Skip to main content Accessibility help
×
  • Cited by 42
  • James T. Kinard, Institute for Cognitive Literacy, Chicago, Alex Kozulin, International Center for the Enhancement of Learning Potential, Jerusalem
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
2008
Online ISBN:
9780511814655

Book description

This book demonstrates how rigorous mathematical thinking can be fostered through the development of students' cognitive tools and operations. This approach seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children's cognitive functions cannot be viewed as following a natural maturational path: they should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches – Vygotsky's theory of psychological tools and Feuerstein's concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.

Reviews

'… The book raises some interesting ideas and should give rise to some productive reflections.'

Source: American Journal of Psychology

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
×

Contents

References
Alexandrova, E. I. (1998). Matematika: Uchebnik dlia 1 klassa (Mathematics for the 1st grade). Moscow: Dom Pedagogiki.
,American Association for the Advancement of Science. (1990). Science for all Americans: Project 2061. New York: Oxford University Press.
,American Association for the Advancement of Science. (1993). Benchmarks for Science Literacy: Project 2061. New York: Oxford University Press.
Anderson, N. (1996). A functional theory of cognition. Mahwah, NJ: Lawrence Erlbaum.
Atahanov, R. (2000). Matematicheskoe myshlenie I metodiki opredelenija urovnej ego razvitija (Mathematical reasoning and methods of the assessment of the stages of its development). Riga, Latvia: Eksperiments.
Boyer, C. B. (2004). History of analytic geometry. Mineola, NY: Dover Press.
Boyer, C., and Merzbach, U. (1991). A history of mathematics. New York: Wiley.
Brown, A., and Ferrara, R. (1985). Diagnosing zones of proximal development. In J. Wertsch (Ed.), Culture, communication and cognition: Vygotskian perspectives (pp. 273–305). New York: Cambridge University Press.
Bruner, J. (1968). Toward a theory of instruction. New York: Norton.
Cajori, F. (1993). A history of mathematical notations. New York: Dover.
Campbell, G. (Winter 1999/2000). Support them and they will come. Issues in Science and Technology Online. Retrieved January 4, 2005, from www.issues.org
Campione, J., and Brown, A. (1987). Linking dynamic assessment with school achievement. In C. Lidz (Ed.), Dynamic assessment (pp. 82–113). New York: Guilford.
Carroll, J. (1993). Human cognitive abilities. Cambridge: Cambridge University Press.
Chaiklin, S. (2003). The Zone of Proximal Development in Vygotsky's analysis of learning and instruction. In A. Kozulin, B. Gindis, V. Ageyev, and S. Miller (Eds.), Vygotsky's educational theory in cultural context (pp. 39–64). New York: Cambridge University Press.
Chazan, D. (2000). Beyond formulas in mathematics and teaching dynamics of the high school algebra classroom. New York: Teachers College Press.
Cioffi, G., and Carney, J. (1983). Dynamic assessment of reading disabilities. The Reading Teacher, 36, 764–768.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum Associates.
Coolidge, J. L. (1942). A history of geometrical methods. Oxford: Oxford University Press.
Crosby, A. (1997). The measure of reality: Quantification and Western society. New York: Cambridge University Press.
Cummins, J. (2000). Learning to read in a second language. In S. Shaw (Ed.), Intercultural education in European classroom. Stone-on-Trent, UK: Trentham Books.
Davydov, V. (1988a). Problems of developmental teaching: Part 1. Soviet Education, 8, 15–97.
Davydov, V. (1988b). Problems of developmental teaching: Part 2. Soviet Education, 9, 3–83.
Davydov, V. (1988c). Problems of developmental teaching: Part 3. Soviet Education, 10, 3–77.
Davydov, V. (1990). Types of generalization in instruction. Reston, VA: National Council of Teachers of Mathematics.
