# Mathematics Education

## Summer 2020

**Tuesday, July 21, 3:00 - 4:30 p.m.**

#### Multiple Concept Definitions for Tangent Lines - The Case of Alex

**Keith Gallagher, West Virginia University**

**Abstract**: *Prior
research has shown that students tend to reason in terms of the informal components
of their concept images rather than rely on formal concept definitions when
working with topics in mathematics. However, students’ concept images may be
incomplete or inaccurate, or students’ evoked concept images may exclude
important features of concepts or classes of examples. This presentation will
describe two students’ evoked concept images of concepts in general topology as
revealed through their completion of proof tasks as well as some of the effects
those images had on their success in proving. We will also discuss the impact
of the students’ exploration of their example spaces on their concept images
and on their proof writing.*

#### Reading Discussion

**Tim McEldowney, West Virginia University**

Epistemic injustice in mathematics education (Tanswell & Rittberg, 2020). Those interested in the paper attached may also choose a companion piece:

Rittberg, C., Tanswell, F., & Van Bendegem, J. (2018). Epistemic injustice in mathematics. *Sythenese*. Available at https://doi.org/10.1007/s11229-018-01981-1.

**Meeting Link:** https://wvu.zoom.us/j/92911275436

**Tuesday, June 23, 3:00 - 4:30 p.m.**

#### Multiple Concept Definitions for Tangent Lines - The Case of Alex

**Abby Sine and Vicki Sealey, Associate Professor |West Virginia University**

**Abstract**: In this study, we analyze the case study of one student’s responses to a series of questions about tangent lines. The student, Alex (pseudonym), was in Calculus 1 and participated in a pilot study to see how student understanding of tangent lines changed throughout the course of a semester. We use Tall and Vinner’s Theory of Concept Images and Definitions to describe Alex’s mental images and definitions about tangent lines. Alex’s interview was particularly interesting because of his dual definition of tangent lines which included both a geometric definition and calculus definition. Despite several attempts by the interviewer to evoke cognitive conflict, Alex kept these two definitions separate throughout the interview and was able to resolve this cognitive conflict without changing his concept image.

#### Reading discussion - "The Lecture as a Transmedial Pedagogical Form: A Historical Analysis"

**Nicole Infante, Associate Professor | West Virginia University**

**Meeting Link:**__https://wvu.zoom.us/j/99575328550__

**Tuesday, May 19, 3:00 - 5:30 p.m.**

#### Feedback
in proof writing** **

__
__

**Dr. David Miller, Professor**

**| West Virginia University**

**Abstract:** Mathematical proof is essential to the field of mathematics and
paramount in upper-level mathematics classes. In these upper-level mathematical
proof courses, Professors assign homework that require students to write proofs
and spend a significant amount of time grading and providing feedback on
students’ proof productions. This feedback is an important tool that points out
both student proof writing errors and parts that are written well or correctly.
Some researchers have remarked that feedback may greatly alter the behavior of
students and may have more impact than any other instructor practice, but there
has been very little research on feedback from either the side of the professor
or the student. In this talk, I will discuss recent research that has been
conducted in an introduction to proof class from two different studies
regarding student feedback preferences, utilization, and revision work after
receiving feedback from the professor. We will end the talk with some teaching
implications.

#### Reading
discussion of ‘What do mathematicians mean by ‘proof’?’

######
**Led by: Ben Davies, Post Doctoral Research Associate ****| West Virginia University**** **

**| West Virginia University**

###### The paper attached
is closely related to some of the ideas presented during April’s meeting. It
will also pair well with aspects of today’s talk on proof, and perhaps have
some overlap with communication as well.

#### Mathematical communication:

######
**Dr. Nicole Infante, Associate Professor ****| West Virginia University**

**Abstract:**
In this talk, I will present thoughts about how we communicate mathematics in
the classroom. We will explore lecture as a primary means of instruction,
including affordances and constraints. Gesture is a natural, often unconscious,
part of our communication that can be leveraged to enhance communication.
Discussion will focus on how we might more consciously incorporate gesture as a
free, easily implementable resource into our teaching practice for both lecture
and active learning strategies.

