[ < Return to the TRUSE Home Page ]

**Date:** June 14 - 18, 2010

**Location:** University of Maine

Theoretical foundations and methodologies: Conceptualizing work in research on undergraduate discipline-based STEM education Assessment: How do we measure outcomes of interest and what is the nature of the claims we make? Transfer of knowledge and concepts within and across domains Nature of knowledge for teaching in the discipline First year courses: How do we best support student success?

This conference will bring together researchers in undergraduate mathematics, physics, and chemistry education to transform and integrate research across disciplines. In addition to plenary sessions there will be poster sessions, working groups to interact and plan with new colleagues, and interactive free time. This is your chance to be part of an emerging community of scholars collaborating across diciplinary lines! Sponsors

This conference is generously sponsored by the National Science Foundation through grants DUE-CCLI # 0941515 and 0941191.

Stacey Lowery Bretz, Miami University, Dept. of Chemistry and Biochemistry

Marilyn Carlson, Arizona State University, Dept. of Mathematics

Renee Cole, University of Central Missouri, Dept. of Chemistry

Melanie Cooper, Clemson University, Dept. of Chemistry

Ayush Gupta, University of Maryland, Dept. of Physics

Tom Holme, Iowa State University, Dept. of Chemistry

Michael Loverude, California State University, Fullerton, Dept. of Physics

Karen Marrongelle, Portland State University, Dept. of Mathematics

David Meltzer, Arizona State University, Mary Lou Fulton Teachers College

Dawn Meredith, University of New Hampshire, Dept. of Physics

Ricardo Nemirovsky, San Diego State University, Dept. of Math & Statistics

Michael Oehrtman, Arizona State University, Dept. of Mathematics

N. Sanjay Rebello, Kansas State University, Dept. of Physics

Bruce Sherin, Northwestern University, Department of Learning Sciences

Vicente Talanquer, University of Arizona, Dept. of Chemistry

Joe Wagner, Xavier University, Dept. of Mathematics

Learning Chemistry through Inquiry: Engaging Underprepared Math Students

Stacey Lowery Bretz

Department of Chemistry and Biochemistry

Miami University

Numerous research studies have identified mathematics knowledge as the single best predictor of success in first year undergraduate chemistry. An intervention grounded in learning theory was designed to reduce attrition of students with weak math backgrounds. Results from multiple cognitive and affective measures will be presented. Examples of the difficulties these students encounter while learning chemistry as well as the inquiry model used to structure the intervention will be provided.

**Quantitative and Covariational Reasoning: Theoretical Foundations for Promoting and Studying Continued Mathematics Learning and Meaningful Mathematical Modeling in the Sciences**

Marilyn P. Carlson

Department of Mathematics

Arizona State University

Well-intentioned faculty who are committed to integrating mathematics and science instruction will likely confront many barriers in their journey to collaborate. Overcoming these barriers can be facilitated by identifying common ways of thinking and understandings that support students in both making interdisciplinary connections and continuing their learning in mathematics and science. This session will describe the approach of one interdisciplinary project when navigating these barriers during a six-year STEM education collaborative. Faculty teams identified quantitative and covariational reasoning as crucial reasoning abilities for modeling in the sciences and learning ideas in calculus and differential equations. Quantitative reasoning (Smith III & Thompson, 2008) refers to a student imagining a situation, conceiving of measurable attributes within this imagined situation (e.g., quantities), and constructing relationships between these quantities. Covariational reasoning entails coordinating the values of two quantities that are changing in tandem (Carlson, et al., 2002). Such reasoning ranges from identifying a general correspondence between the values of two quantities to reasoning about the rate of change of one quantity with respect to another quantity. Illustrations of the meaning and usefulness of these constructs in supporting connections in mathematics and science learning will be provided.

**Adapting a Methodology for Documenting Collective Growth to an Undergraduate Physical Chemistry Class**

Renee Cole

Department of Chemistry

University of Central Missouri

Physical chemistry is a subject that uses mathematical inscriptions to carry chemical meaning. In order to gain understanding, both curricular and pedagogical, of how students build an understanding of mathematical inscriptions that are used in chemistry, it is necessary to document student reasoning and classroom practices. A three-phase approach grounded in Toulmin's argumentation scheme was adapted to trace the growth of ideas in an inquiry mathematics classroom. This method of documenting collective production of meaning was adapted for use in analyzing an inquiry-oriented physical chemistry classroom. The difference in classroom structure between mathematics and physical chemistry necessitated modifications to the application of the methodology, but the analysis provided empirical evidence for common themes that define physical chemistry classroom practices. The presentation will describe the methodology used to analyze the classroom discourse, including the evidence for the utility of the adaptations. The chemistry classroom practices identified using the methodology will be discussed, including a detailed example.

**Investigating the Development of Representational Competence in Chemistry**

Melanie M Cooper

Department of Chemistry

Clemson University

Representational competence, or (as defined by Kozma) the ability to use representations to explain the relationship between physical properties and underlying processes, is a crucial skill for STEM students. This is particularly true in chemistry, where molecular level processes must, by necessity be depicted using representations that “stand in” for the atoms and molecules themselves. Students must learn to use these representations with facility, otherwise they are doomed to memorize and regurgitate, rather than synthesize and use their knowledge in new situations.

OrganicPad is a teaching, learning and research system that allows students to draw freehand Lewis structures and other representations of molecular structure. It can identify what the students have drawn and determine if the structure is correct and provide contextual feedback for students with varying degrees of specificity. Each stroke that the student draws is recorded and stored in a database for further study, and modeling. Using these data, student interviews, and assignments we have been studying how students learn to draw these structures, and how students use them to predict physical and chemical properties.

**Incorporating Emotions in Fine-Grained Cognitive Dynamics**

Ayush Gupta

Department of Physics

University of Maryland

Researchers have argued for students’ epistemology as connected to their affect, but at a coarse grain-size—treating epistemology as a belief or stance toward a discipline, and an emotional stance as applied broadly to a discipline or classroom culture (Boaler and Greeno, 2000). An emerging line of research, however, shows that a student can shift between multiple locally coherent epistemological stances, and such dynamics is better modeled via fine-grained cognitive structures (Hammer & Elby, 2002). To begin uniting these two bodies of literature, toward the long-term goal of incorporating emotions into fine-grained models of in-the-moment cognitive dynamics, we present case studies from clinical interviews and discussion sessions. “Judy,” a sophomore engineering major in a circuits course, shows “annoyance” at the qualitative, conceptual questions on homework and exams. This emotional response stabilizes epistemological stances that conceptual reasoning is useless and an unbridgeable gulf separates real circuits from the ideal circuits targeted by the conceptual questions. But Judy’s epistemological stances are contextual, easily disrupted by an emotionally positive experience during the interview (Gupta, Danielak, & Elby, In Press). My second case comes from an episode of a group of introductory physics students working on a physics tutorial, where emotional sharing among the students changes the epistemological nature of the activity and precipitates a sharing of deep conceptual ideas.

