**Emily Stone**

Email

# 2015 Colloquia

## May 13 - Grant Swicegood

*Doctoral Dissertation Defense*

## An Investigation of the Impact of iPad Usage on Elementary Mathematical Skills and Attitudes

### Grant Swicegood

PhD Candidate, University of Montana

#### Wednesday, May 13, 2015 at 2:10 pm in Math 103

Currently, many schools are implementing one-to-one initiatives, where the goal is to give every student in a classroom a tablet or laptop. However, there is a dearth of research backing up the assumption that they significantly improve student learning. This study explored the effects of these new instructional devices by focusing on two second-grade classrooms implementing a one-to-one iPad program. Specifically, it investigated how iPad usage affects student and teacher attitudes toward mathematics, student mathematics performance in and out of app environments, the instructional purposes for which iPads are used in the classroom, and implementation issues of the technology. This primarily observational study employed a mixed methods approach to capture a picture of an active program to serve as a source for further questions that may be better answered by experimenting with different treatments. Quantitative data was gathered on student performance in two apps, Addimal Adventure and Splash Math 2^{nd} Grade, as well on the frequency and type of iPad usage. Qualitative data came from interviews with six students and two teachers near the beginning and end of the four month research period. In this presentation, I will present these results and discuss their implications for the education community.

## May 12 - Grant Swicegood

*Colloquium*

## An Investigation of the Impact of iPad Usage on Elementary Mathematical Skills and Attitudes

**Grant Swicegood**

PhD Candidate, University of Montana

PhD Candidate, University of Montana

#### Tuesday, May 12, 2015 at 3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109

Currently, many schools are implementing one-to-one initiatives, where the goal is to give every student in a classroom a tablet or laptop. However, there is a dearth of research backing up the assumption that they significantly improve student learning. This study explored the effects of these new instructional devices by focusing on two second-grade classrooms implementing a one-to-one iPad program. Specifically, it investigated how iPad usage affects student and teacher attitudes toward mathematics, student mathematics performance in and out of app environments, the instructional purposes for which iPads are used in the classroom, and implementation issues of the technology. This primarily observational study employed a mixed methods approach to capture a picture of an active program to serve as a source for further questions that may be better answered by experimenting with different treatments.

## April 27 - Alex Philp

*Colloquium*

**The Significance of Applied Mathematics and Statistics in Data Science Driven Corporations.**

**Alex Philp**

Founder and CEO

**Upstream Health Systems**

#### Monday, April 27, 2015 at 3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109

## April 29 - Math Department Awards Ceremony

*Special Event
*

**Math Department Awards Ceremony**

#### Wednesday, April 29, 2015

3:30 - 5:00 p.m.

Dell Brown Room in Turner Hall

## April 20 - Mike Fredenberg, Mathematics Education Candidate

*Colloquium*

## Factors Considered by Elementary Teachers When Modifying Mathematical Tasks to Support or Extend Children’s Mathematical Thinking

### Mike Fredenberg

Mathematics Education Candidate

San Diego State University & University of California SD

Mathematics educators and researchers have aligned themselves with John Dewey’s argument to concentrate on characterizing and organizing the knowledge and activities that enable teachers to bridge the gulf between theory and practice. In this vein, I ask the question, what factors do exemplary elementary teachers consider when modifying a task for students during the enactment of a lesson? In this presentation, I situate my dissertation study within the arena of Cognitively Guided Instruction (CGI), and the theoretical foundations of the professional noticing of children's mathematical thinking. I describe the motivation for the study, the methodology and data analysis, and I present emerging results. I conclude with a discussion of contributions to the field, and thoughts on future research projects.

#### Monday, April 20, 2015 at 3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109

## April 13 - Lia Harrington

*Colloquium*

## Cross-disciplinary training: A vehicle for research collaboration and STEM education promotion

**Lia Harrington**

PhD student, Department of Psychology

PhD student, Department of Psychology

#### Monday, April 13, 2015 at 3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109

Cross-disciplinary training and collaboration is becoming not only a fad, but a true trend of the future as the divisions between fields are crumbling due to the changing landscape of research. Modern researchers often have to understand mathematical concepts when they implement new computational techniques to understand the underlying structure and relationships of the phenomena they are investigating. I will explore how a cross-disciplinary approach can aid and enrich research collaborations. I also will explore cross-disciplinary training as a possible motivating vehicle for promoting STEM education, especially with engaging women to pursue science careers.

