Revisit this collection of articles through the lens of Mathematics Teaching Practice 6: Build procedural fluency from conceptual understanding and Practice 7: Support productive struggle in learning mathematics.

Huinker, DeAnn, and VictoriaBill.2017. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K–5.Reston, VA: National Council of Teachers of Mathematics.

Baroody, Arthur J.2006. “Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them.” Teaching Children Mathematics13 (August): 22–31.

Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

Common Core State Standards Initiative (CCSSI). 2010. )| false

Forbringer, Linda, and AllisonJ. Fahsl.2010. “Differentiating Practice to Help Students Master Basic Facts.” In Responding to Diversity: Grades Pre-K–5, edited by DorothyY. White and JulieS. Spitzer, pp. 7–22. Reston, VA: National Council of Teachers of Mathematics.

Forbringer, Linda, and AllisonJ. Fahsl.2010. “Differentiating Practice to Help Students Master Basic Facts.” In )| false

Henry, Valerie J., and RichardS. Brown.2008. “First-Grade Basic Facts: An Investigation into Teaching and Learning of an Accelerated, High-Demand Memorization Standard.” Journal for Research in Mathematics Education39 (March): 153–83.

Henry, Valerie J., and RichardS. Brown.2008. “First-Grade Basic Facts: An Investigation into Teaching and Learning of an Accelerated, High-Demand Memorization Standard.” )| false

National Council of Teachers of Mathematics (NCTM).2006. Curriculum Focal Points for Pre-kindergarten through Grade 8: A Quest for Coherence.Reston, VA: NCTM.

National Council of Teachers of Mathematics (NCTM).2006. )| false

NationalResearch Council (NRC).2001. Adding It Up: Helping Children Learn Mathematics. Edited by JeremyKilpatrick, JaneSwafford, and BradFindell. Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academies Press.

NationalResearch Council (NRC).2001. Adding It Up: Helping Children Learn Mathematics. Edited by JeremyKilpatrick, JaneSwafford, and BradFindell. )| false

Ramirez, Gerardo, ElizabethA. Gunderson, SusanC. Levine, and SianL. Beilock.2013. “Math Anxiety, Working Memory, and Math Achievement in Early Elementary School.” Journal of Cognition and Development14 (2): 187–202.

Ramirez, Gerardo, ElizabethA. Gunderson, SusanC. Levine, and SianL. Beilock.2013. “Math Anxiety, Working Memory, and Math Achievement in Early Elementary School.” )| false

Van de Walle, John. A., KarenS. Karp, and JenniferM. Bay-Williams. 2013. Elementary and Middle School Mathematics: Teaching Developmentally.Professional Development Edition. New York: Pearson.

Van de Walle, John. A., KarenS. Karp, and JenniferM. Bay-Williams. 2013. )| false

Van de Walle, John A., LouAnn H. Lovin, KarenS. Karp, and JenniferM. Bay-Williams.2014. Teaching Student Centered Mathematics: Grades K–2.2nd edition. New York: Pearson.

Van de Walle, John A., LouAnn H. Lovin, KarenS. Karp, and JenniferM. Bay-Williams.2014. )| false

Barlow, Angela T., NatashaE. Gerstenschlager, and ShannonE. Harmon.2016. “Learning from the Unknown Student.” Teaching Children Mathematics23, no. 2 (September): 74–81.

Buschman, Larry.2003. Share and Compare: A Teacher's Story about Helping Children become Problem Solvers in Mathematics.Reston, VA: National Council of Teachers of Mathematics.

Chapin, Suzanne H., CatherineO'Connor, and NancyCanavan Anderson.2003. Classroom Discussions: Using Math Talk to Help Students Learn (Grades 1–6).Sausalito, CA: Math Solutions Publications.

Chapin, Suzanne H., CatherineO'Connor, and NancyCanavan Anderson.2003. )| false

Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for Mathematics. Washington, DC: The National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf

Common Core State Standards Initiative (CCSSI). 2010. )| false

Rigelman, Nicole. “Fostering Mathematical Thinking and Problem Solving: The Teacher's Role.” 2007. Teaching Children Mathematics13, no. 6 (February): 308–14.

