A Story of African American Students as Mathematics Learners

Crystal Hill Morton
3.846 532

Abstract


Educational systems throughout the world serve students from diverse populations. Often students from minority populations (i.e. racial, ethnic, linguistic, cultural, economic) face unique challenges when learning in contexts based on the cultural traditions and learning theories of the majority population.  These challenges often leave minority populations labeled as incompetent, unmotivated, and cognitively deficit. In the United States, African American female students are among minority populations who are often positioned as deficit when compared to the majority White population. This study investigates middle school African American female perceptions of themselves as learners and students’ knowledge of the meaning of ratio, proportionality, and how to apply and explain their application of proportionality concepts by examining written problem solving strategies over a three-year period. Students’ responses are analyzed according to the strategies they used to reach their final solution.  The categories of strategies include no-response, guess and check, additive build up with and without a pictorial representation, and multiplicative. The majority of students in this study 86.5%, 69.2%, and 68.6% did not attempt or demonstrated no understanding in year one, two, and three respectively.  Additionally, participants reported positive dispositions about themselves as mathematics learners.


Keywords


Problem solving strategies, African American female students, Middle school, proportional reasoning.

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DOI: http://dx.doi.org/10.18404/ijemst.36351

References


Behr, M., Harel, G., Post,T., & Lesh, R. (1992). Rational Number, Ratio, and Proportion. In

D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 296-333). New York: Macmillian Publishing. Berry, R. Q., III, Thunder, K., & McClain, O. L. (2011). Counter narratives: Examining the mathematics and racial identities of Black boys who are successful with school. Journal of African American Males in Education, 2(1), 10–23.

Cai, J. (1997). Beyond Computation and Correctness: Contributions of Open-Ended Tasks in Examining U.S. and Chinese Students’ Mathematical Performance. Educational Measurement: Issues and Practices, Spring, 5-11.

Cai, J. (2000). Mathematical Thinking Involved in U.S. and Chinese Students’ Solving of Process Constrained and Process-Open Problems. Mathematical Thinking and Learning, 2(4), 309-340.

Carpenter, T., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema &

T. A. Romberg (Eds.), Classrooms that Promote Mathematical Understanding (pp. 19-32). Mahwah, NJ: Erlbaum. Cramer, K., & Post, T. (1993). Connecting research to teaching proportional reasoning. Mathematics Teacher, 86(5), 404–407.

Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. Owens (Ed.), Research ideas for the classroom (pp. 159–178). New York: Macmillian.

Gick, M. (1986). Problem-Solving Strategies. Educational Psychologists, 21(1 &2), 99-120.

Gomez, C., Rousseau, C., Steinthorsdottir, O., Valentine, C., Wagner, L., & Wiles, P. (2002) Multiplicative Reasoning: Developing Student’s Shared Meanings. In B. Litwiller & G. Bright (Eds.), Making Sense of Fractions, Ratios, and Proportions (pp. 213-223). Reston: National Council of Teachers of Mathematics. Hiebert, J. & Behr, M. (1988), Introduction: Capturing the major themes. In J. Hibert & M. Behr (Eds.), Number Concepts and operations in the middle grades (pp. 1-18). Reston: National Council of Teachers of Mathematics.

Inhelder, B., & Piaget, J. (1985). The growth of logical thinking from childhood to adolescence. New York: Basic Books.

Johnson, C., & Kritsonis, W. A. (2006). The national dilemma of African American students: Disparities in mathematics achievement and instruction. National Forum of Applied Educational Research Journal, 20(3), 1–8.

Katada, S. & Gray, C. (2008). Double-and triple-minorities in the international relations classroom. International Studies Perspectives, 9(4), 464-468.

Kroll, D.L., & Miller, T. (1993). Insights from research on mathematical problem solving in middle grades. In D. Owens (Ed.), Research ideas for the classroom: Middle grades Mathematics (pp.55-77). New York: MacMillan Publishing Company.

Ladson-Billings, G. 1997. It doesn’t add up: African American students’ mathematics achievement. Journal for Research in Mathematics Education 28: 697–708.

Lamon, S. (2005). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Lawrence Erlbaum Associates.

