Understanding and procedural knowledge in mathematics instruction<sup>1</sup>

Greeno, James G.

doi:10.1080/00461527809529180

Cited by 75 publications

(38 citation statements)

References 13 publications

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“…This is apparent in the separation of conceptual and procedural knowledge (Alexander, 1996;Greeno, 1978), and this dualism has been reified throughout traditional American schooling (Lave & Wenger, 1991;Resnick, 1987). As Cunningham (1992) wrote, "The majority of the pedagogical practices employed in our culture (e.g., lectures, large classes where listening predominates, objective tests with 'true' or 'best' answers) are ideally suited to supporting a dualist perspective" (p. 179).…”

Section: Student Teachermentioning

confidence: 99%

Constructing Virtual Worlds: Tracing the Historical Development of Learner Practices

Barab¹,

Hay²,

Barnett³

et al. 2001

Cognition and Instruction

143

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This study explores learning and instruction within a technology-rich, collaborative, participatory learning environment by tracking the emergence of shared understanding and products through student and teacher practices. The focus is not only on the interactions among students or between students and teachers, but on student-resource interactions, especially student-technology interactions. In a 1-week camp, students worked in activity groups with 3-dimensional modeling software to develop virtual worlds. Holistic accounts of 2 activity groups in the camp are presented, emphasizing the focus of the activity, group dynamics including the role of the teacher, and the historical development of learner practices. Then, a network methodology is used to trace the history of interactions accounting for the emergence, evolution, and diffusion of learner practices. The findings suggest that becoming knowledgeably skillful with respect to a particular practice or concept is a multigenerational process, evolving in terms of contextual demands and available resources. The tracings further reveal the reciprocal nature of learning and doing, with building conceptual understanding occurring in relation to local conditions and practices, and doing practices being a part of student learning.

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Section: Student Teachermentioning

confidence: 99%

Constructing Virtual Worlds: Tracing the Historical Development of Learner Practices

Barab¹,

Hay²,

Barnett³

et al. 2001

Cognition and Instruction

143

View full text Add to dashboard Cite

show abstract

“…In this same era, educationally oriented cognitive psychologists such as Greeno (1978;Greeno & Simon, 1988) were interested in showing that various mathematical task content knowledge and procedures were prerequisites to many classroom activities and tasks, making the point that these are not usually directly taught. Theoretical advances in understanding the cognitive basis of quantitative reasoning emerged (e.g., Newell, 1980;Newell & Simon, 1972;Schoenfeld, 1983Schoenfeld, , 1985Schoenfeld, , 2002.…”

Section: The Development Of Quantitative Reasoning Constructs and Assmentioning

confidence: 99%

What Is Quantitative Reasoning? Defining the Construct for Assessment Purposes

Dwyer

Gallagher

Levin

et al. 2003

ETS Research Report Series

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In order to create fair and valid assessments, it is necessary to be clear about what is to be measured and how the resulting data should be interpreted. For a number of historical and practical reasons described in this paper, adequately detailed statements with both a theoretical and empirical base do not currently exist for the construct of quantitative reasoning for use in assessments. There is also no adequate explanation of the important differences between assessments that measure quantitative reasoning constructs and those that are intended to measure achievement in related mathematical content areas.The literature in psychology, psychometrics, philosophy, and education, while containing much that is relevant to the construct of quantitative reasoning, unfortunately does not provide materials that can be used in research and development to address such practical issues or to explain the basic nature of quantitative reasoning assessments. This paper briefly discusses the importance and use of constructs and the quantitative reasoning and standards literature. It then presents a statement about the construct of quantitative reasoning for assessment purposes within a construct validity framework that includes both a definition of the construct and threats to valid score interpretation. These threats are based on related but distinguishable constructs and other types of construct-irrelevant variance in the assessments.

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“…Several researchers claim that those who solve an unfamiliar variation of a known type of problem rely on conceptual knowledge rather than on a rote execution of the solving procedure (Greeno, 1978;Novak, 1977b;Novak, Gowin, & Johansen, 1983;Wertheimer, 1959). Thus, for this study, the solving procedures presumably would be linked to the solvers' conceptual knowledge.…”

Section: The Problem Condition Has Been Widelymentioning

confidence: 99%

Red Onions, Elodea, or Decalcified Chicken Eggs? Selecting & Sequencing Representations for Teaching Diffusion & Osmosis

Lankford

Friedrichsen

2012

The American Biology Teacher

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This study focused on the knowledge of six outstanding science students who solved an osmosis problem meaningfully. That is, they used appropriate and substantially accurate conceptual knowledge to generate an answer. Three generated a correct answer; three, an incorrect answer. This paper identifies both the accurate ana inaccurate conceptions about osmosis of each correct and incorrect solver. The investigation consisted of a presolving clinical interview, think-aloud solving of the problem, and retrospective report of the solving. Of the 12 accurate conceptions identified here, 2 were especially important in enabling these solvers to generate a correct answer. Of the eight inaccurate conceptions, either of two blocked a correct answer. Four, however, accompanied (and could therefore be concealed by) a correct answer. Teachers could use this information to make a meaningful solving of this problem accessible to more students and to identify more effectively students' inaccurate conceptions about osmosis. (Contains 23 references.) (Author) *********************************************************************** * Reproductions supplied by EDRS are the best that can be made * * from the original document. * *********************************************************************** That is, they used appropriate and substantially accurate conceptual knowledge to generate an answer.

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Understanding and procedural knowledge in mathematics instruction¹

Cited by 75 publications

References 13 publications

Constructing Virtual Worlds: Tracing the Historical Development of Learner Practices

Constructing Virtual Worlds: Tracing the Historical Development of Learner Practices

What Is Quantitative Reasoning? Defining the Construct for Assessment Purposes

Red Onions, Elodea, or Decalcified Chicken Eggs? Selecting & Sequencing Representations for Teaching Diffusion & Osmosis

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Understanding and procedural knowledge in mathematics instruction1

Cited by 75 publications

References 13 publications

Constructing Virtual Worlds: Tracing the Historical Development of Learner Practices

Constructing Virtual Worlds: Tracing the Historical Development of Learner Practices

What Is Quantitative Reasoning? Defining the Construct for Assessment Purposes

Red Onions, Elodea, or Decalcified Chicken Eggs? Selecting & Sequencing Representations for Teaching Diffusion & Osmosis

Contact Info

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Understanding and procedural knowledge in mathematics instruction¹