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Policy implementation and cognition: Reframing and refocusing implementation research
 Review of Educational Research
, 2002
"... Education policy faces a familiar public policy challenge: Local implementation is difficult. In this article we develop a cognitive framework to characterize sensemaking in the implementation process that is especially relevant for recent education policy initiatives, such as standardsbased ref ..."
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Cited by 147 (3 self)
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Education policy faces a familiar public policy challenge: Local implementation is difficult. In this article we develop a cognitive framework to characterize sensemaking in the implementation process that is especially relevant for recent education policy initiatives, such as standardsbased reforms that press for tremendous changes in classroom instruction. From a cognitive perspective, a key dimension of the implementation process is whether, and in what ways, implementing agents come to understand their practice, potentially changing their beliefs and attitudes in the process. We draw on theoretical and empirical literature to develop a cognitive perspective on implementation. We review the contribution of cognitive science frames to implementation research and identify areas where cognitive science can make additional contributions.
Reform and teaching: Exploring patterns of practice in the context of national and state mathematics reforms
 EDUCATIONA LEVALUATION AND POLICY ANALYSIS
, 1999
"... This article investigates teachers' mathematics practice in the context of recent national and state efforts to reform mathematics education. The authors develop a conceptual frame for examining reformers' proposals for mathematics education in classroom teaching in terms of the intersecti ..."
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Cited by 71 (2 self)
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This article investigates teachers' mathematics practice in the context of recent national and state efforts to reform mathematics education. The authors develop a conceptual frame for examining reformers' proposals for mathematics education in classroom teaching in terms of the intersection of classroom tasks and discourse patterns with principled and procedural mathematical knowledge. Applying this framework to examine mathematics instruction in 25 classrooms, classrooms where teachers reported practices consistent with the reforms as well as familiarity and agreement with either national or state mathematics standards, the authors identify distinctly different patterns of practice in response to the reforms. Based on this analysis, the authors identify some dimensions of practice that appear more responsive to reform than others. In light of their analysis, the authors consider issues for policy analysis, policy research. and the design of policy.
The development of expertise: The journey from acclimation to proficiency.
 Educational Researcher,
, 2003
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Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations
 Journal of Educational Psychology
, 2007
"... Encouraging students to share and compare solution methods is a key component of reform efforts in mathematics, and comparison is emerging as a fundamental learning mechanism. To experimentally evaluate the effects of comparison for mathematics learning, the authors randomly assigned 70 seventhgrad ..."
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Cited by 46 (6 self)
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Encouraging students to share and compare solution methods is a key component of reform efforts in mathematics, and comparison is emerging as a fundamental learning mechanism. To experimentally evaluate the effects of comparison for mathematics learning, the authors randomly assigned 70 seventhgrade students to learn about algebra equation solving by either (a) comparing and contrasting alternative solution methods or (b) reflecting on the same solution methods one at a time. At posttest, students in the compare group had made greater gains in procedural knowledge and flexibility and comparable gains in conceptual knowledge. These findings suggest potential mechanisms behind the benefits of comparing contrasting solutions and ways to support effective comparison in the classroom.
Calculational and conceptual orientations in teaching mathematics
 In D. B. Aichele & A. F. Coxford (Eds.), Professional Development for Teachers of Mathematics: 1994 Yearbook. Reston, VA: National Council of Teachers of Mathematics
, 1994
"... and do not necessarily reflect official positions of NSF or Apple Computer. ..."
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Cited by 37 (3 self)
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and do not necessarily reflect official positions of NSF or Apple Computer.
A Historical Perspective on Reading Research and Practice
, 2004
"... At the time the International Reading Association was created in 1956, the reading research community was poised at a new juncture in its history (Monaghan & Saul, 1987). The efforts of researchers during this period gave rise to extensive literature on learners and the learning process that rem ..."
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Cited by 22 (0 self)
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At the time the International Reading Association was created in 1956, the reading research community was poised at a new juncture in its history (Monaghan & Saul, 1987). The efforts of researchers during this period gave rise to extensive literature on learners and the learning process that remains an enduring legacy for the domain of reading. Yet, this was not the only period of significant change the reading community has experienced in the past 50 years. In fact, reading has periodically responded to internal and external forces resulting in both gradual and dramatic transformations to the domain— transformations that have altered reading study and practice. Our purpose here is to position those transformations within a historical framework. As with others (e.g., VanSledright, 2002), we hold that such a historical perspective allows for reasoned reflection and a certain wisdom that can be easily lost when one is immersed in ongoing study and practice. That is because a historical perspective broadens the vista on reading and adds a critical dimension to the analysis of presentday events and issues. To capture
Toward evidence for instructional design principles: Examples from Cognitive Tutor Math 6. Invited paper
 in Proceedings of PMENA XXXIII (the North American Chapter of the International Group for the Psychology of Mathematics Education
, 2002
"... There is a significant gap between theories of general psychological functions on one hand (e.g., memory) and theories of mathematical content knowledge on the other (e.g., content of algebra). To better guide the design of ground breaking and demonstrably better mathematics instruction, we need ins ..."
