Investigations Bibliography

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In developing the second edition of Investigations, the authors drew on current research and practice. The following list is a selection of some of the resources and references the authors found useful in their work and which also may be of interest to users of the curriculum.

  • Ball, D. L. (1997). What do students know? Facing challenges of distance, context, and desire in trying to hear children. In T. Biddle, T. Good, & I. Goodson (Eds.), International handbook on teachers and teaching (pp. 769-817). Dordrecht, Netherlands: Kluwer Press.

    Ball, D. L. & Bass, H. (2000). Making believe: The collective construction of public mathematical knowledge in the elementary classroom. In D. Phillips (Ed.), Yearbook of the National Society for the Study of Education, Constructivism in Education (pp. 193-224). Chicago: University of Chicago Press.

  • Ball, D. L. & Bass, H. (2003). Making mathematics reasonable in school. In J. Kilpatrick, W. G. Martin, and D. Schifter (Eds.), A Research Companion to Principles and Standards for School Mathematics (pp. 27-44). Reston, VA: National Council of Teachers of Mathematics.
  • Bastable, V. & Schifter, D. (2007). Classroom stories: Examples of elementary students engaged in early algebra. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.). Algebra in the Early Grades (pp. 165-184). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Bass, H. (2003). Computational Fluency, Algorithms, and Mathematical Proficiency: One Mathematician’s Perspective. Teaching Children Mathematics, 9(6), 322-327.
  • Blanton, M. L. & Kaput, J. J. (October 2003). Developing Elementary Teachers’ “Algebra Eyes and Ears”. Teaching Children Mathematics, (10)2, 70-77.
  • Blanton, M., Schifter, D., Inge, V., Lofgren, P., Willis, C., Davis, F. & Confrey, J. (2007). Early Algebra. In V.J. Katz (Ed.). Algebra: Gateway to a Technological Future (pp. 7-14). Washington, D.C.: The Mathematical Association of America.
  • Boaler, J. (2003). When Learning No Longer Matters: Standardized Testing and the Creation of Inequality. Phi Delta Kappan, 84(7), 502-506.
  • Brownell, W. A. (2003). Meaning and Skill – Maintaining Balance. Teaching Children Mathematics, 9 (6), 310-316.
  • Cahnmann, M., & Remillard, J. T. (2002). What counts and how: Mathematics teaching in culturally, linguistically, and socioeconomically diverse urban settings. Urban Review, 34(3), 179-205.
  • Carpenter, T., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999). Children’s Mathematics: Cognitively Guided Instruction. Portsmouth, NH: Heinemann.
  • Carpenter, T. & Franke, M. (2001). Developing algebraic reasoning in the elementary school: Generalization and proof. In H. Chick, K. Stacey, J. Vincent, and J. Vincent (Eds.), Proceedings of the 12th ICMI Study Conference (Vol. 1, pp. 155-62). University of Melbourne, Australia.
  • Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
  • Carraher, D. W., Schliemann, A. D. & Schwartz, J. L. Early Algebra Is Not the Same as Algebra Early. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.). Algebra in the Early Grades (pp. 235-272). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Falkner, K. P., Levi, L., & Carpenter, T. (1999). Children’s Understanding of Equality: A Foundation for Early Algebra. Teaching Children Mathematics (Early Childhood Corner), 6(4), 232-236.
  • Flowers, J., Kline, K., & Rubenstein, R. N. (2003). Developing teachers’ computational fluency: examples in subtraction. Teaching Children Mathematics, 9(6), 330-334.
  • Fosnot, C. & Dolk, M. (2001). Young Mathematicians at Work: Constructing Multiplication and Division. Westport, CT: Heinemann.
  • Fosnot, C. & Dolk, M. (2001). Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction. Westport, CT: Heinemann.
  • Hiebert, J., Carpenter, T. P., Fennema, E., Ruson, K. C., Wearne, D., Murray, H., et al. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
  • Huinker, D., Freckman, J. L., & Steinmeyer, M. B. (2003). Subtraction Strategies from Children's Thinking: Moving toward Fluency with Greater Numbers. Teaching Children Mathematics, 9(6), 347-53.
  • Izsak, A. & Fuson, K. (2000). Students’ understanding and use of multiple representations while learning two-digit multiplication. In M. Fernandez (Ed.), Proceedings of the Twenty-Second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 715-721). Tucson, AZ.
  • Jackson, K., & Remillard, J. T. (2005). Rethinking parent involvement: African American mothers construct their roles in the mathematics education of their children. School Community Journal, 15(1), 51-74.
  • Kerekes, J. & Fosnot, C. T. (1998). Using Pictures with Constraints to Develop Multiplication Strategies. The Constructivist, 13(2), 15-20.
  • Keith, A. (2006). Mathematical argument in a second grade class: Generating and justifying generalized statements about odd and even numbers. In Smith, S. Z. & Smith, M. E. (Eds.), Teachers engaged in research: Inquiry into mathematics classrooms, grades pre-K-2 (pp. 35-68). Greenwich, CT: Information Age Publishing.
