CRIMSTED Resources
Bibliography for Mathematics Knowledge of Elementary Teachers
- Ball, Deborah Loewenberg (1991). Research on teaching mathematics: making subject matter knowledge part of the equation. In J. Brophy (Ed.), Advances in research on teaching: Vol. 2, 1-47. Greenwich, CT: JAI Press.
- Ball, D. L. (1993). Halves, pieces, and twoths: Constructing representational contexts in teaching fractions. In T. Carpenter, E. Fennema, & T. Romberg, (Eds.), Rational numbers: An integration of research (pp. 157-196). Hillsdale, NJ: Erlbaum.
- Ball, Deborah Loewenberg (1993). With an eye on the mathematical horizon: dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93, No. 4, 373-397.
- Ball, Deborah Loewenberg (1990). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21, No. 9, 132-144.
- Ball, Deborah Loewenberg (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90, No. 4, 449-467
- Ball, Deborah Loewenberg (date unknown). The subject matter preparation of prospective mathematics teachers: challenging the myths. Unpublished manuscript.
- Heaton, Ruth M. (1992). Who is minding the mathematics content? A case study of a fifth-grade teacher. The Elementary School Journal, 93, No. 2, 153-162.
- Hutchison, Linda (1997). Learning for teaching: A case of constructing the bridge between subject matter knowledge and pedagogical content knowledge. Unpublished manuscript.
- Lehrer, Richard, & Franke, Megan Loef (1992). Applying personal construct psychology to the study of teachers' knowledge of fractions. Journal for Research in Mathematics Education, 23, No. 3, 223-241.
- Mewborn, Denise S. (2000). An analysis of the research on k-8 teachers' mathematical knowledge. Paper presented at the annual meeting of the American Educational Research Association.
- Putnam, Ralph T., & Reineke, James W. (1993). Teaching and learning mathematics for understanding in the fifth-grade classroom. Elementary subjects center series No. 91. Available from the Center for Learning and Teaching of Elementary Subjects, Institute for Research on Teaching, 252 Erickson Hall, Michigan State University, East Lansing, MI.
- Shifter, Deborah (1998). Learning mathematics for teaching: From a teachers' seminar to the classroom. Journal of Mathematics Teacher Education, 1, 55-87.
- Silver, Edward A. & Burkett, Mary Lee (1994). The posing of division problems by preservice elementary school teachers: Conceptual knowledge and contextual connections. A paper presented at the Annual Meeting of the American Educational Research Association. New Orleans, LA.
- Simon, Martin A. & Blume, Glendon W. (1992). Mathematization as a component of the concept of ratio-as-measure: A study of prospective elementary teachers. A paper presented at the Annual Meeting of the American Educational Research Association. San Francisco, CA.
- Stoddart, Trish, Connell, Michael, Stofflett, Rene, & Peck, Donald (1993). Reconstructing elementary teacher candidates' understanding of mathematics and science content. Teacher & Teacher Education, 9, No. 3, 229-241.
- Taplin, Margaret (1998). Preservice teachers' problem-solving processes. Mathematics Education Research Journal. 10 No 3, 59-75.
- Zazkis, Rina, & Campbell, Stephen. (1995). Divisibility and multiplicative structure of natural numbers: preservice teachers' understanding. A paper presented at the Annual Meeting of the American Educational Research Association. New Orleans, LA.
- Battista, M.T. & Clements, D.H. (1998). Students' understanding of three-dimensional cube arrays. Findings from a research and curriculum development project. In R. Lehrer & D. Chazan (Eds.), Designing learning and environments for developing understanding of geometry and space, 227-248. Mahwah, NJ: Erlbaum.
- Clements, D. H., Battista, M.T., Sarama, J., & Swaminathan, S. (1996). Development of turn and turn measurement concepts in a computer-based instructional unit. Educational studies in Mathematics, 30, 313-337.
- Confrey, J. (1995). Students voice in examining “splitting” as an approach to ratio proportion, and fractions. Paper presented at the International Conference for the Psychology of Mathematics Education, Universidade Federal de Permanbuco, Recife, Brazil.
- DeLoache, J.S. (1989). The development if representation in young children. In H.W. Reese (Ed.), Advances in child development and behavior, 22, 1-39. New York Academic Press.
- Hiebert, J. (1981). Cognitive development and learning linear measurement. Journal for Research in Mathematics Education, 12 197-211.
- Hiebert, J. (1981). Units of measure: Results and implications from national assessment. Arithmetic Teacher, 28, 38-43.
- Hiebert, J. (1984). Why do some children have trouble learning measurement concepts?, Arithmetic Teacher, 31, 19-24.
- Horvath, J. Lehrer, R. (2000). The design of a case-based hypermedia teaching tool. International journal of computers and mathematical learning, 5, 115-141.
- Lehrer, R., Jacobson, C., Kemeny, V. & Stron, D. (1999). Building on children's intuitions to develop mathematical understanding of space. In E. Fennema & T. Romberg (Eds.), Mathematics classrooms that promote understanding, 63-87. Mahwah, NJ: Erlbaum.
- Lehrer, R., Jacobson, C., Thoyre, G., Kemeny, V., Strom, D., Horvath, J., Gance, S., & Koehler, M. (1998). Developing understanding of space and geometry in the primary grades. In R. Lehrer & D. Chazan (Eds.). Designing learning environments for developing understanding of geometry and space, 169-200. Mahwah, NJ: Erlbaum.
- Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of children's reasoning about space and geometry. In R. Lehrer & D. Chazan (Eds.). Designing learning environments for developing understanding of geometry and space, 137-167. Mahwah, NJ: Erlbaum.
- Leslie, A.M. (1987). Pretense and representations: The origins of “theory of mind.” Psychological Review, 94, 412-426.
- Miller, K.F. (1994). Child as measurer of all things: Measurement procedures and the development of quantitative concepts. In C. Sophian (Ed.), Origins of cognitive skills, p 193-228. Hillsdale NJ: Erlbaum.
- Piaget, J. Inhelder, B. & Szeminska, A. (1960). The child's concept of geometry. New York: Basic Books.
- Putnam, R.T., Heaton, R.M., Prawat, R.S., & Remillart, J. (1992). Teaching mathematics for understanding: Discussing case studies of four fifth-grade teachers. Elementary School Journal, 93, 213-228.
- Michelmore, M. (1992). Children's concepts of perpendiculars. In W. Geeslin & K. Graham (Eds.), Proceedings of the 16 th Psychology in Mathematics Education Conference, 2, p 120-127. Durham, NJ: Program Committee of the 16 th Psychology in Mathematics Education Conference.
- Nieuwoudt, H.D., & van Niekerk, R. (1997, March). The spatial competence of young children through the development of solids. Paper presented at the meeting of the American Educational Research Association, Chicago.
- Clements, D.H., & Battista, M.T. (1992). Geometry and spatial reasoning. In D.A. Grows (Ed.), Handbook of research on mathematics teaching and learning, 420-464. New York: Macmillan.
- Clements, D.H., Battista, M.T., & Sarama, J. (2001). Logo and geometry. Journal for Research in Mathematics Education Monograph Series, 10.
- Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematic Education Monograph 3.
- Guitiérrez, A., Jaime, A., & Fortuny, J.M. (1991). An alternative paradigm to evaluate the acquisition of the van Hiele levels. Journal for Research in Mathematics Education, 22, 237-251.
- Sommerville , S.C. , Bryant, P.E., Mazzocco, M.M.M., & Johnson, S.P. (1987, April). The early development of children's use of spatial coordinates. Paper presented at the meeting of the Society for Research in Child Development, Baltimore.
- Nitabach, E., & Lehrer, R. (2002). Developing spatial sense through area measurement. In D.L. Chambers (Ed.), Putting Research into practice in the elementary grades, 183-187. Reston VA: National Council of Teachers of Mathematics.
- Jacobson, C., & Lehrer, R. (2002). Teacher appropriation and student learning of geometry through design. In J. Sowder & B. Schappelle (Eds.), Lessons learned from research, 85-91. Reston VA: National Council of Teachers of Mathematics.
- Stephen M., & Clements. D.H. (2003). Linear and Area Measurement in Prekindergarten to Grade 2. In D.H. Clements & G. Bright (Eds.), Learning and Teaching Measurement 2003 Yearbook, 3-16. Reston VA: National Council of Teachers of Mathematics.
- Barrett, J.E., Jones, G., Thornton, C., & Dickson, S. (2003). Understanding children's developing strategies and concepts for length.
