Bart, W., Post, T., Behr,
M., Lesh, R. (1994). A diagnostic analysis of a proportional reasoning test
item: An introduction to the properties of a semi-dense
item. *Focus
on Learning Problems in Mathematics,* 16(3), 1-11.
Behr, M. & Harel, G.
(1990). Understanding
the Multiplicative Structure.
In G. Booker, P. Cobb, & T.N. de Merldicutti (Eds.) *Proceedings of the PME XIV Conference Volume III* (pp. 27-34). Mexico: Consejo Nacional de Ciencia y Technologia,
Gobierno del Estado de Morelos.
Behr, M., Harel, G., Post, T., & Lesh, R. (1994). Units of quantity: A conceptual
basis common to additive and multiplicative structures.
In G. Harel & J. Confrey (Eds.),* The development
of multiplicative reasoning in the learning of mathematics* (pp. 123-180). Albany, NY: SUNY Press.
Behr, M., Harel, G., Post,
T., & Lesh, R. (1993). Rational
Numbers: Toward a Semantic Analysis - Emphasis on the
Operator Construct.
In T. Carpenter, E. Fennema & T. Romberg (Eds.), *Rational
Numbers: An Integration of Research* (pp. 13-47). Hillsdale,
NJ: Lawrence Erlbaum Associates.
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). NY: Macmillan
Publishing.
Behr, M., Harel, G., Post,
T. & Lesh, R. (1991). The
Operator Construct of Rational Number.
In F. Furinghetti (Ed.) *Proceedings of PME XV Conference* (pp. 120-127). Assisi, Italy: PME.
Behr, M., Harel, G., Post,
T., & Lesh, R. (1987). Theoretical
analysis: Structure and hierarchy, missing value proportion
problems. In J.
Bergeron, N. Herscovics, & C. Kieran (Eds.), *Proceedings
of the Eleventh International Conference, Psychology of
Mathematics Education PMR - XI* Volume II (pp. 269-274).
Montreal, Canada: PME.
Behr, M., Khoury, H., Harel,
G., Post, T., Lesh, R., (1997) Conceptual
Units Analysis of Preservice Elementary School Teachers'
Strategies on a Rational-Number-as-Operator Task. *Journal of Mathematics Education*, *28(1), *48-69*.*
Behr, M., Lesh, R., Post,
T., & Silver E. (1983). Rational
Number Concepts.
In R. Lesh & M. Landau (Eds.), *Acquisition of Mathematics
Concepts and Processes,* (pp. 91-125). New York: Academic
Press.
Behr, M. & Post, T.
(1992). Teaching
rational number and decimal concepts.
In T. Post (Ed.), *Teaching mathematics in grades K-8:
Research-based methods* (2nd ed.) (pp. 201-248). Boston:
Allyn and Bacon.
Behr, M., & Post, T.
(1988). Teaching Rational Number and Decimal Concepts.
In T. Post, (Ed.), *Teaching Mathematics in Grades K-8:
Research Based Methods* (pp. 190-231). Newton, MA:
Allyn & Bacon, Inc.
Behr, M., & Post, T.
(1986). Estimation
and Children's Concept of Rational Number Size. In H. Schoen & M. Zweng (Eds.) *Estimation and Mental
Computation: 1986 NCTM Yearbook* (pp. 103-111). Reston,
VA: National Council of Teachers of Mathematics.
Behr, M., & Post, T.
(1981). The
Effect of Visual Perceptual Distractors on Children's
Logical-Mathematical Thinking in Rational Number Situations.
In T. Post & M. Roberts (Eds.), *Proceedings of
the Third Annual Meeting of the North American Chapter
of the International Group for the Psychology of Mathematics
Education* (pp. 8-16). Minneapolis: University of Minnesota.
Behr, M., Post, T., &
Lesh R. (1981, July). Construct
Analyses, Manipulative Aids, Representational Systems
and the Learning of Rational Numbers.
In *Proceedings of the Fifth Conference of the International
Group for the Psychology of Mathematics Education.* (pp. 203-209). Grenoble, France: PME.
Behr, M., Post, T., Silver,
E., & Mierkiewicz, D. (1980, August). Theoretical
Foundations for Instructional Research on Rational Numbers.