  • Kilpatrick, J., Martin, W. G., & Schifter, D. (2003). A Research Companion to Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Kline, K. & Flowers, J. (1999). The Impact of Developing Written Computation as a Representation of Mental Computation. In Hitt, F. & Santos, M. (Eds.), Proceedings of the Twenty First Annual Meeting of the North American Chapter of the International Groups for the Psychology of Mathematics Education (pp. 839-845). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
  • Kline, K. & Grant, T. (2003). Developing the Building Blocks of Measurement with Young Children. In Clements, D (Ed.), The National Council of Teachers of Mathematics 2003 Yearbook, Learning and Teaching Measurement (pp. 46-56).
  • Kline, K. & Grant, T. (2002). Developing Elementary Teachers’ Knowledge of Content and Pedagogy Through Implementation of a Standards-Based Mathematics Curriculum. In Guyton, E. & Rainer, J. (Eds.), Teacher Education Yearbook X: Meeting and Using Standards in the Preparation of Teachers (pp. 67-80). Dubuque, Iowa: Kendall/Hunt Publishing Group.
  • Kline, K. & Grant, T. (2002). What Do Elementary Teachers Learn From Reform Mathematics Textbooks? In Thompson, D (Ed.), Proceedings of the Twenty Fourth Annual Meeting of the North American Chapter of the Psychology of Mathematics Education (pp. 1505-1513). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
  • Kline, K. & Grant, T. (2001). What Impacts Teachers as They Implement a Reform Curriculum?: The Case of One Fifth Grade Teacher. In Speiser, R. & Maher, C. (Eds.), Proceedings of the Twenty Third Annual Meeting of the North American Chapter of the Psychology of Mathematics Education (pp. 691-698). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
  • Kline, K., Grant, T., & Archer, M. K. (2006.) Using Your Own Teaching as a Site for Research Into Practice. In S. Z. Smith and M. E. Smith (Eds.) Teachers Engaged in Research: Inquiry into mathematics classrooms, grades pre-K-2 (pp. 15-34). Greenwich, CT: Information Age Publishing.
  • Kline, K., Grant, T., Crumbaugh, C., Kim, O. K., & Cengiz, N. (2005). Exploring Elementary Teachers’ Use of a New Mathematics Curriculum. In Lloyd, G. M., Wilson, M., Wilkins, J. L. M., & Behm, S. L. (Eds.), Proceedings of the 27th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, [CD ROM] Eugene, OR: All Academic.
  • Kline, K., Grant, T., Crumbaugh, C., Kim, O. K., & Cengiz, N. (Forthcoming, 2008). Analyzing whole-group discussion to explore teachers’ emergent curriculum use. In J. Remillard, G. Lloyd & B. Herbel-Eisenman (Eds.), Teachers’ Use of Mathematics Curriculum Materials: Research Perspectives on Relationships Between Teachers and Curriculum. Routledge.
  • Ladson-Billings, G. (2002). I ain’t writin’ nuttin’: Permission to fail and demands to succeed in urban classrooms. In L. Delpit & J. K. Dowdy (Eds.), The skin that we speak: Thoughts on language and culture in the classroom (pp. 107-120). New York: The New Press.
  • Ladson-Billings, G. (1995). Making Mathematics meaningful in multicultural contexts. In W. Secada (Ed.), New Directions for Equity in Mathematics Education (pp. 126-145). Cambridge: Cambridge University Press.
  • Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32, 465-491.
  • Lampert, M. (1992). Teaching and Learning Long Division for Understanding in School. In G. Leinhardt, R. Putnam, & R. A. Hattrup (Eds.), Analysis of Arithmetic for Mathematics Teaching (pp. 221-282). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Lampert, M. (2001). Teaching Problems and the Problems of Teaching. New Haven, CT: Yale University Press.
  • Lappan, G. & Bouck, M. (1998). Developing Algorithms for Adding and Subtracting Fractions. In The NCTM Yearbook: The Teaching and Learning of Algorithms in School Mathematics (pp. 183-197). Reston, VA: NCTM.
  • Ma, L. (1999). Knowing and Teaching Elementary School Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Madell, R. (1985). Children’s Natural Processes. Arithmetic Teacher, 32(7), 20-22.
  • Moschkovich, J. (1999). Supporting the participation of English language learners in mathematical discussions. For the Learning of Mathematics, 19(1), 11-19.
  • Moses, R. P. & Cobb, C. E. (2002). Radical Equations: Civil Rights from Mississippi to the Algebra Project. Beacon Press.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • 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.
  • National Research Council. (1989). Everybody counts: A report to the nation on the future of mathematics education. Washington, D.C.: National Academy Press.
  • National Research Council. (2002). Helping Children Learn Mathematics. Mathematics Learning Study Committee, J.Kilpatrick and J.Swafford, Editors. Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
  • Obidah, J. & Teel, K. M. (2001). Because of the kids. New York: Teachers College Press.
  • Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211-246.
  • Remillard, J. T., & Bryans, M. B. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications for curricular change. Journal of Research in Mathematics Education, 35(5), 352-388.
