Handbook of psychology volume 7 educational psychology

References

387

Giere, R. N. (1992). Cognitive models of science. Minneapolis:

University of Minnesota Press.

Goldenberg, E. P., Cuoco, A. A., & Mark, J. (1998). A role for geom-

etry in general education. In R. Lehrer & D. Chazan (Eds.),

Designing learning environments for developing understanding

of geometry and space (pp. 3–44). Mahwah, NJ: Erlbaum.

Goodman, N. (1976). Languages of art. Indianapolis, IN: Hackett.

Goodnow, J. (1977). Children’s drawings. Cambridge, MA:

Harvard University Press.

Goodwin, C. (1994). Professional vision. American Anthropologist,

96(3), 606–633.

Goodwin, C. (2000). Practices of color classification. Mind, culture,

and activity, 7(1 & 2), 19–36.

Greeno, J. G. (1998). The situativity of knowing, learning, and

research. American Psychologist, 53, 5–26.

Hall, R. (1990). Making mathematics on paper: Constructing repre-

sentations of stories about related linear functions. Unpublished

doctoral dissertation, University of California at Irvine.

Hall, R. (1996). Representation as shared activity: Situated cogni-

tion and Dewey’s cartography of experience. The Journal of the

Learning Sciences, 5(3), 209–238.

Hall, R. (1999). The organization and development of discursive

practices for “having a theory.” Discourse Processes, 27, 187–

218.

Hall, R., Stevens, R., & Torralba, T. (in press). Disrupting represen-

tational infrastructure in conversations across disciplines. Mind,

Culture, and Activity, 9(3).

Halliday, M. A. K. (1978). Sociolinguistics aspects of mathematical

education. In M. Halliday (Ed.), Language as social semiotic: The

social interpretation of language and meaning (pp. 195–204).

London: University Park Press.

Hanna, G. (1991). Mathematical proof. In D. Tall (Ed.), Advanced

mathematical thinking (pp. 54–61). Dordrecht, The Netherlands:

Kluwer Academic Publishers.

Hanna, G. (1995). Challenges to the importance of proof. For the

Learning of Mathematics, 15, 42–49.

Harel, G. (1998). Greek versus modern mathematical thought and

the role of Aristotelian causality in the mathematics of the

Renaissance: Sources for understanding epistemological obsta-

cles in college students’ conceptions of proof. Plenary talk given

at the International Linear Algebra Society Conference, Madison,

WI.

Harel, G., & Sowder, L. (1998). Students’ proof schemes. In E.

Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research on colle-

giate mathematics education (Vol. 3, pp. 234–283). American

Mathematical Society.

Harel, I., & Papert, S. (1991). Constructionism. Norwood, NJ: Ablex.

Harris, P. J., & Leevers, H. J. (2001). Reasoning from false

premises. In P. Mitchell & K. J. Riggs (Eds.), Children’s reason-

ing and the mind (pp. 67–86). UK: Psychology Press, Taylor and

Francis.

Hartmann, C., & Lehrer, R. (2000). Quilt design as incubator for

geometric ideas and mathematical habits of mind. Proceedings

of the 22nd annual meeting of the North American Chapter of the

International Group for the Psychology of Mathematics Educa-

tion, Tucson, AZ.

Hatano, G., & Ito, Y. (1965). Development of length measuring

behavior. Japanese Journal of Psychology, 36, 184 –196.

Haverty, L. A., Koedinger, K. R., Klahr, D., & Alibali, M. W.

(2000). Solving inductive reasoning problems in mathematics:

Not-so-trivial pursuit. Cognitive Science, 24, 249 –298.

Hawkins, J., Pea, R. D., Glick, J., & Scribner, S. (1984). “Merds that

laugh don’t like mushrooms.” Developmental Psychology, 20,

584 –594.

Healy, L., & Hoyles, C. (2000). A study of proof conceptions in

algebra. Journal for Research in Mathematics Education, 31,

396 – 428.

Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and stu-

dent cognition: Classroom-based factors that support and inhibit

high-level mathematical thinking and reasoning. Journal for

Research in Mathematics Education, 28(5), 524 –549.

