Advertisement

Cognition, Interdisciplinarity, and Equity

Living reference work entry
  • 198 Downloads

Abstract

Research that focuses on mathematical cognition as an individual activity continues to contribute to the field’s understanding of ways that people make sense of mathematical ideas. However, such research is often positioned as separate or even competing with research that focuses on examining the role of mathematics and mathematics education in reproducing societal inequities. This chapter reviews studies and research programs that focus on the intersection of cognition and equity. The review begins with insights from ethnomathematics research, funds of knowledge research, and other studies informed by cultural anthropology. The main section of the review focuses on studies of individual cognition that explicitly challenge unjust power allocations of mathematics in education and society. An analysis of the literature reveals diverse approaches for research that focuses on individual cognition to engage the politics of mathematical thinking and learning. Dominant deficit narratives in society together with the continued use of mathematical expertise as a proxy for intelligence serves as a unique opportunity for studies of individual cognition to contribute to efforts in restoring the dignity of students from marginalized communities.

Keywords

Cognition Equity Mathematical thinking Sociopolitical perspective 

References

  1. Adiredja AP (2019) Anti-deficit narratives: engaging the politics of mathematical sense making. J Res Math Educ 50(4):401–435Google Scholar
  2. Adiredja AP, Andrews-Larson C (2017) Taking the sociopolitical turn in postsecondary mathematics education research. Int J Res Undergrad Math Educ 3(3):444–465CrossRefGoogle Scholar
  3. Adiredja AP, Zandieh M (2017) Using intuitive examples from women of color to reveal nuances about basis. In: Weinberg A, Rasmussen C, Rabin J, Wawro M, Brown S (eds) Proceedings of the 20th annual conference on research in undergraduate mathematics education. San Diego, California, pp 346–359Google Scholar
  4. Adiredja AP, Zandieh M (in press) The lived experience of linear algebra: A Counter-story about women of color in mathematics. Educ Stud MathGoogle Scholar
  5. Andrews J, Yee WC, Greenhough P, Hughes M, Winter J (2005) Teachers’ funds of knowledge and the teaching and learning of mathematics in multi-ethnic primary schools: two teachers’ views of linking home and school. ZDM 37(2):72–80Google Scholar
  6. Barton B (1996) Making sense of ethnomathematics: Ethnomathematics is making sense. Educ Stud Math 31:201–233zbMATHCrossRefGoogle Scholar
  7. Barwell R, Clarkson P, Halai A, Kazima M, Moschkovich J, Planas N, Phakeng MS, Valero P, Ubillús MV (2016) Introduction: an ICMI study on language diversity in mathematics education. In: Mathematics education and language diversity. Springer, Cham, pp 1–22zbMATHCrossRefGoogle Scholar
  8. Bell KE, Orbe MP, Drummon DK, Camara SK (2000) Accepting the challenge of centralizing without essentializing: black feminist thought and African American women’s communicative experiences. Women’s Stud Commun 23(1):41–62. https://doi.org/10.1080/07491409.2000.11517689CrossRefGoogle Scholar
  9. Berry RQ III, Ellis MW, Morton CH, Yow JA (2015) I am a teacher. That’s what I’ve done almost all my life. I teach. J Urban Math Educ 8(1):1–9Google Scholar
  10. Bishop AJ (1988) Mathematical enculturation: a culturation perspective on mathematics education. Kluwer, DordrechtCrossRefGoogle Scholar
  11. Cai J (1997) Beyond computation and correctness: contributions of open-ended tasks in examining U.S. and Chinese students’ mathematical performance. Educ Meas Issues Pract 16:5–11CrossRefGoogle Scholar
  12. Cammarota J (2017) Youth participatory action research: a pedagogy of transformational resistance for critical youth studies. J Crit Educ Policy Stud 15(2):188–213Google Scholar
  13. Cammarota J, Fine M (2008) Revolutionizing education: youth participatory action research in motion. Routledge, New YorkGoogle Scholar
  14. Carraher TN, Carraher DW, Schliemann AD (1985) Mathematics in the street and in schools. Br J Dev Psychol 3:21–29CrossRefGoogle Scholar