**Research and Development of Enhanced Assessment Tools in Chemistry**

Thomas A. Holme

Department of Chemistry

Iowa State Unviersity

The ACS Exams Institute has produced standardized exams for chemistry courses for over 75 years. Recent changes in expectations for assessment, however, are driving the needs of instructors and researchers beyond the traditional norm-referenced exams of the past. The ability to transform a venerable icon such as standardized, norm-referenced exams into more flexible tool for teaching requires research and development along several avenues. First, to provide criterion referencing, there must first be a process for determining content criteria at the college level of instruction. Second, alignment of exam items to a content criterion map provides a challenge that requires both enhanced cognitive characterization and novel perspectives on content within the curriculum. Finally, once an exam has moved beyond norm-referencing and the inherent averaging of measurement error, the characterization of error sources within objectively graded exams becomes more important. The experience of ACS Exams with these components of assessment development will be described in this talk.

**Knowledge for Teaching and Teaching for Knowledge: How Much Is ‘What to do in the Classroom?’ Discipline-Specific?**

Karen Marrongelle

Department of Mathematics

Portland State University

The problem of how teachers can proactively support their students’ learning in the classroom is not unique to any one STEM discipline. Constructs such as Shulman’s (1986) pedagogical content knowledge and Ball, Hill, and Bass’s (2005) mathematical knowledge for teaching imply that at least a certain part of what it takes to be an effective teacher is discipline-specific. On the other hand, scholars and educators have long suggested that at least part of what it takes to be an effective teacher transcends individual subjects (e.g., Gage, 1978). However, most teaching strategies that are discipline-general involve practices such as classroom management and other strategies for general behavior management.

In this talk, I take up the question of whether discipline- and theoretical-based strategies for teaching can transcend the discipline in which they were developed. I will explicate answers to this question by drawing upon examples from undergraduate STEM education, and undergraduate mathematics education in particular.

**No, your peanut butter is in my chocolate…**

Michael Loverude

Department of Physics

California State University, Fullerton

Like the characters in a no-longer-recent commercial, instructors (and students) often act as though they value purity of their chocolate, or at least their disciplines. Courses are taught with the assumption that students have mastered prerequisites and that there exist clean separations between disciplinary content. Conversations about pedagogy rarely seem to cross disciplinary lines. And yet, our disciplines are nevertheless deeply interconnected, and students pass back and forth between our programs in a haphazard way, making assumptions about prior knowledge treacherous. In this talk I will describe work performed in the context of of an NSF-funded collaboration including research on student learning and curriculum development in the context of upper-division courses in thermal physics. We have performed extensive studies of student understanding in the context of upper-division course in thermodynamics and statistical physics at several universities. This presentation will focus on parts of the research and curriculum development efforts that approach, and even cross disciplinary boundaries, including ongoing projects on student understanding of probability and statistics as well as ideal gas behavior and particulate models of matter.

**The Value and the Challenge of Interdisciplinary Research in STEM Education**

David E. Meltzer

Mary Lou Fulton Teachers College

Arizona State University

Collaborative research and development work among diverse STEM education fields is not only potentially fruitful, it is necessary in order to realize the full potential of research-based educational innovations. At the same time, such work brings many challenges that must be acknowledged and effectively addressed. I will discuss these ideas from three different perspectives informed by 10 years of ongoing interdisciplinary work: (1) Undergraduate students typically encounter foundational STEM concepts in multiple courses in diverse fields of study. Innovative efforts to improve instruction in one field will inevitably fall short of their potential if educators in other fields fail to take account of these changes and make appropriate adjustments to instruction in their own areas; (2) STEM education researchers who collaborate on joint projects will often find their divergent backgrounds and viewpoints allow them to see things from very different perspectives, and to provide insights and recognize potential where long-term habituation can make similar perceptions practically inaccessible to workers in their own field; (3) Effective communication among researchers in different fields is crucial, yet challenging. Technical terms and even non-technical words frequently have significantly different meanings or connotations in different fields. Issues that pose major concerns for one field may be non-issues for the other, considered to be outside the area of interest and thus not worth attention or investigation. Effective work requires careful attention and sustained effort to becoming familiar and comfortable with each others' language, idiom, and conventions. This includes symbolic and diagrammatic representations, guiding themes, and major conceptual issues.

**Connecting Physics, Mathematics, Biology and Meaning**

Dawn Meredith

With Jessica Bolker, Gertrud Kraut, Christopher Shubert, James Vesenka,

Department of Physics

University of New Hampshire

We report on three years' experience developing and assessing an introductory physics course for life science majors. This course (co-developed with a zoologist) was designed to have significant biological applications, and to emphasize topics such as fluids that are especially relevant to life science students. One goal is to demonstrate to students the value of physics in understanding biological phenomena. A second goal is to provide experiences that help students connect meaning and mathematics, as this cohort tends to be math phobic and/or disinterested. Examples of our students' work illustrate both difficulties and successes they encounter as they learn to transfer their knowledge across disciplinary boundaries. This work was funded by NSF CCLI Grant 0737458.

**What are concepts?: On the physicality of symbol-use in science and mathematics**

Ricardo Nemirovsky

Department of Mathematics & Statistics

San Diego State University

This talk is an attempt to address questions on the nature of mathematical and scientific concepts in light of embodied cognition. Traditionally concepts were conceived of in opposition to percepts, the idea being that conceptions allow us to overcome the particulars of perceptual appearances subsuming them within abstract and mental categories and entities. According to perspectives emerging from embodied cognition, all thinking and understanding takes place in streams of perceptuo-motor activity. This stance re-opens numerous questions about the nature of conceptions and abstractions. A foundational thesis that concepts are modal patterns of perceptuo-motor activity will be explored on the basis of two case studies. The first case is an episode with undergraduates in a mathematics class for pre-service high school mathematics teachers. The second case is based on an interview with a topologist about a paper of his published in 1999 in the "Geometry & Topology" journal. In both cases we conducted microanalyses to study the physicality of symbol-use, encompassing talk, gesture, gaze, posture, writing, and drawing.