Lamon, S. (1993). Ratio and Proportions: Children’s Cognitive and Metacognitive Processes. In T. Carpenter, E. Fennema, & T. Romberg (Eds.), Rational Numbers: An Integration of Research (131Landis, J. & Koch, G. (1977). The Measurement of Observer Agreement for Categorical Data Models. Biometrics, 33,159-174.

Lobato, J. Ellis, A, Charles, R., & Zbiek, R. (2010). Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning. Reston, VA: NCTM.

Lubienski, S. T., & Bowen, A. (2000). Who‘s counting? A survey of mathematics education research 1982– 19 Journal for Research in Mathematics Education, 31, 626– 633

Malloy, C. & Jones, G.M. (1998). An Investigation of African American students’ mathematical problem solving. Journal of Research in Mathematics Education, 29, 143-163.

Malloy, C. (2009). Instructional Strategies and Dispositions of Teachers Who Help African American Students Gain Conceptual Understanding. In D. Martin (Ed.), Mathematics Teaching, Learning, and Liberation in the Lives of Black Children (88-122). New York, NY: Routledge.

Malloy, C. & Malloy, W. (1998). Issues of Culture in Mathematics Teaching and Learning. Urban Review 30(3), 245-257.

Martin, D. (2009). Mathematics Teaching, Learning, and Liberation in the Lives of Black Children. New York, NY: Routledge.

Morton, C.H. (2008). Making the Invisible Visible: An Examination of African American Students’ Strategy Use During Mathematical Problem Solving. Unpublished doctoral dissertation, University of North Carolina at Chapel Hill.

Moskal, B. M. & Magone, M. E. (2000). Making Sense of What Students Know: Examining the Referents, Relationships, and Modes Students Displayed in Response to a Decimal Task. Educational Studies in Mathematics, 43, 313-335.

National Council of Teachers of Mathematics (2000). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: The Council.

National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.

Polya, G. (1981). Mathematical Discovery: On Understanding , Learning, and Teaching Problem Solving (Combined Edition). New York, NY: John Wiley & Sons.

Pugalee, D. (2004). A Comparison of Verbal and Written Descriptions of Students’ Problem Solving Processes. Educational Studies in Mathematics, 55, 27-47.

Resnick, L. & Singer, J. (1993). Protoquantitative origins of ratios constructed by two sixth-grade students. Educational Studies in Mathematics, 16, 181-204.

Reyes, L., and G. Stanic. 1988. Race, sex, socioeconomic status, and mathematics. Journal for Research in Mathematics Education 19: 26–43.

Schoenfeld, A. (1985). Mathematical Problem Solving. Orlando, Florida: Academic Press.

Siegler, R. (1998). Children’s Thinking (3 rd . Ed.). Upper Saddle River, New Jersey: Prentice-Hall.

Steinthorsdottir, O. & Sriraman, B. (2009). Icelandic 5 th -Grade Girls’ Developmental Trajectories in Proportional Reasoning. Mathematics Education Research Journal, 21 (1), 6-30.

Tate,W., and C. Rousseau (2002). Access and opportunity: The political and social context of mathematics education. In L. English (Ed.), Handbook of international research in mathematics education (271-300). Mahwah, NJ: Erlbaum.

Tourniaire, F., & Pulos, S. (1985). Proportional Reasoning: A Review of the Literature. Educational Studies in Mathematics, 16, 181-204. Appendix A

Conceptual Understanding Scoring Rubric A class has 28 students. The ratio of girls to boys is 4 to 3. How many girls are in the class? Concepts Assessed Understand and apply proportional reasoning used in scaling. Understand that a fraction always represents a part-to-whole relationship. Understand that a ratio can represent part-to-part or part-to-whole relationships. Scoring Rubric Level Identifiers Examples of student responses Understanding No work or states they do not understand with no answer given. “I don’t understand.” No attempt 1 No evidence of understanding concepts related to fractions or proportionality. 2 Written or symbolic explanation shows an understanding the meaning of a ratio, but does not apply the ratio to solve the problem. Correct written or drawing work but provides no explanation of how the answer was found. 3 Explanation is accurate does not thoroughly explain the rationale used in solving the problem. The explanation is procedural rather than conceptual. 4 Evidence of full understanding of proportionality either verbally or visually (scaling 4:3 or using and explaining the proportion 4/7 = 16/28).




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