## April 6 - Frederick Peck, Mathematics Education Candidate

*Colloquium*

## Beyond rise over run! Learning slope in a cascade of artifacts

### Frederick Peck

University of Colorado- Boulder

Mathematics Education Candidate

#### Monday, April 6, 2015 at 3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109

In this talk I address two questions. The first is, how can we understand the role of culture in school mathematics? The second is, how do students in Algebra I learn slope? To explore these questions, I conducted a design experiment as a teacher-researcher in my own Algebra I classroom. In discussing the results, I’ll introduce the concept of a cascade of artifacts to describe learning from a cultural perspective, and I’ll present a local instructional theory for how students learn slope. I’ll conclude with a plan for how I will marshal my current body of work into a robust agenda of future research.

## March 16 - Christopher I. Vahl

*Colloquium*

## Equivalence criteria in the safety evaluation of a genetically modified crop

**Christopher I. Vahl**

Kansas State University

#### Monday, March 16, 2015 at 3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109

The safety evaluation of a genetically modified (GM) crop is accomplished by establishing its substantial equivalence to conventional non-GM food crops with a history of safe use. Toward this end, equivalence testing rather than difference testing is the more appropriate statistical approach. A pivotal step in this process is to specify a reasonable equivalence criterion that encompasses a measure of the discrepancy between the GM and reference crops as well as a regulatory threshold. We explore several possible equivalence criteria and discuss their pros and cons. Each criterion will be shown to address one of three ordered classes of equivalence. Their implications will be examined over an array of parameter values estimated from a real-world dataset. Furthermore, our literature search indicates that the linear mixed model proposed by the European Food Safety Authority is adequate for assessing substantial equivalence despite its lack of genotype-by-environment interaction terms.

## March 9 - Jaikumar Radhakrishnan

*Colloquium*

**Set membership with two bit probes**

**Jaikumar Radhakrishnan**

Professor, Tata Institute of Fundamental Research, Mumbai

and Visiting Scientist, Simons Institute for the Theory of Computing, Berkeley

Professor, Tata Institute of Fundamental Research, Mumbai

and Visiting Scientist, Simons Institute for the Theory of Computing, Berkeley

#### Monday, March 9, 2015 at 3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109

We will consider the bit-probe complexity of the set membership problem, where a set \(S\) of size at most \(n\) from a universe of size \(m\) is to be represented as a short bit vector in order to answer membership queries of the form "Is \(x\) in \(S\)?" by adaptively probing the bit vector at \(t\) places. Let \(s(m,n,t)\) be the minimum number of bits of storage needed for such a scheme. Alon and Feige showed that for \(t=2\) (two bit probes), such schemes can be obtained from dense graphs with large girth. In particular, they showed that for \(n < \log m\),

$$s(m,n,2) = O(m n \log((\log m) / n) / \log m).$$

We improve their analysis and obtain a better upper bound and a corresponding lower bound.

Upper bound: There is a constant \(C>0,\) such that for all large \(m\),

$$s(m,n,2) \leq C \cdot m^{1-\frac{1}{(4n+1)}}.$$

Lower bound: There is a constant \(D>0,\) such that for \(n\geq 4\) and all large \(m\), we have

$$s(m,n,2) \geq D \cdot m^{1-\frac{1}{\lfloor n/4 \rfloor}}.$$

(This is joint work with Mohit Garg.)