Meeting link: https://wvu.zoom.us/j/800309787

## Spring 2020

**Tuesday, February 18, 4 – 6 p.m.**

#### Interpreting Undergraduate Student Complaints about Graduate Student Instructors through the Lens of the Instructional Practices Guide

**Nick Papalia, Graduate Student | West Virginia University**

**Abstract:** College and department administrators take undergraduate student
complaints about Graduate Student Instructors (GSIs) seriously. However, little
research has been done to examine the nature of undergraduate student complaints
across multiple mathematics departments from the lens of student-centered instruction.
In this study, we compared formal (i.e. documented in writing by the student) undergraduate
mathematics student complaints about GSIs at two universities over five years.
Complaints were analyzed by coding the contextualized concerns described in the
complaints using the Mathematical Association of America’s Instructional Practices
Guide to align complaints with topics discussed as best-teaching practices. Results
demonstrated that concerns about classroom and assessment practices were the most
prevalent. Concerns about classroom practices were slightly more abundant and more
pervasive throughout the semester than concerns about assessment practices. Additionally,
an outside-of-class issue undergraduate students raised was regarding the effectiveness
of GSIs communication via emails.

#### Discussion led by Ben Davies, WVU Postdoctoral Research Associate

Schoenfeld, A., (2000). Purposes and Methods of Research in Mathematics Education, Notices of the American Mathematical Society, 47 (6), pp. 641-649

**Tuesday, March 24, 4 – 6 p.m.**

#### Student Understanding of the Definite Integral When Solving Second-Semester Volume Problems

**Krista Bresock, Graduate Student and Instructor | West Virginia University**

**Abstract:** Finding the volume of 3-dimensional solids is a standard application
of the definite integral that students encounter in second-semester calculus. Research
has shown that students have better success with integral application problems
when they are attending to the underlying structure of the definite integral as
the limit of a sum of products, as opposed to only viewing integration as finding
area or calculating an antiderivative. The goal of this study was to examine student
understanding and use of the definite integral when solving second-semester volume
problems. Of the ten students interviewed, four were able to discuss their volume
integrals with 3D explanations corresponding to the underlying Riemann sum structure
of the definite integral. The response of “volume is the integral of area” corresponded
with success in the revolution volume problem but not with the free-standing geometric
solid problems that had no revolution element. Overall, students who lacked the
conceptual understanding of the definite integral could solve revolution problems
successfully but had little success with the non-revolution volume problems. Students
with a more solid conceptual understanding could discuss the underlying structure
of the definite integral but had trouble converting their conception into useable
mathematical formulas in order to solve the problem completely.

#### Discussion led by Matthew Schraeder, WVU Teaching Assistant Professor

Sagher, Y., & Siadat, M. V., (1997). Building Study and Work Skills in a College Mathematics Classroom, Research Report

#### Understanding Exams as Access or Barriers to Mathematics Graduate Programs

**Tim McEldowney, Postdoctoral Research Associate | West Virginia University**

**Abstract: **Written mathematics graduate entrance exams are a major barrier
in the completion of the PhD and often determine if a student even gets to attempt
mathematics research. However, there are few existing studies on the purpose or
effect of these exams. To begin the conversation on modernizing these exams, we
plan to investigate three questions related to these types of exams. What do these
exams, and their administration, look like at different departments? What purpose
do these exams fulfill? What are the differences in pass rates, if any exist, for
different groups of students? This study design will be submitted to the NSF for
review on February 28.

**Tuesday, April 21, 2020**

**Tuesday, April 21, 2020**#### Becoming One Who Proves: An Introduction to Deleuze and Guattari.

**Josh Case, Graduate Student**

**| West Virginia University**

**Abstract: **Gilles Deleuze and Félix Guattari, major
figures in the French post-structural tradition, were philosophers whose
concepts and ideas disrupted traditional Western scientific and political
thought. Their philosophies often question the centrality of psychological and
cognitive research approaches, and while their work has influenced research in
education generally (e.g., Jackson and Mazzei, 2012; St. Pierre, 1997),
connections to the field of RUME seem limited. In this
presentation, I discuss Deleuze and Guattari's ontology, focusing on issues of
being and becoming, and use these ideas to pose questions related to my own
dissertation plans concerning undergraduate proof and proving. These questions
include: How does a mathematical argument "become" a proof and how
does an individual "become" one who proves? I will also touch on my
own Deleuze and Guattari inspired methodological plans for attempting to answer
these kinds of questions.