Teaching Practice Recommendations

Clarke, Shirley. Enriching Feedback in the Primary Classroom. London: Hodder and Stoughton, 2003. Clarke, Shirley, Helen Timperley, and John Hattie. Unlocking Formative Assessment: Practical Strategies for Enhancing Students’ Learning in the Primary and Intermediate Classroom. Auckland, New Zealand: Hodder Moa Beckett, 2004. 

Haystead, Mark W., and Robert J. Marzano. Meta-Analytic Synthesis of Studies Conducted at Marzano Research Laboratory on Instructional Strategies. Englewood, Colo.: Marzano Research Laboratory, 2009. 

Hiebert, James, and Douglas A. Grouws. “The Effects of Classroom Mathematics Teaching on Students’ Learning.” In Second Handbook of Research on Mathematics Teaching and Learning, edited by Frank K. Lester, Jr., pp. 371–404. Charlotte, N.C.: Information Age; Reston, Va.: National Council of Teachers of Mathematics, 2007. 

Hiebert, James, Anne K. Morris, Dawn Berk, and Amanda Jansen. “Preparing Teachers to Learn from Teaching.” Journal of Teacher Education 58, no. 1 (2007): 47–61. 

Kazemi, E. & Stipek, D. (2002). Motivating students by teaching for understanding. In J. T. Sowder & B. P. Schappelle (Eds.), Lessons Learned from Research (pp. 17-22). 

Marzano, Robert J. What Works in Schools: Translating Research into Action. Alexandria, Va.: Association of Supervision and Curriculum Development, 2003. 

———. Designing and Teaching Learning Goals and Objectives: Classroom Strategies That Work. Bloomington, Ind.: Marzano Research Laboratory, 2009. 

Pesek, D. D., & Kirshner, D. (2000). Interference of instrumental instruction in subsequent relational learning. Journal for Research in Mathematics Education, 31(5), 524-540.

Wiliam, Dylan. “Content Then Process: Teacher Learning Communities in the Service of Formative Assessment.” In Ahead of the Curve: The Power of Assessment to Transform Teaching and Learning, edited by Douglas Reeves, pp. 183–204. Bloomington, Ind.: Solution Tree Press, 2007b. 

———. “Keeping Learning on Track: Classroom Assessment and the Regulation of Learning.” In Second Handbook of Mathematics Teaching and Learning, edited by Frank K. Lester, Jr., pp. 1053–98. Charlotte, N.C.: Information Age; Reston, Va.: National Council of Teachers of Mathematics, 2007a.

 ———. Embedded Formative Assessment. Bloomington, Ind.: Solution Tree Press, 2011. 

Zimmerman, Barry J. “Theories of Self-Regulated Learning and Academic Achievement: An Overview and Analysis.” In Self-Regulated Learning and Academic Achievement: Theoretical Perspectives, edited by Barry J. Zimmerman and Dale H. Schunk, pp. 1–65. Mahwah, N.J.: Erlbaum, 2001. 

Boaler, Jo, and Megan Staples. “Creating Mathematical Futures through an Equitable Teaching Approach: The Case of Railside School.” Teachers College Record 110, no. 3 (2008): 608–45. 

Crespo, Sandra, Andreas O. Kyriakides, and Shelly McGee. “Nothing Basic about Basic Facts.” Teaching Children Mathematics 12, no. 2 (2005): 61–67. 

Harkey, E. B., Early, K., Hall, R. D., & Strutchens, M. E. (2023). Model It! Revamping High School Schedules. Mathematics Teacher: Learning and Teaching PK-12, 116(10), 808-812.

Hiebert, James, and Diana Wearne. “Instructional Tasks, Classroom Discourse, and Students’ Learning in Second-Grade Arithmetic.” American Educational Research Journal 30, no. 2 (1993): 393–425.