Davydov, V. (1992). The psychological analysis of multiplication procedures. Focus on Learning Problems in Mathematics, 14, 3–67.
Davydov, V., Gorbov, S., Mikulina, G., and Saveleva, O. (1999). Mathematics: Class 1. Binghamton, NY: State University of New York.
Davydov, V., and Tsvetkovich, Z. (1991). On the objective origin of the concept of fractions. Focus on Learning Problems in Mathematics, 14, 3–67.
Descartes, R. (2001). Discourse on method, optics, geometry, and meteorology. P. J. Oscamp (Tr.). Indianapolis, IN: Hachett.
Duckworth, E. (1987). The having of wonderful ideas. New York: Teachers College Press.
Ekstrom, R. B., French, J. W., Harman, H. H., and Dermen, D. (1976). Manual for kit of factor-referenced cognitive tests. Princeton, NJ: Educational Testing Service.
Ekstrom, R. B., French, J. W., and Harman, H. H. (1979). Cognitive factors: Their identification and replication. Multivariate Behavioral Research Monograph, 79(2), 1–85.
Eves, H. (1990). An introduction to the history of mathematics. Austin, TX: Holt, Rinehart & Winston.
Feuerstein, R. (1990). The theory of structural cognitive modifiability. In B. Presseisen (Ed.), Learning and thinking styles (pp. 68–134). Washington, DC: National Education Association.
Feuerstein, R., Krasilovsky, D., and Rand, Y. (1978). Modifiability during adolescence. In J. Anthony (Ed.), The child and his family: Children and their parents in a changing world (pp. 197–217). London: Wiley.
Feuerstein, R., Rand, Y., and Hoffman, M. (1979). Dynamic assessment of retarded performers. Baltimore, MD: University Park Press.
Feuerstein, R., Rand, Y., Hoffman, M., and Miller, R. (1980). Instrumental Enrichment. Baltimore, MD: University Park Press.
Feuerstein, R., Rand, Y., Falik, L., and Feuerstein, R. S. (2002). Dynamic assessment of cognitive modifiability. Jerusalem: ICELP Press.
Foshay, A. (2007). Brief history of IEA. International Association for the Evaluation of Educational Achievement. Retrieved July 14, 2007, from http://www.iea.nl/brief_ history_of_iea.html
Fosnot, C. T. (Ed.). (1996). Constructivism: Theory, perspectives, and practice. New York: Teachers College Press.
Gerber, M. (2000). Dynamic assessment for students with learning disabilities. In C. Lidz and J. Elliott (Eds.), Dynamic assessment: Prevailing models and applications (pp. 263–292). New York: Elsevier Science.
Gillings, R. J. (1972). Mathematics in the time of the Pharaohs. Mineola, NY: Dover.
Ginsburg, A., Cooke, G., Leinwand, S., Noell, J., and Pollock, E. (2005). Reassessing U.S. international mathematics performance: New findings from the 2003 TIMSS and PISA. Washington, DC: American Institute for Research.
Glasersfeld, E. (1995). Radical constructivism. London: Falmer.
Guthke, J., and Beckmann, J. (2000). Learning test concept and dynamic assessment. In A. Kozulin and Y. Rand (Eds.), Experience of mediated learning (pp. 175–190). Oxford: Pergamon.
Guthke, J., and Wingenfeld, S. (1992). The learning test concept: Origins, state of art, and trends. In C. Haywood and D. Tzuriel (Eds.), Interactive assessment (pp. 64–93). New York: Springer.
Harpaz, Y. (2007). Approaches to teaching thinking: Toward a conceptual mapping of the field. Teachers College Record, 109(8), 1845–1874.
Hatano, G. (1997). Learning arithmetic with an abacus. In T. Nunes and P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 209–232). Hove, UK: Psychology Press.
Haycock, K. (2001). Closing the achievement gap. Educational Leadership, 58(6), 6–11.
Haywood, C., and Lidz, C. (2007). Dynamic assessment in practice. New York: Cambridge University Press.
Henningsen, M., and 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.
Herrenstein, R., and Murrey, C. (1994). The bell curve. New York: Free Press.
Hiebert, J., and Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning. New York: Macmillan.
Hiebert, J., Stigler, J., Jacobs, J., Givvin, K., Garnier, H., Smith, M., Hollingworth, H., Monaster, A., Wearne, D., and Gallimore, R. (2005). Mathematics teaching in the United States today and tomorrow. Results from the TIMSS 1999 Video Study. Educational Evaluation and Policy Analysis, 27, 111–132.
Huang, G. (2000). Mathematics achievement by immigrant children. Educational Policy Analysis Archives, 8(25), 1–15.
Jacobson, D., and Kozulin, A. (2007). Dynamic assessment of proportional reasoning: Human vs. computer-based mediation. Paper presented at the 12th European Conference for Research on Learning and Instruction, Budapest.
Karpov, Y. (2003a). Vygotsky's doctrine of scientific concepts. In Kozulin, A., Gindis, B., Ageyev, V., and Miller, S. (Eds.), Vygotsky's educational theory in cultural context (pp. 65–82). New York: Cambridge University Press.
Karpov, Y. (2003b). Development through the life-span: A neo-Vygotkian approach. In Kozulin, A., Gindis, B., Ageyev, V., and Miller, S. (Eds.), Vygotsky's educational theory in cultural context (pp. 138–155). New York: Cambridge University Press.
Kinard, J. (2001). Cognitive, affective and academic changes in specially challenged inner city youth. In Kozulin, A., Feuerstein, R., and Feuerstein, R. S. (Eds.), Mediated learning experience in teaching and counseling (pp. 55–64). Jerusalem: ICELP Press.
Kinard, J., and Kozulin, A. (2005). Rigorous mathematical thinking: Mediated learning and psychological tools. Focus on Learning Problems in Mathematics, 22, 1–29.
Kline, M. (1972). Mathematical thought from ancient to modern times. New York: Oxford University Press.
Kozulin, A. (1995). The learning process: Vygotsky's theory in the mirror of its interpretations. School Psychology International, 16, 117–129.
Kozulin, A. (1998a). Psychological tools: A sociocultural approach to education. Cambridge, MA: Harvard University Press.
Kozulin, A. (1998b). Profiles of immigrant students' cognitive performance on Raven's progressive matrices. Perceptual and Motor Skills, 87, 1311–1314.
Kozulin, A. (2000). Diversity of Instrumental Enrichment applications. In A. Kozulin and Y. Rand (Eds.), Experience of mediated learning (pp. 257–273). Oxford: Elsevier Scientific.
Kozulin, A. (2005a). Integration of culturally different students in mainstream classes. Paper presented at the International Conference on Inclusive and Cognitive Learning in Schools, Prague.
Kozulin, A. (2005b). Who needs metacognition more: Teachers or students? Paper presented at the Annual Meeting of the American Educational Research Association, Montreal.
Kozulin, A., and Garb, E. (2002). Dynamic assessment of EFL text comprehension. School Psychology International, 23, 112–127.
Kozulin, A., and Garb, E. (2004). Dynamic assessment of literacy: English as a third language. European Journal of Psychology of Education, 19, 65–78.
Kozulin, A., Gindis, B., Ageyev, V., and Miller, S. (Eds.). (2003). Vygotsky's educational theory in cultural context. New York: Cambridge University Press.
Kozulin, A., Kaufman, R., and Lurie, L. (1997). Evaluation of the cognitive intervention with immigrant students from Ethiopia. In A. Kozulin (Ed.), The ontogeny of cognitive modifiability. Jerusalem: ICELP Press.
Levi-Strauss, C. (1969). The elementary structures of kinship. London: Eyre.
Lidz, C., and Gindis, B. (2003). Dynamic assessment of the evolving cognitive functions in children. In A. Kozulin, B. Gindis, V. Ageyev, and S. Miller (Eds.), Vygotsky's educational theory in cultural context (pp. 99–118). New York: Cambridge University Press.
Luria, A. (1976). Cognitive development: Its cultural and social foundations. Cambridge, MA: Harvard University Press.
Lindquist, M. (Ed.). (1989). Results from the 4th mathematics assessment of the National Assessment of Mathematical Progress. Reston, VA: NCTM.
Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ: Lawrence Erlbaum.
Marzano, R. J. (2000). Transforming classroom grading. Alexandria, VA: Association for Supervision and Curriculum Development.
Marzano, R. J. (2006). Classroom assessment and grading that work. Alexandria, VA: Association for Supervision and Curriculum Development.
Mead, G. H. (1974). Mind, self and society. Chicago: University of Chicago Press.
Menninger, K. (1969). Number words and number symbols. Cambridge, MA: MIT Press.
Morris, A. (2000). A teaching experiment: Introducing 4th graders to fractions from the viewpoint of measuring quantities using Davydov's mathematics curriculum. Focus on Learning Problems in Mathematics, 22, 32–84.
National Commission on Mathematics and Science Teaching for the 21st Century and submitted to former U.S. Secretary of Education, Riley, Richard W.. (2000). Before it's too late. Retrieved January 3, 2004, from http://www.ed.gov/inits/Math/glenn/report.pdf
,National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
,National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: NCTM.
,National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics. Reston, VA: NCTM.
,National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
,National Council of Teachers of Mathematics. (2001). Navigating in algebra in grades 6–8. Reston, VA: NCTM
,National Research Council. (1996). National science education standards. Washington, DC: National Academy Press.
,National Science Foundation. (2000). America's investment in the future. Arlington, VA: NSF.
Newton, X. (2007). Reflections on math reforms in the U.S.: A cross-national perspective. Phi Delta Kappan, 88(9), 681–685.
Nunes, T. (1999). Mathematics learning and the socialization of the mind. Mind, Culture, and Activity, 6, 33–52.
O'Donnell, B., and Taylor, A. (2006/2007). A lesson plan as professional development?: You've got to be kidding!Teaching Children Mathematics: National Council of Teachers of Mathematics, 13(5), 272–278.
Olson, D. (1994). The world on paper: The conceptual and cognitive implications of writing and reading. New York: Cambridge University Press.
Olson, S. (1999). Candid camera [Electronic version]. Teacher Magazine, May/June. Retrieved January 3, 2005, from www.ed.gov/inits/Math/glenn/report.pdf
Otis, A. S., and Lennon, R. T. (1996). Otis-Lennon school ability test. San Antonio, TX: Harcourt Brace.
Perkins, D., and Salomon, G. (1989). Are cognitive skills content bound?Educational Researcher, 18, 16–25.
Piaget, J. (1947/1969). Psychology of intelligence. Totowa, NJ: Littlefield, Adams & Co.
Piaget, J. (1970). Structuralism. New York: Basic Books.
Pullan, J. M. (1968). The history of abacus. London: Books That Matter.
Reese, C., Miller, K., Mazzeo, J., and Dossey, J. (1997). NAEP 1996 mathematics report card for the nation and the states. Washington, DC: National Center for Education Statistics.
Reys, B., and Lappan, G. (2007). Consensus or confusion?: The intended math curriculum in state-level standards. Phi Delta Kappan, 88(9), 676–680.
Rogoff, B. (1990). Apprenticeship in thinking. Oxford: Oxford University Press.
Rogoff, B. (2003). The cultural nature of human development. New York: Oxford University Press.
Rothman, R. (2006). (In)Formative assessments: New tests and activities can help teachers guide student learning. Harvard Education Letter, 22(6). Retrieved January 3, 2006, from http://www.timeoutfromtesting.org/0519_article_harvard.php
Schmittau, J. (2003). Cultural historical theory and mathematics education. In A. Kozulin, B. Gindis, V. Ageyev, and S. Miller (Eds.), Vygotsky's educational theory in cultural context (pp. 225–245). New York: Cambridge University Press.
Schmittau, J. (2004). Vygotskian theory and mathematical education. European Journal of Psychology of Education, 19, 19–44.
Schoultz, J., Saljo, R., and Wyndhamn, J. (2001). Heavenly talk: Discourse, artifacts and children's understanding of elementary astronomy. Human Development, 44, 103–118.
Scribner, S., and Cole, M. (1981). Psychology of literacy. Cambridge, MA: Harvard University Press.
