Pedagogical Content Knowledge

Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof

Year:
2020
Short Description:

This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses - particular conceptions of argumentation, justification, and proof - researchers consider the implications of how each conception shapes empirical outcomes. In each section, organized by grade band, authors adopt particular conceptions of argumentation, justification, and proof, and they analyse one data set from each perspective. In addition, each section includes a synthesis chapter from an expert in the field to bring to the fore potential implications, as well as new questions, raised by the analyses. Finally, a culminating section considers the use of each conception across grade bands and data sets.

Domain appropriateness and skepticism in viable argumentation

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.

A Framework of Construct-Irrelevant Variance for Contextualized Constructed Response Assessment

Estimating and monitoring the construct-irrelevant variance (CIV) is of significant importance to validity, especially for constructed response assessments with rich contextualized information. To examine CIV in contextualized constructed response assessments, we developed a framework including a model accounting for CIV and a measurement that could differentiate the CIV. Specifically, the model includes CIV due to three factors: the variability of assessment item scenarios, judging severity, and rater scoring sensitivity to the scenarios in tasks.

Author/Presenter:
Xiaoming Zhai
Kevin C. Haudek
Christopher Wilson
Molly Stuhlsatz
Year:
2021
Short Description:

Estimating and monitoring the construct-irrelevant variance (CIV) is of significant importance to validity, especially for constructed response assessments with rich contextualized information. To examine CIV in contextualized constructed response assessments, we developed a framework including a model accounting for CIV and a measurement that could differentiate the CIV.

Resource(s):

“Well That's How the Kids Feel!”—Epistemic Empathy as a Driver of Responsive Teaching

While research shows that responsive teaching fosters students' disciplinary learning and equitable opportunities for participation, there is yet much to know about how teachers come to be responsive to their students' experiences in the science classroom. In this work, we set out to examine whether and how engaging teachers as learners in doing science may support responsive instructional practices.

Author/Presenter:
Lama Z. Jaber
Vesal Dini
David Hammer
Year:
2021
Short Description:

In this article, the authors present evidence from teachers' reflections that this stability was supported by the teachers' intellectual and emotional experiences as learners. Specifically, they argue that engaging in extended scientific inquiry provided a basis for the teachers having epistemic empathy for their students—their tuning into and appreciating their students' intellectual and emotional experiences in science, which in turn supported teachers' responsiveness in the classroom.

Strengthening STEM Teaching in Native American Serving Schools through Long-Term, Culturally Responsive Professional Development

Principal Investigator:

This is a 4-year, level II Exploratory study within the teaching strand of DRK12. The research explores the functioning and impact of a nationally-developed STEM professional development model within the Navajo Nation. Teacher participants represent the entire K-12 grade range and multiple content areas, and they all participate in an innovative STEM-content, culturally responsive, 8-month professional development fellowship. We explore the extent to which culturally responsive principles are evident in their self-authored curriculum units.

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Target Audience:

Aligning the Science Teacher Education Pathway: A Networked Improvement Community

Principal Investigator:

The A-STEP project fosters collaboration between university faculty and pathway partners to implement common set of tools (Next Gen ASET Toolkit) across a science teacher training and development pathway. Partnerships across steps function under shared goals and paradigm shifts for pedagogical reform along the teacher pathway. A-STEP promotes change across our Networked Improvement Community (NIC) and the local pathway partners working with each university, ultimately impacting the enactment of the NGSS in respective K-12 classrooms.

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Target Audience: