Our resources are designed to embody the vision of the Common Core State Standards for Mathematics and have been field-tested in a wide variety of classrooms. In addition, we have drawn on the large body of educational research carried out over the past 40 years on the development of students’ mathematical thinking, which includes the following resources:
Baroody, A. J., & Ginsburg, H. P. (1986). The relationship between initial meaning and mechanical knowledge of arithmetic. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Erlbaum.
Bergeron, J. C., & Herscovics, N. (1990). Psychological aspects of learning early arithmetic. In P. Nesher, & J. Kilpatrick (Ed.), Mathematics and cognition: A research synthesis by the International Group for the Psychology of Mathematics Education (Chap. 2). Cambridge, England: Cambridge University Press.
Brenner, Mary E.., “Development of Mathematical Communication in Problem Solving Groups By Language Minority Students.” Bilingual Research Journal, vol.22 (Spring, Summer, and Fall 1998), pp. 103-128.
Carpenter, Thomas P., et al. “Models of Problem Solving: A Study of Kindergarten Children’s Problem- Solving Processes.” Journal for Research in Mathematics Education, vol. 24 (November 1993), pp. 428-441.
Carpenter, Thomas P., James M. Moser, and Harriet C. Bebout, “Representation of Addition and Subtraction Word Problems.” Journal for Research in Mathematics Education, vol. 19 (July 1988), pp. 345-357.
Carpenter, T., M. L. Franke, L. Levi, and S. Empson. (1999) Children’s Mathematics: Cognitively Guided Instruction. Portsmouth, NH: Heinemann.
Carpenter, T., M. L. Franke, and L. Levi. (2003) Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School, Portsmouth, NH: Heinemann.
Chapin, S., C. O’Connor, and N. C. Anderson. (2003) Classroom Discussions: Using Math Talk to Help Students Learn, Grades 1-6. Sausalito, CA: Math Solutions Publications.
Clements, Douglas H., Sudha Swaminathan, Mary Anne Zeitler, and Julie Sarama.“Young Children’s Concepts of Shape.” Journal for Research in Mathematics Education, vol. 30 (March 1999), pp. 192-212.
Clements, D., and G. Bright, eds. 2003. Learning and Teaching Measurement. Reston: VA: National Council of Teachers of Mathematics.
Cobb, P., & Merkel, G. (1989). Thinking strategies: Teaching arithmetic through problem solving. In P. Trafton (Ed.), New directions for elementary school mathematics: 1989 yearbook. Reston, VA: National Council of Teachers of Mathematics.
Empson, Susan B. “Low-Performing Students and Teaching Fractions for Understanding: An Interactional Analysis.” Journal for Research in Mathematics Education, vol. 34 (July 2003), pp. 305-343.
Fischer, Florence E. “A Part-Part-Whole Curriculum for Teaching Number in the Kindergarten.” Journal for Research in Mathematics Education, vol. 21 (May 1990), pp. 207-215.
Fosnot, C.T., and M. Dolk. (2001a.) Young Mathematicians at Work: Constructing Multiplication and Division. Portsmouth, NH: Heinemann.
______, (2001b.) Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction. Portsmouth, NH: Heinemann.
______, (2002) Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents. Portsmouth, NH: Heinemann.
Fuson, K. 1992. “Research on Whole Number Addition and Subtraction.” In Handbook of Research on Mathematics Teaching and Learning, edited by D. Grouws, 243-75. New York: Macmillan.
Gelman, R., & Gallistel, C. R. (1978). The Child’s Understanding of Number. Cambridge, MA: Harvard University Press.
Gelman, R., Meck, E., & Merkin, S. (1986). Young children’s numerical competence. Cognitive Development 1: 1-29.
Heibert, James, “Signposts for Teaching Mathematics through Problem Solving.” In Teaching Mathematics through Problem Solving Prekindergarten-Grade 6.Edited by Frank K. Lester and Randall I. Charles, pp. 53-61. Reston, VA: NCTM, 2003.
Heibert, James, and Thomas P. Carpenter, “Learning and Teaching with Understanding.” In Handbook of Research on Mathematics Teaching and Learning. Edited by Douglas A. Grouws, pp. 65-97, New York: Macmillan 1992.
Heibert, James, and Diane Wearne, “Links between Teaching and Learning Place Value with Understanding in First Grade.” Journal for Research in Mathematics Education, vol. 23 (March 1992), pp. 98-122.
Hiebert, J. (1988). A theory of developing competence with written mathematical symbols. Educational Studies in Mathematics 19: 333-355.
Janvier, C. (Ed.) (1987). Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Erlbaum.
Kamii, C. K. (1994). Young Children Continue to Invent Arithmetic, 3rd Grade. New York: Teachers College Press.
Kamii, C., & Joseph, L. (1988). Teaching place value and double-column addition. Arithmetic Teacher 35 (6): 48-52.
Kato, Yasuhiko, et al. “Young Children’s Representations of Groups of Objects: The Relationship Between Abstraction and Representation.” Journal for Research in Mathematics Education, vol. 33 (January 2002), pp. 30-45.
Kelly, Catherine A. “Using Manipulatives in Mathematical Problem Solving: A Performance- Based Analysis.” The Montana Mathematics Enthusiast, vol. 3 (2006), pp. 184-193.
Lampert, M. “Knowing, Doing, and Teaching Multiplication.” Cognition and Instruction, vol. 3 (Winter 1986), pp. 305-342.
Liljedahl, P. (2016). Building thinking classrooms: Conditions for problem solving. In P. Felmer, J. Kilpatrick, & E. Pekhonen (eds.) Posing and Solving Mathematical Problems: Advances and New Perspectives. New York, NY: Springer.
Mulligan, Joanne T., and Michael C. Mitchelmore. “Young Children’s Intuitive Models of Multiplication and Division.” Journal for Research in Mathematics Education, vol. 28 (May 1997), pp. 309-330.
Pyke, Curtis L. “The Use of Symbols, Words, and Diagrams as Indicators of Mathematical Cognition: A Causal Model.” Journal for Research in Mathematics Education, vol. 34 (November 2003), pp. 406-432.
Rubenstein, Rheta N. “Strategies to Support the Learning of the Language of Mathematics.” In Communication in Mathematics, K-12 and Beyond: 1996 Yearbook. Edited by Portia C. Elliott and Margaret J. Kenney, pp. 214-218. Reston, VA: National Council of Teachers of Mathematics, 1996
Schoenfeld, A., ed. 1994. Mathematical Thinking and Problem Solving. Hillsdale, NJ: Lawrence Erlbaum.
Van de Walle, John A. “Designing and Selecting Problem-Based Tasks.” In Teaching Mathematics through Problem Solving Prekindergarten-Grade 6. Edited by Frank K. Lester and Randall I. Charles, pp. 67-80. Reston, VA: NCTM, 2003.
Van de Walle, John A., and Karen Bowman Watkins. “Early Development of Number Sense.” In Research Ideas for the Classroom: Early Childhood Mathematics. Edited by Robert J. Jensen, pp.127-150. New York: Macmillan, 1993.
Wilson, Patricia S., and Ruth Rowland. “Teaching Measurement.” In Research Ideas for the Classroom: Early Childhood Mathematics. Edited by Robert J. Jensen, pp. 171-194. New York: Macmillan, 1993.