Herbst, P. (2002). Understanding the work of the teacher getting stu-

dents to prove. Journal of Research in Mathematics Education,

33, 176 –203.

Hersh, R. (1993). Proving is convincing and explaining. Educa-

tional Studies in Mathematics, 24(4), 389–399.

Hershkowitz, R., & Schwarz, B. B. (1999). Reflective processes

in a mathematics classroom with a rich learning environment.

Cognition and Instruction, 17, 65–91.

Hesse, M. B. (1965). Forces and fields. Totowa, NJ: Littlefield,

Adams.

Hestenes, D. (1992). Modeling games in the Newtonian world.

American Journal of Physics, 60, 440 – 454.

Hiebert, J. (1981a). Cognitive development and learning linear

measurement. Journal for Research in Mathematics Education,

12, 197–211.

Hiebert, J. (1981b). Units of measure: Results and implications from

national assessment. Arithmetic Teacher, 28, 38– 43.

Hiebert, J. (1984). Why do some children have trouble learning

measurement concepts? Arithmetic Teacher, 31, 19–24.

Hildreth, D. J. (1983). The use of strategies in estimating measure-

ments. Arithmetic Teacher, 30, 50 –54.

Hodgson, T., & Riley, K. J. (2001). Real-world problems as contexts

for proof. Mathematics Teacher, 94(9), 724–728.

Hoyles, C. (1997). The curricular shaping of students’ approaches to

proof. For the Learning of Mathematics, 17, 7–16.

Izsak, A. (2000). Inscribing the winch: Mechanisms by which

students develop knowledge structures for representing the

physical world with algebra. The Journal of the Learning

Sciences, 9(1), 31–74.

Jackiw, N. (1995). The geometer’s sketchpad. Berkeley, CA: Key

Curriculum Press.

388

Mathematical Learning

Jacobson, C., & Lehrer, R. (2000). Teacher appropriation and

student learning of geometry through design. Journal for

Research in Mathematics Education, 31, 71–88.

Joram, E., Subrahmanyam, K., & Gelman, R. (1998). Measurement

estimation: Learning to map the route from number to quantity

and back. Review of Educational Research, 68, 413– 449.

Jorgensen, J. C., & Falmagne, R. J. (1992). Aspects of the meaning of

if . . . then for older preschoolers: Hypotheticality, entailment, and

suppositional processes. Cognitive Development, 7, 189 –212.

Kaiser, D. (2000). Stick-figure realism: Conventions, reification,

and the persistence of Feynman diagrams, 1948–1964. Repre-

sentations, 70, 49–86.

Kaput, J. (1992). Technology and mathematics education. In D. A.

Grouws (Ed.), Research on mathematics teaching and learning

(pp. 515–556). New York: Macmillan.

Kaput, J. (1999). Teaching and learning a new algebra. In E.

Fennema & T. A. Romberg (Eds.), Mathematics classrooms that

promote understanding (pp. 133–155). Mahwah, NJ: Erlbaum.

Kaput, J., & Shaffer, D. (in press). On the development of human

representational competence from an evolutionary point of view.

In K. Gravemeijer, R. Lehrer, B. Van Oers, & L. Verschaffel

(Eds.), Symbolizing, modeling, and tool use in mathematics edu-

cation (pp. 269–286). Dordrecht, The Netherlands: Kluwer Aca-

demic.

Karmiloff-Smith, A. (1992). Beyond modularity. Cambridge, MA:

MIT Press.

Kelly, A. E., & Lesh, R. A. (Eds.). (2000). Handbook of research

design in mathematics and science education. Mahwah, NJ:

Erlbaum.

Kemeny, V. (2001). Discursive construction of mathematical mean-

ing: A study of teaching mathematics through conversation in the

primary grades. Unpublished doctoral dissertation, University

of Wisconsin, Madison.

Kerr, D. R., & Lester, S. K. (1976). An error analysis model for mea-

surement. In D. Nelson & R. E. Reys (Eds.), Measurement in

school mathematics (pp. 105–122). Reston, VA: National Coun-

cil of Teachers of Mathematics.