Sertima, I. V. (Ed.). (1984). Blacks in science, ancient and modern. New Brunswick, NJ: Transaction Books.
Sfard, A. (1998). On two metaphors for learning and the danger of choosing just one. Educational Researcher, 27(2), 4–13.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(1), 4–14.
Smeltzer, D. (2003). Man and number. Mineola, NY: Dover.
Smith, D. E. (1958). History of mathematics. New York: Dover.
Smith, I., Martin, M., Mullis, I., and Kelly, D. (2000). Profiles of student achievement in science at the TIMSS international benchmarks. Chestnut Hill, MA: Boston College.
Stafylidou, S., and Vosniadou, S. (2004). The development of students' understanding of fractions. Learning and Instruction, 14(5), 503–518.
Stech, S. (2007). Special features of cognition and learning in the school context. Transylvanian Journal of Psychology, 2, 63–76.
Sternberg, R. (1980). Sketch of a componental subtheory of human intelligence. Behavioral and Brain Sciences, 3, 573–584.
Sternberg, R., and Grigorenko, E. (2002). Dynamic testing. New York: Cambridge University Press.
Stigler, J., Chalip, L., and Miller, K. F. (1986). Consequences of skill: The case of abacus training in Taiwan. American Journal of Education, 94(4), 447–479.
Stigler, J., and Hiebert, J. (1997). Understanding and improving classroom mathematics instruction: An overview of TIMSS video study. Phi Delta Kappan, 79(1), 14–21.
Sunderman, G., and Orfield, G. (2006). Domesticating a revolution: No Child Left Behind reforms and state administrative response. Harvard Educational Review, 76, 526–555.
Vamvakoussi, X., and Vosniadou, S. (2004). Understanding the structure of the set of rational numbers. Learning and Instruction, 14(5), 453–467.
Verschaffel, L. (1999). Realistic mathematical modeling and problem solving in the upper elementary school. In J. H. M. Hamers, J. E. H. Van Luit, and B. Csabo (Eds.), Teaching and learning thinking skills (pp. 215–240). Lisse: Swets & Zeitlinger.
Vinovskis, M. A. (2007). Overseeing the nation's report card: The creation and evolution of the National Assessment Governing Board (NAGB). Washington, DC: National Assessment Governing Board, U.S. Department of Education.
Vygotsky, L. (1978). Mind in society. Cambridge, MA: Harvard University Press.
Vygotsky, L. (1979). Instrumental method in psychology. In J. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 134–143). Armonk, NY: Sharpe.
Vygotsky, L. (1986). Thought and language (rev. ed.). Cambridge, MA: MIT Press.
Vygotsky, L. (1998). Child psychology: The collected works of L. S. Vygotsky (Vol. 5). New York: Plenum.
Vygotsky, L., and Luria, A. (1993). Studies on the history of behavior. Hillsdale, NJ: Lawrence Erlbaum.
Werner, H., and Kaplan, B. (1984). Symbol formation. Hillsdale, NJ: Lawrence Erlbaum.
Wixson, K. K., Dutro, E., and Athan, R. G. (2003). The challenge of developing content standards. Review of Research in Education, American Educational Research Association, 27, 69–82.
Wood, D. (1999). Teaching the young child: Some relationships between social interaction, language, and thought. In P. Lloyd and C. Fernyhough (Eds.), Lev Vygotsky: Critical assessments (Vol. 3, pp. 259–275). London: Routledge.
Xie, X. (2002). The cultivation of problem-solving and reason in NCTM and Chinese national standards. Nanjing: Nanjing Normal University, School of Education.
Zaslavsky, C. (1984). The Yoruba number system. In I. V. Sertima (Ed.), Blacks in science, ancient and modern (pp. 110–126). New Brunswick, NJ: Transaction Books.
Zuckerman, G. (2003). The learning activity in the first years of schooling. In A. Kozulin, B. Gindis, V. Ageyev, and S. Miller (Eds.), Vygotsky's educational theory in cultural context (pp. 177–199). New York: Cambridge University Press.
Zuckerman, G. (2004). Development of reflection through learning activity. European Journal of Psychology of Education, 19, 9–18.

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.