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The duality between ways of thinking and ways of understanding: Implications for learning trajectories in mathematics education
Institution:1. College of Education, Oregon State University, Furman Hall 304L, Corvallis, OR 97331, United States;2. Department of Mathematics, Oregon State University, Kidder Hall, Corvallis, OR 97331, United States;1. Department of Psychology and Human Development, Vanderbilt University, United States;2. Wisconsin Center for Education Research, University of Wisconsin-Madison, United States;1. University College Dublin, Ireland;2. University of Oklahoma, USA;1. Department of Mathematics Education, Faculty of Mathematics and Physics, Charles University, Czech Republic;2. University of Puerto Rico at Mayagüez, Mayagüez, PR, USA;3. Instituto Tecnológico Autónomo de México, Mexico;1. TERC, 2067 Massachusetts Avenue, Cambridge, MA 02140, USA;2. City College, The City University of New York, 160 Convent Avenue, New York, NY 10031, USA
Abstract:
Keywords:Ways of thinking  Ways of understanding  Mathematical knowledge  Learning trajectories  Learning progressions
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