Classroom Interactions Around Problem Contexts and Task Authenticity in Middle School Mathematics

References

• Aguirre, J. M., Turner, E. E., Bartell, T. G., Kalinec-Craig, C., Foote, M. Q., McDuffie, A. R., & Drake, C. (2012). Making connections in practice: How prospective elementary teachers connect to children’s mathematical thinking and community funds of knowledge in mathematics instruction. Journal of Teacher Education, 62(2), 178–192.
   Google Scholar
• Boaler, J. (1993). The role of contexts in the mathematics classroom: Do they make mathematics more real’? For the Learning of Mathematics, 13(2), 12–17.
   Google Scholar
• Bonotto, C. (2005). How informal out-of-school mathematics can help students make sense of formal in-school mathematics. Mathematical Thinking and Learning, 7(4), 313–344. doi:10.1207/s15327833mtl0704_3
   Google Scholar
• Bonotto, C. (2007). How to replace word problems with activities of realistic mathematical modeling. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI Study (pp. 185–192). New York, NY: Springer.
   Google Scholar
• Bonotto, C., & Basso, M. (2001). Is it possible to change the classroom activities in which we delegate the process of connecting mathematics with reality? International Journal of Mathematics Education in Science and Technology, 32(3), 395–399. doi:10.1080/00207390110040201
   Google Scholar
• Brenner, M. E. (2002). Everyday problem solving and curriculum implementation: An invitation to try pizza. Journal for Research in Mathematics Education. Monograph 11, Everyday and Academic Mathematics in the Classroom, 11, 63–92. doi:10.2307/749965
   Google Scholar
• Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32–42. doi:10.3102/0013189X018001032
   Google Scholar
• Busse, A. (2011). Upper secondary students’ handling of real-world contexts. In G. Kaiser, W. Blum, R. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 37–46). New York: Springer.
   Google Scholar
• Carpenter, T. P., Lindquist, M. M., Matthews, W. & Silver, E. A. (1983). Results of the third NAEP mathematics assessment: Secondary school. Mathematics Teacher, 76, 652–659.
   Google Scholar
• Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and schools. British Journal of Developmental Psychology, 3, 21–29.
   Web of Science ®Google Scholar
• Certo, J. L., Cauley, K. M., Moxley, K. D., & Chafin, C. (2008). An argument for authenticity: Adolescents’ perspectives on standards-based reform. The High School Journal, 91(4), 26–39.
   Google Scholar
• Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62(2), 211–230. doi:10.1007/s10649-006-7834-1
   Google Scholar
• Chapman, O. (2007). Mathematical modeling in high school mathematics: Teachers’ thinking and practice. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education, The 14th ICMI study (pp. 325–332). New York, NY: Springer.
   Google Scholar
• Chazan, D. (2000). Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom. New York: Teachers College Press.
   Google Scholar
• Christiansen, I. M. (1997). When negotiation of meaning is also negotiation of task: Analysis of communication in an applied mathematics high school course. Educational Studies in Mathematics, 34(1), 1–25. doi:10.1023/A:1002944413332
   Google Scholar
• Civil, M. (2002). Chapter 4: Everyday mathematics, mathematicians’ mathematics, and school mathematics: Can we bring them together? Journal for Research in Mathematics Education Monograph, 11, 40–62. doi:10.2307/749964
   Google Scholar
• Cobb, P. (1986). Contexts, goals, beliefs, and learning mathematics. For the Learning of Mathematics, 6(2), 2–9.
   Google Scholar
• Corbin, J. (2005). Grounded theory. In B. Somekh, & C. Lewin (Eds.), Research methods in the social sciences (pp. 49–52). New Delhi, India: Vistaar Publications.
