Reasoning With Tools and Inscriptions

Cobb, Paul

doi:10.1207/s15327809jls11,2-3n_3

Cited by 45 publications

(25 citation statements)

References 19 publications

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“…This definition relates to the semiotic classification of a sign as icon, index, or symbol. In accordance with Cobb (2002), we see inscriptions as intimately related to the notion of symbolising in mathematics. Meaningmaking and ways of symbolising are co-evolving and mutually constitutive processes.…”

mentioning

confidence: 55%

Reasoning with paper and pencil: The role of inscriptions in student learning of geometric series

Carlsen¹

2009

Math Ed Res J

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The purpose of this article is to analyse how students use inscriptions as tools for thinking and learning in mathematical problem-solving activities. The empirical context is that of learning about geometric series in a small group setting. What has been analysed is how students made use of inscriptions, self-made as well as those provided by text books and teachers, and the role these inscriptions played in the coordination of students' learning/communication. Through the use of inscriptions (made on the chalkboard and with paper and pencil), the students externalised their thinking while engaging in mathematical reasoning on the topic of geometric series. The inscriptions were significant as anchor points for arguments in the ongoing discussions. Three main issues are highlighted: (a) how the inscriptions used contribute to the process of appropriation, (b) how the students use inscriptions to externalise and clarify their ideas and attempts at meaning-making, and (c) how the inscriptions are conducive to closing the gap between the original problem as given in the text book and the mathematisation necessary. It is argued that inscriptions, through their material nature, play a decisive role in learning mathematical reasoning.This study is an attempt to document and analyse how students are using inscriptions in reasoning and learning about geometric series. Following a sociocultural perspective on learning and development (Rogoff, 1990;Säljö, 2005; Wertsch, 1998), it is important to study students' actions and use of artifacts in problem-solving settings to gain insight into how they appropriate mathematical concepts and modes of reasoning. The focus of the present study is on how students rely on and use the specific type of cultural tools that we refer to as inscriptions when engaging in mathematical problem solving. Inscriptions are understood as artifacts such as graphs, drawings, and mathematical symbols used for cognitive, communicative, mathematical, and problem-solving purposes in interactional settings 1 . The inscriptions may appear in text books, they may be made by the teacher for instructional purposes, or they may be self-made by learners while engaging in problem solving.

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mentioning

confidence: 55%

Reasoning with paper and pencil: The role of inscriptions in student learning of geometric series

Carlsen¹

2009

Math Ed Res J

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“…We took inquiry as a process of collaboratively addressing complex, ambiguous tasks that require negotiation and mathematical evidence. The norms of mathematical inquiry follow those proposed by other researchers (e.g., Cobb, 1999;2002;Franke et al, 2015;McClain & Cobb, 2001;Yackel & Cobb, 1996) that go beyond simply explaining one's own work to engage with others' ideas (e.g., active listening, explaining and justifying ideas, building on others ideas, and sharing incomplete ideas). Our focus on argumentation practices in inquiry emphasised the negotiation and classroom discourse aspects.…”

Section: Norms Of Argumentation-based Inquirymentioning

confidence: 87%

“…By norms, we refer to classroom level cognitive and social structures operationalised through the collective expectations of the teacher and students about what count as appropriate activities and interactions (Cobb, 2002;Enyedy & Stevens, 2015;Webb et al, 2014). Practices encompass the broader space of classroom activities and interactions; as they are negotiated into shared norms, they often become tacit unless violated (Cobb, 2002). Accepted norms and practices in mathematical inquiry include "explaining and justifying solutions, attempting to make sense of explanations given by others, indicating agreement or disagreement, and questioning [conflicting] alternatives" (Cobb, 1999, p. 7).…”

Section: Developing Norms and Practices Of Argumentation-based Inquirymentioning

confidence: 99%

“…Accepted norms and practices in mathematical inquiry include "explaining and justifying solutions, attempting to make sense of explanations given by others, indicating agreement or disagreement, and questioning [conflicting] alternatives" (Cobb, 1999, p. 7). Cobb (2002) argued that three key types of norms constitute classroom mathematical practice: normative purpose (shared goals of an activity), normative standards of argumentation (what counts as a legitimate argument in terms of claims and support that would be expected by the teacher and students), and normative ways of reasoning with tools and representations. Translating these into an argumentation-based inquiry classroom, normative practices would focus on having a shared goal of authentically responding to the inquiry question, generating a legitimate and justifiable solution, being explicit about the evidence and process of solution, anticipating critique, and privileging expectations to think and reason mathematically.…”

Section: Developing Norms and Practices Of Argumentation-based Inquirymentioning

confidence: 99%

“…These represent Cobb's (2002) norms of a shared purpose to understand and improve the solutions of others, standards of argument, expecting legitimate claims and evidence, and by including representations in explaining solutions.…”

Section: Billmentioning

confidence: 99%

See 2 more Smart Citations

Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom

Makar

Bakker

Ben‐Zvi

2015

ZDM Mathematics Education

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Exploring middle school students' use of inscriptions in project-based science classrooms

Wu¹,

Krajcik²

2006

Sci. Ed.

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This study explores seventh graders' use of inscriptions in a teacher-designed project-based science unit. To investigate students' learning practices during the 8-month water quality unit, we collected multiple sources of data (e.g., classroom video recordings, student artifacts, and teacher interviews) and employed analytical methods that drew from a naturalistic approach. The findings showed that throughout the unit, provided with the teachers' scaffold and social, conceptual, and material resources, the seventh graders were able to use various inscriptions (e.g., digital pictures, Web pages, and models) to demonstrate meaningful inscriptional practices such as creating and using inscriptions to make arguments, to represent conceptual understandings, and to engage in thoughtful discussions. Inscriptions and associated practices provided students with experiences and understandings about certain ways to organize, transform, and link data or scientific ideas. However, when constructing inscriptions, students did not consider how the inscriptions could serve certain reasoning purposes. In addition, more scaffolds were needed to help students use multiple inscriptions to make a coherent argument.

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Reasoning With Tools and Inscriptions

Cited by 45 publications

References 19 publications

Reasoning with paper and pencil: The role of inscriptions in student learning of geometric series

Reasoning with paper and pencil: The role of inscriptions in student learning of geometric series

Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom

Exploring middle school students' use of inscriptions in project-based science classrooms

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