References and Research
Research from which this resource is derived
Other references including early research

Research from which this resource is derived (most recent first)

Stacey, K. (2005). Travelling the road to expertise: A longitudinal study of learning. In Chick, H. L. & Vincent, J. L. (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 19-36). Melbourne: PME.
| Abstract | Full-Text | Powerpoint |

Steinle, V. (2004). Changes with Age in Students’ Misconceptions of Decimal Numbers. Unpublished doctoral thesis, University of Melbourne.
| Abstract | Full-Text |

Steinle, V. (2004). Detection and Remediation of Decimal Misconceptions. In B. Tadich, S. Tobias, C. Brew, B. Beatty, & P. Sullivan (Eds.), Towards Excellence in Mathematics (pp. 460-478). Brunswick: The Mathematical Association of Victoria.
| Abstract | Full-Text | Powerpoint |
Steinle, V., & Stacey, K. (2004a). A longitudinal study of students' understanding of decimal notation: An overview and refined results. In I. Putt, R. Faragher & M. McLean (Eds.), Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 541-48). Townsville: MERGA.
| Abstract |
Steinle, V., & Stacey, K. (2004b). Persistence of decimal misconceptions and readiness to move to expertise. In M.J. Hoines & A.B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 225 - 232). Bergen, Norway: PME.
| Abstract |
Stacey, K., Sonenberg, E., Nicholson, A., Boneh, T., & Steinle, V. (2003). A teaching model exploiting cognitive conflict driven by a Bayesian network. In P. Brusilovsky, A. T. Corbett, and F. De Rosis (Eds.), Lecture Notes in Artificial Intelligence (Ninth International Conference on User Modeling UM2003) 2702/2003, 352362. Springer-Verlag, Heidelberg.
| Abstract |

Steinle, V., & Stacey, K. (2003a). Grade-related trends in the prevalence and persistence of decimal misconceptions. In N.A. Pateman, B.J. Dougherty & J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp. 259-266). Honolulu: PME.
| Abstract |

Steinle, V., & Stacey, K. (2002). Further evidence of conceptual difficulties with decimal notation. In B. Barton, K. Irwin, M. Pfannkuch & M. Thomas (Eds.), Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 633-640). Auckland: MERGA.
| Abstract |
Stacey, K., Helme, S., Archer, S., & Condon, C. (2001). The effect of epistemic fidelity and accessibility on teaching with physical materials: A comparison of two models for teaching decimal numeration. Educational Studies in Mathematics. 47, 199-221.
| Abstract |
Stacey, K., Helme, S., & Steinle, V. (2001). Confusions between decimals, fractions and negative numbers: A consequence of the mirror as a conceptual metaphor in three different ways. In M. v. d. Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 217-224). Utrecht: PME. (Included here with permission).
| Abstract | Full-Text |
Stacey, K., Helme, S., Steinle, V., Baturo, A., Irwin, K., & Bana, J. (2001). Preservice Teachers' Knowledge of Difficulties in Decimal Numeration. Journal of Mathematics Teacher Education, 4(3), 205-225.
| Abstract |
Steinle, V., & Stacey, K. (2001). Visible and invisible zeros: Sources of confusion in decimal notation. In J. Bobis, B. Perry & M. Mitchelmore (Eds.), Numeracy and Beyond. Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 434-441). Sydney: MERGA.
| Abstract |
Helme, S., & Stacey, K. (2000a). Can minimal support for teachers make a difference to students' understanding of decimals? Mathematics Teacher Education and Development. 2, 105 - 120. (Included here with permission).
| Abstract | Full-Text |
Steinle, V., & Stacey, K. (1998a). Students and decimal notation: Do they see what we see? In J. Gough & J. Mousley (Eds.), 35th Annual Conference of the Mathematics Association of Victoria (Vol. 1, pp. 415-422). Melbourne: MAV. (Included here with permission).
| Abstract | Full-Text |

Top

Other references including early research (alphabetically ordered)

Archer, S., & Condon, C (1999). Linear arithmetic blocks: A concrete model for teaching decimals, Department of Science and Mathematics Education, Faculty of Education, University of Melbourne.
| Further Information |

Asp, G., Chambers, D., Scott, N., Stacey, K., & Steinle, V. (1997). Using Multimedia for the Teaching of Decimal Notation. In Clarke, D., Clarkson, P., Gronn, D., Horne, M., MacKinlay, M., & McDonough, A. (Eds.), Mathematics - Imagine the Possibilities. Proceedings of the Thirty-fourth Annual Conference of the Mathematical Association of Victoria. (pp. 60-67) Melbourne: Mathematical Association of Victoria. (Included here with permission).
| Abstract | Full-Text |

Australian Council for Educational Research (ACER) (1964). Primary School Mathematics: Report of a Conference of Curriculum Officers of State Education Departments. Held at Melbourne 16-20 March, 1964. Hawthorn, Vic: ACER.