In R. Karplus (Ed.) *Proceedings of Fourth Annual Conference
of International Group for Psychology of Mathematics Education* (pp. 60-67). Berkeley, CA: Lawrence Hall of Science.
Behr, M., Reiss, M., Harel,
G., Post, T., & Lesh, R. (1986, July). Qualitative
Proportional Reasoning: Description of Tasks and Development
of Cognitive Structures.
In *Proceedings of the Tenth International Conference
for the Psychology of Mathematics Education* (PME-10)
(pp. 235-240). London, England.
Behr, M., Wachsmuth, I.,
& Post, T. (1988). Rational
Number Learning Aids: Transfer From Continuous Models
To Discrete Models. *Focus on Learning Problems in Mathematics,* 10(4),
1-17.
Behr,
M., Wachsmuth, I., & Post, T. (1985, March). Construct
a Sum: A Measure of Children's Understanding of Fraction
Size.
Journal for Research in Mathematics Education, 16(2),
120-131. A condensed earlier version appeared as On Children's
Quantitative Concept of Rational Number: Construct and
Estimate the Sum. In J. Bergeron & N. Herscovics (Eds.), *Proceedings of the North American Chapter of the International
Group for the Psychology of Mathematics Education* Volume II (pp. 272-79). Montreal, Canada: September 1983.
Behr, M., Wachsmuth, I.,
& Post, T. (1984, August). Tasks
to Assess Children's Perception of the Size of a Fraction.
In A. Bell, B. Low & J. Kilpatrick (Eds.), *Theory,
Research and Practice in Mathematical Education* (pp.
179-18). Fifth International Congress on Mathematical
Education, South Australia: Shell Centre for Mathematics
Education.
Behr, M., Wachsmuth, I.,
Post T., & Lesh R. (1984, November). Order
and Equivalence of Rational Numbers: A Clinical Teaching
Experiment. *Journal
for Research in Mathematics Education,* 15(5), 323-341.
Bezuk, N., & Cramer,
K. (1989). Teaching
About Fractions: What, When, and How?
In P. Trafton (Ed.), *National Council of Teachers of
Mathematics 1989 Yearbook: New Directions For Elementary
School Mathematics* (pp. 156-167). Reston, VA: National
Council of Teachers of Mathematics.
Bright, G., Behr, M., Post,
T., & Wachsmuth, I. (1988, May). Identifying
fractions on number lines. *Journal for Research in Mathematics Education.,* 19(3), 215-232.
Conner, G., Harel, G., &
Behr, M. (1988). The
effect of structural variables on the level of difficulty
of missing value proportion problems.
In M. Behr, C. Lacampagne, & M. Wheeler (Eds.), *Proceedings
of the Ninth Annual Conference of PME-NA* (pp. 65-71).
DeKalb, IL: PME.
Cramer K., Ahrendt, S., Monson, D., Wyberg, T., & Colum K. (2017) Fractions, Number Lines, and Third Graders. *Teaching Children Mathematics, 24 (3).*
Cramer, K., Ahrendt, S., Monson, D., Wyberg, T., & Miller, C. (2016). Making Sense of Third Grade Students’ Misunderstandings of the Number Line. *Investigations in Mathematics Learning* (pp. 19-37). Volume 9 Issue 1.
Cramer, K., Behr,
M., Post T., Lesh, R., (2013) Rational Number Project: Initial Fraction Ideas - Abridged for Grade Three
Abridged edition authors: Kathleen Cramer, Terry Wyberg, Susan Ahrendt, Debbie Monson, Christina Miller.
Abridged from
Cramer,
K., Behr, M., Post T., Lesh, R., (2009) Rational Number Project: Initial Fraction Ideas.
Originally published in 1997 as Rational Number Project: Fraction Lessons for the Middle
Grades - Level 1, Kendall/Hunt Publishing Co., Dubuque Iowa.
Cramer,
K., Behr, M., Post T., Lesh, R., (2009) Rational Number Project: Initial Fraction Ideas.
Originally published in 1997 as Rational Number Project: Fraction Lessons for the Middle
Grades - Level 1, Kendall/Hunt Publishing Co., Dubuque Iowa.
Cramer, K., Wyberg, T., & Leavitt, S. (2009). Fraction Operations and
Initial Decimal Ideas. [Companion module to
RNP: Fraction Lessons for
the Middle Grades]
Cramer, K., & Wyberg, T. (2007). When getting the right answers is not always enough. In M. Strutchens & W. G. Martin (Eds). The learning of mathematics :2007 National Council of Teachers of Mathematics Yearbook (pp. 205 – 220). Reston, VA: NCTM.