   Google Scholar
• Cordova, D. I., & Lepper, M. R. (1996). Intrinsic motivation and the process of learning: Beneficial effects of contextualization, personalization, and choice. Journal of Educational Psychology, 88(4), 715–730. doi:10.1037/0022-0663.88.4.715
   Web of Science ®Google Scholar
• Coxford, A. F. (2003). Mathematics curriculum reform: A personal view. In G. M. A. Stanic, & J. Kilpatrick (Eds.), A history of school mathematics (pp. 599–622). Reston, VA: NCTM.
   Google Scholar
• Curris, C. C., & Welner, K. G. (2005). Closing the achievement gap by detracking. Phi Delta Kappan, 86(8), 594–598. doi:10.1177/003172170508600808
   Web of Science ®Google Scholar
• English, L. D. (2006). Mathematical modeling in the primary school: Children’s construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303–323. doi:10.1007/s10649-005-9013-1
   Google Scholar
• Futrell, M. H., & Gomez, J. (2008). How tracking creates a poverty of learning. Educational Leadership, 65(8), 74–78.
   Web of Science ®Google Scholar
• Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11(3), 199–219. doi:10.1007/s10857-007-9070-8
   Google Scholar
• Gerofsky, S. (1996). A linguistic and narrative view of word problems in mathematics education. For the Learning of Mathematics, 16(20), 36–45.
   Google Scholar
• Gerofsky, S. (2004). A man left Albuquerque heading east: Word problems as genre in mathematics. New York, NY: Peter Lang Publishing, Inc.
   Google Scholar
• Gerofsky, S. (2010). The impossibility of ‘real-life’ word problems (according to Bakhtin, Laca, Zizek and Baudrillard. Discourse: Studies in the Cultural Politics of Education, 31(1), 61–73.
   Web of Science ®Google Scholar
• Glaser, B. (1965). The constant comparative method of qualitative analysis. Social Problems, 12(4), 436–445. doi:10.2307/798843
   Web of Science ®Google Scholar
• Glaser, B., & Strauss, A. (1967). The discovery of grounded theory: Strategies for qualitative research. Chicago, IL: Aldine.
   Google Scholar
• Gould, H., & Wasserman, N. H. (2014). Striking a balance: Students’ tendencies to oversimplify or overcomplicate in mathematical modeling. Journal of Mathematics Education at Teachers College, 5(1), 27–34.
   Google Scholar
• Gutstein, E. (2003). Teaching and learning for social justice in an urban, Latino school. Journal for Research in Mathematics Education, 34(1), 37–73. doi:10.2307/30034699
   Web of Science ®Google Scholar
• Hamacher, H. W., & Kreußler, J. (2013). Merging educational and applied mathematics: The example of locating bus stops. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings of the eighth congress of the European society for research in mathematics education (pp. 1087–1096). Ankara, Turkey: European Society for Research in Mathematics Education.
   Google Scholar
• Hegret, W., & Torres-Skoumal, M. (2007). Picture (im)perfect mathematics! In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education, The 14th ICMI study (pp. 379–386). New York, NY: Springer.
   Google Scholar
• Henningsen, M. A., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549. doi:10.2307/749690
   Web of Science ®Google Scholar
• Jablonka, E. (2007). The relevance of modeling and applications: Relevant to whom and for what purpose? In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education, The 14th ICMI study (pp. 193–200). New York, NY: Springer Science+Business Media, LLC.