Jackson, Kara, Anne Garrison, Jonee Wilson, Lynsey Gibbons, and Emily Shahan. “Exploring Relationships between Setting Up Complex Tasks and Opportunities to Learn in Concluding Whole-Class Discussions in Middle-Grades Mathematics Instruction.” Journal for Research in Mathematics Education 44, no. 4 (2013): 646–82. 

Kisker, Ellen Eliason, Jerry Lipka, Barbara L. Adams, Anthony Rickard, Dora AndrewIhrke, Eva Evelyn Yanez, and Ann Millard. “The Potential of a Culturally-Based Supplemental Math Curriculum to Reduce the Math Performance Gap between Alaska Native and Other Students.” Journal for Research in Mathematics Education 43, no. 1 (2012): 75–113. 

Livers, S. D. (2023). Model It! Poultry Egg-States. Mathematics Teacher: Learning and Teaching PK-12, 116(10), 764-770.

Smith, Margaret S., and Mary Kay Stein. 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, Va.: National Council of Teachers of Mathematics, 2011. 

———. “Selecting and Creating Mathematical Tasks: From Research to Practice.” Mathematics Teaching in the Middle School 3, no. 5 (1998): 344–49. 

Stein, Mary Kay, Barbara W. Grover, and Marjorie Henningsen. “Building Student Capacity for Mathematical Thinking and Reasoning: An Analysis of Mathematical Tasks Used in Reform Classrooms.” American Educational Research Journal 33, no. 2 (1996): 455–88. 

Stein, Mary Kay, and Suzanne Lane. “Instructional Tasks and the Development of Student Capacity to Think and Reason: An Analysis of the Relationship between Teaching and Learning in a Reform Mathematics Project.” Educational Research and Evaluation 2, no. 1 (1996): 50-80. 

Stein, Mary K., Janine Remillard, and Margaret S. Smith. “How Curriculum Influences Student Learning.” In Second Handbook of Research on Mathematics Teaching and Learning, edited by Frank K. Lester, Jr., pp. 319–69. Charlotte, N.C.: Information Age; Reston, Va.: National Council of Teachers of Mathematics, 2007. 

Stein, Mary Kay, Jennifer Russell, and Margaret Schwan Smith. “The Role of Tools in Bridging Research and Practice in an Instructional Improvement Effort.” In Disrupting Tradition: Research and Practice Pathways in Mathematics Education, edited by William F. Tate, Karen D. King, and Celia Rousseau Anderson, pp. 33–44. Reston, Va.: National Council of Teachers of Mathematics, 2011. 

Stein, Mary Kay, and Margaret S. Smith. “Mathematical Tasks as a Framework for Reflection: From Research to Practice.” Mathematics Teaching in the Middle School 3, no. 4 (1998): 268–75. 

Stein, Mary Kay, Margaret S. Smith, Marjorie Henningsen, and Edward A. Silver. Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development. 2nd ed. New York: Teachers College Press, 2009. 

Stigler, James W., and James Hiebert. The Teaching Gap: Best Ideas from the World’s Teachers for Improving Education in the Classroom. New York: Simon and Schuster, 1999. 

———. “Improving Mathematics Teaching.” Educational Leadership 61, no. 5 (2004): 12–16. 

Wager, Anita A. “Incorporating Out-of-School Mathematics: From Cultural Context to Embedded Practice.” Journal of Mathematics Teacher Education 15, no. 1 (2012): 9–23. 

Ghousseini, H. (2015). Core practices and problems of practice in learning to lead classroom discussions. The Elementary School Journal, 115(3), 334-357.

Ghousseini, H., & Herbst, P. (2016). Pedagogies of practice and opportunities to learn about classroom mathematics discussions. Journal of Mathematics Teacher Education, 19, 79-103.

Hiebert, James, and Diana Wearne. “Instructional Tasks, Classroom Discourse, and Students’ Learning in Second-Grade Arithmetic.” American Educational Research Journal 30, no. 2 (1993): 393–425.

Jacobs, V. R., Martin, H. A., Ambrose, R. C., & Philipp, R. A. (2014). Warning Signs. Recognize Three Common Instructional Moves That Are Generally Followed by Taking over Children’s Thinking, 21(2), 107-113.

