Research-validated References:
Thinking Strategies for Mastering Math® bases its methodology on studies by the authors listed below. All studies meet the requirements of scientific research as set forth by the U.S. Department of Education. David Harpster, Ed. D., has reviewed each study and serves as consultant and editor of Thinking Strategies ensuring the authors of Thinking Strategies for Mastering Math® methodology aligns with the methodology proposed in the studies.
Ashcraft, M.H., and Stazyk, E.H.
“Mental Addition: A Test of Three Verification Models.” In Memory and Cognition 9 (1981): pp. 185 - 196.
Devlin, Keith
Descriptions of the term “number sense” generally run along the lines of “fluidity and flexibility with numbers, a sense of what numbers mean, and an ability to use mental mathematics to negotiate the world and make comparisons.”
Mathematician; Executive Director, H-STAR Institute, Stanford; Author, Finding Fibonacci.
Banchoff, Thomas F.
“Dimension.” On the Shoulders of Giants: New Approaches to Numeracy, edited by Lynn Arthur Steen, pp. 11 - 59. Washington, D. C.: National Academy Press, 1990.
Baroody, Arthur J.
“Mastery of Basic Number Combinations: Internalization of Relationships or Facts?” edited by Jeremy Kilpatrick. Journal for Research in Mathematics Education 16 (1985): 83 - 96.
Barnard, J. S.
Poor Concept Formation in Mathematics: A Diagnostic Perspective. Human Sciences Research council Pretoria, South Africa. 1989, pp. 1 - 89.
Baroody, Arthur J.
“The Development of Preschoolers’ Counting Skills and Principles.” In Pathways to Number: Children’s Developing Numerical Abilities, edited by Jacqueline Bideaud, Claire Meljac, and Jean-Paul Fischer, pp 99 - 126. Hillsdale, N. J.: Lawerence Erlbaum Associates, 1992.
Van Hiele, Pierre M.
Structure and Insight: A theory of Mathematics Education. Orlando, Fla.: Academic Press, 1986. (van Hiele's Level 1, Analysis; Level 0 Visualization)
Van de Walle, J. A., Karp, K., and Bay-Williams, J. M. (2010).
Elementary and Middle School Mathematics: Teaching Developmentally (Seventh ed.). Boston: Allyn and Bacon.
Burger, William F., and J. Michael Shaughnessy.
“Characterizing the van Hiele Levels of Development in Geometry.” Journal for Research in Mathematics Education 17 (January 1986): 31 - 48.
California State Department of Education.
A Question of Thinking: A First Look at Students’ Performance on Open-Ended Questions in Mathematics. Sacramento, Calif.: California Assessment Program, California State Department of Education, 1989.
Carpenter, Thomas P. and James M. Moser.
“The Acquisition of Addition and Subtraction Concepts in Grades One through Three.” Journal for Research in Mathematics Education 15 (May 1984): 179 - 202.
Clements, Douglas H.
“Geometric and Spatial Thinking in Young Children.” In Mathematics in the Early Years, edited by Juanita V. Copley, pp. 66 - 79. Reston, Va.: National Council of Teachers of Mathematics, 1999b.
Clements, Douglas H., Micheal T. Battista, Julie Sarama, and Sudha Swaminathan.
“Development of Students’s Spatial Thinking in a Unit on Geometric Motions and Area.” Elementary School Journal 98, no. 2 (1997): 171 - 186.
Clements, Douglas H., Sudha Swaminathan, Mary Anne Zeitler Hannibal, and Julie Sarama.
“Young Children’s Concepts of Shape.” Journal for Research in Mathematics Education 30 (March 1999): 192 - 212.
Cobb, Paul, and Grayson Wheatley.
“Children’s Initial Understandings of Ten.” Focus on Learning Problems in Mathematics 10, no. 3 (1988): 1 - 28.
Dossey, John A., Ina V.S. Mullis, and Chancey O. Jones.
Can Students Do Mathematical Problem Solving? Results from Constructed-Response Questions in NAEP’s 1992 Mathematics Assessment. 23-FR-01. Washington, D.C.: National Center for Education Statistics, August 1993.