Watanabe, Tad. “Can Fifth Graders Derive Area Formulae? Implications from Japanese Curriculum Materials.” Presentation at the Georgia Mathematics Conference, Rock Eagle, GA, October15–17, 2008.

Watanabe, Tad. “Can Fifth Graders Derive Area Formulae? Implications from Japanese Curriculum Materials.” )| false

Carpenter, Thomas P., MeganL. Franke, VictoriaR. Jacobs, ElizabethFennema, and SusanB. Empson. “A Longitudinal Study of Invention and Understanding in Children's Multidigit Addition and Subtraction.” Journal for Research in Mathematics Education29 (January1998): 3–20.

Carpenter, Thomas P., MeganL. Franke, VictoriaR. Jacobs, ElizabethFennema, and SusanB. Empson. “A Longitudinal Study of Invention and Understanding in Children's Multidigit Addition and Subtraction.” )| false

Fuson, Karen C., DianaWearne, JamesC. Hiebert, HanlieG. Murray, PieterG. Human, AlwynI. Olivier, ThomasP. Carpenter, and ElizabethFennema. “Children's Conceptual Structures for Multidigit Numbers and Methods of Multidigit Addition and Subtraction.” Journal for Research in Mathematics Education28 (March1997): 130–62.

Fuson, Karen C., StevenT. Smith, and AnaMaria Lo Cicero. “Supporting Latino First Graders' Ten-Structured Thinking in Urban Classrooms.” Journal for Research in Mathematics Education28 (December1997): 738–66.

Kamii, Constance, and AnnDominick. ”The Harmful Effects of Algorithms in Grades 1–4.” In The Teaching and Learning of Algorithms in School Mathematics, 1998 Yearbook of the National Council of Teachers of Mathematics (NCTM), edited by LornaJ. Morrow.Reston, VA.: NCTM, 1998.

McClain, Kay, PaulCobb, and JanetBowers. “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 (NCTM), edited by LornaJ. Morrow.Reston, VA.: NCTM, 1998.

McClain, Kay, PaulCobb, and JanetBowers. “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 (NCTM), edited by LornaJ. Morrow.Reston, VA.: NCTM, 1998.)| false

Stigler, James W., and JamesHiebert. “Understanding and Improving Classroom Mathematics Instruction: An Overview of the TIMSS Video Study.” Phi Delta Kappa79 (September1997): 14–21.

Stigler, James W., and JamesHiebert. “Understanding and Improving Classroom Mathematics Instruction: An Overview of the TIMSS Video Study.” Phi Delta Kappa79 (September1997): 14–21.)| false

Whitenack, Joy W., NancyKnipping, SueNovinger, and GailUnderwood. “Second Graders Circumvent Addition and Subtraction Difficulties.” Teaching Children Mathematics8 (December2001): 228–33.

Whitenack, Joy W., NancyKnipping, SueNovinger, and GailUnderwood. “Second Graders Circumvent Addition and Subtraction Difficulties.” Teaching Children Mathematics8 (December2001): 228–33.10.5951/TCM.8.4.0228)| false

Wilson, Linda D., and RolfK. Blank. “Improving Mathematics Education: Using Results from the NAEP and TIMSS.” ERIC document no. ED 431 001, 1999.

Wilson, Linda D., and RolfK. Blank. “Improving Mathematics Education: Using Results from the NAEP and TIMSS.” ERIC document no. ED 431 001, 1999.)| false

Carpenter, Thomas P., MeganL. Franke, VictoriaR. Jacobs, ElizabethFennema, and SusanB. Empson. “A Longitudinal Study of Invention and Understanding in Children's Multidigit Addition and Subtraction.” Journal for Research in Mathematics Education29 (January1998): 3–20.

Carpenter, Thomas P., MeganL. Franke, VictoriaR. Jacobs, ElizabethFennema, and SusanB. Empson. “A Longitudinal Study of Invention and Understanding in Children's Multidigit Addition and Subtraction.” Journal for Research in Mathematics Education29 (January1998): 3–20.10.2307/749715)| false

Chapin, Suzanne H., and ArtJohnson.Math Matters, Grades K-6: Understanding the Math You Teach.Sausalito, Calif: Math Solutions Publications, 2000.

