Keith Weber

Rutgers University

84Publications

18H-index

1,554Citations

Publications 90

Newest

Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions, domain restrictions, and the arcsine function

Abstract Prospective secondary mathematics teachers are typically required to take advanced university mathematics courses. However, many prospective teachers see little value in completing these courses. In this paper, we present the instantiation of an innovative model that we have previously developed on how to teach advanced mathematics to prospective teachers in a way that informs their future pedagogy. We illustrate this model with a particular module in real analysis in which theorems abo...

#1Keith Weber (RU: Rutgers University)H-Index: 18

#2Kristen Lew (Texas State University)

Last.Juan Pablo Mejía-Ramos (RU: Rutgers University)H-Index: 12

view all 3 authors...

AbstractIn mathematics education, researchers commonly infer students’ standards of conviction from the justifications that they produce. Specifically, if students justify a mathematical statement ...

An Evaluation of ULTRA; an Experimental Real Analysis Course Built on a Transformative Theoretical Model

Most prospective secondary mathematics teachers in the United States complete a course in real analysis, yet view the content as unrelated to their future teaching. We leveraged a theoretically-motivated instructional model to design modules for a real analysis course that could inform secondary teachers’ actionable content knowledge and pedagogy. The theoretical model and designed curriculum launches the study of advanced mathematics content, in this case, real analysis, via authentic 7–12 clas...

#1Will McGuffey (Francis Marion University)

#2Ruby Quea (RU: Rutgers University)

Last.Juan Pablo Mejia Ramos (Francis Marion University)

view all 6 authors...

ABSTRACTProspective secondary mathematics teachers are usually required to complete several university advanced mathematics courses before being certified to teach secondary mathematics. However, t...

Correction to: designing advanced mathematics courses to influence secondary teaching: fostering mathematics teachers’ “attention to scope”

#1Nicholas H. Wasserman (Columbia University)H-Index: 7

#2Keith Weber (RU: Rutgers University)H-Index: 18

Last.William McGuffey (Francis Marion University)H-Index: 1

view all 4 authors...

Designing advanced mathematics courses to influence secondary teaching: fostering mathematics teachers’ “attention to scope”

#1Nicholas H. Wasserman (Columbia University)H-Index: 7

#2Keith Weber (RU: Rutgers University)H-Index: 18

Last.William McGuffey (Francis Marion University)H-Index: 1

view all 4 authors...

Most prospective secondary mathematics teachers complete a course in real analysis, yet view the content as unrelated to their future teaching. We leveraged a theoretically motivated instructional model to design modules for a real analysis course that could inform secondary teachers’ pedagogy, focusing on how this model was implemented in a single module about “attending to scope.” The central aim is to document how teachers’ experience in this real analysis course influenced their subsequent t...

#1Keith Weber (RU: Rutgers University)H-Index: 18

In this paper, we explore the role of syntactic representations in set theory. We highlight a common inferential scheme in set theory, which we call the Syntactic Representation Inferential Scheme, in which the set theorist infers information about a concept based on the way that concept can be represented syntactically. However, the actual syntactic representation is only indicated, not explicitly provided. We consider this phenomenon in relation to the derivation indicator position that assert...

#1Keith Weber (RU: Rutgers University)H-Index: 18

#2Jennifer A. Czocher (Texas State University)H-Index: 4

ABSTRACTWe report the results of a study in which we asked 94 mathematicians to evaluate whether five arguments qualified as proofs. We found that mathematicians disagreed as to whether a visual argument and a computer-assisted argument qualified as proofs, but they viewed these proofs as atypical. The mathematicians were also aware that many other mathematicians might not share their judgment and viewed their own judgment as contextual. For typical proofs using standard inferential methods, the...

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