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**ORAL THESIS DEFENSE**

MST Candidate

**Shahram Shawn Firouzian
**Thesis Advisor: Natasha Speer

Thesis Committee:

Natasha M. Speer

Robert Franzosa

John Thompson

Submitted in Partial Fulfillment of the

Requirements for the Degree of

Master of Science in Teaching

May, 2014

**Correlations Between Students’ Multiple Ways of Thinking About the Derivative and Their Abilities to Solve Applied Derivative Problems**

There is extensive research on students’ understanding, thinking and difficulties with the derivative and applied derivative problems, however there are very little works correlating the two fields. In this study, the correlations between students’ multiple ways of thinking about the derivative and their abilities in solving the applied derivative problems such as related rate and graphing problems are investigated. Fine-grained analysis of the students’ written surveys and clinical interviews revealed that students’ having two or more ways of thinking about the derivative correlate to their higher abilities in solving applied derivative problems.

**Wednesday, April 9, 2014
4:30 p.m.
Arthur St. John Hill Auditorium, ESRB**

**ORAL THESIS DEFENSE**

MST Candidate

**Jon Janelle
**Thesis Advisor: Natasha Speer

Submitted in Partial Fulfillment of the

Requirements for the Degree of

Master of Science in Teaching

May, 2014

**PROOF CONCEPTIONS OF COLLEGE CALCULUS STUDENTS**

Mathematicians and mathematics education researchers have consistently asserted the crucial and multifaceted roles that deductive reasoning and proof play in mathematics. In contrast, students at many levels of education have been found hold severely limited views of proof that may lead them to view mathematics as a rigid, formal, and largely meaningless discipline. Improving students’ understandings and attitudes of reasoning and proof is necessary to motivate a greater number to consider careers in STEM fields and to prevent attrition in mathematically-intensive degree programs.

This study consisted of an investigation into 59 undergraduate calculus students’ views about the nature and purposes of mathematical proof, the forms of empirical arguments they perceived as valid proofs, and the connection between their proof construction and validation practices. Previous studies of student proof conceptions have primarily focused on three groups: students in secondary geometry courses, pre-service and in-service teachers, and advanced undergraduate and graduate students who have received formal instruction in the creation of deductive proofs. However, little attention has been given to the connection between students’ proof constructions and validations or to examining students’ conceptions after the completion of a high school geometry course, but before enrollment in proof-based mathematics course. Using data obtained from written surveys and interviews, this study was designed to fill this gap in the literature.

Findings suggest that a majority, more than 80%, of college calculus students believe that the inspection of a few examples and the testing of a single extreme case are valid forms of mathematical proof. In addition, students who incorrectly validated empirical arguments as proofs were significantly more likely than their peers to construct empirical arguments when asked to verify a conjecture. Consistent with the findings of past researchers, approximately half accepted false arguments based on their proof-like surface features, for example the use of variables or formal mathematical language. While two-thirds of students were able to describe at least one purpose for proof consistent with descriptions generated by the mathematical community, many were unable to acceptably describe a single meaningful use. The pedagogical implications and limitations of these findings are discussed.

** **

**Thursday, April 17, 2014
2:00-4:30 pm
207 Boardman Hall**

*Maine Center for Research in STEM Education
(RiSE Center) *

**Presents**

**Eric Pandiscio
**Department of Exercise Science and STEM Education

Maine RiSE Center, University of Maine

** Differentiated student thinking while solving **

** a distance vs. time graph problem**

This study probes the thinking of students at different stages of mathematical experience: college students who have taken calculus; college students who have not taken calculus; current high school mathematics teachers; graduate students in a discipline-based mathematics education program. The study asks:

- what is the nature of student thinking when solving a distance/time graph problem?
- do students with different levels of mathematical experience solve graph problems differently from each other?

