School tracking practices have been documented repeatedly as having negative effects on students’ identity development and attainment, particularly for those students placed in lower tracks. Despite this documentation, tracking persists as a normative practice in American high schools, perhaps in part because we have few models of how departments and teachers can successfully organize instruction in heterogeneous, high school mathematics classes. This paper offers one such model through a qualitative and quantitative analysis.
Focus of Study
In an effort to better the field's understanding of equitable and successful teaching, we conducted a longitudinal study of three high schools. At one school, Railside, students demonstrated greater gains in achievement than students at the other two schools and higher overall achievement on a number of measures. Furthermore, achievement gaps among various ethnic groups at Railside that were present on incoming assessments disappeared in nearly all cases by the end of the second year. This paper provides an analysis of Railside's success and identifies factors that contributed to this success.
Participants
Participants included approximately 700 students as they progressed through three California high schools. Railside was an urban high school with an ethnically, linguistically, and economically diverse student body. Greendale was situated in a coastal community with a more homogeneous, primarily White student body. Hilltop was a rural high school with primarily White and Latino/a students.
Research Design
This longitudinal, multiple case study employed mixed methods. Three schools were chosen to offer a range of curricular programs and varied student populations. Student achievement and attitudinal data were evaluated using statistical techniques, whereas teacher and student practices were documented using qualitative analytic techniques such as coding.
Findings/Results
One of the findings of the study was the success of Railside school, where the mathematics department taught heterogeneous classes using a reform-oriented approach. Compared with the other two schools in the study, Railside students learned more, enjoyed mathematics more and progressed to higher mathematics levels. This paper presents large-scale evidence of these important achievements and provides detailed analyses of the ways that the Railside teachers brought them about, with a focus on the teaching and learning interactions within the classrooms.
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References
1.
BeckerJ., and JacobB. (2000). California school mathematics politics: The anti-reform of 1997-1999. Phi Delta Kappan, 81, 529—537.
2.
BlackP., and WiliamD. (1998). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80, 139—148.
3.
BoalerJ. (1997). Experiencing school mathematics: Teaching styles, sex and setting. Buckingham, England: Open University Press.
4.
BoalerJ. (2000). Mathematics from another world: Traditional communities and the alienation of learners. Journal of Mathematical Behavior, 18(4), 379—397.
5.
BoalerJ. (2002a). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student learning. (Revised and expanded edition.) Mahwah, NJ: Lawrence Erlbaum Associates.
6.
BoalerJ. (2002b). Learning from teaching: Exploring the relationship between reform curriculum and equity. Journal for Research in Mathematics Education, 33, 239—258.
7.
BoalerJ. (2002c). The development of disciplinary relationships: Knowledge, practice and identity in mathematics classrooms. For the Learning of Mathematics, 22(1), 42—47.
BoalerJ., and BrodieK. (2004). The importance of depth and breadth in the analysis of teaching: A framework for analysing teacher questions. In the Proceedings of the 26th Meeting of the North America Chapter of the International Group for the Psychology of Mathematics Education. Toronto, Ontario.
10.
BoalerJ., and GresalfiM. S. (in preparation). What is learning? The importance and nature of disciplinary relationships in mathematics.
11.
BriarsD., and ResnickL. (2000). Standards, assessments–and what else? The essential elements of standards-based school improvement. Unpublished manuscript.
12.
ChazanD. (2000). Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom. New York: Teachers College Press.
13.
CohenD., and BallD. L. (2001). Making change: Instruction and its improvement. Phi Delta Kappan, 83, 73—77.
14.
CohenE. (1994). Designing groupwork. New York: Teachers College Press.
15.
CohenE., and LotanR. (Eds.). (1997). Working for equity in heterogeneous classrooms: Sociological theory in practice. New York: Teachers College Press.
16.
CorbettD., and WilsonB. (1995). Make a difference with, not for, students. Educational Researcher, 24, 12—17.
17.
Darling-HammondL. (1998). Teachers and teaching: Testing policy hypotheses from a National Commission Report. Educational Researcher, 27(1), 5—15.
18.
DelpitL. (1988). The silenced dialogue: Power and pedagogy in education other people's children. Harvard Educational Review, 58(3), 280—298.
19.
EisenhartK. (2002) Building theories from case study research. In HubermanA. M., and MilesM. (Eds.). The qualitative researcher's companion, (pp. 3—36). Thousand Oaks, CA: Sage Publications.
20.
FendelD., ResekD., AlperL., and FraserS. (1997). Interactive mathematics program- Year 1. Berkeley, CA: Key Curriculum Press.
21.
FioriN., and BoalerJ. (2004). What discussions teach us about mathematical understanding: Exploring and assessing students’ mathematical work in classrooms. In the Proceedings of the 26th Meeting of the North America Chapter of the International Group for the Psychology of Mathematics Education. Toronto, Ontario.
22.
FreedmanS. W., DelpV., and CrawfordS. M. (2005). Teaching English in untracked classrooms. Research in the teaching of English, 40(1), 62—126.
23.
GeertzC. (2000). The interpretation of cultures. New York: Basic Books.
24.
GlesneC., and PeshkinA. (1992). Becoming qualitative researchers. White Plains, NY: Longman.
25.
GreenoJ. G. (1997). Theories and practices of thinking and learning to think. American Journal of Education, 106, 85—126.
GutiérrezK., LarsonJ., and KreuterB. (1995). Cultural tensions in the scripted classroom: The value of the subjugated perspective. Urban Education, 29(4), 410—442.
