Development of Numberline and Measurement Concepts

Petitto, Andrea L.

doi:10.1207/s1532690xci0701_3

Cited by 87 publications

(115 citation statements)

References 5 publications

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“…Similarly, the Piagetians argued that meaningful measurement and indirect comparison using transitive reasoning is impossible until children conserve length. However, children do not necessarily need to develop conservation before they can learn some measurement ideas (Clements, 1999;Hiebert, 1981;Petitto, 1990). Thus, children have an intuitive understanding on which to base reasoning about distance and length, but that reasoning develops over years, possibly requiring specific educational experiences to build concepts and skills that enable children to (1) align endpoints (Piaget et al, 1960), (2) use a third object and transitivity to compare the length of two objects that cannot be compared directly (Hiebert, 1981), (3) place length units along objects to find their lengths and associate higher counts with longer objects (Hiebert, 1981;Stephan, Bowers, Cobb, & Gravemeijer, 2003), (4) understand the need for equal-length units (Ellis, Siegler, & Van Voorhis, 2003), (5) use rulers accurately and meaningfully (Lehrer, 2003;Stephan et al, 2003), and (6) make inferences about the relative size of objects (e.g., if the number of units are the same, but the units are different, the total size is different) (Nunes & Bryant, 1996).…”

Section: Original Length Learning Trajectorymentioning

confidence: 99%

Evaluation of a learning trajectory for length in the early years

Sarama

Clements

Barrett

et al. 2011

ZDM Mathematics Education

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Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited, especially compared to topics such as number and operations. To contribute to the establishment of a research base for instruction in measurement, we evaluated and refined a previously developed learning trajectory in early length measurement, focusing on the developmental progressions that provide cognitive

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Section: Original Length Learning Trajectorymentioning

confidence: 99%

Evaluation of a learning trajectory for length in the early years

Sarama

Clements

Barrett

et al. 2011

ZDM Mathematics Education

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“…The emphasis on paths and movement might help students focus on intervals or line segments as units of length, instead of on points (Cannon, 1992). Further, connections between mathematical symbols and graphics may promote in students a belief in the necessity of equal-interval units, another significant conceptual advance (Petitto, 1990). In addition, these connections may help students build mental connections between numerical and geometric ideas.…”

mentioning

confidence: 99%

Students' Development of Length Concepts in a Logo-Based Unit on Geometric Paths

Clements¹,

Battista²,

Sarama³

et al. 1997

Journal for Research in Mathematics Education

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We investigated the development of linear measure concepts within an instructional unit on paths and lengths of paths, part of a large-scale curriculum development project funded by the National Science Foundation (NSF). We also studied the role of noncomputer and computer interactions in that development. Data from paper-and-pencil assessments, interviews, and case studies were collected within the context of a pilot test of this unit with 4 third graders and field tests with 2 thirdgrade classrooms. Three levels of strategies for solving length problems were observed: (a) apply general strategies such as visual guessing of measures and naive guessing of numbers or arithmetic operations; (b) draw hatch marks, dots, or line segments to partition lengths to serve as perceptible units to quantify the length; (c) no physical partitioning-use an abstract unit of length, a "conceptual ruler," to project onto unsegmented objects. Those students who had connected numeric and spatial representations evinced different and more powerful problem-solving strategies in geometric situations than those who had forged fewer such connections.

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“…As the number line is central to the LMR curriculum, we are able to build on and contribute to literatures in the learning sciences on children's developing understandings of the number line [Booth & Siegler, 2008;Earnest, 2012;Petitto, 1990;Saxe, Earnest, Sitabkhan, Haldar, Lewis, & Zheng, 2010;Siegler & Opfer, 2003] as well as linear representations [Barrett, Sarama, Clements, Cullen, McCool, Witkowski-Rumsey, & Klanderman, 2012;Lehrer, 2003;Núñez, 2011;Piaget & Inhelder, 1956;Piaget, Inhelder, & Szeminska, 1960;Saxe, Shaughnessy, Gearhart, & Haldar, 2013b]. As a whole, these literatures reveal that young children show capabilities to order numbers along a linear dimension; however, only later do children show capabilities to generate uniform metric properties in their ordering of numbers.…”

Section: The Lmr Curriculum Unit and Its Register Of Mathematical Defmentioning

confidence: 99%

Studying Cognition through Time in a Classroom Community: The Interplay between “Everyday” and “Scientific Concepts”

et al. 2015

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This paper presents an analytic approach for understanding the interplay through time between “scientific” and “everyday concepts” in a mathematics classroom community. To illustrate the approach, we focus on an elementary classroom implementing an integers and fractions lesson sequence that makes use of the number line as a principal representational context. In our analysis of the community's emerging collective practices (recurring structures of joint activity), we trace the interplay between children's sensorimotor actions (displacing, counting, and splitting) and the mathematical definitions supported in the classroom, like definitions of unit interval or equivalent fractions. In our illustrative analysis, we find that the teacher orchestrated collective practices to support the use of actions to make sense of the formal definitions, and the use of definitions to regulate actions. Though we illustrate the analytic approach for a particular classroom community, the approach illuminates teaching-learning dynamics that transcend any particular classroom or subject matter domain.

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Development of Numberline and Measurement Concepts

Cited by 87 publications

References 5 publications

Evaluation of a learning trajectory for length in the early years

Evaluation of a learning trajectory for length in the early years

Students' Development of Length Concepts in a Logo-Based Unit on Geometric Paths

Studying Cognition through Time in a Classroom Community: The Interplay between “Everyday” and “Scientific Concepts”

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