Using a covariational framework (Carlson, Jacobs, Coe, Larsen & Hsu, 2002), preliminary data reveal many students have difficulty working with phenomena that display varying rates of change. Data also indicate many students estimate answers, even when an exact answer is possible. Data were collected via written surveys and semi-structured oral interviews. This work builds on, yet diverges from, prior research in physics education (McDermott, Rosenquist & van Zee, 1987; Thornton & Sokoloff, 1990; Kim & Kim, 2005), and mathematics education (Chiu, Kessel, Moschkovich & Munch-Nunez, 2001; Moschkovich, 1996) that describes difficulties students have with graph interpretation.

**Monday, April 7, 2014
3:00-4:00 pm
Arthur St. John Hill Auditorium, 165 Barrows Hall**

*Maine Center for Research in STEM Education
Colloquia & Seminar Series*

**Presents**

**Warren Christensen**

North Dakota State University

Assistant Professor of Physics

Director of Growing Up STEM REU

**Student reasoning about matrix multiplication: **

** a window for investigating math/physics frame shifts**

In principle, a student who has completed both Linear Algebra and Quantum Mechanics should have a wealth of conceptual and procedural knowledge that has been attained from classes in mathematics and physics. However in practice, it seems that many students come into our physics courses with a lack of skills that we know were taught in math courses. Do students fail to retain this information or do students possess this information but only within specific contexts? This investigation casts light on students’ thinking about matrix multiplication and how their thinking appears to be influenced by their framing of the problem as either a mathematics or physics question. We use the framework of Framing and Resources to describe a single student’s thinking during an interview. Using an interview protocol written by mathematicians from a study in Mathematics Education, we explicitly probed mathematical thinking, and investigated if (and when) students attempted to relate mathematical problems to physics. Using lexicon analysis, we find students seem to shift from a “mathematical frame” to a “physics frame” and back again, but struggle to successfully transfer concepts between those frames. I will highlight the markers for these frame shifts and explore the potential instructional consequences of this work.

**Friday, March 21, 2014
3:00 – 4:00 pm
Arthur St. John Hill Auditorium, 165 Barrows Hall**

*Maine Center for Research in STEM Education (RiSE Center)
Colloquia & Seminar Series*

**Presents**

Lauren Barth-Cohen, PhD

Post-Doctoral Research and Teaching Associate

Center for Research in STEM Education, University of Maine

**Evidence Construction in a Field Geology Environment**

**Abstract:** Evidence is key to many scientific practices including argumentation, explanation, and modeling. For learners engaged in scientific practices, often we aim for them to construct scientific evidence from observations in the world, but the details of how learners go from observation to verbal accounts of evidence in support of a claim in a complicated environment has been overlooked. In this talk we argue that much can be learned about scientific practices from examining how evidence is constructed from human sensory data. We present a case of one teacher who was involved in an evidence construction activity as part of a professional development workshop in a field geology environment. Using theoretical machinery from coordination class theory we model the evidence construction process, specifically how observations as connected with prior knowledge turn into evidence for a claim. Use this model we illuminate the teacher constructing evidence to support a claim for the relative ages of two types of rocks in the field, and we also use the model to illustrate her constructing hypothetical evidence to support an alternative claim. This case illustrates the importance of a commonly overlooked dimension of scientific practices, and implications suggest that evidence construction is applicable to both instruction and professional development.

**Monday, March 17, 2014
3:00 pm**

** Arthur St. John Hill Auditorium, 165 Barrows Hall**

Image Description: Maine Center for Research in STEM Education

*Maine Center for Research in STEM Education (RiSE Center)
Colloquia & Seminar Series*

**Presents**

**Paula Lemons**

Assistant Professor of Biochemistry and Molecular Biology

University of Georgia

**Helping Biology Students Develop Problem-Solving Skills**

Based on economic projections, about one million more U.S. STEM professionals will be needed over the next decade to fill positions in fast-growing occupations that require problem solving. Yet little is known about the development of problem-solving skills among undergraduate biology students. It is also not known how to support college faculty who want to change their courses in order to promote problem solving. Dr. Lemons developed a method for creating biology questions that encourage problem solving, and she used these questions to document the particular problem-solving steps used by students. Her work revealed that students practice a mixture of helpful and not helpful problem-solving steps. Faculty can use this research by coaching their students to use helpful problem-solving steps. Unfortunately, many faculty who want to guide their students in problem solving face the challenge of transitioning from instructor-centered to learner-centered teaching. Dr. Lemons studied faculty who were making this transition. Her work shows that faculty focus primarily on personal experience, not empirical evidence, when making decisions about teaching. These studies point to ways to increase the amount of learning about problem solving in undergraduate biology classrooms by supporting both students and faculty.