Kline, M. (1980). Mathematics: The loss of certainty. Oxford, UK:

Oxford University Press.

Koedinger, K. R. (1998). Conjecturing and argumentation in high-

school geometry students. In R. Lehrer & D. Chazan (Eds.),

Designing learning environments for developing understanding

of geometry and space (pp. 319 –347). Mahwah, NJ: Erlbaum.

Koedinger, K. R., & Anderson, J. R. (1990). Abstract planning and

perceptual chunks: Elements of expertise in geometry. Cognitive

Science, 14, 511–550.

Konold, C., & Pollatsek, A. (in press). Data analysis as the search

for signals in noisy processes. Journal for Research in Mathe-

matics Education.

Kotovsky, L., & Gentner, D. (1996). Comparison and categorization

in the development of relational similarity. Child Development,

67, 2797–2822.

Krummerheuer, G. (1995). The ethnography of argumentation. In

P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical

meaning (pp. 229–269). Mahwah, NJ: Erlbaum.

Krummerheuer, G. (1998). Formats of argumentation in the mathe-

matics classroom. In H. Steinbring, M. G. Bartolini Bussi, & A.

Sierpinska (Eds.), Language and communication in the mathe-

matics classroom (pp. 223–234). Reston, VA: National Council

of Teachers of Mathematics.

Kuhn, D. (1977). Conditional reasoning in children. Developmental

Psychology, 13, 342–353.

Kuhn, D. (1989). Children and adults as intuitive scientists. Psycho-

logical Review, 96, 674–689.

Kuhn, D. (1991). The skills of argument. Cambridge, UK:

Cambridge University Press.

Kuhn, D. (1992). Thinking as argument. Harvard Educational

Review, 62, 155–178.

Kuhn, D. (2001). How do people know? Psychological Science,

12(1), 1–8.

Kuhn, D., Amsel, E., & O’Loughlin, M. (1988). The development of

scientific thinking skills. New York: Academic Press.

Kuhn, D., Shaw, V., & Felton, M. (1997). Effects of dyadic instruc-

tion on argumentative reasoning. Cognition and Instruction, 15,

287–315.

Lakatos, I. (1976). Proofs and refutations. Cambridge, UK:

Cambridge University Press.

Lakoff, G., & Nunez, R. E. (1997). The metaphorical structure of

mathematics: Sketching out cognitive foundations for a mind-

based mathematics. In L. D. English (Ed.), Mathematical reason-

ing. Analogies, metaphors, and images (pp. 21–89). Mahwah, NJ:

Erlbaum.

Lakoff, G., & Nunez, R. E. (2000). Where mathematics comes from.

New York: Basic Books.

Lampert, M. (2001). Teaching problems and the problems of teach-

ing. New Haven, CT: Yale University Press.

Lampert, M., Rittenhouse, P., & Crumbaugh, C. (1996). Agreeing

to disagree: Developing sociable mathematical discourse. In

D. Olson & N. Torrance (Eds.), The handbook of education and

human development (pp. 731–764). Cambridge, MA: Blackwell.

Latour, B. (1986). Visualization and cognition: Thinking with eyes

and hands. Knowledge and Society: Studies in the Sociology of

Culture Past and Present, 6, 1–40.

Latour, B. (1987). Science in action: How to follow scientists and

engineers through society. Cambridge, MA: Harvard University

Press.

Lee, K., Karmiloff-Smith, A., Cameron, C. A., & Dodsworth, P.

(1998). Notational adaptation in children. Canadian Journal of

Behavioural Science, 30, 159–171.

Lehrer, R. (2002). Developing understanding of measurement. In

J. Kilpatrick, G. Martin, & D. Schifter (Eds.), A research com-

panion to the Standards and Principles. Reston, VA: National

Council of Teachers of Mathematics.

References

389

Lehrer, R., Guckenberg, T., & Lee, O. (1988a). Comparative study

of the cognitive consequences of inquiry-based Logo instruction.

Journal of Educational Psychology, 80(4), 543–553.

