George B. N. 2011. Defeating Dictators: Fighting Tyranny in Africa and around the World. New York, NY: Palgrave Macmillan.
- Ayittey, George B. N. 1999. Africa in Chaos. New York, NY: Palgrave Macmillan.
- Ayittey, George B. N. 1993. Africa Betrayed. New York, NY: Palgrave Macmillan.
- Bangura, Abdul Karim (ed.). 2013. Fractal Complexity in the Works of Major Black Thinkers, Volumes One and Two. San Diego, CA: Cognella Press.
- Bangura, Abdul Karim. 2012. A mathematical exploration of fractal complexity among the axioms on the African state in the Journal of Third World Studies: From John Mukum Mbaku to Pade Badru. Journal of Third World Studies xxix, 2:11-64.
- Bangura, Abdul Karim. 2012. Fractal complexity in Cheikh Anta Diop’s Precolonial Black Africa: A pluridisciplinary analysis. CODESRIA Bulletin 1&2:10-19.
- Bangura, Abdul Karim. 2012. Fractal complexity in Mwalimu Chinua Achebe’s Things Fall Apart: A mathematical exploration. Critical Interventions 9/10:106-121.
- Bangura, Abdul Karim. 2008. African Peace Paradigms. Dubuque, IA: Kendall Hunt Publishing Company.
- Bangura, Abdul Karim. 2005. Ubuntugogy: An African educational paradigm that transcends pedagogy, andragogy, ergonagy, and heutagogy. Journal of Third World Studies xxii, 2:13-53.
- Bangura, Abdul Karim. 2002. Sojourner- Douglass College=s Philosophy in Action: An African-Centered Creed. San Jose, California: Writers Club Press.
- Bangura, Abdul Karim. 2000. Chaos Theory and African Fractals. Washington, DC: The African Institution.
- Brown, Clifford and Larry Liebovitch. 2010. Fractal Analysis. Thousand Oaks, CA: Sage Publications.
- Brown, Gillian and George Yule. 1983. Discourse Analysis. Cambridge, UK: Cambridge University Press.
- Cabral, Amicar. 1995. Identity and dignity in the context of the national liberation struggle. In F. L. Hord (Mzee Lasana Okpara) and J. S., eds. I Am Because We Are: Readings in Black Philosophy. Amherst, MA: University of Massachusetts Press.
- Chafe, Wallace L. 1972. Discourse structure and human knowledge. In R. O. Freedle and J. B. Carroll (eds.). Language Comprehension and the Acquisition of Knowledge. Washington, DC: V. M. Winston.
- Cooper, Anna Julia. 1995. Womanhood: A vital element in the regeneration of progress. In F. L. Hord (Mzee Lasana Okpara) and J. S., eds. I Am Because We Are: Readings in Black Philosophy. Amherst, MA: University of Massachusetts Press.
- Davis, Philip J. 1993. Spirals: From Thoedorus to Chaos. Wellesley, MA: A. K. Peters.
- Diop, Cheikh Anta. 1981/trans. 1991. Civiliza- tion or Barbarism: An Authentic Anthropology. Brooklyn, NY: Lawrence Hill Books.
- Diop, Cheikh Anta. 1974a. The African Origin of Civilization: Myth and Reality. Chicago, IL: Lawrence Hill (Africa World Press edition).
- Diop, Cheikh Anta. 1974b. Black Africa: The Economic Basis for a Federated State. Chicago, IL: Lawrence Hill (Africa World Press edition).
- Diop, Cheik Anta. 1962. The Cultural Unity of Negro Africa. Paris, France: Presence Africaine.
- Diop, Cheikh Anta. 1960/trans. 1987. Precolonial Black Africa: A Comparative Study of the Political and Social Systems of Europe and Black Africa, from Antiquity to the Formation of Modern States (translated from the French by Harold Salemson). Chicago, IL: Lawrence Hill Books.
- Eglash, Ron. 1999. African Fractals: Modern Computing and Indigenous Design. New Brunswick, NJ: Rutgers University Press.