  15. Charlton JI (2000) Nothing about us without us: disability oppression and empowerment. University of California Press, BerkeleyGoogle Scholar
  16. Civil M (2007) Building on community knowledge: An avenue to equity in mathematics education. In: Nassir N, Cobb P (eds) Improving access to mathematics: Diversity and equity in the classroom. Teachers College Press, New York, pp 105–117Google Scholar
  17. Civil M, Andrade R (2002) Transitions between home and school mathematics: rays of hope amidst the passing clouds. In: de Abreu G, Bishop AJ, Presmeg NC (eds) Transitions between contexts of mathematical practices. Kluwer, Boston, pp 149–169CrossRefGoogle Scholar
  18. D’Ambrosio U (1985) Ethnomathematics and its place in the history and pedagogy of mathematics. Learn Math 5(1):44–48MathSciNetGoogle Scholar
  19. D’Ambrosio U (1999) Ethnomathematics and its first international congress. ZDM 31(2):50–53Google Scholar
  20. Da Rocha Falcão JT (2005) Conceptualisation en acte, conceptualisation explicite: Quels apports théoriques à offrir à la didactique des mathématiques et des sciences? Actes du Colloque Les processus de conceptualisation en debat-hommage a Gérard Vergnaud. Association pour la Recherche sur le Développement des Compétences, ParisGoogle Scholar
  21. De Freitas E, Sinclair N (2017) Concept as generative devices. In: de Freitas E, Sinclair N, Coles A (eds) What is a mathematical concept? Cambridge University Press, New YorkzbMATHCrossRefGoogle Scholar
  22. Delgado-Gaitan C (1994) Socializing young children in Mexican-American families: an intergenerational perspective. In: Greenfield PM, Cocking RR (eds) Cross-cultural roots of minority child development. Lawrence Erlbaum, Hillsdale, pp 55–86Google Scholar
  23. Frade C, Acioly-Régnier N, Jun L (2013) Beyond deficit models of learning mathematics: socio-cultural directions for change and research. In: (Ken) Clements MA, Bishop A, Keitel-Kreidt C, Kilpatrick J, Leung FK-S (eds) Third international handbook of mathematics education. Springer, New York, pp 101–144Google Scholar
  24. Fuson KC, Smith ST, Lo Cicero AM (1997) Supporting Latino first graders’ ten structured thinking in urban classrooms. J Res Math Educ 28:738–766CrossRefGoogle Scholar
  25. Gerdes P (1992) On the history of mathematics in Africa South of the Sahara. AMUCHMA Newsletter 9, Higher Pedagogical Institute, Maputo, pp 3–32Google Scholar
  26. González N (2005) Beyond culture: the hybridity of funds of knowledge. In: Gonzáles N, Moll LC, Amanti C (eds) Funds of knowledge: theorizing practices in households, communities, and classrooms. Lawrence Erlbaum Associates, Mahwah, pp 29–46Google Scholar
  27. González N, Moll L, Amanti C (2005) Introduction: theorizing practice. In: Gonzáles N, Moll LC, Amanti C (eds) Funds of knowledge: theorizing practices in households, communities, and classrooms. Lawrence Erlbaum Associates, Mahwah, pp 29–46Google Scholar
  28. Goos M (2018) A review of research on understanding and promoting students’ mathematical thinking published in Educational Studies in Mathematics 2014–2018. In: Gómez DM (ed) Proceedings of the first PME regional conference: South America. PME, Rancagua, pp 1–16Google Scholar
  29. Gutiérrez R (2002) Enabling the practice of mathematics teachers in context: towards a new equity research agenda. Math Think Learn 4(2 & 3):145–187. https://doi.org/10.1207/S15327833MTL04023_4CrossRefGoogle Scholar
  30. Gutiérrez R (2008) A “gap gazing” fetish in mathematics education? Problematizing research on the achievement gap. J Res Math Educ 39(4):357–364Google Scholar
  31. Gutiérrez R (2009) Framing equity: helping students “play the game” and change the game. Teach Excell Equity Math 1(1):5–7Google Scholar
  32. Gutiérrez R (2013) The sociopolitical turn in mathematics education. J Res Math Educ 44(1):37–68CrossRefGoogle Scholar
  33. Gutiérrez KD, Rogoff B (2003) Cultural ways of learning: individual traits or repertoires of practice. Educ Res 32(5):19–25CrossRefGoogle Scholar
  34. Harel G (2010) The role of mathematics in mathematics education research: question for public debate. Paper presented at the research pre-session of the annual meeting of the National Council of Teachers of Mathematics, San DiegoGoogle Scholar