## March 2 - Johnathan M. Bardsley

*Colloquium*

**Using numerical optimization techniques for sampling in statistical inverse problems**

**Johnathan M. Bardsley**

**Department of Mathematical Sciences**

#### Monday, March 2, 2015 at 3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109

Many solution methods for inverse problems compute the maximum a posteriori (MAP) estimator, or equivalently, the regularized solution, by solving an optimization problem. Uncertainty quantification (UQ), on the other hand, typically requires sampling from the Bayesian posterior density function. In this talk, we bring these two ideas together and present posterior sampling methods that make use of existing algorithms for computing regularized solutions/MAP estimators. Theoretically correct samplers for both linear and nonlinear inverse problems will be presented.

## February 23 - Grant Swicegood

**Mobile Educational Technology and the Mathematics Classroom**

**Grant Swicegood**

**PhD Candidate, Department of Mathematical Sciences**

#### Monday, February 23, 2015 at 3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109

In this talk, I will discuss the current state of mobile educational technology initiatives involving tablets (e.g. iPads), laptops, and other mobile electronic devices. What does this mean to the modern mathematics classroom at the elementary or high school level? What does the implementation actually look like? In addition to exploring these questions, I will demonstrate the functionality of several popular educational mathematics apps and discuss the possible impacts on student learning. Against this background, I will describe the iPad initiative at Paxson School in Missoula and my current research there in second grade classrooms.

## December 7 - Peter Coffee

## November 30 - Cody Palmer

## November 23 - Beth Burroughs & Mary Alice Carlson

## November 16 - Leonid Kalachev

## November 9 - Tiangang Cui

## November 2 - Jesse Johnson, Department of Computer Science

## October 5 - Bitty Balducci

*Colloquium*

**A Forum on Philanthropy at the College and Department**

**Bitty Balducci **

Assistant Director of Development, College of Humanities and Sciences

University of Montana Foundation

*Assistant Director of Development, College of Humanities and Sciences*

University of Montana Foundation

Please join us for a discussion of existing efforts in the Math. Dept. for philanthropic development, and the incorporation of new strategies

**Monday, October 5, 2015 at 3:10 p.m. in Math 103**

4:00 p.m. Refreshments in Math Lounge 109

4:00 p.m. Refreshments in Math Lounge 109

## September 28 - Michael Reid

*Colloquium*

**Budget Development**

### Michael Reid

**VP Administration & Finance at the UM**

### Monday, September 28, 2015 at 3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109

## September 15 - Matthew Yancey

*Colloquium*

**Spectral algorithms to find communities with special structure**

### Matthew Yancey

IDA/CCS

A recent trend in data-mining is to find communities in a graph. Generally speaking, a community of a graph is a vertex set such that the number of edges contained entirely inside the set is "significantly more than expected." These communities are then used to describe families of proteins in protein-protein interaction networks, among other applications. Community detection is known to be NP-hard; there are several methods to find an approximate solution with rigorous bounds.

We present a new goal in community detection: to find good bipartite communities. A bipartite community is a pair of disjoint vertex sets *S*, *S*' such that the number of edges with one endpoint in *S* and the other endpoint in *S*' is "significantly more than expected." We claim that this additional structure is natural to some applications of community detection. In fact, using other terminology, they have already been used to study correlation networks, social networks, and two distinct biological networks. We will show how the spectral methods for classical community detection can be generalized to finding bipartite communities, and we will prove sharp rigorous bounds for their performance. Additionally, we will present how the algorithm performs on public-source data sets.

### Tuesday, September 15, 2015 at 10:10 a.m. in Math 103

11:00 a.m. Refreshments in Math Lounge 109

## September 14 - Gerrit Stols

*Colloquium*

**Teaching and learning of Mathematics using technology: opportunities and pitfalls**

### Gerrit Stols

Head of the Department of Science, Mathematics, and Technology Education at the University of Pretoria

In this talk, I will give an overview of the different kinds of software that are used in mathematics classes. Teachers and lecturers technology use can be categorized as the use of technology *outside the classroom* (to improve the effectiveness and professionalism) and *inside the classroom* to enhance the conceptual development of their students. Both uses generate new opportunities, but if used incorrectly, can impede students’ conceptual development. I will therefore reflect on the importance and limitations of technology use. Lastly I will focus on the question: Why do teachers and lecturers, in general, not use technology in their classrooms?