**Discovering Application on the Way to Abstraction: Connecting Design Research in Calculus and Differential Equations to Science and Engineering**

Michael Oehrtman

Department of Mathematics

Arizona State University

My initial research on students' spontaneous reasoning about limit concepts identified aspects of approximation and error analyses as a potential foundation for conceptual development throughout introductory calculus and differential equations courses. I conducted subsequent design research to develop instruction with the criteria to i) reflect the structure of formal definitions of limits, ii) be based on natural language and ideas directly accessible to students, iii) be coherent in its application to all concepts defined in terms of limits, iv) have coherent meaning and structure across multiple representations, and v) be amenable to instructional techniques based on a constructivist theory of abstraction. Although the initial goals for this research were to foster rigorous mathematical reasoning with an eye toward eventual abstraction and formalization, results from early teaching experiment and interviews with colleagues in physics, biology and engineering suggested that a greater value of the approach was its focus on modeling, numerical methods and error analyses for students in applied sciences. In this talk, I will explore the connections of my work with current research and instructional innovation in undergraduate science and engineering education and outline future directions for this research with potential synergy with education researchers across STEM disciplines.

**From text to vectors: Automating the analysis of interview data**

Bruce Sherin

School of Education and Social Policy

Northwestern University

As science educators, we frequently want to get inside the heads of our students. One way that we do this is through the medium of words, both written and spoken. We ask students questions, listen to their responses, and try to make inferences about the knowledge they possess. However, as researchers in science education, we want to make these inferences in a systematic way. To date, this has generally been accomplished by relying on the hand-coding of the spoken or written data.

In this talk, I will discuss my attempts to automate the coding of data by using techniques from computational linguistics. Beginning with data in the form of raw interview transcripts, I will show how it is possible both to induce coding categories and code the transcripts, all without supervision from a human coder. In this work, I make use of a data corpus consisting of clinical interviews in which students were asked to explain the seasons. The computational techniques I will describe are principally based on vector space models, including techniques similar to Latent Semantic Analysis.

Vicente Talanquer

Department of Chemistry and Biochemistry

University of Arizona

Dual-process theories propose that there are two distinct modes of thinking or processing, commonly labeled System 1 and System 2, which may run in series or parallel in our mind. The first of these systems includes processes that are preconscious, implicit, automatic, fast, and effortless (heuristic operations), while processes in System 2 are conscious, explicit, controlled, slow, and high effort (analytic operations). System 1 and System 2 modes of reasoning correspond, respectively, to our common sense notions of intuitive and analytical thinking. Although most of the research on heuristic reasoning has been completed in non-academic contexts, there is ample evidence that this mode of thinking is also common in science and math classrooms. In particular, in the past few years we have directed our research efforts to investigate the reasoning heuristics used by undergraduate chemistry students when solving academic tasks that demand qualitative reasoning (e.g., classification, ranking, evaluation, design) and require the identification and coordination of multiple cues for their successful completion. In this seminar, I will summarize results from our investigations that are relevant to teaching and learning in the different STEM disciplines, and discuss the challenges that the identification and characterization of heuristic reasoning processes pose.

**Representational Fluency in Learning and Problem Solving in Physics**

N. Sanjay Rebello

Elizabeth Gire

Kansas State University

The use of multiple external representations in instruction has been widely recognized to facilitate learning. Similarly, the ability of learners to express their ideas in multiple representations has also been shown to result in improved performance on problem solving tasks. In this talk I will describe ongoing efforts at Kansas State University to utilize physical and virtual representations of simple machines and to assess their impact on learning in a conceptual physics class. I will also describe studies with students in a calculus-based physics course to facilitate transfer of problem solving skills across problems using graphical, functional and numerical representations. Results from both studies have helped highlight the affordances and constraints provided by various representations. Our results also show interesting sequencing effects when more than one representation is used in learning and problem solving.

Joe Wagner

Department of Mathematics

Xavier University

Many approaches to the transfer problem argue that transfer depends on the recognition of the same or similar abstract structure in two different problems or situations. However, mainstream cognitive perspectives and contrasting Piagetian constructivist accounts differ in their conceptualizations of structure. These differences are not clearly articulated in the literature, yet they have significant implications for accounts of transfer processes. In particular, Piagetian (as well as "radical") constructivism raises problematic questions concerning how individuals can, on the one hand, be active constructors of their own, often idiosyncratic, knowledge while, on the other hand, still learn to see "the same structure" across different situations. I will offer an introduction to my "transfer-in-pieces" account of transfer and, using data not previously published, discuss how diSessa's "knowledge-in-pieces" epistemology and my own transfer approach can be used to foster a constructivist account of transfer that begins to address these difficulties. Using interview data involving undergraduate students learning elementary principles of probability and statistics, I examine how what experts consider a single mathematical concept or principle may come to be recognized through a variety of assimilatory cognitive resources whose usefulness is influenced by contextual factors. That is, an individual might actively structure two contextually dissimilar situations differently while still perceiving the same mathematical principle at work in both. Similarly, two or more individuals may agree on the relevance of a particular mathematical concept in a given situation, even though each structures the situation quite differently.

Nicole Becker

Marcy Towns

Purdue University

Upper-level undergraduate physical chemistry courses require students to be proficient in calculus in order to develop an understanding of thermodynamics concepts. This poster will present the findings of a study that examines the relationship between math and chemistry in two undergraduate physical chemistry courses. Students participated in think-aloud interviews in which they responded to a set of questions involving mixed second partial derivatives with either abstract symbols or thermodynamics variables. Preliminary results and analysis of the study will be discussed.

**In-time remedial help sessions: An attempt to improve academic performance of at-risk general chemistry students **

Derek Behmke

Charles Atwood

University of Georgia

Previous research has made it clear that at-risk students must be exposed to additional instructional approaches in order to be successful in chemistry. We have developed and tested a definition of at-risk students. These students are identified immediately after the completion of a homework using our computerized homework and testing system, JExam. A brief look at this definition is followed by a detailed description of the cooperative learning based remedial help sessions at-risk students are invited to attend. Numerous comparisons are made between students who were identified as at-risk and attended a help session and those who chose not to attend in order to determine the effect the remedial help sessions have on student performance. These comparisons include analysis of performance on targeted test questions as well as overall test and course grades.