28.
GutiérrezK., Baquedano-LopezP., and TejedaC. (1999). Rethinking diversity: Hybridity and hybrid language practices in the third space. Mind, Culture, & Activity: An International Journal, 6(4), 286—303.
29.
GutiérrezR. (1996). Practices, beliefs and cultures of high school mathematics departments: Understanding their influence on student advancement. Journal of Curriculum Studies, 28(5), 495—529.
30.
GutiérrezR. (1999). Advancing urban Latina/o youth in mathematics: Lessons from an effective high school mathematics department. Urban Review, 31(3), 263—281.
31.
GutiérrezR. (2000). Is the multiculturalization of mathematics doing us more harm than good? In MalalinghamR., and McCarthyC. (Eds.), Multicultural Curriculum: New Directions for Social Theory, Practice and Policy (pp. 119—219). New York: Routledge.
32.
HabermanM. (1991) The pedagogy of poverty versus good teaching, Phi Delta Kappan, 73, 290—294.
33.
HandV. (2003). Reframing participation: Meaningful mathematical activity in diverse classrooms. Unpublished dissertation, Stanford University, Stanford, CA.
34.
HeathS. B. (1983). Ways with words: Language, life, and work in communities and classrooms. New York: Cambridge University Press.
35.
HollandD., LachiotteW., SkinnerD., and CainC. (1998). Identity and agency in cultural worlds. Cambridge, MA: Harvard University Press.
36.
HornI. S. (2002). Learning on the job: Mathematics teachers’ professional development in the contexts of high school reform. Unpublished Ph.D. Dissertation, University of California, Berkeley.
37.
HornI. S. (2005). Learning on the job: A situated account of teacher learning in two high school mathematics departments. Cognition & Instruction, 23(2), 207—236.
38.
KnappM. S., ShieldsP. M., and TurnbullB. J. (1992). Academic challenge for the children of poverty. Summary report. Washington, DC: U.S. Department of Education.
39.
Ladson-BillingsG. (1994). Dreamkeepers: Successful teachers of African-American children. San Francisco, CA: Jossey-Bass Publishers.
40.
Ladson-BillingsG. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32(3), 465—491.
41.
LampertM. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.
42.
LeeC. (1995). A culturally based cognitive apprenticeship: Teaching African American high school students skills in literary interpretation. Reading Research Quarterly, 30(4), 608—630.
43.
LinchevskiL., and KutscherB. (1998). Tell me with whom you're learning, and I'll tell you how much you've learned: Mixed-ability versus same-ability grouping in mathematics. Journal for Research in Mathematics Education, 29(5), 533—554.
44.
LubienskiS. (2000). Problem solving as a means towards mathematics for all: An exploratory look through the class lens. Journal for Research in Mathematics Education, 31, 454—482.
45.
MadisonB. L., and HartT. A. (1990). A challenge of numbers: People in the mathematical sciences. Washington, DC: National Academy Press.
46.
MartinoA., and MaherC. (1999). Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us. Journal of Mathematical Behavior, 18(1), 52—78.
47.
McLaughlinM., and TalbertJ. (2001). Professional communities and the work of high school teaching. Chicago: University of Chicago Press.
48.
MosesB., and CobbC. (2001). Radical equations: Math literacy and civil rights. Boston: Beacon Press.
49.
OakesJ. (1985). Keeping track: How schools structure inequality. New Haven, CT: Yale University Press.
RAND. (2002, October). Mathematical proficiency for all students: Toward a strategic research and development program in mathematics education (Dru-2773-OERI). Arlington, VA: RAND Education & Science and Technology Policy Institute.
52.
RosenL. (2001). Myth making and moral order in a debate on mathematics education policy. In SuttonM., and LevinsonB.A.U. (Eds.), Policy as practice: Toward a comparative socio-cultural analysis of educational policy (Vol. 1, pp. 295—316). Westport, CT: Ablex Publishing.
53.
RosenholtzS. J., and WilsonB. (1980). The effect of classroom structure on shared perceptions of ability. American Educational Research Journal, 17, 175—182.
54.
SalleeT., KyshJ., KasimatisE., and HoeyB. (2000). College preparatory mathematics. Sacramento, CA: CPM Educational Program.
55.
SchoenfeldA. (2002). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 13—25.
56.
SilverE. A., SmithM. S., and NelsonB. S. (1995). The QUASAR project: Equity concerns meet mathematics education reform in the middle school. In FennemaE., SecadaW., and AdajianL.B. (Eds.), New directions for equity in mathematics education (pp. 9—56). New York: Cambridge University Press.
57.
SimpsonC. (1981). Classroom structure and the organization of ability. Sociology of Education, 54, 120—132.
58.
SiskinL. S. (1994). Realms of knowledge: Academic departments in secondary schools. Washington, DC: Falmer Press.
59.
SteinM. K., SmithM., HenningsenM., and SilverE. (2000). Implementing standards-based mathematics instruction: A case book for professional development. New York: Teachers College Press.
60.
TalbertJ., and McLaughlinM. (1996). Teacher professionalism in local school contexts. In Goodson, and Hargreaves (Eds.), Teachers’ professional lives (pp. 127—153). Washington, DC: Falmer Press.
61.
TharpR., and GallimoreR. (1988). Rousing minds to life: Teaching, learning, and schooling in social context. New York: Cambridge University Press.
62.
YackelE., and CobbP. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458—477.
63.
YinR. K. (1994). Case study research: Design and methods. Thousand Oaks, CA: Sage Publications.
