Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory

By Martin A. Simon, Ron Tzur. 2004

434 citations recorded by the source corpus.

Subfields: Developmental and Educational Psychology, Education

View Paper: https://www.semanticscholar.org/paper/775c98693043be78e1a2b5457fbf156c2b7ef8b7

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In Developmental and Educational Psychology

In Education

Citations in the corpus

Fine grain assessment of students’ mathematical understanding: participatory and anticipatory stagesin learning a new mathematical conception (2007, background): “The general constructs were formulated in three recent theoretical papers (Simon and Tzur 2004; Simon et al. 2004; Tzur and Simon 2004) as an elaboration on six constructivist 274 R.”
Conceptualizing Perseverance in Problem Solving as Collective Enterprise (2017, background): “…mathematical practices—from making sense of problems, to modeling and reasoning about them, to monitoring or changing directions in their problem solving approach (Boaler & Sengupta-Irving, 2016; CCSI, 2010; Parker, 2009; Sengupta-Irving, 2016; Sengupta-Irving & Enyedy, 2014; Simon & Tzur, 2004).”
Developing a Hypothetical Multi-Dimensional Learning Progression for the Nature of Matter. (2009, background): “These smaller steps are similar to learning trajectories, a construct that has been employed by the mathematics education community to organize instruction of important ideas in the discipline (Gravemeijer, 2004; Simon & Tzur, 2004).”
A Learning Trajectory in 6-Year-Olds' Thinking about Generalizing Functional Relationships. (2015, background): “…instructional sequence and the associated tasks is tightly coupled with hypotheses about students’ learning within a task (Barrett & Battista, 2014; Simon & Tzur, 2004), and the progression that results represents only one possible path of learning (Baroody et al., 2004; Stevens, Shin, & Krajcik,…”
Seeing an Exercise as a Single Mathematical Object: Using Variation to Structure Sense-Making (2006, methodology): “Even the hypothetical version offered by Simon and Tzur (2004, p. 100) seems to assume that something sequential can be said about learning, but in our experience this over-simplifies the responses to experience that can occur in or out of a classroom. Nevertheless, when planning, thinking in terms ”
NOTICING: Roots and Branches (2011, background): “In order to learn intentionally from experience, we must withdraw from action and reflect on or reconstruct that action and its effects (Simon & Tzur, 2004).”
A Local Instruction Theory for the Development of Number Sense (2010, neutral): “2004; Jones, et al, 2001; Simon, 1995; Simon & Tzur, 2004; Stephan, Bowers, Cobb, &”
Content-Focused Coaching: Five Key Practices (2016, background): “…is generally consistent with the substantial body of work in mathematics education, science education, and the learning sciences on the process of developing, testing, and revising designs for supporting learning (Cobb & Gravemeijer, 2008; Lehrer & Schauble, 2004; Simon, 1995; Simon & Tzur, 2004).”
Key Developmental Understandings in Mathematics: A Direction for Investigating and Establishing Learning Goals (2006, background): “My colleagues and I have been working on a framework that can guide pedagogical approaches to the development of KDUs (Simon & Tzur, 2004; Simon et al., 2004).”
Participatory and Anticipatory Stages of Mathematical Concept Learning: Further Empirical and Theoretical Development. (2016, background): “1 LTA grew out of Tzur’s (1995) dissertation research, Simon’s (1995) early work on hypothetical learning trajectories, and the collaboration of Simon and Tzur (1996–2001).”
Connecting changes in secondary mathematics teachers’ knowledge to their experiences in a professional development workshop (2013, background): “Though teachers’ ability to select high-level instructional tasks is essential in promoting students’ learning (NCTM 2000; Simon and Tzur 2004; Stein et al. 2000), teachers typically do not analyze or select instructional tasks by attending to the type or level of thinking that the task can elicit…”
Meeting the Challenges of Mathematics Teacher Education through Design and Use of Tasks that Facilitate Teacher Learning (2008, background): “In this chapter I focus specifically on the teacher-educator role as task designer.1 There is a consensus among mathematics educators that learning occurs through engagement in tasks (Krainer, 1993; Simon & Tzur, 2004; Zaslavsky, 2005).”
Mathematical problem solving: an evolving research and practice domain (2007, background): “The Case Study includes two related phases: (a) A research team (formed by a math educator, two graduate students, and two high school teachers) selects or designs a series of tasks and each task is discussed in depth to identify students’ potential or hypothetical learning trajectories ( Simon & Tz”