Mercer, N.: Words and Minds: Development through dialogue, pp. 131–166. Routledge, London (2000).

Michaels, Sarah, Mary Catherine O’Connor, and Lauren Resnick. “Deliberative Discourse Idealized and Realized: Accountable Talk in the Classroom and in Civic Life.” Studies in Philosophy and Education 27, no. 4 (2008): 283–97. 

Rothermel Rawding, M., & Wills, T. (2012). Discourse: Simple moves that work. Mathematics Teaching in the Middle School, 18(1), 46–51. 

Smith , M. S., Hughes , E. K., Engle , R. A., & Stein, M. K. (2009). Orchestrating Discussion. Mathematics Teaching in the Middle School, 14(9), 548–556.

Boaler, Jo, and Karin Brodie. “The Importance, Nature, and Impact of Teacher Questions.” In Proceedings of the 26th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, vol. 2, pp. 773–81. Toronto: Ontario Institute for Studies in Education of the University of Toronto, 2004.

Hiebert, James, and Diana Wearne. “Instructional Tasks, Classroom Discourse, and Students’ Learning in Second-Grade Arithmetic.” American Educational Research Journal 30, no. 2 (1993): 393–425.

Martin, Danny Bernard. “Hidden Assumptions and Unaddressed Questions in Mathematics for ALL Rhetoric.” Mathematics Educator 13, no. 2 (2003): 7.

McTighe, Jay, and Grant P. Wiggins. Essential Questions: Opening Doors to Student Understanding. Alexandria, Va.: Association for Supervision and Curriculum Development, 2013.

Rathmell, Edward C. Basic Facts: Questions, Answers, and Comments. Cedar Falls, Iowa: Thinking with Numbers, 2005.http://www.thinkingwithnumbers.com. 

Crespo, Sandra, Andreas O. Kyriakides, and Shelly McGee. “Nothing Basic about Basic Facts.” Teaching Children Mathematics 12, no. 2 (2005): 61–67. 

Fuson, Karen C. “Toward Computational Fluency in Multidigit Multiplication and Division.” Teaching Children Mathematics 9, no. 6 (2003): 300–305.

Fuson, Karen C., and Sybilla Beckmann. “Standard Algorithms in the Common Core State Standards.” National Council of Supervisors of Mathematics Journal of Mathematics Education Leadership 14, no. 1 (2012/2013): 14–30.

Fuson, Karen C., Mindy Kalchman, and John D. Bransford. “Mathematical Understanding: An Introduction.” In How Students Learn: History, Mathematics, and Science in the Classroom, edited by M. Suzanne Donovan and John D. Bransford, Committee on How People Learn: A Targeted Report for Teachers, National Research Council, pp. 217–56. Washington, D.C.: National Academies Press, 2005.

Fuson, Karen C., and Aki Murata. “Integrating NRC Principles and the NCTM Process Standards to Form a Class Learning Path Model That Individualizes within Whole Class Activities.” National Council of Supervisors of Mathematics Journal of Mathematics Education Leadership 10, no. 1 (2007): 72–91.

Isaacs, Andrew C., and William M. Carroll. “Strategies for Basic-Facts Instruction.” Teaching Children Mathematics 5, no. 9 (1999): 508–15. 

Karp, K. S., Bush, S. B., & Dougherty, B. J. (2014). 13 rules that expire. Teaching Children Mathematics, 21(1), 18-25. https://doi.org/10.5951/teacchilmath.21.1.0018

Pashler, Harold, Patrice M. Bain, Brian A. Bottge, Arthur Graesser, Kenneth Koedinger, Mark McDaniel, and Janet Metcalfe. Organizing Instruction and Study to Improve Student Learning. IES Practice Guide (NCER 2007-2004). Washington, D.C.: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education, 2007. http://ncer.ed.gov. 