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Cited by 22 (13 self)
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There is a significant gap between theories of general psychological functions on one hand (e.g., memory) and theories of mathematical content knowledge on the other (e.g., content of algebra). To better guide the design of ground breaking and demonstrably better mathematics instruction, we need instructional principles and associated design methods to fill this gap in a way that is not only consistent with psychological and content theories but prompts and guides us beyond what those theories can do. Toward this goal, I reflect on lessons from past and current Cognitive Tutor mathematics projects. From this experience, I have abstracted four instructional bridging principles, SituationAbstraction, ActionGeneralization, VisualVerbal, and ConceptualProcedural, and associated methods for applying them. I illustrate these in the context of the design of the successful Cognitive Tutor Algebra course (now in more than 800 schools) and the ongoing research and development of a Cognitive Tutor course for 6 th grade mathematics.
Smallgroup reflections: parallels between teacher discourse and student behavior in peerdirected groups
 The Journal of Learning Sciences
, 2006
"... Prior research on smallgroup collaboration identifies several behaviors that significantly predict student learning, such as exchanging explanations and applying help received. Previous reports focus on student behavior to understand why many students do not engage in behaviors predictive of learni ..."
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Cited by 16 (1 self)
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Prior research on smallgroup collaboration identifies several behaviors that significantly predict student learning, such as exchanging explanations and applying help received. Previous reports focus on student behavior to understand why many students do not engage in behaviors predictive of learning, leaving unexplored how teachers may influence smallgroup interaction. Consequently, this article describes established teacher practices and examines whether and how students reproduce teacher discourse in the context of a semesterlong program of cooperative learning in four middle school mathematics classrooms. This article illustrates changes that emerged and factors that made change difficult. The research concludes that student behavior largely mirrored the discourse modeled by and the expectations communicated by teachers. Teachers tended to give unlabeled calculations, procedures, or answers instead of labeled explanations. Teachers often instructed using a recitation approach in which they assumed primary responsibility for solving the problem, having students only provide answers to discrete steps. Finally, teachers rarely encouraged students to verbalize their thinking or to ask questions. Students adopting the role of helpgiver showed behavior very similar to that of the teacher: doing most of the
Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving
 Journal of Educational Psychology
, 2009
"... Researchers in both cognitive science and mathematics education emphasize the importance of comparison for learning and transfer. However, surprisingly little is known about the advantages and disadvantages of what types of things are being compared. In this experimental study, 162 seventh and ei ..."
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Cited by 16 (2 self)
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Researchers in both cognitive science and mathematics education emphasize the importance of comparison for learning and transfer. However, surprisingly little is known about the advantages and disadvantages of what types of things are being compared. In this experimental study, 162 seventh and eighthgrade students learned to solve equations (a) by comparing equivalent problems solved with the same solution method, (b) by comparing different problem types solved with the same solution method, or (c) by comparing different solution methods to the same problem. Students ’ conceptual knowledge and procedural flexibility were best supported by comparing solution methods and to a lesser extent by comparing problem types. The benefits of comparison are augmented when examples differ on relevant features, and contrasting methods may be particularly useful in mathematics learning.
Concept maps: Theory, methodology, technology
, 2004
"... Abstract. In this article we combine the use of a thematic approach and concept maps to propose a methodological approach for technology courses, in our case, computer networks. The thematic approach offers a good way to increase students ’ motivation and presents a new way of elaborating a curricul ..."
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Cited by 15 (7 self)
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Abstract. In this article we combine the use of a thematic approach and concept maps to propose a methodological approach for technology courses, in our case, computer networks. The thematic approach offers a good way to increase students ’ motivation and presents a new way of elaborating a curriculum. The concept maps, which are the principal tool of the assimilation theory, help in the organization of contents, facilitating the process of concept acquisition by learners. These ideas are synthesized in a Web application which can be used as an aid or guide for teachers and learners of computer networks to organize and to improve their educational activities. 1