- Ball, D. L. (1988). Research on teaching mathematics: Making subject matter knowledge part of the equation. In J. Brophy (Ed.), Advances in research on teaching: Vol. 2. Teachers' subject matter knowledge and classroom instruction (pp. 1-44). Greenwich, CT: JAI Press. (page 6)
- Ball, D. L. (1990). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21(4), 132-144. (page 133)
- Ball, D. L., & Mosenthal, J. H. (June 1990). The construction of new forms of teaching: Subject matter knowledge in inservice teacher education. Research Report 90-8 (pp. 3-38), East Lansing, MI: The National Center for Research on Teacher Education. (page 6)
- Ball, D. L. (Sept. 1988). The subject matter preparation of prospective mathematics teachers: Challenging the myths. Research Report 88-3 (pp. 1-28), East Lansing, MI: The National Center for Research on Teacher Education. (pages 2, 18)
- Heaton, R. M. (1992). Who is minding the mathematics content? A case study of a fifth-grade teacher. The Elementary School Journal, 93(2), 153-162. (pages 156, 157)
- Hungerford, T. W. (Jan. 1994). Future elementary teachers: The neglected constituency. American Mathematical Monthly, 101(1), 15-21. (page 17)
- Mewborn, D. S. (2000). An analysis of the research on K-8 teachers' mathematical knowledge (pp 1-40). Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, LA. (page 20)
- Mosenthal, J. H., & Ball, D. L. (1992). Constructing new forms of teaching: Subject matter knowledge in inservice teacher education. Journal of Teacher Education, 43(5), 347-356. (page 350)
- Putnam, R. T., Heaton, R. M., Prawat, R. S., & Remillard, J. (1992). Teaching mathematics for understanding: Discussing case studies of four fifth-grade teachers. The Elementary School Journal, 3(2), 213-228. (page 214)
- Carlson, A., Floto, D., & Mays, B. (1997). Using children's literature to develop and advance problem solving and critical thinking in mathematics (pp. 1-76). Action Research Project Submitted to Graduate Faculty for Master of Arts in Teaching and Leadership, Saint Xavier University, Chicago, Illinois. (page 8)
- Stein, M. K., Baxter, J. A., & Leinhardt, G. (1990). Subject-matter knowledge and elementary instruction: A case from functions and graphing. American Educational Research Journal, 27(4), 639-663. (pages 639, 641, 643, 653, 656)
- Stoddart, T., Connell, M., Stofflett, R., & Peck, D. (1993). Reconstructing elementary teacher candidates' understanding of mathematics and science content. Teacher and Teacher Education, 9(3), 229-241. (pages 231, 233, 234)
- Kilpatrick, J., Swafford, J., & Findell, B. (Eds). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. (pages 262, 263)
- Begg, A., & Edwards, R. (1999). Teachers Ideas About Teaching Statistics.
- Konold, C. & Higgins, T. (2003). Reasoning about data. A Research Companion to Principles and Standards for School Mathematics. Reston, VA: NCTM.
- Shaughnessy, J. M. (2003). Research on students' understandings of probability. A Research Companion to Principles and Standards for School Mathematics. Reston, VA: NCTM.
- Fischbein, E., Nello. M. S., & Marino, M. S. (1991). Factors affectin probabilistic judgments in students and adolescents. Educational Studeis in Mathematics, 22, 523-549.
- Putnam, R., Heaton, R. Prawat, R. & Remillard, J. (1992). Teaching mathematics for understanding: Discussing case studies for four fifth grade teachers. The Elementary School Journal Vol 93 #2
- Quinn, R. (1997) Nov/Dec #2 Effects of Mathematics methods courses on the mathematical attitudes and content knowledge of preservice teachers. The Journal of Educational Research. (p. 109)
- Jones, G. A., Langrall, C. W., Thornton, C. A., Mooney, E. S., Wares, A., Jones, M. R., Perry, B., Putt, I. A., & Nisbet, S. (2001). Using students' statistical thinking to inform instruction. Journal of Mathematical Behavior, 20, 109-144.
- Mokros, J., & Russell, S. J. (1995). Children's concepts of average and representativeness. Journal for Research in Mathematics Education, 26, 20-39.
- Strauss, S., Bichler, E. (1988) The development of children's concepts of the arithmetic average. Journal for Research in Mathematics Education, 19, 64-80.
- Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1999). Students' probabilistic thinking in instruction. . Journal for Research in Mathematics Education, 30, 487-519.
- Bright, G. W., & Friel, S. N. (1998). Graphical representations: Helping students interpret data. In S. P. LaJoie (Ed.), Reflections on statistics: Learning, teaching, and assessment in grades K-12 (pp. 63-88). Mahwah, NJ: Erlbaum.
- Putt, I. J., Jones, G. A., Thornton, C. A., Perry, B., Langrall, C. W., & Mooney, E. S. (1999). Young students' informal statistical knowledge. Teaching Statistics, 21, 74-77.
- Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1997). A framework for assessing and nurturing young children's thinking in probability. Educational Studies in Mathematics, 32, 101-125.