Paulo Borges

University of Toronto

In this work, a curriculum proposal has been developed for the introduction of modern Physics theories in the high school and course's early years in natural sciences and engineering. As theoretical foundations, the epistemology of Gaston Bachelard and the Jean Piaget's genetic epistemology were chosen. To this theoretical basis was added the research results in Mathematics and Science Education on student's previous conceptions, as well as the logical and psychological difficulties and obstacles to learning. The History of Science influence in the previous ideas shape is discussed along with the use of that history to overcome the learning difficulties of Quantum Theory concepts. A review of the evolution of the concept of atom from the Greeks to the twentieth century was also done. It will be used to identify the differences between the Chemistry point of view and other sciences of nature in relation to the concept of atom and substance. Finally, a discussion of the many interpretations of Quantum Theory influence on education will be presented. As a result, a proposal for curriculum organization directed towards senior high school and university education is done.

**Calculus II Students' Reasoning about Convergence and Divergence **

Danielle Champney

University of California, Berkeley

This study-in-progress aims to investigate students' understanding of and reasoning around convergence and divergence in the context of infinite series, and how this understanding was shaped by real-life experiences and classroom instruction, both in calculus and other courses. Commonly taught in Calculus II at American universities, the chapter on infinite series, and in particular convergence testing, is fertile ground for teaching college students both mathematical content and reasoning/critical thinking skills. However, in most current textbooks and college calculus classes, this material is presented in such a way that provides alarmingly few opportunities for sense-making, and as something procedural and memorized. By critically examining students' experience with the phenomena of convergence and divergence, researchers can better understand the origins of student struggles and misunderstandings, toward improving the teaching of this content in future courses.

**Student understanding of slope and derivative after multivarible calculus**

Warren Christensen

John Thompson

North Dakota State University

There is a small but growing body of work showing that student difficulties with mathematics concepts may underlie many of the difficulties we encounter in physics. The primary motivation for this study came from PER investigations in upper-level thermal physics. We perceived student physics difficulties may have roots in the underlying mathematics. Concern about student framing of math questions (which are essentially physics-less physics questions) in a physics classroom led us to ask questions in the prerequisite third semester course on multivariable calculus.

**Investigations in the Impact of Visual Cognition and Spatial Ability on Student Comprehension in Physics and Space Science**

Ximena Cid

R. E. Lopez

University of Texas, Arlington

Physics and Space Science (including Planetary Science) examine topics that are highly spatial in nature (e.g. electricity and magnetism, quantum mechanics, seasons, lunar phases, etc.). Students are required to visualize a given system, manipulate that system (e.g. rotate it, progress in time, zoom in to a specific location, etc.), and then solve a given problem regarding that system. Doing all of this, simultaneously, can lead to a cognitive overload where the student is unable to correctly solve the problem. Some of the difficulties may be rooted in conceptual difficulties with the material, whereas another set of difficulties may arise from student difficulties with spatial intelligence and visual cognition. Thus in some cases, students might have created an incorrect mental image of the problem to begin with, and it is this misconception, not the lack of content knowledge, that has caused an incorrect answer. It has been shown that there is a correlation between achievement in Science Technology Engineering and Mathematics (STEM) fields and spatial ability. My work focuses on several discrete investigations in topics that relate to student learning in physics and space science and the relationship to spatial ability.

**Decorating with arrows: Students' use of mechanisms in organic chemistry **

Nathaniel Grove ** **

Melanie M. Cooper

Kelli M. Rush

Clemson University

The use of the curved-arrow or electron-pushing formalism for conveying mechanistic processes is ubiquitous throughout the organic chemistry curriculum. Practicing organic chemists rely upon these symbolisms to not only depict the flow of electrons during chemical reactions but to also predict the products of new reactions or to deconstruct target compounds during retrosynthetic analyses. Lingering questions remain, however, about the utility and meaning that students derive from their use. This poster will focus on our use of OrganicPad, an innovative and user-friendly program that has been designed to allow students to draw organic mechanisms by using the natural user interface of a Tablet PC, to document how students use mechanisms to assist in the prediction of reaction products and how those uses evolve over time. Preliminary results from this study will be discussed as will the practical implications of the research.

**Modeling Mathematical Behavior**

Tim Fukawa-Connelly

The University of New Hampshire

This poster considers a set of techniques that can be used to understand and improve the context of a traditional (i.e., lecture-based) math classroom, and which could help students develop higher order thinking skills. These techniques, which I call “Modeling Mathematical Behaviors” (MMBs), consist of the instructor demonstrating good mathematical habits by thinking out loud and questioning students during whole-class discussions. I contend that a class taught using MMBs may, in part, dampen the standard criticisms of lecture-based teaching. It appears that mathematicians already incorporate MMBs into their teaching, and asking them to be more explicit about the fact that they are doing so, and explicitly describing to the students what behaviors they are modeling, may improve student learning.

**A Case for a Multi-dimensional Categorization Scheme for Student Understanding of Limits **

Gillian Galle

University of New Hampshire

Most calculus courses define the concepts of derivation and integration in terms of limits. For most students then, a solid understanding of limits is necessary in order to make sense of the later concepts that are introduced. While analyzing data from student interviews to assess student understanding of limits for four first year calculus students, the application of the 7 Step Genetic Decomposition created by Cottrill, et. al. (1996) indicated that the interviewed students possessed no higher than a 3rd step understanding. However, despite being unable to clearly articulate their understanding in terms of the expected lexicon, two students were able to draw highly specific graphs as examples and counterexamples to the points they were making and one student was able to draw on additional knowledge from other parts of calculus. This suggests that the students possess a far more sophisticated understanding of the limit concept than they were able to articulate. Thus, a case is made that the 7 Step Genetic Decomposition accounts for only one dimension of student understanding of limits and that additional criterion that accounts for other relevant aspects of limit knowledge be taken into account in order to accurately diagnose student understanding of the limit concept. In particular, inspired by the work of Fuller, et. al. (2009), dimensions should be added that reflect justification (the types of examples students use when explaining their answers), logical structure (the student's ability to see the applicability of an example to the problem they are trying to solve), and method (the strategy a student applies to solving a limit problem).

**Integration and area: Student misconceptions of a fundamental relationship**

William Hall Jr.

University of Maine

Studies have shown that students are prone to develop a computationally-based view of integration, only associating it with finding an area under a curve. While it is true that definite integrals and area under the curve are inextricably related, it is equally true that this association does not describe the whole of integration. Students view area under the curve as something that must be tangible, something with physical qualities; therefore, they fail to grasp the true nature of the definite integral: an accumulation function. These issues may be thoroughly ingrained in students as studies have also shown that their conceptions of area may also be focused on computation. In this study, 25 students were interviewed about the definite and indefinite integral. It is shown that their understanding of integration is intimately tied to area under the curve. Students were unable to correctly define the definite integral as a limit of Riemann sums and some described area under the curve as if it were a literal representation of a situation or a tangible object such as farmland. Additionally, students extended their area-conception to the indefinite integral stating that it computed the boundless area under the curve. These associations show that students may have a poor understanding of area under the curve and subsequently, may not appreciate the power of integration.