  • Remillard, J. T., & Cahnmann, M. (2005). Researching mathematics teaching in bilingual-bicultural classrooms. In T. McCarty (Ed.), Language, learning, power, and schooling. Hillsdale, NJ: Erlbaum.
  • Remillard, J. T., & Geist, P. (2002). Supporting teachers professional learning through navigating openings in the curriculum. Journal of Mathematics Teacher Education, 5(1), 7-34.
  • Remillard, J. T., & Jackson, K. (2006). Old math, new math: Parents’ experiences with standards-based reform. Mathematical Thinking and Learning, 8(3), 231-259.
  • Richardson, K. (1997). Too Easy for Kindergarten, Just Right for First Grade. Teaching Children Mathematics (Early Childhood Corner), 3(8), 432-37.
  • Russell, S. J. (2000). Developing computational fluency with whole numbers. Teaching Children Mathematics, 7(3), 154-158.
  • Russell, S. J. (1999). Mathematical reasoning in the elementary grades. In Lee V. Stiff & Frances R. Curcio (Eds.), Developing mathematical reasoning in grades K-12, 1999 Yearbook (pp. 1-12). Reston, VA: National Council of Teachers of Mathematics.
  • Russell, S. J. (2006). What does it mean that 5 has a lot?: From the world to data and back. In G. Burrill (Ed.), Thinking and reasoning with data and chance, 2006 Yearbook. Reston, VA: National Council of Teachers of Mathematics.
  • Russell, S. J., Eston, R., Rook, J., Scott, M., & Sweeney, L. (2003). How to focus the mathematics curriculum on solving problems. In F. K. Lester & R. I. Charles (Eds.), Teaching mathematics through problem solving, prekindergarten-grade 6 (pp. 85-100). Reston, VA: National Council of Teachers of Mathematics.
  • Russell, S. J., Schifter, D. & Bastable, V. (January/February, 2006). Is It 2 More or Less? Algebra in the Elementary Classroom. Connect, Volume 19, Issue 3, 1-3.
  • Russell, S. J., & Vaisenstein, A. (September/October 2008). Computational fluency: Working with a struggling student. Connect, Volume 12 Issue 1, 8-12.
  • Schifter, D. (2001). Learning to see the invisible: What skills and knowledge are needed to engage with students’ mathematical ideas? In T. Wood, B.S. Nelson, J. Warfield (Eds.). Beyond Classical Pedagogy: Teaching Elementary School Mathematics (pp. 109-134). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Schifter, D. (1999). Reasoning about Operations: Early Algebraic Thinking, Grades K through 6. In L. Stiff and F. Curio, (Eds.) Mathematical Reasoning, K-12: 1999 NCTM Yearbook (pp. 62-81). Reston, VA: National Council of Teachers of Mathematics.
  • Schifter, D. (2009). Representation-Based Proof in the Elementary Grades. In D.A. Stylianou, M. Blanton, & E. Knouth (Eds), Teaching and learning proof across the grades: A K-16 Perspective. Oxford: Routledge – Taylor Francis and National Council of Teachers of Mathematics.
  • Schifter, D., Bastable, V., Russell, S. J., Riddle, M. & Seyferth, L. (2008). Algebra in the K-5 Classroom: Learning Opportunities for Students and Teachers. In Greenes, C. E. and Rubenstein, R. (Eds.), Algebra and Algebraic Thinking in School Mathematics: 70th Yearbook (pp. 263-277). Reston, VA: NCTM.
  • Schifter, D., Monk, S., Russell, S. J., & Bastable, V. (2007). Early Algebra: What Does Understanding the Laws of Arithmetic Mean in the Elementary Grades? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.) Algebra in the early grades (pp. 413-447). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Schifter, D. & Szymaszek, J. (2003). Structuring a Rectangle: Teachers Write to Learn about Their Students’ Thinking. In D. Clements and G. Bright (Eds.) Learning and Teaching Measurement: 2003 NCTM Yearbook (pp. 143-156). Reston, VA: National Council of Teachers of Mathematics.
  • Schoenfeld, A. H. (2002). Making Mathematics Work for All Children: Issues of Standards, Testing, and Equity. Educational Researcher, 31(1), 13-15.
  • Schweitzer, K. (2006). Teacher as researcher: Research as a partnership. In Smith, S. Z. & Smith, M. E. (Eds.), Teachers engaged in research: Inquiry into mathematics classrooms, grades pre-K-2 (pp. 69-94). Greenwich, CT: Information Age Publishing.
  • Tierney, C. & Monk, S. Children’s Reasoning about Change over Time. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.). Algebra in the Early Grades (pp. 185-200). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Vaisenstein, A. (2006). A Look at a Child’s Understanding of Mathematical Ideas through His Representations. In Smith, S. Z. & Smith, M. E. (Eds.), Teachers engaged in research: Inquiry into mathematics classrooms, grades pre-K-2 (pp. 95-108). Greenwich, CT: Information Age Publishing.
  • Whitenack, J. & Yackel, E. (2002). Making Mathematical Arguments in the Primary Grades: The Importance of Explaining and Justifying Ideas. (Principles and Standards). Teaching Children Mathematics, 8(9), 524-527.