- Acredolo, C., O'Connor, J., Banks, L., & Horobin, K. (1989). Students' ability to make probability estimates: Skills revealed through application of Anderson's functional measurement methodology. Student Development, 60, 933-945.
- Shaughnessy, J. M. (1992). Research on probability and statistics: Reflections and directions. In D. Grouws (Ed.), Handbook of research on the teaching and learning of mathematics (pp. 465-494). New York: Macmillan.
Bibliography for Mathematics Knowledge of Middle School Teachers
| N1 | Silver, E. A. and et al. (1993). "Sense Making and the Solution of Division Problems Involving Remainders: An Examination of Middle School Students' Solution Processes and Their Interpretations of Solutions." Journal for Research in Mathematics Education 24(2): 117. |
| N2 | Lamon, S. J. (1993). "Ratio and Proportion: Connecting Content and Children's Thinking." Journal for Research in Mathematics Education 24(1): 41. |
| N3 | Heller, P. M. and et al. (1990). "Qualitative and Numerical Reasoning about Fractions and Rates by Seventh- and Eighth-grade Students." Journal for Research in Mathematics Education 21(5): 388. |
| N4 | Sowder, J., B. Armstrong, et al. (1998). "Educating Teachers to Teach Multiplicative Structures in the Middle Grades." Journal of Mathematics Teacher Education 1(2): 127. |
| N5 | Chinnappan, M. (2000). "Preservice Teachers' Understanding and Representation of Fractions in a JavaBars Environment." Mathematics Education Research Journal 12(3): 234. |
| N6 | Saxe, G. B., M. Gearhart, et al. (2001). "Enhancing Students' Understanding of Mathematics: A Study of Three Contrasting Approaches to Professional Support." Journal of Mathematics Teacher Education 4(1): 55. |
| N7 | Bruno, A., M. C. Espinel, et al. (1997). "Prospective Teachers Solve Additive Problems with Negative Numbers." Focus on Learning Problems in Mathematics 19(4): 36. |
| N8 | Wilson, M. R. (1994). "Implications for Teaching of One Middle School Mathematics Teacher's Understanding of Fractions." |
| N9 | Putnam, R. T. and J. W. Reineke (1993). "Teaching and Learning Mathematics for Understanding in a Fifth-Grade Classroom. Elementary Subjects Center Series No. 91." |
| N10 | Simon, M. A. (1993). "Prospective Elementary Teachers' Knowledge of Division." Journal for Research in Mathematics Education 24(3): 233. |
| N11 | Borko, H. and et al. (1992). "Learning to Teach Hard Mathematics: Do Novice Teachers and Their Instructors Give Up Too Easily?" Journal for Research in Mathematics Education 23(3): 194. |
| N12 | Ball, D. L. (1990). "Prospective Elementary and Secondary Teachers' Understanding of Division." Journal for Research in Mathematics Education 21(2): 132. |
| N13 | Lehrer, R. and M. L. Franke (1992). "Applying Personal Construct Psychology to the Study of Teachers' Knowledge of Fractions." Journal for Research in Mathematics Education 23(3): 223. |
| N14 | Graeber, A. O. and et al. (1989). "Brief Reports: Preservice Teachers' Misconceptions in Solving Verbal Problems in Multiplication and Division." Journal for Research in Mathematics Education 20(1): 95. |
| N15 | Fisher, L. C. (1988). "Strategies Used by Secondary Mathematics Teachers to Solve Proportion Problems." Journal for Research in Mathematics Education 19(2): 157. |
| N16 | Jackson, M. B. and E. R. Phillips (1983). "Vocabulary Instruction in Ratio and Proportion for Seventh Graders." Journal for Research in Mathematics Education 14(5): 337. |
| N17 | Keijzer, R. and J. Terwel (2001). "Audrey's Acquisition of Fractions: A Case Study into the Learning of Formal Mathematics." Educational Studies in Mathematics 47(1): 53. |
| N18 | Dole, S. (2000). "Promoting Percent as a Proportion in Eighth-Grade Mathematics." School Science and Mathematics 100(7): 380. |
| N19 | Singh, P. (2000). "Understanding the Concepts of Proportion and Ratio Constructed by Two Grade Six Students." Educational Studies in Mathematics 43(3): 271. |
| N23 | Tzur, R. (1999). "An Integrated Study of Children's Construction of Improper Fractions and the Teacher's Role in Promoting That Learning." Journal for Research in Mathematics Education 30(4): 390. |
| N27 | Reys, R., B. Reys, et al. (1999). "Assessing Number Sense of Students in Australia, Sweden, Taiwan, and the United States." School Science and Mathematics 99(2): 61. |