   Google Scholar
• Jackson, K. (2011). Approaching participation in school-based mathematics as a cross-setting phenomenon. Journal of the Learning Sciences, 20(1), 111–150. doi:10.1080/10508406.2011.528319
   Web of Science ®Google Scholar
• Jackson, K., Garrison, A., Wilson, J., Gibbons, L., & Shahan, E. (2013). Exploring relationships between setting up complex tasks and opportunities to learn in concluding whole-class discussions in middle-grades mathematics instruction. Journal for Research in Mathematics Education, 44(4), 646–682. doi:10.5951/jresematheduc.44.4.0646
   Web of Science ®Google Scholar
• Jansen, A. (2008). An investigation of relationships between seventh-grade students’ beliefs and their participation during mathematics discussions in two classrooms. Mathematical Thinking and Learning, 10, 68–100. doi:10.1080/10986060701820327
   Google Scholar
• Jurdak, M. E. (2006). Contrasting perspectives and performance of high school students on problem solving in real world, situated, and school contexts. Educational Studies in Mathematics, 63, 283–301. doi:10.1007/s10649-005-9008-y
   Google Scholar
• Kilpatrick, J., & Izsák, A. (2008). A history of algebra in the school curriculum. In C. Greenes & R. Rubenstein (Eds.),Algebra and algebraic thinking in school mathematics (pp. 3–18). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Kliebard, H. M., & Franklin, B. M. (2003). The ascendance of practical and vocational mathematics, 1893-1945: Academic mathematics under siege. In G. M. A. Stanic, & J. Kilpatrick (Eds.), A history of school mathematics (pp. 399–440). Reston, VA: NCTM.
   Google Scholar
• Lappan, G., Fey, J. T., Friel, S. N., Fitzgerald, W. M., & Phillips, E. D. (2006). Connected mathematics 2. Boston, MA: Prentice Hall.
   Google Scholar
• Lappan, G., & Phillips, E. (2009). A designer speaks: Glenda Lappan and Elizabeth Phillips. Educational Designer, 1(3), 1–19.
   Google Scholar
• Lappan, G., Phillips, E. D., & Fey, J. T. (2007). The case of connected mathematics. In C. R. Hirsch (Ed.), Perspectives on the design and development of school mathematics curricula (pp. 67–79). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Lave, J. (1988). Cognition in practice: Mind, mathematics, and culture in everyday life. New York: Cambridge University Press.
   Google Scholar
• Lobato, J. (2006). Alternative perspectives on the transfer of learning: History, issues, and challenges for future research. The Journal of the Learning Sciences, 15(4), 431–449. doi:10.1207/s15327809jls1504_1
   Web of Science ®Google Scholar
• Lubienski, S. T. (2000). Problem solving as a means toward mathematics for all: An exploratory look through a class lens. Journal for Research in Mathematics Education, 31(4), 454–482. doi:10.2307/749653
   Web of Science ®Google Scholar
• Martin, D. (2000). Mathematical success and failure among African-American youth. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
   Google Scholar
• Masingila, J. O. (1993). Learning from mathematics practice in out-of-school situations. For the Learning of Mathematics, 13(2), 18–22.
   Google Scholar
• Meyer, M. R., Dekker, T., & Querelle, N. (2001). Context in mathematics curricula. Mathematics Teaching in the Middle School, 6(9), 522–527.
   Google Scholar
• Middleton, J. A., & Jansen, A. (2011). Motivation matters and interest counts: Fostering engagement in mathematics. Reston, VA: NCTM.
   Google Scholar
• Nasir, N. S., Hand, V., & Taylor, E. V. (2008). Culture and mathematics in school: Boundaries between ‘cultural’ and ‘domain’ knowledge in the mathematics classroom and beyond. Review of Research in Education, 32, 187–240. doi:10.3102/0091732X07308962
   Web of Science ®Google Scholar
• National Center for Research in Mathematical Sciences Educational Staff. (1998). Mathematics in context. Chicago, IL: Encyclopedia Britannica Educational Corporation.
   Google Scholar
• National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
   Google Scholar
• National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
   Google Scholar
• National Council of Teachers of Mathematics. (2009). Focus on high school mathematics: Reasoning and sense-making. Reston, VA: Author.
   Google Scholar
• National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.
   Google Scholar
• National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Authors.
   Google Scholar
• Nicol, C. (2002). Where’s the math? Prospective teachers visit the workplace. Educational Studies in Mathematics, 50, 289–309. doi:10.1023/A:1021211207232
   Google Scholar
• Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education, The 14th ICMI study (pp. 1–32). New York, NY: Springer Science+Business Media, LLC.