Cramer, K.; Numerical Reasoning: Number Systems, Ratio, and Proportional Relationships. In M. Battista (Ed.), *Reasoning and Sense making in the Elementary Grades 6-88* (pp. 25 – 46).Reston, VA: NCTM
Cramer, K.; Numerical Reasoning: Number and Operations with Fractions. In M. Battista (Ed.), *Reasoning and Sense making in the Elementary Grades 3-5* (pp. 43 - 66).Reston, VA: NCTM
Cramer,
K. (2003) Using a translation model
for curriculum development and classroom instruction.
In Lesh, R., Doerr, H. (Eds.) *Beyond Constructivism.
Models and Modeling Perspectives on Mathematics Problem
Solving, Learning, and Teaching.* Lawrence Erlbaum
Associates, Mahwah, New Jersey.
Cramer,
Kathleen (2003). Mathematics for Elementary
and Middle School Teachers: Functions and Proportionality
Course. Unpublished curriculum.
Cramer,
K., (2001) Using
Models to Build Middle-Grade Students' Understanding of
Functions. *Mathematics Teaching in the Middle School. *6 (5),
310-318.
Cramer, K., Behr, M., &
Bezuk, N. (1989, October). Proportional
Relationships and Unit Rates. *Mathematics Teacher,* 82 (7), 537-544.
Cramer, K., Henry, A., (2002) Using
Manipulative Models to Build Number Sense for Addition
of Fractions. *National Council of Teachers of Mathematics
2002 Yearbook: Making Sense of Fractions, Ratios, and
Proportions* (pp. 41-48). Reston, VA: National Council
of Teachers of Mathematics.
Cramer,
K. & Lesh, R. (1988). Rational
number knowledge of preservice elementary education teachers.
In M. Behr (Ed.), *Proceedings of the 10th Annual Meeting
of the North American Chapter of the International Group
for Psychology of Mathematics Education *(pp. 425-431).
DeKalb, Il.: PME.
Kathleen Cramer, Debra Monson, Susan Ahrendt, Terry Wyberg, Christy Pettis & Chelsey Fagerlund (2018) Reconstructing the unit on the number line: Tasks to extend fourth graders’ fraction understandings, *Investigations in Mathematics Learning*
DOI: 10.1080/19477503.2018.1434594
Cramer, K., Monson, D., Ahrendt, S., Wiley, B., Colum, K, & Wyberg, T. (2015). 5 indicators of decimal sense. *Teaching Children Mathematics*, 22 (3), (pp. 186-195).
Cramer, Kathleen; Monson, Debra; Whitney, Stephanie; Leavitt, Seth; Wyberg, Terry. (2010, February). Dividing Fractions and Problem Solving. *Mathematics Teaching in the Middle School* v15 n6 p338-346 Feb 2010.
Cramer, Kathleen A.; Monson, Debra S.; Wyberg, Terry; Leavitt, Seth; Whitney, Stephanie B. (2009, September). Models for initial decimal ideas. *Teaching Children Mathematics*, v16 n2 p106-117 Sept 2009.
Cramer, K., & Post, T.
(1995). Facilitating
children's development of rational number knowledge.
In D. Owens, M. Reed, and G. Millsaps (Eds.), *Proceedings
of the Seventeenth Annual Meeting of PME-NA.* (pp.
377-382). Columbus, OH: PME.
Cramer, K. & Post, T.
(1993, May). Connecting
Research To Teaching Proportional Reasoning. *Mathematics Teacher,* 86(5), 404-407.
Cramer, K. & Post, T.
(1993, February). Making
connections: A Case for Proportionality. *Arithmetic Teacher,* 60(6), 342-346.
Cramer, K., Post, T., &
Behr, M. (1989, September). Interpreting
Proportional Relationships. *Mathematics Teacher,* 82 (6), 445-452.
Cramer, K., Post, T., &
Behr, M. (1989, January). Cognitive
Restructuring Ability, Teacher Guidance and Perceptual
Distracter Tasks: An Aptitude Treatment Interaction Study. *Journal for Research in Mathematics Education,* 20(1), 103-110.