Ball, D. (1992). Manipulatives and the reform of math education, American Educator, Summer, 14-18, 46-47.

Baturo, A., & Cooper, T (1997). Reunitising hundredths: Prototypic and non-prototypic representations. In E. Pehkonen (Ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education, (Vol. 2 pp. 57-64). Lahti, Finland: PME.

Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio and proportion. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296-333). New York: MacMillan.

Bell, A. W., Costello, J., & Kuchemann, D.E. (1983). A Review of Research in Mathematical Education, Part A. Windsor, Berks.: NFER-Nelson.

Board of Studies (1995). Curriculum and Standards Framework (Mathematics). Melbourne, Board of Studies (Victoria).

Booker, G., Bond, D., Briggs, J., & Davey, G. (1997). Teaching Primary Mathematics, Melbourne: Longman.

Brown, M. (1981). Place value and decimals. In K. Hart (Ed.), Children's Understanding of Mathematics, 11-16 (pp. 48-65). London: John Murray.

Carpenter, T., Corbitt, M., Kepner, H., Lindquist, M., & Reys, R. (1981). Decimals: Results and implications from national assessment. Arithmetic Teacher, April, 34-37.

Chambers, D., Stacey, K., & Steinle, V. (2003). Making Educational Research Findings Accessible for Teacher Education: From Research Project to Multimedia Resource. Society for Information Technology and Teacher Education International Conference 2003 (1), 2865-2872. Albuquerque, NM. [Online]. Available: http://dl.aace.org/12362

Cheeseman, J. (1994). Making sense of decimals - How can calculators help? In C. Beesey, & D. Rasmussen (Eds.), Mathematics Without Limits (pp. 169-172). Mathematics Association of Victoria.

Condon, C., & Hinton, S. (1999). Decimal Dilemmas, Australian Primary Mathematics Classroom, 4 (3), 26 - 31.

Condon, C., & Archer, S. (1999). Lesson ideas and activities for teaching decimals, Department of Science and Mathematics Education, Faculty of Education, University of Melbourne.
| Further Information |

Courant, R., & Robbins, H. (1996). What is Mathematics? An elementary approach to ideas and methods. (2nd edition, revised by Ian Stewart) London: Oxford University Press.

Dantzig, T. (1954). Number, the Language of Science; a critical survey written for the cultured non-mathematician. New York: Macmillan.

English, L., & Halford, G. (1995). Mathematics Education: Models and Processes. Mahwah, NJ: Lawrence Erlbaum.

Graeber, A., & Johnson, M. (Eds.), (1991). Insights into Secondary School Students' Understanding of Mathematics. College Park, University of Maryland, MD.

Grossman, A. S. (1983). Decimal notation: An important research finding. Arithmetic Teacher, 30, 32-33.

Hayes, R. L. (1998). Teaching Negative Number Operations. Doctor of Education Thesis, University of Melbourne.

Helme, S., & Stacey, K. (2000b). Improved decimal understanding: Can targeted resources make a difference. In J. Bana & A. Chapman (Eds.), Mathematics education beyond 2000. (Proceedings of the 23rd annual conference of the Mathematics Education Research Group of Australasia, pp 299-306). Fremantle: MERGA.

Hiebert, J. (1984). Children's mathematical learning: The struggle to link form and understanding. Elementary School Journal, 84(5), 497-513.

Hiebert, J. (1985). Children's Knowledge of Common and Decimal Fractions. Education and Urban Society, 17(4), 427-437.

Hiebert, J., Wearne, D., & Taber, S. (1991). Fourth Graders' Gradual Construction of Decimal Fractions during Instruction Using Different Physical Representations, The Elementary School Journal, 91 (4), 321-341.

Irwin, K. (1996). Making Sense of Decimals. In J. Mulligan & M. Mitchelmore (Eds.) Children's Number Learning (pp. 243 - 257). Adelaide: Australian Association of Mathematics Teachers.

Irwin, K. (1997). What conflicts help students learn about decimals? In F. Biddulph & K. Carr (Eds.), Proceedings of Twentieth Annual Conference of the Mathematics Education Research Group of Australasia (pp. 247-254). University of Waikato: MERGA.

Lokan, J., Ford, P., & Greenwood, L. (1996). Maths and Science on the Line. Australian Junior Secondary Students' Performance in the Third International Mathematics and Science Study. Australian Council for Educational Research: Melbourne.

Lokan, J., Ford, P., & Greenwood, L. (1997). Maths and Science on the Line. Australian Middle Primary Students' Performance in the Third International Mathematics and Science Study. Australian Council for Educational Research: Melbourne.

MacGregor M., & Moore R. (1991). Teaching Mathematics in the Multicultural Classroom. Melbourne: University of Melbourne. Available from Australian Association of Mathematics Teachers.