Pesek, D. D., & Kirshner, D. (2000). Interference of instrumental instruction in subsequent relational learning. Journal for Research in Mathematics Education, 31(5), 524-540.

Rathmell, Edward C. Basic Facts: Questions, Answers, and Comments. Cedar Falls, Iowa: Thinking with Numbers, 2005. http://www.thinkingwithnumbers.com. 

Rohrer, Doug. “The Effects of Spacing and Mixed Practice Problems.” Journal for Research in Mathematics Education 40, no. 1 (2009): 4–17.

Rohrer, Doug, and Kelli Taylor. “The Shuffling of Mathematics Problems Improves Learning.” Instructional Science 35, no. 6 (2007): 481–98.

Seeley, Cathy L. Faster Isn’t Smarter: Messages about Math, Teaching, and Learning in the 21st Century. Sausalito, Calif.: Math Solutions, 2009. 

Thornton, Carol A. “Emphasizing Thinking Strategies in Basic Fact Instruction.” Journal for Research in Mathematics Education (1978): 214–27. 

Ball, Deborah Loewenberg, and Francesca M. Forzani. “Building a Common Core for Learning to Teach and Connecting Professional Learning to Practice.” American Educator 35, no. 2 (2011): 17–21. 

Banilower, Eric R., Sally E. Boyd, Joan D. Pasley, and Iris R. Weiss. Lessons from a Decade of Mathematics and Science Reform. Chapel Hill, N.C.: Horizon Research, 2006. 

Barkatsas, Anastasios Tasos, and John Malone. “A Typology of Mathematics Teachers’ Beliefs about Teaching and Learning Mathematics and Instructional Practices.” Mathematics Education Research Journal 17, no. 2 (2005): 69–90. 

Donovan, M. Suzanne, and John D. Bransford, eds. How Students Learn: History, Mathematics, and Science in the Classroom. National Research Council, Committee on How People Learn: A Targeted Report for Teachers. Washington, D.C.: National Academies Press, 2005. 

Duit, Reinders, and David F. Treagust. “Conceptual Change: A Powerful Framework for Improving Science Teaching and Learning.” International Journal of Science Education 25, no. 6 (2003): 671–88. 

Grossman, Pam, Karen Hammerness, and Morva McDonald. “Redefining Teaching, Re‐ imagining Teacher Education.” Teachers and Teaching: Theory and Practice 15, no. 2 (2009): 273–89. 

Hiebert, James, and Douglas A. Grouws. “The Effects of Classroom Mathematics Teaching on Students’ Learning.” In Second Handbook of Research on Mathematics Teaching and Learning, edited by Frank K. Lester, Jr., pp. 371–404. Charlotte, N.C.: Information Age; Reston, Va.: National Council of Teachers of Mathematics, 2007. 

Hlas, Anne Cummings, and Christopher S. Hlas. “A Review of High‐Leverage Teaching Practices: Making Connections between Mathematics and Foreign Languages.” Foreign Language Annals 45, no. s1 (2012): s76–s97. 

Kapur, Manu. “Productive Failure in Mathematical Problem Solving.” Instructional Science 38, no. 6 (2010): 523–50. 

Mayer, Richard E. “Rote versus Meaningful Learning.” Theory into Practice 41, no. 4 (2002): 226–32. 

McDonald, Morva, Elham Kazemi, and Sarah Schneider Kavanagh. “Core Practices and Pedagogies of Teacher Education: A Call for a Common Language and Collective Activity.” Journal of Teacher Education 64, no. 5 (2013): 378–86. 

Raslan, G. (2024). The Impact of the Zone of Proximal Development Concept (Scaffolding) on the Students Problem Solving Skills and Learning Outcomes. In: Al Marri, K., Mir, F.A., David, S.A., Al-Emran, M. (eds) BUiD Doctoral Research Conference 2023. Lecture Notes in Civil Engineering, vol 473. Springer, Cham. https://doi.org/10.1007/978-3-031-56121-4_6.