Lehrer, R., Jacobson, C., Kemeny, V., & Strom, D. (1999). Building

on children’s intuitions to develop mathematical understanding

of space. In E. Fennema & T. A. Romberg (Eds.), Classrooms that

promote mathematical understanding (pp. 63–87). Mahwah,

NJ: Erlbaum.

Lehrer, R., Jacobson, C., Thoyre, G., Kemeny, V., Strom, D., Horvath,

J., Gance, S., & Koehler, M. (1998). Developing understanding of

geometry and space in the primary grades. In R. Lehrer &

D. Chazan (Eds.), Designing learning environment for develop-

ing understanding of geometry and space (pp. 169–200).

Mahwah, NJ: Erlbaum.

Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of

children’s reasoning about space and geometry. In R. Lehrer & D.

Chazan (Eds.), Designing learning environment for developing

understanding of geometry and space (pp. 137–167). Mahwah,

NJ: Erlbaum.

Lehrer, R., & Pritchard, C. (in press). Symbolizing space into being.

In K. Gravemeijer, R. Lehrer, B. Van Oers, & L. Verschaffel

(Eds.), Symbolizing, modeling, and tool use in mathematics edu-

cation. Dordrecht, The Netherlands: Kluwer Academic Press.

Lehrer, R., Randle, L., & Sancilio, L. (1989). Learning pre-proof

geometry with LOGO. Cognition and Instruction, 6, 159–184.

Lehrer, R., & Schauble, L. (2000). Modeling in mathematics and

science. In R. Glaser (Ed.), Advances in Instructional Psychol-

ogy (pp. 101–159). Mahwah, NJ: Erlbaum.

Lehrer, R., & Schauble, L. (2002). Symbolic communication in

mathematics and science: Co-constituting inscription and

thought. In E. Amsel & J. Byrnes (Eds.), The development of

symbolic communication (pp. 167–192). Mahwah, NJ: Erlbaum. 

Lehrer, R., Schauble, L., Carpenter, S., & Penner, D. E. (2000). The

inter-related development of inscriptions and conceptual

understanding. In P. Cobb, E. Yackel, & K. McClain (Eds.),

Symbolizing and communicating in mathematics classrooms:

Perspectives on discourse, tools, and instructional design

(pp. 325–360). Mahwah, NJ: Erlbaum.

Lehrer, R., Strom, D., & Confrey, J. (in press). Grounding metaphors

and inscriptional resonance: Children’s emerging understanding

of mathematical similarity. Cognition and Instruction.

Leinhardt, G., & Schwarz, B. B. (1997). Seeing the problem: An

explanation from Polya. Cognition and Instruction, 15, 395– 434.

Lesh, R. (2002). Research design in mathematics education: Focus-

ing on design experiments. In L. English (Ed.), The international

handbook of research design in mathematics education (pp. 241–

287). Hillsdale, N.J.: Erlbaum.

Lesh, R., & Doerr, H. (1998). Symbolizing, communicating, and

mathematizing: Key components of models and modeling. In

P. Cobb & E. Yackel (Eds.), Symbolizing and communicating

in mathematics classrooms (pp. 361–383). Mahwah, NJ:

Erlbaum.

Lesh, R., & Harel, G. (in press). Problem solving, modeling and

local conceptual development. Models and modeling in mathe-

matics education [Monograph for International Journal for

Mathematical Thinking and Learning]. Hillsdale, NJ: Erlbaum. 

Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Princi-

ples for developing thought revealing activities for students and

teachers. In A. Kelly & R. Lesh (Eds.), The handbook of research

design in mathematics and science education (pp. 591–646).

Hillsdale, NJ: Erlbaum.

Leslie, A. M. (1987). Pretense and representation: The origins of

“theory of mind.” Psychological Review, 94, 412–426.

Levi, I. (1996). For the sake of the argument. Cambridge, England:

Cambridge University Press.

Lindquist, M. (1989). The measurement standards. Arithmetic

Teacher, 37, 22–26.

Lynch, M. (1990). The externalized retina: Selection and mathemati-

zation in the visual documentation of objects in the life sciences.

In M. Lynch & S. Woolgar (Eds.), Representation in scientific

practice (pp. 153–186). Cambridge, MA: MIT Press.

Martin, W. G., & Harel, G. (1989). Proof frames of preservice

elementary teachers. Journal for Research in Mathematics

Education, 20, 41–51.

McClain, K., & Cobb, P. (2001). An analysis of development of

sociomathematical norms in one first-grade classroom. Journal

for Research in Mathematics Education, 32, 236–266.

McClain, K., Cobb, P., Gravemeijer, K., & Estes, B. (1999).

Developing mathematical reasoning within the context of mea-

surement. In L. V. Stiff & F. R. Curcio (Eds.), Developing

mathematical reasoning in grades K-12 (pp. 93–106). Reston,

VA: National Council of Teachers of Mathematics.

Meira, L. (1995). The microevolution of mathematical representa-

tions in children’s activity. Cognition and Instruction, 13, 269–

313.

Meira, L. (in press). Mathematical representations as systems of

notations-in-use. In K. Gravemeijer, R. Lehrer, B. Van Oers, & L.

Verschaffel (Eds.), Symbolizing, modeling, and tool use in mathe-

matics education (pp. 89–106). Dordrecht, The Netherlands:

Kluwer.

Miller, C. S., Lehman, J. F., & Koedinger, K. R. (1999). Goals and

learning in microworlds. Cognitive Science, 23, 305–336.

Miller, K. F. (1984). Child as the measurer of all things: Measure-

ment procedures and the development of quantitative concepts.

In C. Sophian (Ed.), Origins of cognitive skills (pp. 193–228).

Hillsdale, NJ: Erlbaum.

Miller, K. F., & Baillargeon, R. (1990). Length and distance: Do

preschoolers think that occlusion bring things together? Devel-

opmental Psychology, 26, 103–114.

Moschkovich, J. N. (1996). Moving up and getting steeper: Negoti-

ating shared descriptions of linear graphs. The Journal of the

Learning Sciences, 5, 239–277.

Moss, J., & Case, R. (1999). Developing children’s understanding

of the rational numbers: A new model and an experimental

390

Mathematical Learning

curriculum. Journal for Research in Mathematics Education, 30,

122–147.

Munn, P. (1998). Symbolic function in pre-schoolers. In C. Donlan

(Ed.), The development of mathematical skills (pp. 47–71).

Hove, UK: Psychology Press, Taylor & Francis.

Nemirovsky, R., & Monk, S. (2000). “If you look at it the other

way . . .”:  An  exploration into the nature of symbolizing. In

P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and

communicating in mathematics classrooms. Perspectives on

discourse, tools, and instructional design (pp. 177–221).

Mahwah, NJ: Erlbaum.

Nemirovsky, R., Tierney, C., & Wright, T. (1998). Body motion and

graphing. Cognition and Instruction, 16, 119–172.

Newcombe, N. S., & Huttenlocher, J. (2000). Making space.

Cambridge, MA: MIT Press.

Noss, R., & Hoyles, C. (1996). Windows on mathematical meaning.

Amsterdam: Kluwer Academic.

Nunes, T. (1999). Mathematics learning as the socialization of the

mind. Mind, Culture, and Activity, 6, 33–52.

Nunes, T., Light, P., & Mason, J. (1993). Tools for thought: The

measurement of length and area. Learning and Instruction, 3,

39–54.

O’Brien, D., Dias, M., Roazzi, A., & Braine, M. (1998). Conditional

reasoning: The logic of supposition and children’s understanding

of pretense. In M. D. S. Braine & D. P. O’Brien (Eds.), Mental

logic (pp. 245–272). Mahwah, NJ: Erlbaum.

Ochs, E., Jacoby, S., & Gonzales, P. (1994). Interpretive journeys:

How physicists talk and travel through graphic space. Configu-

rations, 2, 151–171.

Ochs, E., Taylor, C., Rudolph, D., & Smith, R. (1992). Storytelling

as a theory-building activity. Discourse Processes, 15, 37–72.