Marston, K., & Stacey, K. (2001). Foundations for Teaching Arithmetic (CD-ROM) Melbourne: University of Melbourne, Department of Science and Mathematics Education, Faculty of Education.
| Further Information |

McIntosh, J., Stacey, K., Tromp, C., & Lightfoot, D. (2000). Designing constructivist computer games for teaching about decimal numbers. In J. Bana & A. Chapman (Eds.), Mathematics Education Beyond 2000. Proceedings of the 23rd annual conference of the Mathematics Education Research Group of Australasia. (pp. 409-416). Fremantle: MERGA.

Moloney, K., & Stacey, K. (1996). Understanding Decimals. The Australian Mathematics Teacher, 52(1), 4-8.

Moloney, K., & Stacey, K. (1997). Changes with Age in Students' Conceptions of Decimal Notation. Mathematics Education Research Journal, 9(1), 25-38.

Moloney, K. (1994). The Evolution of Concepts of Decimals in Primary and Secondary Students, Unpublished Master of Education Thesis, University of Melbourne.

Mullis, I., Martin, M., Beaton, A., Gonzalez, E., Kelly D., & Smith, T. (1997). Mathematics Achievement in the Primary School Years. Boston: CSTEEP, Boston College.

Nesher, P., & Peled, I. (1986). Shifts In Reasoning: The Case of Extending Number Concepts. Educational Studies In Mathematics, 17, 67-79.

Peled, I., & Shahbari, J. A. (2003). Improving decimal number conception by transfer from fractions to decimals. In N.A. Pateman, B.J. Dougherty & J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp. 1-6). Honolulu: PME.

Resnick, L. B., 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(1), 8-27.

Sackur-Grisvard, C., & Leonard, F. (1985). Intermediate Cognitive Organizations in the Process of Learning a Mathematical Concept: The Order of Positive Decimal Numbers, Cognition and Instruction, 2, (2), 157-174.

Stacey, K., & Flynn, J. (2003). Evaluating an adaptive computer system for teaching about decimals: Two case studies. In V. Aleven, U. Hoppe, J. Kay, R. Mizoguchi, H. Pain, F. Verdejo, & K. Yacef (Eds.), AI-ED2003 Supplementary Proceedings of the 11th International Conference on Artificial Intelligence in Education, (pp. 454 460). Sydney: University of Sydney. Available at http://www.it.usyd.edu.au/~aied/Supp_procs.html#vol8

Stacey, K., & Steinle, V. (1998). Refining the Classification of Students' Interpretations of Decimal Notation. Hiroshima Journal of Mathematics Education, 6, 49-70.
| Abstract |

Stacey, K., & Steinle, V. (1999a). A longitudinal study of children's thinking about decimals: A preliminary analysis. In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, Vol. 4. pp 233-240. Haifa: PME. (Included here with permission).
| Abstract | Full-Text |

Stacey, K., & Steinle, V. (1999b). Understanding decimals: The path to expertise. In J. M. Truran & K. M. Truran (Eds.), Making the difference. Proceedings of the 22nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 446-453). Adelaide: MERGA.
| Abstract |

Stacey, K., & Steinle, V. (2005). Relative risk analysis of educational data. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce & A. Roche (Eds.), Building Connections: Research, theory and practice. Proceedings of the 28th Annual Conference of the Mathematics Education Research Group of Australasia, (Vol. 2, pp. 696-703). Melbourne: MERGA.
| Abstract |
Stacey, K., Steinle, V., & Moloney, K. (1998). Students' Understanding of Decimals: An Overview.
| Abstract | Full-Text |

Steinle, V., & Stacey, K. (1998b). The incidence of misconceptions of decimal notation amongst students in Grades 5 to 10. In C. Kanes, M. Goos, & E. Warren (Eds.), Teaching Mathematics in New Times. Proceedings of the 21st Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 548-555). Gold Coast, Australia: MERGA. (Included here with permission).
| Abstract | Full-Text |

Steinle, V., & Stacey, K. (2003b). Exploring the right, probing questions to uncover decimal misconceptions. In L. Bragg, C. Campbell, G. Herbert & J. Mousley (Eds.), Proceedings of the 26th Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 634-641). Geelong: MERGA.
| Abstract |
Steinle, V., & Stacey, K. (2005). Analysing longitudinal data on students' decimal understanding using relative risk and odds ratio. In H.L. Chick & J.L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp. 217224). Melbourne: PME.
| Abstract |

Swan, M. (1983a). The Meaning and Use of Decimals (Pilot edition). Nottingham: Shell Centre for Mathematical Education.

Swan, M. (1983b). Teaching Decimal Place Value: A Comparative Study of "Conflict" and "Positive only" Approaches. Nottingham: Shell Centre for Mathematics Education.

Thompson, P. (1992). Notations, conventions, and constraints: Contributions to effective uses of concrete materials in elementary mathematics, Journal for Research in Mathematics Education, 23(2), 123-147.

Tromp, C. (1999). Number Between: Making a game of decimal numbers, Australian Primary Mathematics Classroom, 4(3), 9-11.

Top