  35. Harel G (2017) The learning and teaching of linear algebra: observations and generalizations. J Math Behav 46:69–95Google Scholar
  36. Heid MK (2010) Where’s the math (in mathematics education research)? J Res Math Educ 41(2):102–103Google Scholar
  37. Kamii C (1985) Young children reinvent arithmetic: implications of Piaget’s theory. Teachers College Press, New YorkGoogle Scholar
  38. Knijnik G (2002) Ethnomathematics: culture and politics of knowledge in mathematics education. Learn Math 22(1):11–14Google Scholar
  39. Knijnik G, Wanderer F, Oliveira C (eds) (2004) Etnomatemática: Curriculo e formação de professors [Ethnomathematics: curricula and teacher education], Santa Cruz do Sol, EduniscGoogle Scholar
  40. Larnell GV, Bullock EC, Jett CC (2016) Rethinking teaching and learning mathematics for social justice from a critical race perspective. J Educ 196(1):19–29CrossRefGoogle Scholar
  41. Lave J, Wenger W (1991) Situated learning: legitimate peripheral participation. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  42. Lerman S (2000) The social turn in mathematics education perspectives in mathematics education research. In: Boaler J (ed) Multiple perspectives in mathematics teaching and learning. Alex, WestportGoogle Scholar
  43. Lewis KE (2014) Difference not deficit: Reconceptualizing mathematical learning disabilities. J Res Math Educ 45(3):351–396Google Scholar
  44. Lewis KE, Lynn DM (2018a) An insider’s view of a mathematics learning disability: compensating to gain access to fractions. Investig Math Learn 10(3):159–172CrossRefGoogle Scholar
  45. Lewis KE, Lynn DM (2018b) Access through compensation: emancipatory view of a mathematics learning disability. Cogn Instr 36(4):424–459CrossRefGoogle Scholar
  46. Malloy C (2009) Instructional strategies and dispositions of teachers who help African American students gain conceptual understanding. In: Martin DB (ed) Mathematics teaching, learning, and liberation in the lives of black children. Routledge, London, pp 88–122Google Scholar
  47. Malloy CE, Jones MG (1998) An investigation of African American students’ mathematical problem solving. J Res Math Educ 29:143–163. https://doi.org/10.2307/749896CrossRefGoogle Scholar
  48. Martin DB, Gholson ML, Leonard J (2010) Mathematics as gatekeeper: power and privilege in the production of knowledge. J Urban Math Educ 3(2):12–24Google Scholar
  49. McKinney de Royston M, Sengupta-Irving T (2019) Another step forward: engaging the political in learning. Cogn Inst. Advanced online copy. https://doi.org/10.1080/07370008.2019.1624552
  50. Miura IT, Okamoto Y, Kim CC, Steere M, Fayol M (1993) First graders’ cognitive representation of number and understanding of place value: cross-national comparisons – France, Japan, Korea, Sweden, and the United States. J Educ Psychol 85:24–30CrossRefGoogle Scholar
  51. Moll LC, Amanti C, Neff D, González N (1992) Funds of knowledge for teaching: using a qualitative approach to connect homes and classrooms. Theory Pract 21(2):132–141. https://doi.org/10.1080/00405849209543534CrossRefGoogle Scholar
  52. Morton C (2014) A story of African American students as mathematics learners. Int J Educ Math Sci Technol 2(3):234–245CrossRefGoogle Scholar
  53. Nasir N (1996) Statistics in practice: African American youth in the play of basketball. Unpublished master’s thesis, University of California, Los AngelesGoogle Scholar
  54. Nasir NS (2000) Points ain’t everything: emergent goals and average and percent understanding in the play of basketball among African American students. Anthropol Educ Q 31:283–305CrossRefGoogle Scholar
  55. Nasir NS (2007) Identity, goals, and learning: The case of basketball mathematics. In: Nasir NS, Cobb P (eds) Diversity, equity, and access to mathematical ideas. Teachers College Press, New York. pp 130–143Google Scholar
  56. Nasir NS, Hand V, Taylor EV (2008) Culture and math in school: boundaries between “cultural” and “domain” knowledge in the mathematics classroom and beyond. Rev Res Educ 32:187–232CrossRefGoogle Scholar
  57. Nasir N, Snyder CR, Shah N, Ross KM (2013) Racial storylines and implications for learning. Hum Dev 55(5–6):285–301Google Scholar