- Frege, Gottlob. 1892/1952. On sense and reference. In P. T. Geach and M. Black. Translations from the Philosophic Writings of Gottlob Frege. Oxford, England: Blackwell.
- Gangoueus, Chez. Dimanche 22 Juin 2008. Cheikh Anta Diop: L’Afrique noir précoloniale. Retrieved on January 23, 2012 from http://gangoueus.blogspot.com/2008/06/cheikh-anta-diop lafrique-noire...
- Grice, Herbert Paul. 1975. Logic and conversation. In P. Cole. (ed.). Syntax and Semantics: vol. 3: Speech Acts. New York, NY: Academic Press.
- Hargittai, István and Cliff A. Pickover. (eds.). 1992. Spiral Symmetry. Singapore, Malaysia: World Scientific Publishing Company.
- Howe, Stephen. 1999. Afrocontricism: Mythical Pasts and Imagined Homes. New York, NY: Verso Books.
- Kates, Carol A. 1980. Pragmatics and Semantics: An Empiricist Theory. Ithaca, New York: Cornell University Press.
- Levinson, Stephen. 1983. Pragmatics. Cambridge, UK: Cambridge University Press.
- Luthuli, Chief Albert John. 1952 speech. Speeches and Statements by Luthuli.
- Stanger, KwaDukuya, South Africa. Retrieved on January 13, 2013 from http:/ /www.luthulimuseum.org.za/luthulis-life-/ speeches Mazonde, Isaac and Pradip Thomas (eds.). 2007. Indigenous Knowledge Systems and Intellectual Property in the Twenty-First Century: Perspectives from Southern Africa. Dakar, Senegal: Council for the Development of Social Science Research in Africa (CODESRIA) Publications.
- Mokhtar, G. 1990. Ancient Civilizations of Africa. Berkeley, CA: University of California Press.
- Nabudere, Dani W. 2003. Towards the establishment of a Pan-African university: A strategic concept paper. African Journal of Political Science 8, 1:1-30.
- Senghor, Léopold Sédar. n.d. The Poetry of Sédar-Senghor—DISA. Retrieved on January 13, 2013 from http://www.disa.ukzn.ac.za/webpages/DC/asjul58.22/asjul58.22.pdf
- Setati, Mamokgethi. 2008. Access to mathematics versus access to the language of power: The struggle in multilingual mathematics classrooms. South African Journal of Education 28:103-116.
- Setati, Mamokgethi. 2005a. Teaching mathematics in a primary multilingual classroom. Journal for Research in Mathematics Education 36, 5:447-466.
- Setati, Mamokgethi. 2005b. Researching teaching and learning from "with" or "on" teachers to "with" and "on" teachers. Perspectives in Education 23, 1:91-101.
- Setati, Mamokgethi. 2003. ‘Re’-presenting qualitative data from multilingual mathematics classrooms. ZDM (Zentralblatt für Didaktik der Mathematik): The International Journal on Mathematics Education 35, 6:294-300.
- Setati, Mamokgethi. 2002. Researching mathematics education and language in multilingual South Africa. The Mathematics Educator 12, 2:6-20.
- Setati, Mamokgethi. 1998. Code-switching in a senior primary class of second-language mathematics learners. For the Learning of Mathematics 18, 1:34-40.
- Shuy, Roger W. 1982. Topic as the unit of analysis in a criminal law case. In D. Tannen. (ed.).
- Analyzing Discourse: Text and Talk. Washington, DC: Georgetown University Press.
- Steen, Lynn A. (ed.). 1988. Introduction to Contemporary Mathematics. New York, NY: W. H. Freeman and Company.
- Strawson, Peter F. 1952. Introduction to Logical Theory. London, England: Methuen.
- Touré, Sékou. 1989. A dialectical approach to culture. In R. Chrisman and N. Hare, eds.
- Contemporary Black Thought. Indianapolis, IN and New York, NY: The Bobbs-Merrill Co, Inc./MacMillan Press.
- Winters, Clyde Ahmad. 1998. The Afrocentric. The Western Journal of Black Studies 22.
References
Adeleke, Tunde. 2009. The Case against Afrocentrism. Jackson, MS: University Press of Mississippi.