**Students' responses to different representations of a vector addition question**

Jeffrey Hawkins

John R. Thompson, Michael C. Wittmann, Eleanor C. Sayre, Jessica W. Clark

The Univeristy of Maine

Students use multiple methods to add vectors graphically [1], some of them leading to correct solutions, some of them not. We discuss students' responses to four different representations of a single graphical vector addition question, designed to elicit different solution methods. These four questions have vectors arranged in either a head-to-tail or a tail-to-tail orientation and either with and without a grid. These questions were administered to several hundred students at two different universities. We present the prevalence of different methods in students' responses on the four different types of questions. Furthermore, we describe the types of language they used as well as inconsistencies between students' explanations and drawings. Supported in part by NSF Grants REC-0633951. References [1] J. M. Hawkins, J. R. Thompson, and M. C. Wittmann, AIP Conf. Proc. 1179, 161 (2009)

**Lexical Ambiguities in Statistics: Helping Students Understand Random and Randomness **

Jennifer Kaplan Michigan State University

Neal Rogness, Grand Valley State University

Diane Fisher, University of Louisiana-Lafayette

Language plays a crucial role in the classroom. The use of specialized language in a domain can cause a subject to seem more difficult to students than it actually is. When words that are part of everyday English are used differently in a domain, these words are said to have lexical ambiguity. Studies in other fields, such as mathematics and chemistry education suggest that in order to help students learn vocabulary instructors should exploit the lexical ambiguity of the words. Lemke (1990) observed that people connect what they hear to what they have heard and experienced in the past. If a commonly used English word is co-opted by a technical domain, the first time students hear the word used in that domain they may incorporate the technical usage as a new facet of the features of the word they had learned previously. The use of words with lexical ambiguity, therefore, may encourage students to make incorrect associations between words they know and words that sound similar but have specific meanings in statistics that are different from the common usage definitions. We will report the results of a study that is part sequence of studies designed to understand the effects of and develop techniques for exploiting lexical ambiguities in the statistics classroom. In particular, it will describe the everyday meanings students have for the word random at the beginning of a statistics class, the statistical meanings and misconceptions that are developed by students during the class and activities that instructors can use to help students better understand what statisticians mean by random or randomness.

**Qualitative analysis of student difficulties with damped harmonic motion**

Adam Kaczynski

Brian Frank

Michael Wittmann

University of Maine

Damped harmonic motion is a core topic in the University of Maine's sophomore-level mechanics course. In the Intermediate Mechanics Tutorials [1, 2], we have a series of tutorials that address this topic from two different perspectives: first by reasoning conceptually about the dynamics of the physical situation, and later by examining the differential equation of its motion. In each case, students are asked to draw a qualitatively correct graph of the position versus time graph for the damped harmonic oscillator. We observe that the majority of students, regardless of tutorial, only note the change in amplitude, neglecting the change in period and location at which the maximum speed occurs compared to the simple harmonic oscillator. We present examples of common student responses taken from ungraded take-home pretests and classroom video.

**MINDSET: Mathematics Instruction using Decision Science and Engineering Tools **

Karen Keene

North Carolina State University

This poster will describe an integrated mathematics education and industrial engineering project that is an ongoing NSF project. Faculty from four departments (two math ed and two industrial engineering) are working together to design and implement a fourth year high school mathematics project. There are many possibilities of extending this curriculum development and research to the university level.

**The Chem-Math Project & Using Structural Equation Modeling to Determine Freshmen At-Risk in General Chemistry **

Cary Kilner

University of New Hampshire

In my experience as a former high school chemistry teacher I collaborated with a colleague, an exemplary mathematics teacher, to determine what particular mathematics skills students are taught in their mathematics classes vis a vis what such skills chemistry students must have in order to be successful problem-solvers. Through this process I have isolated 25 skill areas I call the Chem-Math Units. I have presented them to practicing high school and college chemistry and physics teachers at many conferences and used their feedback to refine these Units, which can then be used to inform and guide instruction. The Chem-Math Project is best taught in recitation for the less well-prepared students who must then be identified. Hence the use of SEM (structural equation modeling) in order to integrate and appropriately weight the indicator/predictor variables. My emerging protocol is expected to be a more precise placement tool than merely using the SAT-math, a mathematics placement test, or even the Toledo exam as is often done.

**The Emotional Toll of Learning - How Students Experience Programming Assignments
Comp **

Päivi Kinnunen

Beth Simon

UCSD

This study explores how a group of computer science majors experienced the process of doing programming assignments in an introductory programming course taught with a media computation approach and using pair programming. We used Grounded Theory to explicate the experience students have with programming assignments. Using a set of four longitudinal interviews with a purposeful sample of nine students, we see that students experience distinct emotional episodes relating to getting started with their assignment, encountering difficulties, dealing with difficulties, succeeding, submitting assignment, and finishing. Additionally, we observed overarching emotional experiences. Ubiquitously in these various stages of experience were issues of self-efficacy assessment and auxiliary emotional load. The goal of the study is to develop a theory of students' programming assignment experience, rich in detail and grounded in student experience. When completed such a theory may lead to curricular supports, interventions, or tools, to help steer student experience away from the most harmful of emotional tolls.

**Can Freshmen Learn Equilibrium using Simultaneous Equations?**

Eileen Kowalski

US Military Academy

Equilibrium systems are often described by multiple reactions and systems of equations in physical or analytical chemistry courses. In General Chemistry courses, these systems are typically simplified to one or two reactions and one equation with one unknown (usually called concentration or reaction tables). Simplifying these systems was especially important before common access to calculators with solve functions or computers with math solvers and spreadsheet programs. However, now that most students have these tools available, we no longer need to be constrained by a lack of technology. Because simplifying the system sometimes obscures the chemistry concepts, we may be able to teach equilibrium more effectively by adopting the method with simultaneous equations. Can college freshmen learn equilibrium using multiple reactions described by multiple equations? Our results indicate yes.

This poster compares the results of using systems of equations and the traditional table method to teach equilibrium concepts in General Chemistry. Comparing students' scores on quizzes, tests, and the final exam showed that students using either method performed equally well. Qualitative data from student and faculty surveys supported the systematic method. Results from Think-Aloud interviews with students in each group will also be presented.

