Cultivating inquiry about space in a middle school mathematics classroom

Lehrer, Richard; Kobiela, Marta; Weinberg, Paul

doi:10.1007/s11858-012-0479-x

Cited by 16 publications

(8 citation statements)

References 24 publications

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“…Instructional design. The students' work with definitions was situated within a larger project aimed at engaging students in mathematical inquiry about geometry and spatial mathematics (Lehrer et al, 2013). The students spent the first week of the school year working within a Connected Mathematics Project (CMP) unit on polygons.…”

Section: Methodsmentioning

confidence: 99%

“…In the figure, "Qs" stands for "questions," "Def" for "definitions," "Quads" for "quadrilaterals," and "Prop" for "properties." intervention and the impact on students' learning, see Lehrer et al, 2013. )…”

Section: Methodsmentioning

confidence: 99%

“…Hence, learning to participate in aspects of definitional practice and learning about the mathematics of space co-originated. Further, as we have mentioned, defining created the common ground for the development of related practices, such as posing questions worthy of investigation (for more information about this work, see Lehrer et al, 2013).…”

Section: Providing a View Of Developmentmentioning

confidence: 99%

“…Because students are rarely well versed in disciplinary practices, mathematical practices and conceptual understanding must co-originate (Harel, 2008), in contrast to experts for whom existing well-formed practices inform the development of new disciplinary understandings (Lakatos, 1976;Wilkerson-Jerde & Wilensky, 2011;Wineburg, 1998). To investigate how emerging mathematical practices and concepts could be coconstituted, we conducted a 6-month design study in which middle school students had opportunities to engage in the mathematical practices of definition, conjecture, refutation, inquiry, and proof as they investigated shape and form on the plane (Lehrer, Kobiela, & Weinberg, 2013). In this article, we examine how student participation in the practice of defining influenced their emerging conceptions of the geometry of shape and form and how emerging conceptions of shape and form provided opportunities to exercise and elaborate this form of practice.…”

mentioning

confidence: 99%

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The Codevelopment of Mathematical Concepts and the Practice of Defining

Kobiela

Lehrer

2015

JRME

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We examined the codevelopment of mathematical concepts and the mathematical practice of defining within a sixth-grade class investigating space and geometry. Drawing upon existing literature, we present a framework for describing forms of participation in defining, what we term aspects of definitional practice. Analysis of classroom interactions during 16 episodes spanning earlier and later phases of instruction illustrate how student participation in aspects of definitional practice influenced their emerging conceptions of the geometry of shape and form and how emerging conceptions of shape and form provided opportunities to develop and elaborate aspects of definitional practice. Several forms of teacher discourse appeared to support students' participation and students' increasing agency over time. These included: (a) requesting that members of the class participate in various aspects of practice, (b) asking questions that serve to expand the mathematical system, (c) modeling participation in aspects of practice, (d) proposing examples that create contest (i.e., monsters), and (e) explicitly stating expectations of and purposes for participating in the practice.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Providing a View Of Developmentmentioning

confidence: 99%

mentioning

confidence: 99%

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The Codevelopment of Mathematical Concepts and the Practice of Defining

Kobiela

Lehrer

2015

JRME

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“…Existing inquiry-based educational practices have shown an effort to address students' spatial ability development. As an illustration, during 6 months of geometry instruction that aimed to engage students in mathematical inquiry, secondary students were able to formulate questions that reflected thoughtful mathematical reasoning and spatial reasoning (Lehrer et al, 2013).…”

Section: Engaging Students In Spatial Thinking Through Scientific Inq...mentioning

confidence: 99%

Fostering spatial ability development in and for authentic STEM learning

et al. 2023

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Empirical interdisciplinary research has explored the role of spatial ability in STEM learning and achievement. While most of this research indicates that fostering spatial thinking in educational contexts has the potential to positively impact students’ enrollment and performance in STEM subjects, there is less agreement on the best approach to do so. This article provides an overview of various types of effective spatial interventions and practices in formal or informal educational contexts, including targeted training of STEM-relevant spatial skills, spatialized curricula embedded in schools, integrated STEM practices addressing students’ use of spatial skills, and spatial activities in informal STEM education. Gender and socio-economic status of students – two variables that have been found to moderate the relationship between students’ spatial ability and their STEM performance – are also discussed in this article. Drawing on a wide spectrum of perspectives on situating spatial ability research in STEM education contexts, this article underscores the need for further inquiry into opportunities for developing K-12 students’ spatial ability through integrated and informal STEM practices. This article proposes a conjecture that the relationship between developing students’ spatial ability and enhancing their abilities to solve spatially complex STEM problems is bidirectional. Recommendations for future research are made on lingering questions about the effect of interventions, untapped resources for spatial ability training in formal and informal STEM education, and educational strategies for developing students’ spatial ability in authentic learning environments.

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