Learning Trajectories for Vertical Coherence

Confrey, Jere. 1988. “Multiplication and Splitting: Their Role in Understanding Exponential Functions." In Proceedings of the 10th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, pp. 250–59, Dekalb, Illinois, December 3–5, 1988.

Confrey, Jere. 1988. “Multiplication and Splitting: Their Role in Understanding Exponential Functions." In Proceedings of the 10th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, pp. 250–59, Dekalb, Illinois, December 3–5, 1988.)| false
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Confrey, Jere. 1995. “Student Voice in Examining ‘Splitting’ as an Approach to Ratio, Proportions, and Fractions." In Proceedings of the 19th Psychology of Mathematics Education (PME) Conference. Universidade Federal de Pernambuco, Recife, Brazil, pp. I-3–I-29, July 22–27, 1995.

Confrey, Jere. 1995. “Student Voice in Examining ‘Splitting’ as an Approach to Ratio, Proportions, and Fractions." In Proceedings of the 19th Psychology of Mathematics Education (PME) Conference. Universidade Federal de Pernambuco, Recife, Brazil, pp. I-3–I-29, July 22–27, 1995.)| false
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Confrey, Jere, Garron Gianopulos, William McGowan, Meetal Shah, and Michael Belcher. 2017. “Scaffolding Learner-Centered Curricular Coherence Using Learning Maps and Diagnostic Assessments Designed around Mathematics Learning Trajectories." ZDM: The International Journal on Mathematics Education 49, no. 5 (May): 717–34.

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Confrey, Jere, Garron Gianopulos, William McGowan, Meetal Shah, and Michael Belcher. 2017. “Scaffolding Learner-Centered Curricular Coherence Using Learning Maps and Diagnostic Assessments Designed around Mathematics Learning Trajectories." ZDM: The International Journal on Mathematics Education 49, no. 5 (May): 717–34.10.1007/s11858-017-0869-1)| false
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Confrey, Jere, Alan P. Maloney, Kenny H. Nguyen, and André A. Rupp. 2014. “Equipartitioning, a Foundation for Rational Number Reasoning." In Learning over Time: Learning Trajectories in Mathematics Education, edited by Alan Maloney, Jere Confrey, and Kenny H. Nguyen, pp. 61–96. Charlotte, NC: Information Age Publishing.

Confrey, Jere, Alan P. Maloney, Kenny H. Nguyen, and André A. Rupp. 2014. “Equipartitioning, a Foundation for Rational Number Reasoning." In Learning over Time: Learning Trajectories in Mathematics Education, edited by Alan Maloney, Jere Confrey, and Kenny H. Nguyen, pp. 61–96. Charlotte, NC: Information Age Publishing.)| false
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Confrey, Jere, and Grace Hotchkiss Scarano. 1995. “Splitting Reexamined: Results from a Three-Year Longitudinal Study of Children in Grades Three to Five." In Proceedings of the 17th Psychology of Mathematics Education, North American Chapter, pp. 421–26. Ohio State University, Columbus, OH, October 21–25, 1995.

Confrey, Jere, and Grace Hotchkiss Scarano. 1995. “Splitting Reexamined: Results from a Three-Year Longitudinal Study of Children in Grades Three to Five." In Proceedings of the 17th Psychology of Mathematics Education, North American Chapter, pp. 421–26. Ohio State University, Columbus, OH, October 21–25, 1995.)| false
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Freudenthal, Hans. 1987. “Mathematics Starting and Staying in Reality." In Proceedings of the USCMP Conference on Mathematics Education on Development in School Mathematics around the World. Reston, VA: National Council of Teachers of Mathematics.

Freudenthal, Hans. 1987. “Mathematics Starting and Staying in Reality." In Proceedings of the USCMP Conference on Mathematics Education on Development in School Mathematics around the World. Reston, VA: National Council of Teachers of Mathematics.)| false
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Harel, Guershon, and Jere Confrey, eds. 1994. Development of Multiplicative Reasoning in the Learning of Mathematics. Albany, NY: The SUNY Press.

Harel, Guershon, and Jere Confrey, eds. 1994. Development of Multiplicative Reasoning in the Learning of Mathematics. Albany, NY: The SUNY Press.)| false
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Kapur, Manu. 2008. “Productive Failure." Cognition and Instruction 26, no. 3 (July–September): 379–424.

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Kapur, Manu. 2008. “Productive Failure." Cognition and Instruction 26, no. 3 (July–September): 379–424.10.1080/07370000802212669)| false
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National Governors Association Center for Best Practices (NGA Center) and Council of Chief State School Officers (CCSSO). 2010. Common Core State Standards for Mathematics Washington, DC: NGA Center and CCSSO. http://www.corestandards.org.

National Governors Association Center for Best Practices (NGA Center) and Council of Chief State School Officers (CCSSO). 2010. Common Core State Standards for Mathematics Washington, DC: NGA Center and CCSSO. http://www.corestandards.org.)| false
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Siemon, Dianne, Margarita Breed, and Jo Virgona. 2005. “From Additive to Multiplicative Thinking—The Big Challenge of the Middle Years." In Mathematics: Celebrating Achievement. Proceedings of the Annual Conference of the Mathematical Association of Victoria . Melbourne: MAV.

Siemon, Dianne, Margarita Breed, and Jo Virgona. 2005. “From Additive to Multiplicative Thinking—The Big Challenge of the Middle Years." In Mathematics: Celebrating Achievement. Proceedings of the Annual Conference of the Mathematical Association of Victoria . Melbourne: MAV.)| false
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Vergnaud, Gerard. 1988. “Multiplicative Structures." In Number Concepts and Operations in the Middle Grades, edited by James Hiebert and Merlyn Behr, pp. 141–61. Reston, VA: National Council of Teachers of Mathematics.

Vergnaud, Gerard. 1988. “Multiplicative Structures." In Number Concepts and Operations in the Middle Grades, edited by James Hiebert and Merlyn Behr, pp. 141–61. Reston, VA: National Council of Teachers of Mathematics.)| false
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