REFERENCES
9 THE MATHEMATICAL WORLD
Behr, M., Lesh, R., Post,
T., & Silver, E. (1983). Rational number concepts. In R. Lesh & M. Lindau (Eds.), Acquisition
of mathematical concepts and processes (pp. 91-126). New York: Academic Press.
Bliss, J. (1978). Ideas
of chance and probability in children and adolescents. Physics Education, 13,
408-413.
Burger, W., &
Shaughnessy, J. (1986). Characterizing the van Hiele levels of development in geometry.
Journal for Research in Mathematics Education, 17, 31-48.
Carpenter, T.,
Corbitt, M., Kepner, H., Lindquist, M., & Reys, R. (1981). Decimals: Results and
implications from the second NAEP mathematics assessment. Arithmetic Teacher, 28(8),
34-37.
Clements, D., &
Battista, M. (1989). Learning of geometric concepts in a Logo environment. Journal for
Research in Mathematics Education, 20, 450 467.
Clements, D., &
Battista, M. (1990). The effects of Logo on children's conceptualizations of angle and
polygons. Journal for Research in Mathematics Education, 21, 356-371.
Clements, D., &
Battista, M. (1992). Geometry and spacial reasoning. In D. Grouws (Ed.), Handbook of
research on mathematics teaching and learning (pp. 420-464). New York: Macmillan
Publishing Company.
Clement, J. (1982).
Algebra word problem solutions: Thought processes underlying a common misconception. Journal
for Research in Mathematics Education, 13, 16-30.
Clement, J.
(1989).The concept of variation and misconceptions in Cartesian graphing. Focus on
Learning Problems in Mathematics, 11(1-2), 77-87.
Falk, R., Falk, R., &
Levin, I. (1980). A potential for learning probability in young children. Journal for
Research in Mathematics Education, 11, 181-204.
Fischbein, E., &
Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? Educational
Studies in Mathematics, 15, 1-24.
Fuson, K. (1988). Children's
counting and concepts of number. New York: Springer Verlag.
Fuson, K., Richards, J., &
Briars, D. (1982). The acquisition and elaboration of the number word sequence. In C.
Brainerd (Ed.), Progress in cognitive development research Vol. 1: Children's logical
and mathematical cognition (pp. 33-92). New York: Springer Verlag.
Gal, I., Rothschild, K.,
& Wagner, D. (1990). Which group is better? The development of statistical
reasoning in elementary school children. Paper presented at the American Educational
Research Association, Boston, MA.
Garfield, J., &
Ahlgren, A. (1988). Difficulties in learning probability and statistics: Implications for
research. Journal for Research in Mathematics Education, 19, 44-63.
Greeno, J. (1982,
March). A cognitive learning analysis of algebra. Paper presented at the annual
meeting of the American Educational Research Association, Boston, MA.
Grouws, D. (Ed.)
(1992). Handbook of research on mathematics teaching and learning. New York:
Macmillan Publishing Company.
Hawkins, A., &
Kapadia, R. (1984). Children's conceptions of probability: A psychological and pedagogical
review. Educational Studies in Mathematics, 15, 349-377.
Herscovics, N.
(1989). Cognitive obstacles encountered in the learning of algebra. In S. Wagner & C.
Kieran (Eds.), Research issues in the learning and teaching of algebra (pp.
60-86). Reston, VA: National Council of Teachers of Mathematics.
Hiebert, J. (1992).
Mathematical, cognitive, and instructional analyses of decimal fractions. In G. Leinhardt,
R. Putnam, & R. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp.
283-322). Hillsdale, NJ: Lawrence Erlbaum Associates.
Hiebert, J., &
Behr, M. (Eds.). (1988). Number concepts and operations in the middle grades.
Reston, VA: National Council of Teachers of Mathematics.
Hiebert, J., &
Wearne, D. (1986). Procedures over concepts: The acquisition of decimal number knowledge.
In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics
(pp. 199-223). Hillsdale, NJ: Lawrence Erlbaum Associates.
Kahneman, D., Slovic,
P., & Tversky, A. (1982). Judgment under certainty: Heuristics and biases.
Cambridge: Cambridge University Press.
Kerslake, D. (1981).
Graphs. In K. M. Hart (Ed.), Children's understanding of mathematics: 11-16 (pp.
120-136). London: John Murray.
Kieran, C. (1981).
Concepts associated with the equality symbol. Educational Studies in Mathematics, 12,
317-326.
Kieran, C. (1984). A
comparison between novice and more-expert algebra students on tasks dealing with the
equivalence of equations. In J. Moser (Ed.), Proceedings of the sixth annual meeting
of PME-NA (pp. 83-91). Madison: University of Wisconsin.
Kieran, C. (1988). Two
different approaches among algebra learners. In A. F. Coxford (Ed.), The ideas of
algebra, K-12 (1988 Yearbook, pp. 91-96). Reston, VA: National Council of Teachers of
Mathematics.
Kieran, C. (1989). The
early learning of algebra: A structural perspective. In S. Wagner & C. Kieran (Eds.), Research
issues in the learning and teaching of algebra (pp. 33-56). Reston, VA: National
Council of Teachers of Mathematics.
Kieran, C. (1992). The
learning and teaching of school algebra. In D. Grouws (Ed.), Handbook of research on
mathematics teaching and learning (pp. 390-419). New York: Macmillan Publishing
Company.
Kieren, T. (1992).