   Google Scholar
• Nyabanyaba, T. (1999). Whither relevance? Mathematics teachers’ discussion of the use of ‘real-life’ contexts in school mathematics. For the Learning of Mathematics, 19(3), 10–14.
   Google Scholar
• Oakes, J. (2005). Keeping track: How schools structure inequality (2nd ed.). New Haven, CT: Yale University Press.
   Google Scholar
• Palm, T. (2006). Word problems as simulations of real-world situations: A proposed framework. For the Learning of Mathematics, 26(1), 42–47.
   Google Scholar
• Palm, T. (2008). Impact of authenticity on sense making in word problem solving. Educational Studies in Mathematics, 67, 37–58. doi:10.1007/s10649-007-9083-3
   Google Scholar
• Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211–246. doi:10.3102/00346543075002211
   Web of Science ®Google Scholar
• Romberg, T. A., & Shafer, M. C. (2003). Mathematics in Context (MiC)—Preliminary evidence about student outcomes. In S. Senk, & D. Thompson (Eds.), Standards-based school mathematics curricula: What are they? What do students learn? Mahweh, NJ: Lawrence Erlbaum Associates.
   Google Scholar
• Roth, W. M. (1996). Where is the context in contextual word problems? Mathematical practices and products in grade 8 students’ answers to story problems. Cognition and Instruction, 14(4), 487–527. doi:10.1207/s1532690xci1404_3
   Web of Science ®Google Scholar
• Strauss, A. L., & Corbin, J. M. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Thousand Oaks, CA: Sage.
   Google Scholar
• Sullivan, P., Zevenbergen, R., & Mousley, J. (2003). The contexts of mathematics tasks and the context of the classroom: Are we including all students? Mathematics Education Research Journal, 15(2), 107–121. doi:10.1007/BF03217373
   Google Scholar
• Tomaz, V. S., & David, M. M. (2015). How students’ everyday situations modify classroom mathematical activity: The case of water consumption. Journal for Research in Mathematics Education, 46(4), 455–496. doi:10.5951/jresematheduc.46.4.0455
   Web of Science ®Google Scholar
• Turner, E. E., Gutiérrez, M. V., Simic-Muller, K., & Díez-Palomar, J. (2009). “Everything is math in the whole world”: Integrating critical and community knowledge in authentic mathematical investigations with elementary Latina/o students. Mathematical Thinking and Learning, 11(3), 136–157. doi:10.1080/10986060903013382
   Web of Science ®Google Scholar
• van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessment problems in mathematics. For the Learning of Mathematics, 25(2), 2–10.
   Google Scholar
• Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, Netherlands: Swets & Zeitlinger B.V.
   Google Scholar
• Walkington, C., Sherman, M., & Petrosino, A. (2012). “Playing the game” of story problems: Coordinating situation-based reasoning with algebraic representation. The Journal of Mathematical Behavior, 31, 174–195. doi:10.1016/j.jmathb.2011.12.009
   Google Scholar
• Walkington, C., Sherman, M., & Petrosino, A. (2013). Supporting algebraic reasoning through personalized story scenarios: How situational understanding mediates performance. Mathematical Thinking and Learning, 15(2), 89–102. doi:10.1080/10986065.2013.770717
   Web of Science ®Google Scholar
• Wernet, J. L. W. (2009). The reality of relevance in the classroom: How secondary teachers at Lansing Christian Schools Use Real-World Connections ( Unpublished manuscript). Spring Arbor University, Spring Arbor, MI.
   Google Scholar
• Wernet, J. L. W. (2011). Authenticity and centrality: Attention to and use of problem contexts in secondary mathematics classrooms ( Unpublished manuscript). Michigan State University, East Lansing, MI.
   Google Scholar
• Wyner, J. S., Bridgeland, J. M., & Diiulio, J. J. (2007). Achievement trap: How America is failing millions of high-achieving students from lower-income families. Lansdowne, VA: Jack Kent Cooke Foundation.
   Google Scholar