Disciplinary Content Knowledge

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?

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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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Target Audience:

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Principal Investigator:

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Target Audience:

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Principal Investigator:

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Target Audience:

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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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Principal Investigator:

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Principal Investigator:

Although several middle school science units are emerging with high ratings on an NGSS EQuIP review, few have been subjected to experimental or quasi-experimental study to examine their efficacy with teachers or students. We share the design specifications, development process, and research findings from a quasi-experimental test of a designed-for-NGSS middle school science unit. Treatment students outperformed comparison students on a test of three-dimensional learning (p = .019; d = .300).

Co-PI(s): Betty Stennett and Lindsey Mohan, BSCS Science Learning

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