Cramer, K., Post, T., &
Currier, S. (1993). Learning
and Teaching Ratio and Proportion: Research Implications. In D. Owens (Ed.), *Research Ideas For the Classroom* (pp. 159-178). NY: Macmillan Publishing Company.
Cramer, K. A, Post, T. R., del Mas, R. C. (2002) Initial
Fraction Learning by Fourth- and Fifth-Grade Students:
A Comparison of the Effects of Using Commercial Curricula
With the Effects of Using the Rational Number Project
Curriculum. *Journal for Research in Mathematics
Education.* 33 (2) 111-144.
Cramer, K., & Whitney, S. (2010). Learning rational number concepts and skills in elementary classrooms: Translating research to the elementary classroom. In D. V. Lambdin, & F. K. Lester (Eds.), *Teaching and learning mathematics: Translating research to the elementary classroom* (pp. 15-22). Reston, VA: NCTM.
Cramer, K., Wyberg, T., & Leavitt, S. (2009). Fraction Operations and
Initial Decimal Ideas. [Companion module to RNP: Fraction Lessons for the Middle Grades]
Cramer, K., Wyberg, T., & Leavitt, S. (2009). The Role of Representations in Fraction Addition and Subtraction.* Mathematics Teaching in the Middle School. *13 (8), 490-496.
Cramer, K., & Wyberg, T. (2009). Efficacy of different concrete models for teaching the part-whole construct for fractions. *Mathematical Thinking and Learning*, 11 (4), 226-258.
Harel, G., & Behr, M.
(1995). Teachers'
solutions for multiplicative problems. *Hiroshima Journal of Mathematics Education,* 3,
31-51.
Harel, G. & Behr, M.
(1990). The
Construct Theory of Rational Numbers: Toward a Semantic
Analysis. In G.
Booker, P. Cobb, & T.N. de Merldicutti (Eds.) *Proceedings
of the PME XIV Conference* (pp. 3-10). Mexico: Consejo
Nacional de Ciencia y Technologia, Gobierno del Estado
de Morelos.
Harel, G., & Behr, M.
(1989). Structure
and Hierarchy of Missing Value Proportion Problems and
Their Representations. *Journal of Mathematical Behavior,* 8(1), 77-119.
Harel, G., Behr, M., Post,
T. & Lesh, R. (1994). Invariance
of ratio: The case of children's anticipatory scheme of
constancy of taste. *Journal for Research in Mathematics Education,* 25(4), 324-345.
Harel, G., Behr, M., Post, T., & Lesh, R. (1994). The impact of number type on the
solution of multiplication and division problems: Further
considerations. In G. Harel & J. Confrey (Eds.),* The development of multiplicative reasoning in the learning
of mathematics* (pp. 365-388). Albany, NY: SUNY Press.
Harel, G., Behr, M., Post,
T., & Lesh, R. (1992). The
Blocks Task: Comparative Analyses of the Task With Other
Proportion Tasks and Qualitative Reasoning Skills of Seventh
Grade Children in Solving the Task. *Cognition and Instruction,* 9(1), 45-96.
Harel, G., Behr, M., Post,
T. & Lesh, R. (1991). Variables
Affecting Proportionality: Understanding of Physical Principles,
Formation of Quantitative Relations, and Multiplicative
Invariance. In
F. Furinghetti (Ed.) *Proceedings of PME XV Conference* (pp. 125-133). Assisi, Italy: PME.
Harel, G., Behr, M., Post,
T., & Lesh, R. (1987). Qualitative
differences among seventh grade children in solving a
non numerical proportional reasoning blocks task. In J. Bergeron, N. Herscovics, & C. Kieran (Eds.), *Proceedings of the Eleventh International Conference,
Psychology of Mathematics Education PMR - XI* Volume
II (pp. 282-288). Montreal, Canada: PME.
Harel, G., Post, T., &
Behr, M. (1988). An
assessment instrument to examine knowledge of multiplication
and division concepts and its implementation with in-service
teachers. In M.
Behr, C. Lacampagne, & M. Wheeler (Eds.), *Proceedings
of the Ninth Annual Conference of PME-NA* (pp. 411-417).
DeKalb, IL: PME.
Harel, G., Post, T., &
Behr, M. (1988, July). On
the textual and semantic structures of mapping rule and
multiplicative compare problems.