Chapin, Suzanne H., and ArtJohnson.Math Matters, Grades K-6: Understanding the Math You Teach.Sausalito, Calif: Math Solutions Publications, 2000.)| false

Fuson, Karen C., DianaWearne, JamesC. Hiebert, HanlieG. Murray, PieterG. Human, AlwynI. Olivier, ThomasP. Carpenter, and ElizabethFennema. “Children's Conceptual Structures for Multi-digit Numbers and Methods of Multidigit Addition and Subtraction.” Journal for Research in Mathematics Education29 (March1997): 130–62.

Fuson, Karen C., DianaWearne, JamesC. Hiebert, HanlieG. Murray, PieterG. Human, AlwynI. Olivier, ThomasP. Carpenter, and ElizabethFennema. “Children's Conceptual Structures for Multi-digit Numbers and Methods of Multidigit Addition and Subtraction.” Journal for Research in Mathematics Education29 (March1997): 130–62.10.2307/749759)| false

Russell, Susan Jo. “Developing Computational Fluency with Whole Numbers.” Teaching Children Mathematics7 (November2000): 154–58.10.5951/TCM.7.3.0154)| false

Scharton, Susan.Growing Mathematicians: Developing Problem Solving through Invention and Communication.University of California, San Diego: Unpublished master's thesis, 2001.

Scharton, Susan.Growing Mathematicians: Developing Problem Solving through Invention and Communication.University of California, San Diego: Unpublished master's thesis, 2001.)| false

Schoenfeld, Alan. “Teaching Mathematical Thinking and Problem Solving.” In Toward a Thinking Curriculum: Current Cognitive Research, edited by L.Resnick and L.Klopfer. Alexandria, VA.: Association of Supervision and Curriculum Development, 1989.

Schoenfeld, Alan. “Teaching Mathematical Thinking and Problem Solving.” In Toward a Thinking Curriculum: Current Cognitive Research, edited by L.Resnick and L.Klopfer. Alexandria, VA.: Association of Supervision and Curriculum Development, 1989.)| false

Barnett-Clarke, Carne, WilliamFisher, RickMarks, and SharonRoss.2010. Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3-5.Reston, VA: National Council of Teachers of Mathematics.

Barnett-Clarke, Carne, WilliamFisher, RickMarks, and SharonRoss.2010. Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3-5.Reston, VA: National Council of Teachers of Mathematics.)| false

Behr, Merlyn, IpkeWachsmuth, ThomasR. Post, and RichardLesh.1984. “Order and Equivalence of Rational Numbers: A Clinical Teaching Experiment.” Journal for Research in Mathematics Education15 (November): 323–41.

Behr, Merlyn, IpkeWachsmuth, ThomasR. Post, and RichardLesh.1984. “Order and Equivalence of Rational Numbers: A Clinical Teaching Experiment.” Journal for Research in Mathematics Education15 (November): 323–41.10.2307/748423)| false

Cramer, Kathleen, DebraMonson, StephanieWhitney, SethLeavitt, and TerryWyberg.2010. “Dividing Fractions and Problem Solving.” Mathematics Teaching in the Middle School15 (February): 338–46.

Cramer, Kathleen, DebraMonson, StephanieWhitney, SethLeavitt, and TerryWyberg.2010. “Dividing Fractions and Problem Solving.” Mathematics Teaching in the Middle School15 (February): 338–46.10.5951/MTMS.15.6.0338)| false

Greeno, James G.1991. “Number Sense as Situated Knowing in a Conceptual Domain.” Journal for Research in Mathematics Education22 (May): 170–218.10.2307/749074)| false

Lamon, Susan J.2007. Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers.New York: Routledge-Taylor Francis Group.

Lamon, Susan J.2007. Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers.New York: Routledge-Taylor Francis Group.)| false

Petit, Marjorie M., RobertE. Laird, and EdwinL. Marsden.2010. A Focus on Fractions: Bringing Research to the Classroom.New York: Routledge-Taylor Francis Group.

Petit, Marjorie M., RobertE. Laird, and EdwinL. Marsden.2010. A Focus on Fractions: Bringing Research to the Classroom.New York: Routledge-Taylor Francis Group.10.4324/9780203855515)| false

Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf

Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf)| false

Aguirre, Julia M., KarenMayfield-Ingram, and DannyBernard Martin.2013. The Impact of Identity in K–8 Mathematics: Rethinking Equity-Based Practices.Reston, VA: National Council of Teachers of Mathematics.

