Disciplinary Content Knowledge

Domain appropriateness and skepticism in viable argumentation

Lead Organization(s)
Year
2020
Short Description

Several recent studies have focused on helping students understand the limitations of empirical arguments (e.g., Stylianides, G. J. & Stylianides, A. J., 2009, Brown, 2014). One view is that students use empirical argumentation because they hold empirical proof schemes—they are convinced a general claim is true by checking a few cases (Harel & Sowder, 1998). Some researchers have sought to unseat students’ empirical proof schemes by developing students’ skepticism, their uncertainty about the truth of a general claim in the face of confirming (but not exhaustive) evidence (e.g., Brown, 2014; Stylianides, G. J. & Stylianides, A. J., 2009). With sufficient skepticism, students would seek more secure, non-empirical arguments to convince themselves that a general claim is true. We take a different perspective, seeking to develop students’ awareness of domain appropriateness (DA), whether the argument type is appropriate to the domain of the claim. In particular, DA entails understanding that an empirical check of a proper subset of cases in a claim’s domain does not (i) guarantee the claim is true and does not (ii) provide an argument that is acceptable in the mathematical or classroom community, although checking all cases does both (i) and (ii). DA is distinct from skepticism; it is not concerned with students’ confidence about the truth of a general claim. We studied how ten 8th graders developed DA through classroom experiences that were part of a broader project focused on developing viable argumentation. 

Eliminating Counterexamples: A Case Study Intervention for Improving Adolescents’ Ability to Critique Direct Arguments

Students’ difficulties with argumentation, proving, and the role of counterexamples in proving are well documented. Students in this study experienced an intervention for improving their argumentation and proving practices.

Author/Presenter

Carolyn Maher

Year
2020
Short Description

Students’ difficulties with argumentation, proving, and the role of counterexamples in proving are well documented. Students in this study experienced an intervention for improving their argumentation and proving practices. The intervention included the eliminating counterexamples (ECE) framework as a means of constructing and critiquing viable arguments for a general claim. This framework involves constructing descriptions of all possible counterexamples to a conditional claim and determining whether or not a direct argument eliminates the possibility of counterexamples. This case study investigates U.S. eighth-grade (age 13) mathematics students’ conceptions about the validity of a direct argument after the students received instruction on the ECE framework. We describe student activities in response to the intervention, and we identify students’ conceptions that are inconsistent with canonical notions of mathematical proving and appear to be barriers to using the ECE framework.

Eliminating Counterexamples: An Intervention for Improving Adolescents’ Contrapositive Reasoning

Students’ difficulties with contrapositive reasoning are well documented. Lack of intuition about contrapositive reasoning and lack of a meta-argument for the logical equivalence between a conditional claim and its contrapositive may contribute to students’ struggles. This case study investigated the effectiveness of the eliminating counterexamples intervention in improving students’ ability to construct, critique, and validate contrapositive arguments in a U.S. eighth-grade mathematics classroom.

Author/Presenter

David Yopp

Lead Organization(s)
Year
2020
Short Description

Students’ difficulties with contrapositive reasoning are well documented. Lack of intuition about contrapositive reasoning and lack of a meta-argument for the logical equivalence between a conditional claim and its contrapositive may contribute to students’ struggles. This case study investigated the effectiveness of the eliminating counterexamples intervention in improving students’ ability to construct, critique, and validate contrapositive arguments in a U.S. eighth-grade mathematics classroom. The intervention involved constructing descriptions of all possible counterexamples to a conditional claim and its contrapositive, comparing the two descriptions, noting that the descriptions are the same barring the order of phrases, and finding a counterexample to show the claim is false or viably arguing that no counterexample exists.

Resource(s)

NCTM Presentation Line of "Good" Fit in Grade 8 Classrooms

Lead Organization(s)
Year
2018
Short Description

This presntation addreses 4 research cquestions

 

What extant criteria do Grade 8 students use to choose the better line
of fit between two lines “fit” to a set of data, when both lines express
the trend of the data?
 
Is a residual criterion accessible and useful to Grade 8 students when
learning about line of fit?
 
How does introducing a residual criterion impact student
understanding of line of fit and their understanding mathematical
modeling process?
 
What stages of learning do students express as they engage in our
lesson?

BioGraph 2.0: Online Professional Development for High School Biology Teachers for Teaching and Learning About Complex Systems

Principal Investigator:

The purpose of this study has been to address the accessibility and efficacy of high quality professional development by modifying a successful in-person PD to be delivered on the edX platform. The PD course introduces BioGraph, a curriculum that uses computer-based simulations to teach biology concepts and complex systems ideas. The study has taken place over the last four years with teachers from across the globe, and in biology classrooms across the US and in India with teachers and students who are working with the BioGraph curriculum.

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Building a Teacher Knowledge Base for the Implementation of High-Quality Instructional Resources through the Collaborative Investigation of Video Cases (Collaborative Research: Murray and Wilson)

Principal Investigator:

Analyzing Instruction in Mathematics using the TRU framework (AIM-TRU) is a research-practice partnership that is investigating the pressing problem of supporting teachers in increasing their capacity to implement high-quality instructional materials in the classroom with fidelity. Drawing upon the design-based research paradigm, the partnership has worked to co-design, investigate, and iteratively form the AIM-TRU Learning Cycle, which gives teachers the opportunity to understand the materials and how they are used in the classroom through a video-based professional learning cycle.

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Getting Unstuck: Designing and Evaluating Teacher Resources to Support Conceptual and Creative Fluency with Programming

Principal Investigator:

We are studying how an online professional learning experience for K-12 computer science teachers can be adapted for use in the classroom. Our goal is to increase teachers' conceptual and creative fluency with the Scratch programming environment. In collaboration with several teachers, we further refined our online professional learning experience for summer 2020. We have also been collaboratively developing and studying educative curriculum materials that promote both teacher and student learning and development.

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Building Environmental and Educational Technology Competence and Leadership Among Educators: An Exploration in Virtual Reality Professional Development

Principal Investigator:

This exploratory project supports the professional development of secondary STEM teachers by providing multiyear training around three specific areas: (1) environmental sciences themed content; (2) technology integration in the classroom, and (3) classroom-based action research within action research communities. Using virtual reality to focus on wetlands and their connection to flooding brings locally relevant STEM concepts in a real-world context that is relatable to minoritized teachers and students living in these areas.

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Leveraging Simulations in Preservice Preparation to Improve Mathematics Teaching for Students with Disabilities (Collaborative Research: Cohen and Jones)

Principal Investigator:

The broader goal of our DRK-12 project is to develop and test whether simulated classroom experience with students with disabilities can improve elementary general educators' preparedness to support these students in mathematics. To support the tools' development, we have interviewed 22 leading mathematics and special educators to unearth tensions and points of convergence in how the respective fields conceptualize mathematics instruction. The poster will discuss implications of these findings for teacher preparation and development.

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High School Students' Climate Literacy Through Epistemology of Scientific Modeling (Collaborative Research: Chandler and Forbes)

Principal Investigator:

We share the conception, design, and some activities from a curriculum based on the use of a global climate model EzGCM in secondary geoscience classrooms. Implemented through the NSF-funded CLiMES (Climate Literacy through Modeling and Epistemology of Science) project, this curriculum facilitated in-depth understanding of climate literacy concepts through model-based reasoning.

Co-PI(s): Mark Chandler, Columbia University

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