**Monday, February 3, 2014
3:00 – 4:00 pm
Arthur St. John Hill Auditorium, 165 Barrows Hall**

Snacks will be provided at 2:45 in the Hill Auditorium Lobby.

for a Printable page, please click Colloq February 3 2013.

Department of Physics & Astronomy

University of Maine

**THESIS DEFENSE**

** & MAINE RISE CENTER COLLOQUIUM**

Benedikt Harrer

Ph.D. Candidate

“IDENTIFYING PRODUCTIVE RESOURCES IN SECONDARY SCHOOL STUDENTS’ DISCOURSE ABOUT ENERGY”

A growing program of research in science education acknowledges the beginnings of disciplinary reasoning in students’ ideas and seeks to inform instruction that responds productively to these disciplinary progenitors in the moment to foster their development into sophisticated scientific practice. This dissertation examines secondary school students’ ideas about energy for progenitors of disciplinary knowledge and practice. Previously, researchers argued that students’ ideas about energy were constrained by stable and coherent conceptual structures that conflicted with an assumed unified scientific conception and therefore needed to be replaced. These researchers did not attend to the productive elements in students’ ideas about energy.

To analyze the disciplinary substance in students’ ideas, a theoretical perspective was developed that extends Hammer et al.’s resources framework (Hammer et al., 2005. Resources, framing, and transfer. In Mestre, Ed., Transfer of Learning: Research and Perspectives, 89-120. Greenwich, CT: Information Age Publishing). This elaboration allows for the identification of disciplinary productive resources—i.e., appropriately activated declarative and procedural pieces of knowledge—in individual students’ utterances as well as in the interactions of multiple learners engaged in group learning activities.

Using this framework, original interview transcripts from one of the most influential studies of students’ ideas about energy (Watts, 1983. Some alternative views of energy. Physics Education, 18/5, 213-217) were analyzed. Disciplinary productive resources regarding the ontology of energy, indicators for energy, and mechanistic reasoning about energy were found to be activated by interviewed students. These valuable aspects were not recognized by the original author. An interpretive analysis of video recorded student-centered discourse in rural Maine middle schools was carried out to find cases of resource activation in classroom discussions. Several cases of disciplinary productive resources regarding the nature of energy and its forms as well as the construction of a mechanistic energy story were identified and richly described.

Like energy, resources are manifested in various ways. The results of this study imply the necessity of appropriate disciplinary training for teachers that enables them to recognize and productively respond to disciplinary progenitors of the energy concept in students’ ideas.