Aguirre, Julia M., KarenMayfield-Ingram, and DannyBernard Martin.2013. The Impact of Identity in K–8 Mathematics: Rethinking Equity-Based Practices.Reston, VA: National Council of Teachers of Mathematics.)| false

Boaler, Jo.2002. “The Development of Disciplinary Relationships: Knowledge, Practice, and Identity in Mathematics Classrooms.” For the Learning of Mathematics22 (1): 42–47.

Boaler, Jo.2002. “The Development of Disciplinary Relationships: Knowledge, Practice, and Identity in Mathematics Classrooms.” For the Learning of Mathematics22 (1): 42–47.)| false

Boaler, Jo, and CathyHumphreys.2005. Connecting Mathematical Ideas: Middle School Video Cases to Support Teaching and Learning.Portsmouth, NH: Heinemann.

Boaler, Jo, and CathyHumphreys.2005. Connecting Mathematical Ideas: Middle School Video Cases to Support Teaching and Learning.Portsmouth, NH: Heinemann.)| false

Grootenboer, Peter, and RobynZevenbergen.2008. “Identity as a Lens to Understand Learning Mathematics: Developing a Model.” In Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia, Vol. 1, edited by MerrilynGoos, RayBrown, and KatieMakar, pp. 243–249, Canberra, Australia: MERGA.

Grootenboer, Peter, and RobynZevenbergen.2008. “Identity as a Lens to Understand Learning Mathematics: Developing a Model.” In Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia, Vol. 1, edited by MerrilynGoos, RayBrown, and KatieMakar, pp. 243–249, Canberra, Australia: MERGA.)| false

Willis, Judy.2010. Learning to Love Math: Teaching Strategies that Change Student Attitudes and Get Results.Alexandria, VA: Association for Supervision and Curriculum Development.

Willis, Judy.2010. Learning to Love Math: Teaching Strategies that Change Student Attitudes and Get Results.Alexandria, VA: Association for Supervision and Curriculum Development.)| false

Hiebert, James, and DouglasA. Grouws.2007. “The Effects of Classroom Mathematics Teaching on Students’ Learning.” In Second Handbook of Research on Mathematics Teaching and Learning, edited by FrankK. LesterJr., pp. 371–404. Charlotte, NC: Information Age Publishing.

Hiebert, James, and DouglasA. Grouws.2007. “The Effects of Classroom Mathematics Teaching on Students’ Learning.” In Second Handbook of Research on Mathematics Teaching and Learning, edited by FrankK. LesterJr., pp. 371–404. Charlotte, NC: Information Age Publishing.)| false

Hiebert, James, and DianaWearne.1993. “Instructional Tasks, Discourse, and Students’ Learning in Second-Grade Arithmetic.” American Educational Research Journal30 (2): 393–425.

Hiebert, James, and DianaWearne.1993. “Instructional Tasks, Discourse, and Students’ Learning in Second-Grade Arithmetic.” American Educational Research Journal30 (2): 393–425.10.3102/00028312030002393)| false

Smith, Margaret.2000. “Reflection on Practice: Redefining Success in Mathematics Teaching and Learning.” Mathematics Teaching in the Middle School5 (January): 378–82; 86.

Smith, Margaret.2000. “Reflection on Practice: Redefining Success in Mathematics Teaching and Learning.” Mathematics Teaching in the Middle School5 (January): 378–82; 86.10.5951/MTMS.5.6.0378)| false

Carpenter, Thomas P., MeganL. Franke, and LindaLevi.2003. Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School.Portsmouth, NH: Heinemann.

Carpenter, Thomas P., MeganL. Franke, and LindaLevi.2003. Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School.Portsmouth, NH: Heinemann.)| false

Ferrucci, Beverly, BerinderjeetKaur, JackA. Carter, and BanHarYeap.2008. “Using a Model Approach to Enhance Algebriac Thinking in the Elementary School Mathematics Classroom.” In Algebra and Algebraic Thinking in School Mathematics, 2008 Yearbook of the National Council of Teachers of Mathematics (NCTM), edited by CaroleE. Greenes and RhetaRubenstein, pp. 195–210. Reston, VA: NCTM.