In A. Borbas (Ed.) *Proceedings of the XII International
Congress, Psychology of Mathematics Education (PME)* Volume II (pp. 372-379). Budapest: PME.
Heller , P., Post, T., &
Behr, M. (1985, October). The Effect of Rate Type, Problem Setting and Rational
Number Achievement on Seventh Grade Students Performance
on Qualitative and Numerical Proportional Reasoning problems.
In S. Damarin & M. Shelton (Eds.), *Proceedings
of the seventh General Meeting of the North American chapter
of the International Group for the Psychology of Mathematics
Education* (pp. 113-122). Columbus, Ohio: PME.
Heller, P., Ahlgren, A.,
Post, T., Behr, M., & Lesh, R. (1989, March). Proportional
Reasoning: The Effect of Two Context Variables, Rate Type
and Problem Setting. *Journal for Research in Science Teaching,* 26(1),
205-220.
Heller, P., Post, T., Behr,
M., & Lesh, R. (1990). Qualitative
and Numerical Reasoning About Fractions and Rates by Seventh
and Eighth Grade Students. *Journal for Research in Mathematics Education,* 21(5), 388-402.
Heller, P., Post, T., Behr,
M., & Lesh, R. (unpublished). The
effect of two context variables on qualitative and numerical
reasoning about rates.
Lacampagne,
C., Post, T., Harel, G., Behr, M. (1988, November). A
model for the development of leadership and the assessment
of mathematical and pedagogical knowledge of middle school
teachers.
In M. Behr, C. Lacampagne, & M. Wheeler (Eds.), *Proceedings
of the Ninth Annual conference of PME-NA* (pp. 418-425).
DeKalb, IL: PME.
Leavitt,
Seth (2003). Creating the Web Pages
for the Rational Number Project.
Unpublished M.Ed. paper.
Lesh, R., Behr, M., &
Post, T. (1987). Rational
Number Relations and Proportions.
In C. Janiver (Ed.), *Problems of Representations in
the Teaching and Learning of Mathematics* (pp. 41-58).
Hillsdale, NJ: Lawrence Erlbaum.
Lesh, R., Cramer, K., Doerr, H., Post, T., Zawojewski,
J., (2003) Model Development Sequences.
In Lesh, R., Doerr, H. (Eds.) *Beyond Constructivism.
Models and Modeling Perspectives on Mathematics Problem
Solving, Learning, and Teaching.* Lawrence Erlbaum
Associates, Mahwah, New Jersey.
Lesh, R., Hoover, M., Hole,
B., Kelly, A., Post, T., (2000) Principles
for Developing Thought-Revealing Activities for Students
and Teachers. In
A. Kelly, R. Lesh (Eds.), *Research Design in Mathematics
and Science Education. *(pp. 591-646). Lawrence Erlbaum
Associates, Mahwah, New Jersey.
Lesh, R., Hoover, M. &
Kelly, A. (1992). Equity,
Technology, and Teacher Development.
In I. Wirszup & R. Streit (Eds.), *Developments
in School Mathematics Education Around the World: Volume
3* (pp. ). Reston, VA: National Council of Teachers
of Mathematics.
Lesh, R., Kelly, A., (2000) Multitiered
Teaching Experiments.
In A. Kelly, R. Lesh (Eds.), *Research Design in Mathematics
and Science Education. *(pp. 197-230). Lawrence Erlbaum
Associates, Mahwah, New Jersey.
Lesh, R. & Lamon, S. (1992) Assessing
Authentic Mathematical Performance. In R. Lesh &
S. Lamon (Eds.), *Assessments of Authentic Performance
in School Mathematics* (pp. 17-62). Washington, DC:
American Association for the Advancement of Sciences Press.
Lesh, R. & Lamon, S. (1992). Introduction: Trends, Goals, and Priorities in Mathematics
Assessment. In R. Lesh & S. Lamon (Eds.), *Assessments
of Authentic Performance in School Mathematics* (pp.
3-16). Washington, DC: American Association for the Advancement
of Sciences Press.
Lesh, R., Lamon, S., Gong, B. & Post, T. (1992) Using
Learning Progress Maps to Improve Educational Decision
Making. In R. Lesh & S. Lamon (Eds.), *Assessments
of Authentic Performance in School Mathematics* (pp.
343-375 ). Washington, DC: American Association for the
Advancement of Sciences Press.