**Participation patterns within arguments constructed by students in small groups **

Ushiri Kulatunga

Jennifer Lewis

University of South Florida

Our current work focuses on the use of Toulmin's argumentation scheme to trace argumentation in peer-led sessions for a General Chemistry _ course. We utilize a coding scheme based on Toulmin's (1958) argumentation model and a framework for assessing arguments based on both their strength and the extent to which students collaborated in their construction. Data was collected by video recording weekly peer-led sessions with a focus on one or two cooperative learning groups. Analysis of the data has revealed that students frequently engage in co-constructed arguments and support their claims with evidence, but do not elaborate on their reasoning to further validate explanations. Peer leader intervention has shown a positive influence on strengthening the arguments, but students are often able to resolve wrong claims on their own without peer leader assistance. This presentation focuses on the participation patterns of the students in the co-construction of arguments within groups, including findings in which some students provide more challenging components such as warrants, backings and rebuttals while other students provide the simple components such as claims and data. Our study also suggests steps that peer leaders (or others who facilitate small group work) can take in order to address such equity issues.

**Toward Expert Problem Solving: Blending Conceptual and Symbolic Reasoning**

Eric Kuo

Michael M. Hull, Andrew Elby, Ayush Gupta

University of Maryland

Physics and engineering education research have developed strategies to teach problem solving (Van Heuvelen, 1991; Heller, Keith, & Anderson, 1992; Gray, Costanzo, & Plesha, 2005; Litzinger et al., 2006). Such problem solving strategies emphasize the physical conceptual understanding of the problem while translating the problem to a relevant diagram and then to the relevant mathematical expressions, but none employ conceptual reasoning to solve the symbolic equations for the solution. In clinical interviews with two students in an introductory physics course, we have found that one of them, Alex, was able to set up and solve the relevant equations in a “plug-and-chug” way while the other student, Pat, was able to expertly blend conceptual and symbolic meanings of the relevant equation to find a shortcut solution. We model Pat's reasoning in terms of “symbolic forms,” (Sherin, 2001) cognitive structures that combine an algebraic symbol template with a conceptual schema. We argue that strategies to develop problem solving expertise should include such blending of the guts of mathematical operations with conceptual meaning.

**Curriculum Development Addressing Multiplicity, Probability and Density of States in Statistical Physics **

Donald B. Mountcastle

John R. Thompson

University of Maine

As part of our research on teaching and learning in the context of upper-division statistical physics, we are creating a small-group guided-inquiry activity (tutorial) that addresses the discrete binomial distribution and its approximation by the continuous normal (Gaussian) distribution. The curriculum emphasizes the distribution dependence on N, the number of binary trials, making extensive use of computational software with graphical displays, allowing N to span more than six orders of magnitude. These activities provide excellent motivation for examining the increasing density of discrete countable states while approaching the continuum limit, where integration of a continuous density function is required. Thus, we have an ideal opportunity for students to engage the summation to integration transition of integral calculus. The tutorial and a second one with significant revisions were implemented during the past two years. Findings include improvement in recognition that the distributions become increasingly narrowed about the mean with increasing N. However, significant confusion remains between the concepts of microstates and macrostates, and the roles they play in determining probability. This curriculum project continues to be a work in progress. Supported in part by NSF Grants #PHY-0406764, DRL-0633951 and DUE-0817282

Kristen Murphy

Karrie Anderson and Peter Geissinger

University of Wisconsin-Milwaukee

According to the American Association for the Advancement of Science (AAAS) science literacy consists of four common themes: systems, models, constancy and change, and scale. These themes pervade any science course, and scientifically literate students would be expected to be successful in these courses. However, of the four themes for science literacy, scale is the only theme not included in the National Science Education Standards. Because these standards are the model for many state standards, the omission of scale means that this key component of scientific thought is likely to be underdeveloped in students who start college. Through individual student activities on spatial scale with students in introductory chemistry courses, we have found particular weaknesses in students' scaling abilities. Through this we developed two class-wide assessments: a scale literacy skills test and a scale concept inventory. Utilizing these, we have found that students in general chemistry on average were at a novice-level for scale literacy. More importantly, we have found that scale literacy is a better predictor for success in general chemistry than math background or prior chemistry content knowledge.

**A framework for comparison of two intentional pedagogical structures for presenting the concept of a group in abstract algebra classes**

Charlene Newton

Mariah Shrey, Tim Fukawa-Connelly

University of New Hampshire

“What is your intended pedagogical structure?” is not a common query among instructors in the STEM disciplines. In fact, such questioning may meet with puzzled or deflective responses demonstrating unfamiliarity with the question or perhaps a lack of interest in pursuing it. Contrary to current practice, teachers can pose this guiding question to develop a reflective teaching practice. An underlying theoretical perspective for this study is the view that no teaching practice is neutral to beliefs about the learning process and the nature of knowledge. It follows that each teacher holds at least an implicit philosophy of teaching and learning with inherent pedagogical intentions. This study describes two distinct approaches to teaching the same topic, definition of a group, as delivered by two professors of undergraduate abstract algebra courses at a northeastern university. We use two models, Mason's (2008) model for the pedagogic structure of a topic and Shoenfeld's (1998) model for fine-grain analyses of teacher decision-making, to understand and analyze what unfolds in the two classrooms based on the teachers' preparatory decisions and their decisions while interacting with students in the moment. We also examine three connected strands of human psychology, awareness (cognition), emotion (affect) and behavior (enaction), to further explicate the intentional pedagogical structure held by each instructor. This study poses questions about effective ways to compare student learning outcomes for disparate pedagogical structures in the STEM disciplines and suggests implications for teacher professional development.

**What makes something a chemical? Investigating fourth-grade children's ideas about chemicals and their properties **

Mary O'Donnell

Miami University

A potential source of difficulty for students learning science arises from the fact that many words used in formal science instruction are used informally outside of the classroom. “Chemical” is one such word with multiple uses and meanings. We qualitatively investigated the ideas about chemicals that children bring to an instructional setting so that these ideas may be appreciated as a necessary piece in the learning process. Data and results from a qualitative investigation of fourth grade children's conceptual knowledge of chemicals will be presented. Our results will focus on how children identify chemicals and describe their properties.