Ferrucci, Beverly, BerinderjeetKaur, JackA. Carter, and BanHarYeap.2008. “Using a Model Approach to Enhance Algebriac Thinking in the Elementary School Mathematics Classroom.” In Algebra and Algebraic Thinking in School Mathematics, 2008 Yearbook of the National Council of Teachers of Mathematics (NCTM), edited by CaroleE. Greenes and RhetaRubenstein, pp. 195–210. Reston, VA: NCTM.)| false

Johnson, Ken, and TedHerr.2001. Problem-Solving Strategies: Crossing the River with Dogs and Other Mathematical Adventures.Emeryville, CA: Key Curriculum Press.

Johnson, Ken, and TedHerr.2001. Problem-Solving Strategies: Crossing the River with Dogs and Other Mathematical Adventures.Emeryville, CA: Key Curriculum Press.)| false

Middleton, James A., and AmandaJansen.2011. Motivation Matters and Interest Counts: Fostering Engagement in Mathematics.Reston, VA: National Council of Teachers of Mathematics.

Middleton, James A., and AmandaJansen.2011. Motivation Matters and Interest Counts: Fostering Engagement in Mathematics.Reston, VA: National Council of Teachers of Mathematics.)| false

Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf

Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf)| false

Klein, Raymond J., and IleneHamilton.1997. “Technology Tips: Using Technology to Introduce Radian Measure.” Mathematics Teacher90, no. 2 (February): 168–72.

Klein, Raymond J., and IleneHamilton.1997. “Technology Tips: Using Technology to Introduce Radian Measure.” Mathematics Teacher90, no. 2 (February): 168–72.10.5951/MT.90.2.0168)| false

AnnenbergLearner.n.d. “The Staircase Problem.” Teaching Math: A Video Library, 9–12. Teacher Resources: Mathematics. https://www.learner.org/resources/series34.html#)| false

Freeburn, Benjamin Louis.2015. “Preservice Secondary Mathematics Teachers’ Learning of Purposeful Questioning and Judicious Telling for Promoting Students’ Mathematical Thinking.” PhD diss., The Pennsylvania State University.

Freeburn, Benjamin Louis.2015. “Preservice Secondary Mathematics Teachers’ Learning of Purposeful Questioning and Judicious Telling for Promoting Students’ Mathematical Thinking.” PhD diss., The Pennsylvania State University.)| false

Lobato, Joanne, DavidClarke, and AmyBurns Ellis.2005. “Initiating and Eliciting in Teaching: A Reformulation of Telling.” Journal for Research in Mathematics Education36, no. 2 (March): 101–36.

Lobato, Joanne, DavidClarke, and AmyBurns Ellis.2005. “Initiating and Eliciting in Teaching: A Reformulation of Telling.” Journal for Research in Mathematics Education36, no. 2 (March): 101–36.)| false

Smith, Margaret S., VictoriaBill, and ElizabethK. Hughes.2008. “Thinking through a Lesson: Successfully Implementing High-level Tasks.” Mathematics Teaching in the Middle School14 (October): 132–38.

Smith, Margaret S., VictoriaBill, and ElizabethK. Hughes.2008. “Thinking through a Lesson: Successfully Implementing High-level Tasks.” Mathematics Teaching in the Middle School14 (October): 132–38.10.5951/MTMS.14.3.0132)| false

Smith, Margaret S., and MaryKay Stein.1998. “From Research to Practice: Selecting and Creating Mathematical Tasks.” Mathematics Teaching in the Middle School3, no. 5 (February): 344–50.

Smith, Margaret S., and MaryKay Stein.1998. “From Research to Practice: Selecting and Creating Mathematical Tasks.” Mathematics Teaching in the Middle School3, no. 5 (February): 344–50.10.5951/MTMS.3.5.0344)| false

Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf)| false

Goldberg, Kenneth.2007. “The Homework Trap.” Paper presented at the annual meeting of the American Educational Research Association, Chicago, April.

Goldberg, Kenneth.2007. “The Homework Trap.” Paper presented at the annual meeting of the American Educational Research Association, Chicago, April.)| false