Open-ended, or implicit, questioning has been described as central to reform teaching in mathematics. However, concerns about equity have caused some researchers to question whether this kind of teaching is productive for all children.
Purpose
This study explores the role that implicit and explicit questions played in encouraging mathematical thinking in an elementary mathematics class taught by a reform-oriented teacher.
Setting
The study took place in a third-grade classroom located in a small urban school.
Participants
Participants in the study were a European American teacher, a student teacher, and 19 third-grade students in an ethnically and socioeconomically diverse classroom.
Research Design
The study drew on ethnographic interpretive methods to collect data through a yearlong observation of 5 focal students in the third-grade classroom. Conversations during mathematics class were audio-recorded and transcribed. Data also included written field notes, student work, informal interviews with children, and formal interviews with the teacher. Analysis began with open coding of the transcripts and field notes and proceeded to more fine-grained coding and examination of other data.
Data Collection and Analysis
Analysis showed that implicit questions seemed to privilege some children, particularly those who shared the language and cultural practices of the teacher, whereas explicit questions allowed a wider variety of children to participate competently in the mathematics classroom.
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References
1.
BallD. L., GoffneyI. M., & BassH. (2005). Guest editorial: The role of mathematics instruction in building a socially just and diverse democracy.The Mathematics Educator, 15(1), 2–5.
2.
BlantonM. L. (2002). Using an undergraduate geometry course to change preservice teachers’ notions of discourse.Journal of Mathematics Teacher Education, 5, 117–152.
3.
BoalerJ. (2002). Learning from teaching: Exploring the relationship between reform curricula and equity.Journal for Research in Mathematics Education, 33, 239–258.
CazdenC. B. (1988). Classroom discourse: The language of teaching and learning. Portsmouth, NH: Heinemann.
6.
CobbP., BoufiA., McClainK., & WhitenackJ. (1997). Reflective discourse and collective reflection.Journal for Research in Mathematics Education, 28, 258–277.
7.
CobbP., GravemeijerK., YackelE., McClainK., & WhitenackJ. (1997). Mathematizing and symbolizing: The emergence of chains of signification in one first-grade classroom. In KirshnerD. & WilsonJ. A. (Eds.), Situated cognition (pp. 151–234). Mahwah, NJ: Erlbaum.
8.
DavidsonE., & HammermanJ. (1993). Homogenized is only better for milk. In CuevasG. & DriscollM. (Eds.), Reaching all students with mathematics (pp. 197–211). Reston, VA: National Council of Teachers of Mathematics.
9.
DelpitL. (1995). Other people's children: Cultural conflict in the classroom. New York: New Press.
10.
DysonA. H. (1997). Writing superheroes: Contemporary childhood, popular culture, and classroom literacy. New York: Teachers College Press.
11.
DysonA. H. (2003). The brothers and sisters learn to write: Popular literacies in childhood and school culture. New York: Teachers College Press.
12.
DysonA. H., & GenishiC. (2005). On the case: Approaches to language and literacy research. New York: Teachers College Press.
13.
EmersonR. M., FretzR. I., & ShawL. L. (1995). Writing ethnographic fieldnotes. Chicago: University of Chicago Press.
14.
EricksonF. (1986). Qualitative methods in research on teaching. In WittrockM. C. (Ed.), Handbook of research on teaching (pp. 119–160). New York: Macmillan.
15.
EricksonF., & GutierrezK. (2002). Culture, rigor, and science in educational research.Educational Researcher, 31(8), 21–24.
16.
FormanE., & AnsellE. (2001). The multiple voices of a mathematical classroom community.Educational Studies in Mathematics, 46(1), 115–142.
17.
GeertzC. (1973). Thick description: Toward an interpretive theory of culture.The interpretation of cultures: Selected essays (pp. 3–32). New York: Basic Books.
18.
GutsteinE., LipmanP., HernandezP., & de los ReyesR. (1997). Culturally relevant mathematics teaching in a Mexican American context.Journal for Research in Mathematics Education, 28, 709–737.
19.
HabermanM. (1991). The pedagogy of poverty versus good teaching.Phi Delta Kappan, 73, 290–294.
20.
HeathS. B. (1982). Questioning at home and at school: A comparative study. In SpindlerG. (Ed.), Doing the ethnography of schooling (pp. 103–127). New York: Holt, Rinehart and Winston.
21.
HeatonR. M. (2000). Teaching mathematics to the new standards: Relearning the dance. New York: Teachers College Press.
22.
Ladson-BillingsG. (1995). But that's just good teaching! The case for culturally relevant pedagogy.Theory Into Practice, 34, 159–165.
23.
Ladson-BillingsG. (1997). It doesn't add up: African American students’ mathematics achievement.Journal for Research in Mathematics Education, 28, 697–708.
24.
LampertM. (1990). When the problem is not the question and the solution is not the answer.American Educational Research Journal, 27, 29–63.
25.
LampertM. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.
26.
LubienskiS. 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, 454–482.
27.
McCroneS. (2005). The development of mathematical discussions: An investigation in a fifth-grade class.Mathematical Thinking and Learning, 7, 111–133.
28.
MewbornD., & HubertyP. D. (1999). Questioning your way to the standards.Teaching Children Mathematics, 6, 243–246.
29.
MosesB., & CobbC. E. (2001). Radical equations: Civil rights from Mississippi to the Algebra Project. Boston: Beacon Press.
30.
MoyerP. S., & MilewiczE. (2002). Learning to question: Categories of questioning used by preservice teachers during diagnostic mathematics interviews.Journal of Mathematics Teacher Education, 5, 293–315.
31.
National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.
32.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
33.
OmiM., & WinantH. (2004). On the theoretical status of the concept of race. In Ladson-BillingsG. & GillbornD. (Eds.), The RoutledgeFalmer reader in multicultural education (pp. 7–15). London: RoutledgeFalmer.
34.
SimonM. A., & SchifterD. (1991). Towards a constructivist perspective: An intervention study of mathematics teacher development.Educational Studies in Mathematics, 22, 309–331.
35.
StarJ. (2005). Reconceptualizing procedural knowledge.Journal for Research in Mathematics Education, 36, 404–411.
TraftonP. R., & ClausA. S. (1994). A changing curriculum for a changing age. In ThorntonC. A. & BleyN. S. (Eds.), Windows of opportunity: Mathematics for students with special needs (pp. 19–39). Reston, VA: National Council of Teachers of Mathematics.
38.
VaccN. (1993). Questioning in the mathematics classroom.The Arithmetic Teacher, 41(2), 88–91.
39.
van de WalleJ. A. (2004). Elementary and middle school mathematics: Teaching developmentally. Boston: Allyn and Bacon.
40.
WhiteD. Y. (2000). Reaching all students mathematically through questioning. In StrutchensM. E., JohnsonM. L., & TateW. F. (Eds.), Changing the faces of mathematics: Perspectives on African Americans (pp. 21–32). Reston, VA: National Council of Teachers of Mathematics.
41.
YackelE., & HannaG. (2003). Reasoning and proof. In KilpatrickJ., MartinW. G., & SchifterD. (Eds.), A research companion to Principles and Standards for School Mathematics (pp. 227–236). Reston, VA: National Council of Teachers of Mathematics.
