Conventional mathematics instruction has failed to help many students in urban schools to develop desirable forms of mathematical proficiency. A promising alternative is offered by instruction that is oriented toward helping students develop a meaningful understanding of mathematical ideas through engagement with challenging mathematical tasks. For 5 years, teachers involved in the QUASAR project have engaged in developing and implementing this alternative style of mathematics instruction in urban middle schools. In this article, some critical features of QUASAR instruction are described and exemplified, and some findings regarding the positive impact of this instruction on students are discussed. Finally, some of the challenges and obstacles encountered in attempting to build the capacity of teachers and schools to offer meaning-oriented mathematics instruction are identified.
Get full access to this article
View all access options for this article.
References
1.
Anyon, J. (1980). Social class and the hidden curriculum of work. Journal of Education, 162(1), 67-92.
2.
Azar, B. (1994, June). Psychology's input leads to better tests. APA Monitor, pp. 1, 15.
3.
Bennett, A. , & Foreman, L. (1991). Visual mathematics. Salem, OR: The Math Leaning Center.
4.
Brown, C. A. , Silver, E. A., & Smith, M. S. (1995, April). Professional development of teachers in the QUASAR project: 7he role of the resource partner. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.
5.
Brown, C. A. , & Smith, M. S. (1994, April). Building capacity for mathematics instructional innovation in urban middle schools: Assisting the development of teachers' capacity. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.
6.
Cohen, E. G. (1984). Talking and working together: Status interaction and learning. In P. Peterson, L. C. Wilkinson, & M. Hallinan (Eds.), Instructional groups in the class-room: Organization and processes (pp. 172-187). Orlando: Academic Press.
7.
Congressional Budget Office . (1987, August). Educational achievement: Explanations and implications of recent trends. Washington, DC: Government Printing Office.
8.
Dossey, J. A. , Mullis, I.V.S., Lindquist, M. M., & Chambers, D. L. (1988). The mathematics report card: Are we measuring up?Princeton, NJ: Educational Testing Service.
9.
Epstein, J. L. , & MacIver, D. J. (1989). Education in the middle grades: Overview of a national survey on practices and trends. Baltimore, MD: Center for Research on Elementary and Middle Schools, Johns Hopkins University.
10.
Fey, J. T. (1981). Mathematics teaching today: Perspectives from three national surveys. Reston, VA: National Council of Teachers of Mathematics.
11.
Fey, J. T. (1990). Quantity. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 61-94). Washington, DC: National Academy Press.
12.
Garcia, E. (1991). Education of linguistically and culturally diverse students: Effective instructional practices (Educational Practice Report: 1). Santa Cruz: University of California, Santa Cruz, National Center for Research on Cultural Diversity and Second Language Learning.
13.
Good, T. L. , & Biddle, B. J. (1988). Research and the improvement of mathematics instruction: The need for observational resources. In D. A. Grouws & T. J. Cooney (Eds.), Effective mathematics teaching (pp. 114-142). Reston, VA: National Council of Teachers of Mathematics.
14.
Grant, G. (1988). The world we created at Hamilton High. Cambridge, MA: Harvard University Press.
15.
Greene, M. (1993). The passions of pluralism: Multiculturalism and the expanding community. Educational Researcher, 22(1), 13-18.
16.
Griffin, S. A. , Case, R., & Siegler, R. S. (1994). Rightstart: Providing the central conceptual prerequisites for first formal learning of arithmetic to students at risk for school failure. In K. McGilly (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 25-49). Cambridge: MIT Press.
17.
Hawkins, B. D. (1993). Math: The great equalizer: Equity 2000 and QUASAR, improving minority standing in gatekeeper courses. Black Issues in Higher Education, 10(6), 38-41.
18.
Henningsen, M. , & Stein, M. K. (in press). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education.
19.
Hiebert, J. (1988). Conceptual and procedural knowledge: 7he case of mathematics. Hillsdale, NJ: Lawrence Erlbaum.
20.
Hiebert, J. , & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York: Macmillan.
21.
Hiebert J. , & Wearne, D. (1993). Instructional tasks, classroom discourse, and students' learning in second-grade arithmetic. American Educational Research Journal, 30, 393-425.
22.
Knapp, M. S. , Adelman, N. E., Marder, C., McCollun, H., Needels, M. C., Shields, P. M., Tumbull, B. J., & Zucker, A. A. (1993). Academic challenge for the children of poverty: Volume 1. Findings and conclusions. Washington, DC: U.S. Department of Education, Office of Policy and Planning.
23.
Kouba, V. L. , Carpenter, T. P., & Swafford, J. O. (1989). Numbers and operations. In M. M. Lindquist (Ed.), Results from the fourth mathematics assessment of the National Assessment of Educational Progress (pp. 64-93). Reston, VA: National Council of Teachers of Mathematics.
24.
Lane, S. (1993). The conceptual framework for the development of a mathematics performance assessment. Educational Measurement: Issues and Practice, 12(2), 16-23.
25.
Lane, S. , & Silver, E. A. (1994, April). Examining students' capacities for mathematical thinking and reasoning in the QUASAR project. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.
26.
Lart, S. , Silver, E. A., & Wang, N. (1995, April). An examination of the performance gains of culturally and linguistically diverse students on a mathematics performance assessment within the QUASAR project. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.
27.
Lesh, R. , Post, T., & Behr, M.(1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum.
28.
Mehan, H. (1979). Learning lessons. Cambridge, MA: Harvard University Press.
29.
Meier, D. (1992). Reinventing teaching. Teachers College Record, 93(1), 594-609.
30.
Mullis, I.V.S. , Dossey, J. A., Owen, E. H., & Phillips, G. W. (1993). NAEP 1992 mathematics report card for the nation and the states. Washington, DC: National Center for Education Statistics.