Warshauer, Hiroko Kawaguchi. “The Role of Productive Struggle in Teaching and Learning Middle School Mathematics.” PhD diss., University of Texas at Austin (2011). 

Weiss, Iris R., and Joan D. Pasley. “What Is High-Quality Instruction?” Educational Leadership 61, no. 5 (2004): 24–28. 

Vygotsky, L.: Mind and society. In: Interaction between Learning and Development, pp. 79–91. Harvard University Press, Cambridge (1978).

Awofala, A. O. A. (2011). Effect of concept mapping strategy on students’ achievement in junior secondary school mathematics. International Journal of Mathematics Trends and Technology-IJMTT, 2.

Hiebert, James, and Diana Wearne. “Instructional Tasks, Classroom Discourse, and Students’ Learning in Second-Grade Arithmetic.” American Educational Research Journal 30, no. 2 (1993): 393–425.

Popelka, S. (2010). Now we're really clicking. Mathematics Teacher, 104(4), 290-295. https://doi.org/10.5951/MT.104.4.0290

Schlosser, M. (2015). Analysis of alternative assessments in the mathematics classroom. Bowling Green Honors Thesis.

Arcavi, Abraham. “The Role of Visual Representations in the Learning of Mathematics.” Educational Studies in Mathematics 52, no. 3 (2003): 215–41.

Conway, B., & Mitchell, M. (2023). Construct It! Intersecting Language and Mathematics with Interlocking Cubes. Mathematics Teacher: Learning and Teaching PK-12, 116(10), 753-757.

Crespo, Sandra, Andreas O. Kyriakides, and Shelly McGee. “Nothing Basic about Basic Facts.” Teaching Children Mathematics 12, no. 2 (2005): 61–67. 

Greeno, James G., and Rogers P. Hall. “Practicing Representation.” Phi Delta Kappan 78, no. 5 (1997): 361–67.

Huntley, M., & Rasmussen, C. (2002). Effects of standards-based mathematics education: A study of the core-plus mathematics algebra and functions strand. In J. Sowder & B. Schappelle (Eds.) Lessons Learned from Research (pp. 163-169). Reston, VA: National Council of Teachers of Mathematics. (Reprinted from “Effects of standards-based mathematics education: A study of the core-plus mathematics algebra and functions strand,” 2000, Journal for Research in Mathematics Education, 31, 328-361).

Johanning, D. (2016). Helping Students Learn to Use Fractions. P. Kenney & E. Silver (Eds). More lessons learned from research (pp. 219-228). NCTM. (Reprinted from “Learning to use fractions: Examining middle school students’ emerging fraction literacy", 2008, Journal for Research in Mathematics Education, 39, 281-310).

Lesh, Richard, Tom Post, and Merlyn Behr. “Representations and Translations among Representations in Mathematics Learning and Problem Solving.” In Problems of Representation in the Teaching and Learning of Mathematics, edited by Claude Janvier, pp. 33–40. Hillsdale, N.J.: Erlbaum, 1987.

Pape, Stephen J., and Mourat A. Tchoshanov. “The Role of Representation(s) in Developing Mathematical Understanding.” Theory into Practice 40, no. 2 (2001): 11.

Pesek, D. D., & Kirshner, D. (2000). Interference of instrumental instruction in subsequent relational learning. Journal for Research in Mathematics Education, 31(5), 524-540.

Stylianou, Despina A., and Edward A. Silver. “The Role of Visual Representations in Advanced Mathematical Problem Solving: An Examination of Expert-Novice Similarities and Differences.” Mathematical Thinking and Learning 6, no. 4 (2004): 353–87.

Tripathi, Preety N. “Developing Mathematical Understanding through Multiple Representations.” Mathematics Teaching in the Middle School 13, no. 8 (2008): 438–4.

Webb, David C., Nina Boswinkel, and Truus Dekker. “Beneath the Tip of the Iceberg: Using Representations to Support Student Understanding.” Mathematics Teaching in the Middle School 14, no. 2 (2008): 110–13.