**Assessing the Effect of Reading Comprehension on Performance in General Chemistry**

Sam Pazicni

Daniel Pyburn, Elizabeth Reily, Victor Benassi

University of New Hampshire

A March 24, 2010 New York Times article entitled “Stagnant National Reading Scores Lag Behind Math” reported that “… scores continue a 17-year trend of sluggish achievement in reading that contrasts with substantial gains in mathematics during roughly the same period.” While mathematical ability has long been implicated as critical for learning Science, the role reading ability (or the sluggish rate at which our nation's students appear to be improving in this area) plays in learning Science has remained largely uninvestigated. Previous work has shown that while most first-year science course require students to read challenging science texts, most enrolled in first-year courses are not proficient at comprehending text that is dense with information. Therefore it is logical to hypothesize that reading ability will correlate in some way with course performance and can be used as a predictor of success in introductory Science courses. The present study investigated the effect of reading ability on performance in a one-semester general chemistry course. Here, we show that reading ability correlates significantly with general chemistry course performance even when more typical factors (mathematical ability, background knowledge, etc.) are controlled for. We also report the use and analysis of a an intervention strategy designed to aid low-skilled readers.

**Student Use of Integrals in Introductory Electromagnetism: Electric Field and Electric Potential Difference **

Jeffrey Polak

Ruth Chabay

North Carolina State University

The calculus concept of integration is important to many of the electromagnetism topics usually introduced in most second semester calculus-based physics courses. Introductory students in both traditional and reformed courses use integration to calculate electric fields from charged objects and to calculate changes in electric potential along paths through regions of electric field. While students have difficulties with both of these types of problems, casual observations from teaching and working with students suggests that they might be treating the concept of integration differently in these two physics contexts. Interviews were conducted with students in a Matter & Interactions course in an attempt to understand how students work with integrals in the contexts of electric field and electric potential difference. Preliminary observations from this data will be presented. An understanding of how students apply integration in different physics contexts may allow for improved instruction that focuses on the important connections between the relevant mathematics and physics concepts.

Videocases for teaching proof

Manya Raman

Jim Sandefur, Kay Somers, Connie Campbell, Geoff Birky

Umeå University

This project uses videocases to teach proof to students at the undergraduate level, typically in an "Introduction to Proof" type course. The idea of using videocases is to make visible the mathematical processes that usually remain invisible, such as how to use examples meaningfully and how to find the right level of detail to communicate a proof idea. With support from NSF, my colleagues and I have made and edited approximately 20 videocases of students working on proofs and piloted them at a number of colleges around the US. I will share a few of these videos, as well an ongoing blog where instructors share their experiences about how to use these videos, and discuss some lines of future research.

**Student understanding of the concepts of substance and chemical change**

Amy Robertson

Peter Shaffer

University of Washington

The Physics Education Group at the University of Washington is currently examining the learning and teaching of the particulate nature of matter. Populations include K-12 teachers and university undergraduates in introductory physics and chemistry courses. As a part of this investigation, conceptual and reasoning difficulties with the basic ideas of substance and chemical change have been identified. Some of the findings, together with comparison of results from previous studies involving K-12 students, will be presented. Instructional strategies for addressing known difficulties will also be discussed. This work has been supported under a National Science Foundation Graduate Research Fellowship.

**Student Ratio Use and Understanding of Molarity Concepts Within Solutions Chemistry **

Stephanie Ryan

Donald J. Wink

University of Illinois at Chicago

Even though students may have proficiency in using ratios in chemical calculations, their conceptual understanding of these ratios may be lacking. In this study, we focus on one such ratio, molarity. Molarity is both an important calculational tool in dilution and concentration problems, as well as in other fields that use chemistry. It is also an important concept in solutions chemistry, since it is a ratio between two extensive properties (moles and volume). Thus many molarity problems involve an understanding of ratio and proportions as well as an understanding of chemistry at the macroscopic, symbolic, particulate, and quantitative levels. As mathematics literature suggests, students have different levels of sophistication when it comes to the use of ratios (e.g. Clark, Berenson, & Cavey 2003). This poster presents an ongoing study of how students are solving various molarity problems that explicitly examines the use of ratio would also be revealing in the diagnostic sense. This research intends to answer three research questions: 1) What are students' interpretations of molarity in solutions chemistry? 2) Are there patterns in how students use ratio in their solving strategies for molarity problems? and 3) Do students' understandings of ratio vary from domain specific tasks to structurally isomorphic tasks? The various understandings that students hold regarding ratio and molarity and how they use ratios while solving molarity will be studied through interviews analyzed by basic interpretive qualitative methods with a grounded theory analysis. This poster will focus on the design of the tasks and interview questions. Preliminary data may be included if any participants are enrolled before the conference.

**Computing Education Research **

Beth Simon

University of California, San Diego

We'll overview the recently revived computing education research community and report a few notable recent results in computing preconceptions, a student-generated online self-assessment environment, and large multi-institutional studies of introductory student performance.

**Addressing student difficulties in statistical mechanics: The Boltzmann factor**

Trevor Smith

John R. Thompson, Donald B. Mountcastle

University of Maine

As part of research into student understanding of topics related to thermodynamics and statistical mechanics at the upper division, we have identified student difficulties in applying concepts related to the Boltzmann factor and the canonical partition function. With this in mind, we have developed a guided-inquiry worksheet activity (tutorial) designed to help students develop a better understanding of where the Boltzmann factor comes from and why it is useful. The tutorial guides students through the derivation of both the Boltzmann factor and the canonical partition function. Preliminary results suggest that students who participated in the tutorial had a higher success rate on assessment items than students who had only received lecture instruction on the topic. We present results that motivate the need for this tutorial, the outline of the derivation used, and results from implementations of the tutorial.

**Collegiate Mathematics Teaching: An Unexamined Practice**

Natasha Speer

University of Maine

Though written accounts of collegiate mathematics teaching exist (e.g., mathematicians’ reflections and analyses of learning and teaching in innovative courses), research on collegiate teachers’ actual classroom teaching practice is virtually non-existent. We advance this claim based on a thorough review of peer-reviewed journals where scholarship on collegiate mathematics teaching is published. To frame this review, we distinguish between instructional activities and teaching practice and present six categories of published scholarship that consider collegiate teaching but are not descriptive empirical research on teaching practice. Empirical studies can reveal important differences among teachers’ thinking and actions, promote discussions of practice, and support learning about teaching. To support such research, we developed a preliminary framework of cognitively-oriented dimensions of teaching practice based on our review of empirical research on pre-college and college teaching.