| N28 | Linchevski, L. and J. Williams (1999). "Using Intuition from Everyday Life in 'Filling' the Gap in Children's Extension of Their Number Concept To Include the Negative Numbers." Educational Studies in Mathematics 39(1-3): 131. |
| G1 | Rickard, A. (1996). "Connections and Confusion: Teaching Perimeter and Area with a Problem-Solving Oriented Unit." Journal of Mathematical Behavior 15(3): 303. |
| G2 | McDonald, J. L. (1989). "Cognitive Development and the Structuring of Geometric Content." Journal for Research in Mathematics Education 20(1): 76. |
| G3 | Bishop, J. (2000). "Linear Geometric Number Patterns: Middle School Students' Strategies." Mathematics Education Research Journal 12(2): 107. |
| G4 | Ben-Chaim, D. and et al. (1988). "The Effect of Instruction on Spatial Visualization Skills of Middle School Boys and Girls." American Educational Research Journal 25(1): 51. |
| G6 | Thompson, T. E. and C. A. Morford (1980). "A Sequential Development of Metric Measurement Activities for Middle School Students Using the Outdoor Environment." School Science and Mathematics 80(7): 609. |
| G7 | Olson, J. and M. Olson (1982). "Activities for the Young Adolescent." School Science and Mathematics 82(4): 300. |
| G8 | Jones, M. L. and R. E. Rowsey (1990). "The Effects of Immediate Achievement and Retention of Middle School Students Involved in a Metric Unit Designed to Promote the Development of Estimating Skills." Journal of Research in Science Teaching 27(9): 901. |
| G11 | Usiskin, Z. and S. Senk (1990). "Evaluating a Test of van Hiele Levels: A Response to Crowley and Wilson." Journal for Research in Mathematics Education 21(3): 242. |
| G13 | Mayberry, J. (1983). "The Van Hiele Levels of Geometric Thought in Undergraduate Preservice Teachers." Journal for Research in Mathematics Education 14(1): 58. |
| A1 | MacGregor, M. and K. Stacey (1997). "Students' Understanding of Algebraic Notation: 11-15." Educational Studies in Mathematics 33(1): 1. |
| A2 | Breidenback, D. and et al. (1992). "Development of the Process Conception of Function." Educational Studies in Mathematics 23(3): 247. |
| A3 | Leinhardt, G. and et al. (1990). "Functions, Graphs, and Graphing: Tasks, Learning, and Teaching." Review of Educational Research 60(1): 1. |
| A4 | MacGregor, M. and K. Stacey (1993). "Cognitive Models Underlying Students' Formulation of Simple Linear Equations." Journal for Research in Mathematics Education 24(3): 217. |
| A9 | Even, R. (1993). "Subject-Matter Knowledge and Pedagogical Content Knowledge: Prospective Secondary Teachers and the Function Concept." Journal for Research in Mathematics Education 24(2): 94. |
| A11 | Bishop, J. (2000). "Linear Geometric Number Patterns: Middle School Students' Strategies." Mathematics Education Research Journal 12(2): 107. |
| A12 | Ferrandez-Reinisch, A.-M. (1985). "The Acquisition of Inverse Proportionality: A Training Experiment." Journal for Research in Mathematics Education 16(2): 132. |
| A15 | Rosnick, P. (1981). "Some Misconceptions concerning the Concept of Variable." Mathematics Teacher 74(6): 418. |
P1 Fischbein, E. and Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics (15)1, 1-24.
P2 Fischbein, E., Nello. M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgments in students and adolescents. Educational Studies in Mathematics, 22, 523-549.
P3 Vahey, P. (March, 1997). Toward an understanding of productive student conceptions of probability: The probability inquiry environment. Paper presented at the Annual Meeting of the American Educational Research Association. Chicago, IL.
P4 Cai, J. (1989) Exploring students' conceptual understanding of the averaging algorithm. School Science and Mathematics, (98)2, 93-98.
P5 Bright, G. W. and Hoeffner, K. (1993). Measurement, probability, statistics and graphing. InD. T. Owens (Ed.), Research Ideas for the Classroom – Middle Grades Mathematics. (pp. 78-98). New York, NY: Macmillan Publishing Company.
P6 Shaughnessy, J. M. (1992). Research on probability and statistics: Reflections and directions. In D. Grouws (Ed.), Handbook of research on the teaching and learning of mathematics (pp. 465-494). New York, NY: Macmillan Publishing Company.
P7 National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.