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Eleventh Annual Symposium Series on
Excellence in Teaching Mathematics and Science:
Research and Practice
ABSTRACTS for PLENARY AND BREAKOUT SESSIONS
February 6 Plenary Talks
Opening plenary session
Mathematics Curriculum and Instruction: A DNR Perspective
Guershon Harel, San Diego University
This talk is on two fundamental questions: what is the mathematics that we should teach in school? and how should we teach it? The goal of the talk is twofold: to present a pedagogical stance on these two questions and to demonstrate this stance with an actual mathematical lesson. The stance is oriented within a broader theoretical framework, called DNR-based instruction in mathematics. The initials D, N, are R stand for three foundational instructional principles in the framework: duality, necessity, and repeated reasoning.
Closing plenary session
Use of the Surveys of Enacted Curriculum for Improving Mathematics and Science Education
Rolf Blank, Council of Chief State School Officers
The Surveys of Enacted Curriculum are a practical, reliable set of data collection tools being used with teachers of Mathematics, Science, English language arts, and Social studies to collect and report consistent, comparable data on current instructional practices and content being taught in classrooms. The resulting data provide an objective method for educators to analyze the degree of alignment between instruction and standards and assessments. Teachers complete the Survey questions through an online, web-based system. The web-based reported data are used by educators and leaders for: a) Aligning classroom instruction with state standards and assessments, b) Evaluating effects of initiatives such as professional development in improving instruction and learning, c) Data-driven school-based improvement of instruction with teachers, particularly to focus on low performance areas, and d) Measuring indicators of instruction and their relationship to student achievement. Annually, the Surveys system is used by over 10,000 teachers in 30 states. The session will focus on strategies for analyzing and using the SEC curriculum data including the three-dimensional maps and charts, comparing practices among teachers, and analyzing gaps between current practice and goals.
February 6 Breakout Sessions
Current Methods of Evaluating Effectiveness of Professional Development for Mathematics and Science Teachers
Rolf Blank, Council of Chief State School Officers
CCSSO is working to assist states in improving evaluations of the quality of professional development for teachers. Towards that objective, CCSSO conducted a study of professional development programs for teachers across the states in relation to research-based characteristics of high quality, effective activities and methods of evaluation. The session will focus on methods used in the study and findings from analysis of a sample of 25 professional development initiatives in 14 states. One-third of the programs reviewed did have well-developed evaluations that produced findings with measurable effects on student achievement or change in instructional practices. Significant effects of professional development programs for teachers of math and science were found when the programs include focus on content knowledge in the math and science subject areas plus training and follow-up pedagogical content knowledge. A rubric for analyzing professional development programs developed by CCSSO effectively analyzed the characteristics of programs based on existing research in the field on predicting effectiveness. Evaluation tools are now broadly available that have been field-tested and allow measurement of effects of programs on teacher knowledge, classroom practices, and student achievement.
Helping Elementary Classroom Teachers Understand and Use Research-Based Math Strategies That Benefit All Students
Angela Giglio Andrews, National-Louis University
Robert Wright’s Learning and Instructional Frameworks in Number will be shared as well as Les Steffe and Paul Cobb’s Stages of Early Arithmetic Learning. Participants will discuss how these research-based findings can be adapted to the classroom in ways that are effective in reaching elementary students, especially those who are struggling to make sense of mathematics. How can they help the classroom teacher to know:
- where the student is now in foundational mathematics?
- where the student needs to go next?
- how to get the student to that next point?
In addition, participants will discuss:
- the important research issues in early number that classroom teachers should be made aware of.
- the importance of these issues to the success students for whom mathematics is not a sense-making experience.
- how to help classroom teachers implement the practices that research indicates are beneficial within the constraints of the existing math curriculum.
Group discussion will follow synopses of some research issues and anecdotal video clips.
Supporting the Developmental Learner On- and Offline
Betty Constance, Colette Currie, Renée Judd, and Elke Kleisch, National-Louis University
Students enter college with a variety of developmental needs that must be met before the student can succeed at college-level coursework. To address the wide range of student needs, a variety of approaches must be taken. In addition to the traditional stand-alone developmental coursework, NLU has developed a program to pair learning specialists with content faculty in designated “PLUS” general education courses. Using traditional content from the PLUS course, the learning specialist works with students to strengthen skills in areas such as writing, reading, basic math, time management, and identifying effective study strategies. Interventions in on-campus courses take the form of in-class workshops and activities and, in some cases, online support in Blackboard CE8. In online classes, the learning specialist contributes activities for assessment and skill building into the online content presentation. PLUS supports are delivered to all students in a PLUS course, not only to those with identified developmental needs, as part of a larger initiative toward universal course design. Data on the outcome of PLUS course design is presently being collected.