  58. Niss M, Bruder R, Planas N, Turner R, Villa-Ochoa JA (2017) Conceptualisation of the role of competencies, knowing and knowledge in mathematics education research. In: Proceedings of the 13th International Congress on Mathematical Education. Springer, Cham, pp 235–248CrossRefGoogle Scholar
  59. Oughton H (2010) Funds of knowledge – a conceptual critique. Stud Educ Adults 42(1):63–78. https://doi.org/10.1080/02660830.2010.11661589CrossRefGoogle Scholar
  60. Pais A (2011) Criticisms and contradictions of ethnomathematics. Educ Stud Math 76(2):209–230CrossRefGoogle Scholar
  61. Parks AN, Schmeichel M (2012) Obstacles to addressing race and ethnicity in the mathematics education literature. J Res Math Educ 43(3):238–252CrossRefGoogle Scholar
  62. Parra-Sanchez A (2017) Ethnomathematical barters. In: Stahler-Pol H, Bohmann N, Pais A (eds) The disorder of mathematics education. Challenging the socio-political dimensions of research. Springer, New York, pp 89–105Google Scholar
  63. Pateman NA, Lim CS (2013) The politics of equity and access in teaching and learning mathematics. In: (Ken) Clements MA, Bishop A, Keitel-Kreidt C, Kilpatrick J, Leung FK-S (eds) Third international handbook of mathematics education. Springer, New York, pp 243–263Google Scholar
  64. Pinto MMF (2018) Making sense of students’ sense-making of mathematics. In: Gómez DM (ed) Proceedings of the first PME regional conference: South America. PME, Rancagua, pp 31–45Google Scholar
  65. Raygoza MC (2016) Striving toward transformational resistance: youth participatory action research in the mathematics classroom. J Urban Math Educ 9(2):122–152Google Scholar
  66. Rios-Aguilar C, Kiyama JM, Gravitt M, Moll LC (2011) Funds of knowledge for the poor and forms of capital for the rich? A capital approach to examining funds of knowledge. Theory Res Educ 9(2):163–184CrossRefGoogle Scholar
  67. Rowlands S, Carson R (2002) Where would formal, academic mathematics stand in a curriculum informed by ethnomathematics? A critical review of ethnomathematics. Educ Stud Math 50(1):79–102CrossRefGoogle Scholar
  68. Schoenfeld AH (2014) Reflections on learning and cognition. ZDM-Int J Math Educ 46:497–503. https://doi.org/10.1007/s11858-014-0589-8CrossRefGoogle Scholar
  69. Shetterley ML (2016) Hidden figures. Harper Collins, New YorkGoogle Scholar
  70. Skovsmose O, Vithal R (1997) The end of innocence: a critique of ‘ethnomathematics’. Educ Stud Math 34:131–158zbMATHCrossRefGoogle Scholar
  71. Stewart S, Thomas MO (2010) Student learning of basis, span and linear independence in linear algebra. Int J Math Educ Sci Technol 41(2):173–188Google Scholar
  72. Terry CL Sr (2011) Mathematical counterstory and African American males: urban mathematics education from a critical race theory perspective. J Urban Math Educ 4(1):23–49Google Scholar
  73. Valencia RR (2010) Dismantling contemporary deficit thinking: educational thought and practice. Routledge, New York. https://doi.org/10.4324/9780203853214CrossRefGoogle Scholar
  74. Valero P (2004) Socio-political perspectives on mathematics education. In: Valero P, Zevenbergen R (eds) Researching the socio-political dimensions of mathematics education. Springer US, Boston, pp 5–23CrossRefGoogle Scholar
  75. Vélez-Ibáñez C, Greenberg J (1992) Formation and transformation of funds of knowledge among US-Mexican households. Anthropol Educ Q 23(4):313–335CrossRefGoogle Scholar
  76. Williams G, Van Dooren W, Dartnell P, Lindmeier A, Proulx J (2017) Topic study group no. 27: learning and cognition in mathematics. In: Proceedings of the 13th International Congress on Mathematical Education. Springer, Cham, pp 501–505CrossRefGoogle Scholar
  77. Willis M (1992) Learning styles of African-American children: review of the literature and interventions. In: Burlew A, Banks W, McAdoo H, Azibo D (eds) African-American psychology. Sage, Newbury Park, pp 260–278Google Scholar
  78. Yang KW (2009) Mathematics, critical literacy, and youth participatory action research. New Dir Youth Dev 2009(123):99–118. https://doi.org/10.1002/yd.317CrossRefGoogle Scholar

Authors and Affiliations

  1. 1.The University of ArizonaTucsonUSA

Section editors and affiliations

  • K. G. Valente
    • 1
  1. 1.Colgate UniversityHamiltonUSA

Personalised recommendations