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2008
Cramer, K., Wyberg, T., Leavitt, S. (2008). The Role of Representations in Fraction
Addition and Subtraction. Mathematics Teaching in the Middle
School. 13 (8), 490-496. |
| | |
2003
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.
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.
Cramer,
Kathleen (2003). Mathematics for
Elementary and Middle School Teachers: Functions and
Proportionality Course. Unpublished curriculum.
Leavitt,
Seth (2003). Creating the Web Pages
for the Rational Number Project.
Unpublished M.Ed. paper.
|
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2002
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., 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.
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2000
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., 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.
|
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1998
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.
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1997
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.
Cramer,
K., Behr, M., Post T., Lesh, R., ( 1997) Rational
Number Project: Fraction Lessons for the Middle Grades
- Level 1, Kendall/Hunt Publishing Co., Dubuque Iowa.
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1995
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.
Harel,
G., & Behr, M. (1995). Teachers' solutions
for multiplicative problems. Hiroshima Journal
of Mathematics Education, 3, 31-51.
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.
Titus,
J. (1995). The concept of fractional
number among deaf and hard of hearing students. American
Annals of the Deaf, 140(3), 255-263.
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1994
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., 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.
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. (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.
Heller,
P., Post, T., Behr, M., & Lesh, R. (unpublished). The
effect of two context variables on qualitative and numerical
reasoning about rates.
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1993
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.
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., & 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.
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.
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1992
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. & 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.
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.
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. (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., 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., 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.
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1991
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.
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.
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.
|
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1990
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.
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.
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.
|
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1989
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.
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., & Behr, M. (1989, September). Interpreting
Proportional Relationships. Mathematics Teacher,
82 (6), 445-452.
Cramer,
K., Behr, M., & Bezuk, N. (1989, October). Proportional
Relationships and Unit Rates. Mathematics Teacher,
82 (7), 537-544.
Harel,
G., & Behr, M. (1989). Structure and
Hierarchy of Missing Value Proportion Problems and Their
Representations. Journal of Mathematical Behavior,
8(1), 77-119.
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.
Post,
T. (1989, September). One Point of
View - Fractions and Other Rational Numbers. Arithmetic
Teacher, 37(1), 3-28.
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.
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1988
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., 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.
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.
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.
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.
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.
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., 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., 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.
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.
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.
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1987
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.
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.
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., 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.
Post,
T., & Cramer, K. (1987, October). Children's
strategies when ordering rational numbers. Arithmetic
Teacher, 35(2), 33-35.
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1986
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., 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.
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., 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.
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.
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1985
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.
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.
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. (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.
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1984
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.
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1983
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.
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.
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.
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1982
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.
|
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1981
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.
Post,
T. (1981, May). Fractions: Results
and Implications from National Assessment. The Arithmetic
Teacher, 28(9), 26-31.
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.
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1980
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.
|
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1979
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., & 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.
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