In this breakout session, math and science faculty and a learning specialist who have participated in PLUS classes and other developmental math initiatives will share their experiences, including insights into what worked and what did not, and lead a discussion on strategies for supporting developmental learners in traditional math and science courses.
Examples from DNR-base instruction in mathematics
Guershon Harel, San Diego University
More examples from the DNR based instruction will be presented in this breakout session. Participants will be given the opportunity to discuss the kind of the curriculum that would be oriented within the conceptual framework presented in the corresponding plenary talk.
Identifying and Characterizing the Influences on Systemic Reform of Mathematics and Science in Chicago Public Schools
Stacy Wenzel, Loyola University Chicago and Rachel Shefner, Center for Science and Math Education, Loyola University Chicago
Chicago’s model for reform of mathematics and science education is “systemic,” involving multiple programs, policies and funding sources that impact district administrators, university partners, principals, teachers, and students from kindergarten through grade 12. We have described and analyzed the processes of this reform model with the support of our current exploratory DRK-12 grant (# 07335500, PI Wenzel). A key product of this grant is a comprehensive document, Math and Science Education Systemic Reform in Chicago, 2002–2008, which includes a systems diagram and conceptual framework. The diagram and framework will be the catalyst for a discussion around the issues and influences identified in these documents, their relative influences on the reform, and the consequences of these influences.
Following an introduction to the topic by the presenters, participants will break into small groups to consider a set of questions, after which a full discussion will take place.
An Apple and Many Ideas, How Do You Want to Teach?
Eun Kyung Ko, National-Louis University
This presentation will include the results from a research project. In addition, there will be a discussion on how to teach students who have different ideas about science. A total of 97 elementary students were participated in this study and actual students’ data and activities will be shared with audience. Results indicated that there was no relationship between students’ understandings of evidence-based explanations and their abilities to develop evidence-based explanations (p>.05). The results of this study do not support the appealing assumption held by many science educators that students’ inquiry skills reflect their understandings about scientific inquiry. Instead, the findings suggest that students’ understandings about evidence-based explanations should be assessed separately and that students’ abilities to develop evidence-based explanations should not be inferred from their understandings about evidence-based explanations. Overall, students’ understandings about evidence-based explanations were not well developed compared to their abilities to develop evidence-based explanations. Therefore, it is necessary for science educators to teach both the understanding of evidence-based explanations and the ability to develop evidence-based explanations.
In this breakout session, the science activities from the research project will be shared and participants will discuss how different students’ ideas can be included in their teaching and assessed.
March 6 Plenary Talks
Opening plenary session
Symbols and Science
William McCallum, University of Arizona
What symbolic literacy do students need for careers in science? Traditional courses in high school and college algebra emphasize procedural fluency and word problems, and reform courses emphasize functions, graphical and numerical representations, and modeling. Does either approach prepare students to reason with the
symbolic expressions they encounter in biology, chemistry, and physics? I will consider some examples from these disciplines that bring out the need for a symbolic literacy: the ability to interpret algebraic form, recognize the structure in algebraic expressions and equations, make strategic choices of algebraic manipulations, and
anticipate the results.
Closing plenary session
Understanding evolution: a multidisciplinary educational challenge.
Michael W. Klymkowsky, University of Colorado
While evolutionary theory, as put forth by Darwin and Wallace 150 years ago, is simple, logical, and based on readily observable facts, understanding how evolution works at the molecular level is difficult, since it requires an appreciation of how random changes in genes can lead to useful adaptations at the organismic level. Without such an understanding, students, and most importantly students training to teach K12 science, are left with a fragile and vulnerable belief in, rather than a robust understanding of, evolutionary processes. Yet, it is all too common to find that biology curricula fail to provide students with the conceptual foundations necessary to understand the nuts and bolts of evolution. Topics such as the creative effects of genetic drift, the mechanism(s) by which mutations produce novel activities, the entropy-driven effects that determine molecular and cellular structure, the ubiquity of gene and genome duplication, together with the formation of chimeric genes, and their roles in facilitating evolutionary novelty, are rarely presented. The problem is not, however, restricted to biology; the physics and chemistry courses required of biology students either do not present, or fail to cultivate a clear understanding of critical concepts needed for an authentic understanding of the structure, behavior, and evolution of biological systems. Topics such as thermodynamics (e.g. energy conservation and entropy as a form of energy), statistical mechanics (associated with diffusive processes and a source of energy for bond breaking), network behavior (involved in adaptive and homeostatic processes), and the energetics of bond formation are typically reserved for “upper division” courses or are presented in a manner that generates more, rather than less confusion. I will present some thoughts as to how this situation can be addressed through course and curricular analysis, conceptual assessments (such as the Biology Concept Inventory), and more effective teaching strategies.