O’Connor, M. C., & Michaels, S. (1993). Aligning academic task and

participation status through revoicing: Analysis of a classroom

discourse. Anthropology and Education Quarterly, 24, 318–335.

O’Connor, M. C., & Michaels, S. (1996). Shifting participant frame-

works: Orchestrating thinking practices in group discussion. In

D. Hicks (Ed.), Discourse, learning, and schooling (pp. 63–103).

Cambridge, UK: Cambridge University Press.

Olson, D. R. (1994). The world on paper. Cambridge, UK: Cambridge

University Press.

Papert, S. (1980). Mindstorms: Children, computers, and powerful

ideas. New York: Basic Books.

Papert, S., Watt, D., diSessa, A., & Weir, S. (1979). Final report of

the Brookline Logo Project: Pt. II. Project summary and data

analysis (Logo Memo No. 53). Cambridge, MA: MIT, Artificial

Intelligence Laboratory.

Penner, E., & Lehrer, R. (2000). The shape of fairness. Teaching

Children Mathematics, 7, 210–214.

Petrosino, A., Lehrer, R., & Schauble, L. (in press). Structuring error

and experimental variation as distribution in the fourth grade.

Mathematical Thinking and Learning.

Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child’s concep-

tion of geometry. New York: Harper and Row.

Pimm, D. (1987). Speaking mathematically: Communication in

mathematics classrooms. London: Routledge & Kegan Paul.

Polya, G. (1945). How to solve it. Princeton, NJ: Princeton University

Press.

Porter, T. M. (1986). The rise of statistical thinking 1820–1900.

Princeton, NJ: Princeton University Press.

Pozzi, S., Noss, R., & Hoyles, C. (1998). Tools in practice, mathe-

matics in use. Educational Studies in Mathematics, 36, 105–122.

Resnick, M. (1994). Turtles, termites, and traffic jams. Cambridge,

MA: MIT Press.

Rips, L. J. (1998). Reasoning and conversation. Psychological

Review, 105, 411–441.

Rips, L. J., Brem, S. K., & Bailenson, J. N. (1999). Reasoning

dialogues. Current Directions in Psychological Science, 8, 172–

177.

Roese, N. (1997). Counterfactual thinking. Psychological Bulletin,

121, 133–148.

Roth, W. M., & McGinn, M. K. (1998). Inscriptions: Toward a the-

ory of representing as social practice. Review of Educational

Research, 68, 35–59.

Rotman, B. (1988). Toward a theory of semiotics of mathematics.

Semiotica, 72, 1–35.

Rotman, B. (1993). Ad Infinitum. Stanford, CA: Stanford University

Press.

Schauble, L. (1996). The development of scientific reasoning in

knowledge-rich contexts. Developmental Psychology, 32, 102–119.

Schoenfeld, A. H. (1988). When good teaching leads to bad results:

The disasters of “well taught” mathematics courses. Educational

Psychologist, 23, 145–166.

Schoenfeld, A. H. (1992). Learning to think mathematically:

Problem solving, metacognition, and sense making in mathe-

matics. In D. A. Grouws (Ed.), Handbook of research on math-

ematics teaching and learning (pp. 334–370). New York:

Macmillan.

Schoenfeld, A. H. (1994). What do we know about mathematics cur-

ricula? Journal of Mathematical Behavior, 13, 55–80.

Schoenfeld, A. H., Smith, J. P., III, & Arcavi, A. (1993). Learning:

The microgenetic analysis of one student’s evolving understand-

ing of a complex subject matter domain. In R. Glaser (Ed.),

Advances in instructional psychology (pp. 55–175). Hillsdale,

NJ: Erlbaum.

Schorr, R., & Clark, K. (in press). Using a modeling approach to

analyze the ways in which teachers consider new ways to teach

mathematics: Models and modeling in mathematics education

[Monograph for International Journal for Mathematical Think-

ing and Learning]. Hillsdale, NJ: Erlbaum.

Schunn, C. D., & Anderson, J. R. (1999). The generality/specificity

of expertise in scientific reasoning. Cognitive Science, 23,

337–370.