Lesh, R., Lamon, S., Lester, F. & Behr, M. (1992) Future
Directions for Mathematics Assessment. In R. Lesh
& S. Lamon (Eds.), *Assessments of Authentic Performance
in School Mathematics* (pp. 379-425). Washington, DC:
American Association for the Advancement of Sciences Press.
Lesh, R., Landau, M. &
Hamilton, E. (1983). Conceptual
models in applied mathematical problem solving research.
In R. Lesh & M. Landau (Eds.), *Acquisition of Mathematics
Concepts & Processes* (pp. 263-343). NY: Academic
Press.
Lesh, R., Post, T., &
Behr, M. (1988). Proportional
Reasoning. In J.
Hiebert & M. Behr (Eds.) *Number Concepts and Operations
in the Middle Grades* (pp. 93-118). Reston, VA: Lawrence
Erlbaum & National Council of Teachers of Mathematics.
Lesh, R., Post, T., &
Behr, M. (1987). Dienes
revisited: Multiple embodiments in computer environments.
In I. Wirsup & R. Streit (Eds.), *Development in
School Mathematics Education Around the World* (pp.
647-680). Reston, VA: National Council of Teachers of
Mathematics.
Lesh, R., Post, T., &
Behr, M. (1987). Representations
and Translations among Representations in Mathematics
Learning and Problem Solving.
In C. Janvier, (Ed.), *Problems of Representations in
the Teaching and Learning of Mathematics* (pp. 33-40).
Hillsdale, NJ: Lawrence Erlbaum.
Monson, D., Ahrendt, S., & Cramer, K., (2017). Working Together to Enhance Children’s Understanding of Fractions. 2017 APME volume *Reflective and Collaborative Processes to Improve Mathematics Teaching* (pp.227-236 ). Reston, VA: NCTM.
Orton, R., Post, T., Behr,
M., Cramer, K., Harel, G., & Lesh, R. (1995). Logical
and psychological aspects of rational number pedagogical
reasoning. *Hiroshima
Journal of Mathematics Education,* 3, 63-75.
Post, T. (1989, September). One
Point of View - Fractions and Other Rational Numbers. *Arithmetic Teacher,* 37(1), 3-28.
Post, T. (1988). Some
notes on the nature of mathematics learning. In T. Post (Ed.), *Teaching Mathematics in Grades K-8:
Research Based Methods* (pp. 1-19). Boston: Allyn &
Bacon.
Post, T. (1981). The
Role of Manipulative Materials in the Learning of Mathematical
Concepts. In *Selected
Issues in Mathematics Education* (pp. 109-131). Berkeley,
CA: National Society for the Study of Education and National
Council of Teachers of Mathematics, McCutchan Publishing
Corporation.
Post, T. (1981, May). Fractions:
Results and Implications from National Assessment. The *Arithmetic Teacher,* 28(9), 26-31.
Post, T. (1979). Making
Time for the Basics: Some Thoughts on Viable Alternatives
Within a Balanced Mathematics Program.
In S. Sharron & R. Reys (Eds.), *Applications in
School Mathematics, 1979 Yearbook* (pp. 352-356). Reston,
VA: National Council of Teachers of Mathematics.
Post, T., Behr, M., &
Lesh, R. (1988). Proportionality
and the development of pre-algebra understandings.
In A. Coxford & A. Shulte (Eds.) *The Idea of Algebra
K-12: Yearbook* National Council of Teachers of Mathematics
(pp. 78-90). Reston, VA: NCTM.
Post, T., Behr, M., &
Lesh, R. (1986). Research-Based
Observations About Children's Learning of Rational Number
Concepts. *Focus
on Learning Problems in Mathematics,* 8(1), 39-48.
Post, T., Behr, M., &
Lesh, R. (1982, April). Interpretations
of Rational Number Concepts.
In L. Silvey & J. Smart (Eds.), *Mathematics for
Grades 5-9, 1982 NCTM Yearbook* (pp. 59-72). Reston,
Virginia: NCTM.
Post, T., Behr, M., Lesh,
R., Wachsmuth, I. (1986, Spring). Selected
Results from the Rational Number Project.