**Assessing Secondary and College Students' Understanding of the Particulate Nature of Matter: Development and Validation of the Structure And Motion of Matter (SAMM) Survey **

Marilyne Stains

Hannah Sevian

Marta Escriu-Sune

Myrna Lisseth Molina Alvarez de Santizo

University of Massachusetts Boston

The development of learning progressions has been at the forefront of science education for several years. While understanding students' conceptual development toward 'big ideas' in science is extremely valuable for researchers, science teachers can also benefit from assessment tools that diagnose their students' levels of understanding and trajectories along these progressions. In this poster, we will describe the development and validation of a teacher-friendly survey (the Structure and Motion of Matter - SAMM - survey) designed to measure students' trajectories along aspects of a research-based learning progression on the particulate nature of matter. Specifically, the survey assesses students' conceptual understanding along four dimensions: the structure of solute and solvent substances in a gas solution, the origin of motion of gaseous solute particles, and their trajectories. Since we also intended the survey and its scoring scheme to be used by science education researchers, the SAMM survey and its scoring scheme have undergone rigorous validation and reliability studies. Results of the criterion validity study indicate that the SAMM survey is well-grounded in theory, and the results of the test-retest study indicate that the survey is also reliable. Finally, inter-rater reliability studies indicate that the an Excel-based scoring scheme associated with the SAMM survey can be used reliably.

**A first-year course in nanoscience: how an interdisciplinary course can "glue" together a student's discipline-based science foundation **

Dan Thomas

Peggy A. Pritchard

University of Guelph

A new major in the B.Sc. program at the University of Guelph was created in Nanoscience in 2008. The field of nanoscience has been growing in significance at the interface between chemistry and physics. While graduate study opportunities have been around for sometime, it has only been recently that work at the undergraduate level has been available. Interestingly enough, while the field is springing up from the Chemistry/Physics/Biology interface, the first undergraduate degree opportunities have all been found in Engineering or Applied Science programs. While recognizing that students require a broad foundation in all of the sciences, we also felt that students needed to be involved in some educational activities in their first year that they could clearly identify with the major they had selected. An introductory course in nanoscience was developed to provide a forum wherein they could explore how their other discipline-based science courses - Biology, Chemistry, Mathematics, and Physics - were woven throughout their newly-chosen field. We hoped to help students understand why they were taking the other courses and to open their minds to future possibilities. Integral to the course was the development of their scientific writing abilities. Throughout the course we provide help with reading scientific papers and writing for a lay scientific audience. A major course component centered around the writing of a nanoscience paper that went through a double-blind peer-review process and culminated in a selection of the student's papers being published in an electronic journal - Da Vinci's Notebook. Students have been enthused by the prospect of being a published author be the end of their first semester and have benefited from the classes in information technology, tutoring with university staff science writing specialists, and participation in the peer reviewing of other's papers. This poster will describe the class, its various activities, and how it has helped develop these transferable skills while also embedding the course content within the traditional disciplines.

**iMAPS: An integrated mathematical and physical science course in first year **

Dan Thomas

University of Guelph

dfthomas@uoguelph.ca

Chemistry

A full-year course entitled "Integrated Mathematical and Physical Sciences" is being developed at the University of Guelph, targeting all entering physical science majors. The single course will constitute 60% of a student's first year credit. The poster will discuss the development process - which is still on-going - other models examined, nature of the interdisciplinary collaboration between development partners, and the process followed to secure institutional approval and support. Concerns surrounding this intensification will be examined as well as the anticipated learning benefits. This is not intended to be an elite program and the greatest beneficiaries are expected to be students in the middle and lower echelon of current classes. Regular, non-graded assessments will be used to identify at risk students even before the first class and continually through out the course. Such students will be directed to various remedial learning activities to help ensure their ultimate success in the course. The overall plan is to create a course which is organized along thematic lines, rather than disciplinary content. The commitment, however, is to develop students that are as prepared or better prepared for continuation into their second year.

**Investigating student understanding of thermodynamics concepts and underlying integration concepts **

John Thompson

Donald Mountcastle

University of Maine

As part of work on student understanding of concepts in advanced thermal physics, we are exploring student understanding of the mathematics underlying physics concepts. One area in which we have done this is with integration in the contexts of thermodynamic (P-V) work, which is process-dependent, and changes in internal energy, a (process-independent) state function. Physics majors answered paired questions, one in a physics context and the other an analogous integration question stripped of physical context, to investigate whether some of the difficulties identified as physics conceptual difficulties could have origins in the mathematics. We found similar difficulties in the work and one-dimensional integral questions. With state functions, student performance strongly favored the physics version. We also asked the math questions to calculus students, with similar results. Our findings have implications for mathematical roots of some physics

**The utility of Lewis structures: A mixed-method study of the students' view of the significance of Lewis structures **

Sonia Underwood

Nathaniel Grove

Melanie M. Cooper

Clemson University

Lewis structures serve as an essential link between chemical structures and their properties. However, our prior research shows that many students fail to recognize this connectivity, instead focusing on a compound's surface features. Using responses from student interviews and open ended questions, a survey instrument was developed to determine students understanding of the purpose of Lewis structures and was administered to students in first and second semester general chemistry and second semester organic chemistry. The results of this study will be presented along with implications for classroom instruction.

**Embodied Mathematics: Gestures and Language as Signs of Emergent Meaning**

Michael C. Wittmann

Katrina E. Black

University of Maine

We often talk about the physics concepts students must learn, their misconceptions when they make mistakes, and the resources they activate when they use intuitions to guide their reasoning -- different kinds of pre-existing ideas to be learned, understood better, or activated. We can also make fewer assumptions about pre-existing ideas and consider responses created dynamically, in immediate response to a question. In this poster, we use gesture and language to look at what students are doing while solving a simple algebra task in the middle of a larger physics problem. We present two examples, one from interviews of wave propagation and the other from videotaped groups involved in the algebraic manipulation of separable differential equations. We suggest that co-incident shifts in language use and gesture are signs of the emergence of newly constructed ideas.

**Revisiting Function Ideas in Undergraduate STEM Courses**

Michelle Zandieh, Arizona State University

Chris Rasmussen, San Diego State University

The goal of this poster presentation is to begin a conversation about the role of function in various undergraduate mathematics and science courses, with an eye toward initiating an interdisciplinary research project that examines the ways that students think about and use function in the context of various undergraduate STEM courses. While the concept of function is pervasive in undergraduate STEM courses, occasions for instructors and students to explicitly revisit this important topic largely go untapped. To begin the discussion, we share preliminary findings from end of the semester individual interviews with 10 linear algebra students. The interviews examined how students thought what a function is and their understandings about ideas related to function such as domain, range, one-to-one, inverse, and composition. The interviews probed students' understandings of each of these ideas in the context of linear transformation, and how their understandings compared to the way they think about function in the context of precalculus or advanced high school algebra. Implications of our findings, especially in relation to prospective secondary school teachers, will be discussed.