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Handbook of the Mathematics of the Arts and Sciences pp 1–26Cite as

Cognition, Interdisciplinarity, and Equity

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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.

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References

  • Adiredja AP (2019) Anti-deficit narratives: engaging the politics of mathematical sense making. J Res Math Educ 50(4):401–435

    Google Scholar 

  • Adiredja AP, Andrews-Larson C (2017) Taking the sociopolitical turn in postsecondary mathematics education research. Int J Res Undergrad Math Educ 3(3):444–465

    Article  Google Scholar 

  • 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 346–359

    Google Scholar 

  • Adiredja AP, Zandieh M (in press) The lived experience of linear algebra: A Counter-story about women of color in mathematics. Educ Stud Math

    Google Scholar 

  • 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):72–80

    Google Scholar 

  • Barton B (1996) Making sense of ethnomathematics: Ethnomathematics is making sense. Educ Stud Math 31:201–233

    Article  MATH  Google Scholar 

  • 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 1–22

    Chapter  MATH  Google Scholar 

  • 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/10.1080/07491409.2000.11517689

    Article  Google Scholar 

  • 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):1–9

    Google Scholar 

  • Bishop AJ (1988) Mathematical enculturation: a culturation perspective on mathematics education. Kluwer, Dordrecht

    Book  Google Scholar 

  • 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 16:5–11

    Article  Google Scholar 

  • Cammarota J (2017) Youth participatory action research: a pedagogy of transformational resistance for critical youth studies. J Crit Educ Policy Stud 15(2):188–213

    Google Scholar 

  • Cammarota J, Fine M (2008) Revolutionizing education: youth participatory action research in motion. Routledge, New York

    Google Scholar 

  • Carraher TN, Carraher DW, Schliemann AD (1985) Mathematics in the street and in schools. Br J Dev Psychol 3:21–29

    Article  Google Scholar 

  • Charlton JI (2000) Nothing about us without us: disability oppression and empowerment. University of California Press, Berkeley

    Google Scholar 

  • 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 105–117

    Google Scholar 

  • 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 149–169

    Chapter  Google Scholar 

  • D’Ambrosio U (1985) Ethnomathematics and its place in the history and pedagogy of mathematics. Learn Math 5(1):44–48

    MathSciNet  Google Scholar 

  • D’Ambrosio U (1999) Ethnomathematics and its first international congress. ZDM 31(2):50–53

    Google Scholar 

  • 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, Paris

    Google Scholar 

  • 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 York

    Chapter  MATH  Google Scholar 

  • 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 55–86

    Google Scholar 

  • 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 101–144

    Google Scholar 

  • Fuson KC, Smith ST, Lo Cicero AM (1997) Supporting Latino first graders’ ten structured thinking in urban classrooms. J Res Math Educ 28:738–766

    Article  Google Scholar 

  • Gerdes P (1992) On the history of mathematics in Africa South of the Sahara. AMUCHMA Newsletter 9, Higher Pedagogical Institute, Maputo, pp 3–32

    Google Scholar 

  • 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 29–46

    Google Scholar 

  • 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 29–46

    Google Scholar 

  • 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 1–16

    Google Scholar 

  • 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_4

    Article  Google Scholar 

  • Gutiérrez R (2008) A “gap gazing” fetish in mathematics education? Problematizing research on the achievement gap. J Res Math Educ 39(4):357–364

    Google Scholar 

  • Gutiérrez R (2009) Framing equity: helping students “play the game” and change the game. Teach Excell Equity Math 1(1):5–7

    Google Scholar 

  • Gutiérrez R (2013) The sociopolitical turn in mathematics education. J Res Math Educ 44(1):37–68

    Article  Google Scholar 

  • Gutiérrez KD, Rogoff B (2003) Cultural ways of learning: individual traits or repertoires of practice. Educ Res 32(5):19–25

    Article  Google Scholar 

  • 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 Diego

    Google Scholar 

  • Harel G (2017) The learning and teaching of linear algebra: observations and generalizations. J Math Behav 46:69–95

    Google Scholar 

  • Heid MK (2010) Where’s the math (in mathematics education research)? J Res Math Educ 41(2):102–103

    Google Scholar 

  • Kamii C (1985) Young children reinvent arithmetic: implications of Piaget’s theory. Teachers College Press, New York

    Google Scholar 

  • Knijnik G (2002) Ethnomathematics: culture and politics of knowledge in mathematics education. Learn Math 22(1):11–14

    Google Scholar 

  • Knijnik G, Wanderer F, Oliveira C (eds) (2004) Etnomatemática: Curriculo e formação de professors [Ethnomathematics: curricula and teacher education], Santa Cruz do Sol, Edunisc

    Google Scholar 

  • Larnell GV, Bullock EC, Jett CC (2016) Rethinking teaching and learning mathematics for social justice from a critical race perspective. J Educ 196(1):19–29