Rational and fractional numbers as mathematical and personal knowledge: Implications for
curriculum and instruction. In G. Leinhardt, R. Putnam, & R. Hattrup (Eds.), Analysis
of arithmetic for mathematics teaching (pp. 323-372). Hillsdale, NJ: Lawrence Erlbaum
Associates.
Kouba, V., Brown, C.,
Carpenter, T., Lindquist, M., Silver, E., & Swafford, J. (1988). Results of the fourth
NAEP assessment of mathematics: Numbers, operations, and word problems. Arithmetic
Teacher, 35(8), 14-19.
Leinhardt, G.,
Zaslavsky, O., & Stein, M. (1990). Functions, graphs, and graphing: Tasks, learning,
and teaching. Review of Educational Research, 60, 1-64.
McDermott, L.,
Rosenquist, M., & van Zee, E. (1987). Student difficulties in connecting graphs and
physics: Example from kinematics. American Journal of Physics, 55, 503-513.
Mokros, J., &
Russell, S. (1992). Children's concepts of average and representativeness. Working
Paper 4-92. Cambridge, MA: TERC.
Mokros, J., &
Tinker, R. (1987). The impact of microcomputer-based labs on children's ability to
interpret graphs. Journal of Research in Science Teaching, 24, 369-383.
Piaget, J., &
Inhelder, B. (1975). The origin of the idea of chance in children. London:
Routledge & Kegan Paul.
Pollatsek, A., Lima,
S., & Well, A. (1981). Concept of computation: Students' understanding of the mean. Educational
Studies in Mathematics, 12, 191-204.
Resnick, L., 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, 8-27.
Saxe, G., Becker, J.,
& Sadeghpour, M. (1989). Developmental differences in children's understanding of
number word conventions. Journal for Research in Mathematics Education, 20,
468-488.
Senk, S. (1989). Van
Hiele levels and achievement in writing geometry proofs. Journal for Research in
Mathematics Education, 20, 309-321.
Shaughnessy, J. M.
(1992). Research in probability and statistics: reflections and directions. In D. Grouws
(Ed.), Handbook of research on mathematics teaching and learning (pp. 465-494).
New York: Macmillan Publishing Company.
Shayer, M., & Adey,
P. (1981). Towards a science of science teaching. London: Heinemann.
Sowder, J. &
Wheeler, M. (1989). The development of concepts and strategies used in computational
estimation. Journal for Research in Mathematics Education, 20, 130-146.
Sowder, J. (1988).
Mental computation and number comparison: Their roles in the development of number sense
and computational estimation. In J. Hiebert & M. Behr (Eds.), Number concepts and
operations in the middle grades (pp. 182-197). Reston, VA: National Council of
Teachers of Mathematics.
Sowder, J. (1992a).
Making sense of numbers in school mathematics. In G. Leinhardt, R. Putnam, & R.
Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp.1-51).
Hillsdale, NJ: Lawrence Erlbaum Associates.
Sowder, J. (1992b).
Estimation and number sense. In D. Grouws (Ed.), Handbook of Research on Mathematics
Teaching and Learning (pp. 371-389). New York: Macmillan Publishing Company.
Sutherland, R.
(1987). A study of the use and understanding of algebra related concepts within a Logo
environment. In J. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the
tenth international conference for the psychology of mathematics education (Vol. I,
pp. 241-247). Montreal: University of Montreal.
Suydam, M. (1985). The
shape of instruction in geometry: Some highlights from research. Mathematics Teacher,
78, 481-486.
Threadgill-Sowder,
J. (1984). Computational estimation procedures of young children. Journal of
Educational Research, 77, 332-336.
Van Hiele, P. (1986).
Structure and insight. Orlando, FL: Academic Press.
Vergnaud, G., &
Errecalde, P. (1980). Some steps in the understanding and the use of scales and axis by
10-13 year old students. In R. Karplus (Ed.), Proceedings of the fourth international
conference for the psychology of mathematics education (pp. 285-291).(ERIC
Reproduction Service No. ED 250 186).
Wagner, S. (1981).
Conservation of equation and function under transformations of variable. Journal for
Research in Mathematics Education, 12, 107-118.
Wagner, S., &
Kieran, C. (Eds.) (1989). Research issues in the learning and teaching of algebra.
Reston, VA: National Council of Teachers of Mathematics.
Wavering, M. (1985,
April). The logical reasoning necessary to make line graphs. Paper presented at
the annual meeting of the National Association for Research in Science Teaching, French
Lick Springs, Indiana. (ERIC Document Reproduction Service No. ED254409).
Wearne, D., &
Hiebert, J. (1988). Constructing and using meaning for mathematical symbols: The case of
decimal fractions. In J. Hiebert & M. Behr (Eds.), Number concepts and operations
in the middle grades (pp. 220-235) Reston, VA: National Council of Teachers of
Mathematics.
Wearne, D., &
Hiebert, J. (1989). Cognitive changes during conceptually based instruction on decimal
fractions. Journal of Educational Psychology, 81, 507-513.
Wirszup, I. (1976).
Breakthroughs in the psychology of learning and teaching geometry. In J. Martin & D.
Bradbard (Eds.), Space and geometry. Papers from a research workshop (pp. 75-97).
Athens, GA: University of Georgia, Georgia Center for the Study of Learning and Teaching
Mathematics. (ERIC Document Reproduction Service No. ED 132 033).