
References and 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. 1936). Melbourne: PME.
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Steinle, V. (2004). Changes with Age in Students’ Misconceptions of Decimal Numbers. Unpublished doctoral thesis, University of Melbourne.
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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. 460478). Brunswick: The Mathematical Association of Victoria.
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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. 54148). Townsville: MERGA.
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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.
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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, 352–362. SpringerVerlag, Heidelberg.
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Steinle, V., & Stacey, K. (2003a). Graderelated 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. 259266). Honolulu: PME.
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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. 633640). Auckland: MERGA.
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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, 199221.
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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. HeuvelPanhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 217224). Utrecht: PME. (Included here with permission).
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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), 205225.
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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. 434441). Sydney: MERGA.
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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).
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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. 415422). Melbourne: MAV. (Included here with permission).
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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 Thirtyfourth Annual Conference
of the Mathematical Association of Victoria. (pp. 6067) Melbourne:
Mathematical Association of Victoria. (Included here with permission).

Abstract  FullText 


Australian Council for Educational Research (ACER) (1964). Primary
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Baturo, A., & Cooper, T (1997). Reunitising hundredths: Prototypic
and nonprototypic representations. In E. Pehkonen (Ed.), Proceedings
of the 21st Conference of the International Group for the Psychology
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Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number,
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Brown, M. (1981). Place value and decimals. In K. Hart (Ed.), Children's
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Carpenter, T., Corbitt, M., Kepner, H., Lindquist, M., & Reys,
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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), 28652872. Albuquerque, NM. [Online]. Available: http://dl.aace.org/12362 

Cheeseman, J. (1994). Making sense of decimals  How can calculators
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Condon, C., & Hinton, S. (1999). Decimal Dilemmas, Australian
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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?
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Dantzig, T. (1954). Number, the Language of Science; a critical
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Graeber, A., & Johnson, M. (Eds.), (1991). Insights into Secondary
School Students' Understanding of Mathematics. College Park,
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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
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the 23rd annual conference of the Mathematics Education Research
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Hiebert, J. (1984). Children's mathematical learning: The struggle
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Hiebert, J. (1985). Children's Knowledge of Common and Decimal
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Hiebert, J., Wearne, D., & Taber, S. (1991). Fourth Graders' Gradual
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Irwin, K. (1996). Making Sense of Decimals. In J. Mulligan &
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 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
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Australasia (pp. 247254). 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
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Lokan, J., Ford, P., & Greenwood, L. (1997). Maths and Science
on the Line. Australian Middle Primary Students' Performance in
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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 (CDROM) 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. 409416). Fremantle: MERGA. 

Moloney, K., & Stacey, K. (1996). Understanding Decimals. The
Australian Mathematics Teacher, 52(1), 48.


Moloney, K., & Stacey, K. (1997). Changes with Age in Students'
Conceptions of Decimal Notation. Mathematics Education Research
Journal, 9(1), 2538.


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, 6779.


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. 16). Honolulu: PME. 

Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S.,
& Peled, I. (1989). Conceptual bases of arithmetic errors: The case
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SackurGrisvard, C., & Leonard, F. (1985). Intermediate Cognitive
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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.), AIED2003 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
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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 233240. Haifa: PME. (Included here with permission).
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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. 446453). Adelaide: MERGA.
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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. 696703). Melbourne: MERGA.
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Stacey, K., Steinle, V., & Moloney, K. (1998). Students' Understanding of Decimals: An Overview.
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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. 548555). Gold Coast, Australia: MERGA. (Included here with permission).
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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. 634641). Geelong: MERGA.
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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. 217–224). Melbourne: PME.

Abstract  

Swan, M. (1983a). The Meaning and Use of Decimals (Pilot edition).
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Swan, M. (1983b). Teaching Decimal Place Value: A Comparative
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Thompson, P. (1992). Notations, conventions, and constraints: Contributions
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Tromp, C. (1999). Number Between: Making a game of decimal numbers,
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