Awoonor, Kofi Nyidevu. 1990. Ghana: A Political History. Accra, Ghana: Sedco Publishing Ltd. and Woeli Publishing Services.
Ayittey, George B. N. 2011. Defeating Dictators: Fighting Tyranny in Africa and around the World. New York, NY: Palgrave Macmillan.
Ayittey, George B. N. 1999. Africa in Chaos. New York, NY: Palgrave Macmillan.
Ayittey, George B. N. 1993. Africa Betrayed. New York, NY: Palgrave Macmillan.
Bangura, Abdul Karim (ed.). 2013. Fractal Complexity in the Works of Major Black Thinkers, Volumes One and Two. San Diego, CA: Cognella Press.
Bangura, Abdul Karim. 2012. A mathematical exploration of fractal complexity among the axioms on the African state in the Journal of Third World Studies: From John Mukum Mbaku to Pade Badru. Journal of Third World Studies xxix, 2:11-64.
Bangura, Abdul Karim. 2012. Fractal complexity in Cheikh Anta Diop’s Precolonial Black Africa: A pluridisciplinary analysis. CODESRIA Bulletin 1&2:10-19.
Bangura, Abdul Karim. 2012. Fractal complexity in Mwalimu Chinua Achebe’s Things Fall Apart: A mathematical exploration. Critical Interventions 9/10:106-121.
Bangura, Abdul Karim. 2008. African Peace Paradigms. Dubuque, IA: Kendall Hunt Publishing Company.
Bangura, Abdul Karim. 2005. Ubuntugogy: An African educational paradigm that transcends pedagogy, andragogy, ergonagy, and heutagogy. Journal of Third World Studies xxii, 2:13-53.
Bangura, Abdul Karim. 2002. Sojourner- Douglass College=s Philosophy in Action: An African-Centered Creed. San Jose, California: Writers Club Press.
Bangura, Abdul Karim. 2000. Chaos Theory and African Fractals. Washington, DC: The African Institution.
Brown, Clifford and Larry Liebovitch. 2010. Fractal Analysis. Thousand Oaks, CA: Sage Publications.
Brown, Gillian and George Yule. 1983. Discourse Analysis. Cambridge, UK: Cambridge University Press.
Cabral, Amicar. 1995. Identity and dignity in the context of the national liberation struggle. In F. L. Hord (Mzee Lasana Okpara) and J. S., eds. I Am Because We Are: Readings in Black Philosophy. Amherst, MA: University of Massachusetts Press.
Chafe, Wallace L. 1972. Discourse structure and human knowledge. In R. O. Freedle and J. B. Carroll (eds.). Language Comprehension and the Acquisition of Knowledge. Washington, DC: V. M. Winston.
Cooper, Anna Julia. 1995. Womanhood: A vital element in the regeneration of progress. In F. L. Hord (Mzee Lasana Okpara) and J. S., eds. I Am Because We Are: Readings in Black Philosophy. Amherst, MA: University of Massachusetts Press.
Davis, Philip J. 1993. Spirals: From Thoedorus to Chaos. Wellesley, MA: A. K. Peters.
Diop, Cheikh Anta. 1981/trans. 1991. Civiliza- tion or Barbarism: An Authentic Anthropology. Brooklyn, NY: Lawrence Hill Books.
Diop, Cheikh Anta. 1974a. The African Origin of Civilization: Myth and Reality. Chicago, IL: Lawrence Hill (Africa World Press edition).
Diop, Cheikh Anta. 1974b. Black Africa: The Economic Basis for a Federated State. Chicago, IL: Lawrence Hill (Africa World Press edition).
Diop, Cheik Anta. 1962. The Cultural Unity of Negro Africa. Paris, France: Presence Africaine.
Diop, Cheikh Anta. 1960/trans. 1987. Precolonial Black Africa: A Comparative Study of the Political and Social Systems of Europe and Black Africa, from Antiquity to the Formation of Modern States (translated from the French by Harold Salemson). Chicago, IL: Lawrence Hill Books.