31.
Mullis, IV.S. , Owen, E. H., & Phillips, G. W. (1990). Accelerating academic achievement: A summary of findings from 20 years of NAEP. Prineton, NJ: Educational Testing Service.
32.
National Council of Teachers of Mathematics . (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
33.
National Council of Teachers of Mathematics . (1991). Professional standards for teaching mathematics. Reston, VA: Author.
34.
National Research Council . (1989). Everybody counts. Washington, DC: National Academy of Sciences.
35.
National Research Council . (1993). Measuring what counts: A conceptual guidefor mathematics assessment. Washington, DC: National Academy of Sciences.
36.
Noddings, N. (1985). Small groups as a setting for research on mathematical problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 345-359). Hillsdale, NJ: Lawrence Erlbanm.
37.
Oakes, J. (1985). Keeping track: How schools structure inequality. New Haven, CT: Yale University Press.
38.
Porter, A. , Floden, R., Freeman, D., Schmidt, W., & Schwille, J. (1988). Content determinants in elementary school mathematics. In D. A. Grouws & T. J. Cooney (Eds.), Effective mathematics teaching (pp. 96-113). Reston, VA: National Council of Teachers of Mathematics.
39.
Raudenbush, S. W. , Rowan, B., & Cheong, Y. F. (1993). Higher order instructional goals in secondary schools: Class, teacher, and school influences. American Educational Research Journal, 30(3), 523-553.
40.
Resnick, L. B. (1987). Education and learning to think. Washington, DC: National Academy Press.
41.
Resnick, L. B. , Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education, 20(1), 8-27.
42.
Romberg, T. A. (1992). Assessing mathematics competence and achievement In H. Berlak (Ed.), Toward a new science of educational testing (pp. 23-52). Albany: State University of New York Press.
43.
Schoenfeld, A. H. (1989). Ideas in the air: Speculations on small group learning, environmental and cultural influences on cognition and epistemology. International Journal of Educational Research, 13, 71-88.
44.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-371). New York: Macmillan.
45.
Secada, W. G. (1992). Race, ethnicity, social class, language, and achievement in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 623-660). New York: Macmillan.
46.
Sigurdson, S. E. , & Olson, A. T. (1992). Teaching mathematics with meaning. The Journal of Mathematical Behavior, 11(1), 37-57.
47.
Sigurdson, S. E. , Olson, A. T., & Mason, R. (1994). Problem solving and mathematics learning. The Journal of Mathematical Behavior, 13(4), 361-388.
48.
Silver, E. A. (1992). Assessment and mathematics education reform in the United States. International Joural of Educational Research, 17(5), 489-502.
49.
Silver, E. A. (1994). Mathematical thinking and reasoning for all students: Moving from rhetoric to reality. In D. F. Robitaille, D. H. Wheeler, & C. Kieran (Eds.), Selected lectures for the 7th International Congress on Mathematical Education (pp. 311-326). Sainte-Foy, Quebec: Les Presses De L'Université Laval.
50.
Silver, E. A. (1995). Rethinking "algebra for all."Educational Leadership, 52(6), 30-33.
51.
Silver, E. A. , & Lane, S. (1993). Assessment in the context of mathematics instruction reform: The design of assessment in the QUASAR project. In M. Niss (Ed.), Assessment in mathematics education and its effects (pp. 59-70). London: Kluwer.
52.
Silver, E. A. , & Lane, S. (1995). Can instructional reform in urban middle schools help narrow the mathematics performance gap? Some evidence from the QUASAR project. Research in Middle Level Education, 18(2), 49-70.
53.
Silver, E. A. , & Smith, M. S. (in press). Building discourse communities in mathematics classrooms: A challenging but worthwhile journey. In P Elliott & M. Kenney (Eds.), Communication in mathematics, K-12. Reston, VA: National Council of Teachers of Mathematics.
54.
Silver, E. A. , Smith, M. S., & Nelson, B. S. (1995). The QUASAR project: Equity concerns meet mathematics education reform in the middle school. In E. Fennema, W. Secada, & L. Byrd (Eds.), New directions for equity in mathematics education (pp. 9-56). New York: Cambridge University Press.
55.
Sleeter, C. , & Grant, C. (1993). Making choices for multicultural education: Five approaches to race, class, and gender. New York: Merrill.
56.
Smith, M. S. , & Silver, E. A. (in press). Meeting the challenges of diversity and relevance. Mathematics Teaching in the Middle School.
57.
Stein, M. K. , Grover, B. W., & Henningsen, M. (in press). Enhanced instruction as a means of building student capacity for mathematical thinking and reasoning. American Educational Research Journal.
58.
Stein, M. K. , & Lane, S. (1995, April). Instructional tasks and student learning: An analysis of the relationship between teaching and learning in the QUASAR project. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.
59.
Stein, M. K. , Silver, E. A., & Smith, M. S. (in press). Mathematics reform and teacher development: A community of practice perspective. In J. Greeno & S. Goldman (Eds.), Thinking practices: A symposium on mathematics and science learning. Hillsdale, NJ: Lawrence Erlbaum.
60.
Stodolsky, S. (1988). The subject matters: Classroom activity in mathematics and social studies. Chicago: University of Chicago Press.
61.
Tate, W. F. (1994). From inner city to ivory tower: Does my voice matter in the academy? Urban Education, 29(3), 245-269.
62.
Webb, N. (1991). Task-related verbal interaction and mathematics learning in small groups. Journal for Research in Mathematics Education, 22, 366-389.
63.
Yackel, E. , Cobb, P., & Wood, T. (1991). Siall-group interactions as a source of learning opportunities in second-grade mathematics. Journal for Research in Mathematics Education, 22(5), 390-408.