In *Proceedings of Ninth Psychology of Mathematics Education
Conference the Netherlands* (pp. 342-351). International
Group for the Psychology of Mathematics Education, ANTWERP
The Netherlands. This paper was reprinted in The Math
Times Journal-Official Journal of the Minnesota Council
of Teachers of Mathematics, Vol. 1, No. 1.
Post, T., & Cramer,
K. (1989, March). Knowledge,
Representation and Quantitative Thinking.
In M. Reynolds (Ed.) *Knowledge Base for the Beginning
Teacher - Special publication of the AACTE* (pp. 221-231).
Oxford: Pergamon Press.
Post, T., & Cramer,
K. (1987, October). Children's
strategies when ordering rational numbers. *Arithmetic Teacher,* 35(2), 33-35.
Post, T., Cramer, K., Behr,
M., Lesh, R., & Harel, G. (1993). Curriculum
implications of Research on the Learning, Teaching, and
Assessing of Rational Number Concepts.
In T. Carpenter, E. F& Harel, G. (In press). Designing
instructionally relevant assessment reports. In T. Carpenter
& E. Fennema (Eds.), *Research on the Learning,
Teaching, and Assessing of Rational Number Concepts.* Lawrence Erlbaum and Associates.
Post, T., Cramer, K., Harel,
G., Kiernen, T., & Lesh, R. (1998) Research
on rational number, ratio and proportionality. *Proceedings of the Twentieth Annual Meeting of the
North American Chapter of the International Group for
the Psychology of Mathematics Education,* *PME-NA
XX *Volume I (pp. 89-93). Raleigh, North Carolina.
Post, T., Harel, G., Behr,
M. & Lesh, R. (1991). Intermediate Teachers' Knowledge of Rational Number Concepts.
In E. Fennema, T. Carpenter, S. Lamon (Eds.),* Integrating
research on teaching and learning mathematics* (pp.
177-198). NY: State University of NY Press.
Post, T., Harel, G., Behr,
M., & Lesh, R. (1988). Intermediate
teachers knowledge of rational number concepts.
In Fennema, et al. (Eds.), *Papers from First Wisconsin
Symposium for Research on Teaching and Learning Mathematics* (pp. 194-219). Madison, WI: Wisconsin Center for Education
Research.
Post, T., & Reys, R.
E. (1979). Abstraction
Generalization and Design of Mathematical Experiences
for Children. In
K. Fuson & W. Geeslin (Eds.), *Models for mathematics
learning.* (pp. 117-139). Columbus, OH: ERIC/SMEAC.
Post T., Wachsmuth I., Lesh
R., & Behr M. (1985, January). Order
and Equivalence of Rational Number: A Cognitive Analysis. *Journal for Research in Mathematics Education,* 16(1), 18-36.
Reiss, M., Behr, M., Lesh,
R., & Post, T. (1988, July) The assessment of cognitive structures in proportional
reasoning. In J.
Bergeron, et al. (Eds.), *Proceedings of the Eleventh
International Conference, Psychology of Mathematics Education
PMR - XI* Volume II (pp. 310-316). Montreal, Canada:
PME.
Reiss, M., Behr, M., Lesh,
R., & Post, T. (1985, July). Cognitive
Processes And Products in Proportional Reasoning.
In L. Streefland (Ed.), *Proceedings of the Ninth International
Conference for the Psychology of Mathematics Education* (pp. 352-356). Noordwijkerhout (Utrecht), Holland: PME.
Titus, J. (1995). The
concept of fractional number among deaf and hard of hearing
students. *American
Annals of the Deaf,* 140(3), 255-263.
Wachsmuth I., Behr M., &
Post T. (1983, July). Children's
perception of fractions and ratios in grade 5.
In R. Hershkowitz (Ed.),* Proceedings of the International
Group for the Psychology of Mathematics Education* VII (pp. 164-169). Rehovot, Israel: Department of Science
Teaching, The Weizmann Institute of Science.
Wachsmuth, I., Bright, G.,
Behr, M., & Post, T. (1986). Assessing
fifth grade children's rational number knowledge in a
non verbal application context: The darts game. *Recherches en Didactique des Mathematiques.,* 7(3),
51-74.
Wyberg,Terry; Whitney, Stephanie R.; Cramer, Kathleen A.; Monson, Debra S.; & Leavitt, Seth. (2011, December) Unfolding Fraction Multiplication *Mathematics Teaching in the Middle School*. 17(5)5, 288-294. |