Eglash, Ron. 1999. African Fractals: Modern Computing and Indigenous Design. New Brunswick, NJ: Rutgers University Press.
Frege, Gottlob. 1892/1952. On sense and reference. In P. T. Geach and M. Black. Translations from the Philosophic Writings of Gottlob Frege. Oxford, England: Blackwell.
Gangoueus, Chez. Dimanche 22 Juin 2008. Cheikh Anta Diop: L’Afrique noir précoloniale. Retrieved on January 23, 2012 from http://gangoueus.blogspot.com/2008/06/cheikh-anta-diop lafrique-noire...
Grice, Herbert Paul. 1975. Logic and conversation. In P. Cole. (ed.). Syntax and Semantics: vol. 3: Speech Acts. New York, NY: Academic Press.
Hargittai, István and Cliff A. Pickover. (eds.). 1992. Spiral Symmetry. Singapore, Malaysia: World Scientific Publishing Company.
Howe, Stephen. 1999. Afrocontricism: Mythical Pasts and Imagined Homes. New York, NY: Verso Books.
Kates, Carol A. 1980. Pragmatics and Semantics: An Empiricist Theory. Ithaca, New York: Cornell University Press.
Levinson, Stephen. 1983. Pragmatics. Cambridge, UK: Cambridge University Press.
Luthuli, Chief Albert John. 1952 speech. Speeches and Statements by Luthuli.
Stanger, KwaDukuya, South Africa. Retrieved on January 13, 2013 from http:/ /www.luthulimuseum.org.za/luthulis-life-/ speeches Mazonde, Isaac and Pradip Thomas (eds.). 2007. Indigenous Knowledge Systems and Intellectual Property in the Twenty-First Century: Perspectives from Southern Africa. Dakar, Senegal: Council for the Development of Social Science Research in Africa (CODESRIA) Publications.
Mokhtar, G. 1990. Ancient Civilizations of Africa. Berkeley, CA: University of California Press.
Nabudere, Dani W. 2003. Towards the establishment of a Pan-African university: A strategic concept paper. African Journal of Political Science 8, 1:1-30.
Senghor, Léopold Sédar. n.d. The Poetry of Sédar-Senghor—DISA. Retrieved on January 13, 2013 from http://www.disa.ukzn.ac.za/webpages/DC/asjul58.22/asjul58.22.pdf
Setati, Mamokgethi. 2008. Access to mathematics versus access to the language of power: The struggle in multilingual mathematics classrooms. South African Journal of Education 28:103-116.
Setati, Mamokgethi. 2005a. Teaching mathematics in a primary multilingual classroom. Journal for Research in Mathematics Education 36, 5:447-466.
Setati, Mamokgethi. 2005b. Researching teaching and learning from "with" or "on" teachers to "with" and "on" teachers. Perspectives in Education 23, 1:91-101.
Setati, Mamokgethi. 2003. ‘Re’-presenting qualitative data from multilingual mathematics classrooms. ZDM (Zentralblatt für Didaktik der Mathematik): The International Journal on Mathematics Education 35, 6:294-300.
Setati, Mamokgethi. 2002. Researching mathematics education and language in multilingual South Africa. The Mathematics Educator 12, 2:6-20.
Setati, Mamokgethi. 1998. Code-switching in a senior primary class of second-language mathematics learners. For the Learning of Mathematics 18, 1:34-40.
Shuy, Roger W. 1982. Topic as the unit of analysis in a criminal law case. In D. Tannen. (ed.).
Analyzing Discourse: Text and Talk. Washington, DC: Georgetown University Press.
Steen, Lynn A. (ed.). 1988. Introduction to Contemporary Mathematics. New York, NY: W. H. Freeman and Company.
Strawson, Peter F. 1952. Introduction to Logical Theory. London, England: Methuen.
Touré, Sékou. 1989. A dialectical approach to culture. In R. Chrisman and N. Hare, eds.
Contemporary Black Thought. Indianapolis, IN and New York, NY: The Bobbs-Merrill Co, Inc./MacMillan Press.
Winters, Clyde Ahmad. 1998. The Afrocentric. The Western Journal of Black Studies 22.