MONDAY, DECEMBER 2, 2013

3:00 pm

ARTHUR ST. JOHN HILL AUDITORIUM

**Maine Center for Research in STEM Education**

presents

**ORAL THESIS DEFENSE**

*MST Candidate*

**Daniel Bragdon
**Thesis Advisor: Dr. Natasha Speer

Submitted in Partial Fulfillment of the

Requirements for the Degree of

Master of Science in Teaching

May 2014

**University Students’ Graph Interpretation and Comprehension Abilities**

There is an increase in demand for individuals to be successful with graph interpretation. Society is currently lacking individuals who have majored in Science, Technology, Engineering and Mathematics (STEM), where most courses require linear graph comprehension as a prerequisite skill. The Common Core for State Standards Initiative for Mathematics, Next Generation Science Standards, and the Maine Revised Learning Results all characterize these as skills to be mastered before a student enters high school. Reading information from graphs and making inferences based on graphically-presented information is challenging for students and researchers have documented a variety of difficulties students have with graph comprehension. These difficulties include, among others, having knowledge of the graph context incorrectly influencing graph comprehension, viewing the graph as an iconic representation of the event and confusing slope and height. Being able to extrapolate and make predictions based on graphs is especially challenging for students. This research on graph comprehension has been primarily focused on students in elementary, middle, and high school and findings do not provide definitive answers as to why these difficulties are prevalent or why certain kinds of questions are so difficult. Despite the important role graph comprehension plays in undergraduate students’ learning of STEM content, little is known about the performance and thinking of this population of students. For the present study, college students in introductory mathematics and physics classes were given linear graph comprehension tasks. Data include both written responses and interviews designed to investigate student thinking were conducted with a subset of students. Findings indicate that students answered extrapolation questions incorrectly more often than other questions. On a written in class survey only 67.6% of students correctly answered an extrapolation question correctly, compared to a success rate of 86.7% on interpolation questions. Interview data analysis generated similar results with only 50% of students consistently answering extrapolation questions correctly. Student responses to interpolation questions can be used as a predictor of a student’s success on extrapolation questions. Implications for instruction are discussed along with directions for further research.

**Monday, November 18, 2013
3:00 pm
Arthur St. John Hill Auditorium (165 Barrows Hall, ESRB)**

*Maine Center for Research in STEM Education (RiSE Center)
Colloquia & Seminar Series*

**Presents**

Erika Allison

Project Director, MainePSP

Susan McKay

Professor of Physics, Director of the Maine Center for Research in STEM Education, and MainePSP Principal Investigator

**The Maine Physical Sciences Partnership (MainePSP)
as a Generator of New Opportunities**

During the last six months, faculty members from the Maine Center for Research in STEM Education Research (RiSE Center) have received over $8 million in grants. This rapid growth in funding, spread among so many different RiSE faculty members, is linked directly to the MainePSP and, in many cases, to the new faculty members that this project has attracted and supported. Those involved with the MainePSP have sought additional funding to build upon and sustain its work. In this colloquium, Erika and Susan, with input from other RiSE Center faculty, will talk informally about these new research and programmatic opportunities and how they are important in sustaining the MainePSP’s work and building capacity for future projects involving UMaine and its partners.

**Monday, November 4, 2013
3:00 pm
Arthur St. John Hill Auditorium, 165 Barrows Hall**

*Snacks will be provided at 2:45 in the Hill Auditorium Lobby.*

*The Maine Center for Research in STEM Education
*

**Oral Thesis Defense
**

**Kalee Gwarjanski (Gurschick)**

**Advisor: Jonathan Shemwell
**

**Friday, November 1, 2013**

**119 Barrows Hall**

**3:15 p.m.**

**PAYING ATTENTION TO THEORY IN SCIENCE
CLASSROOM ARGUMENTATION**

In science classrooms, as in the scientific community, knowledge should be shared, critiqued and advanced through argumentation. Theory construction, in which claims are advanced beyond the empirical facts of an investigation, is essential to scientific argumentation. The present study reports on how a group of 18 middle school teachers, using the Claim-Evidence-Reasoning (CER) framework (McNeill & Krajcik, 2011), developed their knowledge of theory construction in student argumentation during three phases of professional development activities. The first phase illuminated teachers’ initial thinking about theory construction when using CER. The second phase showed how teachers advanced their thinking about theory when they used a modified form of CER with increased support for theory construction. Finally, the third phase explored teachers’ enactment of the modified form of CER during classroom scientific argumentation. Data included surveys, analysis of artifacts and discussion when teachers constructed or critiqued arguments, analysis of student arguments and classroom observation. With unmodified CER, the teachers did not explicitly attend to theory construction when constructing or critiquing arguments. After using theory-enhanced CER, the teachers incorporated more theory into their own arguments, and they better understood and embraced the need for theory in students’ arguments. Still, it was difficult for teachers to discern and make use of varying levels of theory in student arguments. When using the modified CER in their classrooms, teachers supported students in constructing theory, but they tended to use heavy guidance, moving students quickly to high levels of generalization. This result suggests that teachers viewed the process of constructing theory as a straightforward, non-iterative form of learning. I concluded that, in general, teachers and their students would benefit from increased attention to theory within frameworks for supporting scientific argumentation, with particular attention to strategies to support students in the classroom.

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