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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.


Exploring Heuristic Reasoning

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.

Structure, structure everywhere, but not the one unique

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.