    Article  Google Scholar 

  • Lave J, Wenger W (1991) Situated learning: legitimate peripheral participation. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • 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, Westport

    Google Scholar 

  • Lewis KE (2014) Difference not deficit: Reconceptualizing mathematical learning disabilities. J Res Math Educ 45(3):351–396

    Google Scholar 

  • 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):159–172

    Article  Google Scholar 

  • Lewis KE, Lynn DM (2018b) Access through compensation: emancipatory view of a mathematics learning disability. Cogn Instr 36(4):424–459

    Article  Google Scholar 

  • 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 88–122

    Google Scholar 

  • Malloy CE, Jones MG (1998) An investigation of African American students’ mathematical problem solving. J Res Math Educ 29:143–163. https://doi.org/10.2307/749896

    Article  Google Scholar 

  • Martin DB, Gholson ML, Leonard J (2010) Mathematics as gatekeeper: power and privilege in the production of knowledge. J Urban Math Educ 3(2):12–24

    Google Scholar 

  • 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

  • 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 85:24–30

    Article  Google Scholar 

  • 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/10.1080/00405849209543534

    Article  Google Scholar 

  • Morton C (2014) A story of African American students as mathematics learners. Int J Educ Math Sci Technol 2(3):234–245

    Article  Google Scholar 

  • Nasir N (1996) Statistics in practice: African American youth in the play of basketball. Unpublished master’s thesis, University of California, Los Angeles

    Google Scholar 

  • 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 31:283–305

    Article  Google Scholar 

  • 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 130–143

    Google Scholar 

  • 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 32:187–232

    Article  Google Scholar 

  • Nasir N, Snyder CR, Shah N, Ross KM (2013) Racial storylines and implications for learning. Hum Dev 55(5–6):285–301

    Google Scholar 

  • 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 235–248

    Chapter  Google Scholar 

  • Oughton H (2010) Funds of knowledge – a conceptual critique. Stud Educ Adults 42(1):63–78. https://doi.org/10.1080/02660830.2010.11661589

    Article  Google Scholar 

  • Pais A (2011) Criticisms and contradictions of ethnomathematics. Educ Stud Math 76(2):209–230

    Article  Google Scholar 

  • Parks AN, Schmeichel M (2012) Obstacles to addressing race and ethnicity in the mathematics education literature. J Res Math Educ 43(3):238–252

    Article  Google Scholar 

  • 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 89–105

    Google Scholar 

  • 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 243–263

    Google Scholar 

  • 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 31–45

    Google Scholar 

  • Raygoza MC (2016) Striving toward transformational resistance: youth participatory action research in the mathematics classroom. J Urban Math Educ 9(2):122–152

    Google Scholar 

  • 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):163–184

    Article  Google Scholar 

  • 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):79–102

    Article  Google Scholar 

  • Schoenfeld AH (2014) Reflections on learning and cognition. ZDM-Int J Math Educ 46:497–503. https://doi.org/10.1007/s11858-014-0589-8

    Article  Google Scholar 

  • Shetterley ML (2016) Hidden figures. Harper Collins, New York

    Google Scholar 

  • Skovsmose O, Vithal R (1997) The end of innocence: a critique of ‘ethnomathematics’. Educ Stud Math 34:131–158

    Article  MATH  Google Scholar 

  • Stewart S, Thomas MO (2010) Student learning of basis, span and linear independence in linear algebra. Int J Math Educ Sci Technol 41(2):173–188

    Google Scholar 

  • 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):23–49

    Google Scholar 

  • Valencia RR (2010) Dismantling contemporary deficit thinking: educational thought and practice. Routledge, New York. https://doi.org/10.4324/9780203853214

    Book  Google Scholar 

  • 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 5–23

    Chapter  Google Scholar 

  • Vélez-Ibáñez C, Greenberg J (1992) Formation and transformation of funds of knowledge among US-Mexican households. Anthropol Educ Q 23(4):313–335

    Article  Google Scholar 

  • 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 501–505

    Chapter  Google Scholar 

  • 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 260–278

    Google Scholar 

  • 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.317

    Article  Google Scholar 

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Authors and Affiliations

  1. The University of Arizona, Tucson, AZ, USA

    Aditya P. Adiredja

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  1. Aditya P. Adiredja
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Correspondence to Aditya P. Adiredja .

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  1. Dept of Mathematical Sciences, The University of Montana Dept of Mathematical Sciences, Missoula, MT, USA

    Bharath Sriraman

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  1. Colgate University, Hamilton, NY, USA

    K. G. Valente

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Adiredja, A.P. (2020). Cognition, Interdisciplinarity, and Equity. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_73-1

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  • DOI: https://doi.org/10.1007/978-3-319-70658-0_73-1

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