Dossey, John A. and Kathy J. Cook.
“Basic Fact Thinking Strategies for Multiplication-Revisited.” Journal for Research and Mathematics Education 13 (1982): pp. 163 - 171.
Ferrini-Mundy, Joan.
“The Standards Movement in Mathematics Education: Reflections and Hopes.” In Learning Mathematics for a New Century, edited by Maurice J. Burke, pp. 37 - 50. Reston, Va.: National Council of Teachers of Mathematics, 2000.
Harel, G.
“What is Mathematics? A Pedagogical Answer to a Philosophical Question,” in R. B. Gold and R. Simons (eds.), Current Issues in the Philosophy of Mathematics from the Perspective of Mathematicians. Mathematical Association of America, 2008.
Hiebert, James.
“Relationships between Research and the NCTM Standards.” Journal for Research in Mathematics Education 30 (January 1999): 3 - 19.
Hiebert, James and Stigler, James W.
“A Proposal for Improving Classroom Teaching: Lessons from the TIMMS Video Study.” Elementary School Journal 101 (1997): pp. 1 - 20.
Hiebert, 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 Publishing Co., 1992.
Hiebert, James, Thomas P. Carpenter, Elizabeth Fennema, Karen C. Fuson, Diana Wearne, Hanlie Murray, Alwyn Olivier, and Piet Human.
Making Sense: Teaching and Learning Mathematics with Understanding. Portsmouth, N.H.: Heinemann, 1997.
Isaacs, Andrew C., and William M. Carroll.
“Strategies for Basic Facts Instruction.” Teaching Children Mathematics 5 (May 1999): 508 - 515.
Jordan, N. C., Kaplan, D., Ramineni, C., and Locunaik, M. N.
“Early math matters: kindergarten number competence and later mathematics outcomes,”Dev. Psychol. 45, pp. 850 - 867, 2009.
Jordan, N. C., Kaplan, D., Ramineni, C., and Locunaik, M. N.
“Early math matters: kindergarten number competence and later mathematics outcomes,”Dev. Psychol. 45, pp. 850 - 867, 2009.
Mathematics Content Standards for California Public Schools, Kindergarten Through Grade Twelve,(1997)
McClain, Kay, Paul Cobb, and Janet Bowers.
“A Contextual Investigation of Three-Digit Addition and Subtraction.: In The Teaching and Learning of Algorithms in School Mathematics, 1998 Yearbook of the National Council of Teachers of Mathematics, edited by Lorna J. Morrow pp. 141 - 150. Reston, Va.: National Council of Teachers of Mathematics, 1998.
National Assessment Governing Board.
Mathematics Framework for the 2009 National Assessment of Educational Progress. U.S. Department of Education, 2008.
Principles and Standards for School Mathematics.
National Council of Teachers of Mathematics, 2000 pp. 3 - 285.
Rathmell, Edward C.
“Using Thinking Strategies to Teach the Basic Facts.” 1978 of the National Council of Teachers of Mathematics, edited by Marilyn Suydam and Robert E. Reys, pp. 13 - 38.
Robert C. Dixon, Douglas W. Carnine, Dae-Sik Lee, Joshua Wallin, David Chard.
“Report to the California State Board of Education and Addendum to Principal Report.” Review of High Quality Experimental Mathematics Research.(January 1998 Report and March 1998 Addendum): pp. 1 - 100.
Steffe, Leslie P.
“Children’s Multiplying Schemes.” In The Development of Multiplicative Reasoning in the Learning of Mathematics, edited by Guresoh Harel and Jere Confrey, pp. 3 - 39. Albany, N.Y.: State University of New York Press, 1994.
Thornton, Carol A.
“Strategies for the Basic Facts.” In Mathematics for the Young Child, edited by Joseph N. Payne, pp 133 - 151. Reston, Va.: National Council of Teachers of Mathematics, 1990.
U.S. Department of Education.
“What is Scientifically Based Evidence? What is its Logic?” Washington, D.C.: U.S. Department of Education, 2003.