March 6 Breakout Sessions
Breakout abstracts schedules are subject to change.
A complete schedule and abstracts will be provided at the sympoisum.
Designing effective educational scenarios for science and math teachers.
Michael W. Klymkowsky, University of Colorado
An ever-present danger in the context of science education is the tendency to misconstrue memorization and algorithmic proficiency for conceptual understanding. While these are important components of a competent understanding of technical materials, they are not sufficient, and can hide conceptual inadequacies. Particularly when training teachers, unresolved conceptual issues (referred to by McClymer & Knoles as “ersatz learning”) can lead to anxiety, stress and insecurity, all of which have wide-ranging negative effects. To address these issues it is helpful to view lesson/course/curricular design through the lens of the intended, assessed, perceived, and learned curricula. This approach, which borrows from a number of sources, requires the instructor to analyze the goals they want to achieve, determine what (exactly) it looks like for a student to achieve these goals, identify the foundational ideas needed to achieved this level of proficiency, determine and address pre-/misconceptions that might interfere with learning, select forms of assessment that reinforce (rather than undermine) the learning objectives, determine whether these assessments actually measure the intended learning objectives, consider how students perceived these assessments and what they need to learn to pass through them successfully. We will consider strategies on how student thinking can be accessed, how metacognition can be fostered, and how assessments can be crafted to generate the learning we intend.
"Clickers" in Class: Engaging Students with Personal-Electronic Response Systems ssssss ssssssssssssss Martina Bode, Northwestern University, Mary Schuller, Northwestern Memorial Hospital, and Denise Drane, Searle Center for Teaching Excellence
Would you like to acquire immediate feedback on your students' learning? Have you ever wanted to know, within moments of presenting material, how well your students can apply what they've learned? Would you like all students to answer questions during class, rather than the same faithful few? Do you wish you could find out more about the opinions and values of your students? In this session, participants will learn how clickers can stimulate student engagement, increase student participation, and provide immediate feedback about learning.
Math and Algorithms in the Information Age gggggggggggggggg hhhhhhgggggggggggggggggggggggg Andrew Harrington, Loyola University Chicago
This session explores new relationships between math education and technology. Python, a simple, powerful environment for executing algorithms, enables this change when linked with newly developed, inexpensive, small computers. Repetitive numerical and symbolic algorithms in secondary school algebra are traditionally taught by hand. Students develop symbol sense, the ability to manipulate and understand abstract symbols, via hand operation of algorithms such as reducing fraction to lowest terms or simplifying linear expressions. . Specialized packages may be provided, like symbolic computer algebra systems (CAS). CAS are controversial because when results just appear, students do not develop symbol sense. In a Python programming environment students can express basic algorithms in a symbolic fashion themselves, giving them a sophisticated symbol sense, and requiring attention to detail. Thereafter they instantly execute their explicit instructions for tedious calculations. This allows more time for mathematical modeling, including interesting, large, real-world numerical problems. Increased ability in mathematical modeling aids in science classes. The introduction to programming and an appreciation of the role of algorithms are other side benefits in this data-centric age. This session introduces examples using Python for basic algorithms. Participants will discuss the path to this pedagogical change.
Advanced Mathematical Thinking (AMT) in the College Classroom
Keith Nabb, Moraine Valley Community College
The presenter will offer a brief portrait of the growing body of research in math education known as “Advanced Mathematical Thinking” (AMT). The heart of the discussion will center on the construction and development of classroom tasks that foster AMT. Such tasks uphold national and state standards for mathematics instruction and, arguably, plant the seeds to dispelling naïve conceptions about mathematics. The results from recent classroom activities typifying AMT will be shared (these will be pulled from Algebra, Calculus and Differential Equations). Finally, the associated challenges facing students and teachers will be discussed. An atmosphere of open dialogue will be encouraged throughout this session.
Session II
Writing Problems for Algebra
William McCallum, University of Arizona
Participants in this breakout will have the opportunity to work with algebra problems designed to test students' conceptual understanding of the symbolic aspect of algebra. This includes
• Recognizing the symbolic form of an expression: In particular, understanding the difference between an expression and an equation.
• Employing algebraic foresight: Being able to see the form of an expression or a solution to an equation without actually finding it.
• Purposeful manipulation: Choosing the appropriate manipulation to achieve a particular purpose.
Biocalculus Courses and Computer Laboratory Projects s s s s ssssssssssssssss s ssssssssgggggg sssssss ss Timothy D. Comar, Benedictine University
Benedictine University has been offering a rigorous two-semester biocalculus course sequence since 2003. The courses emphasize the integration of biology, mathematics, and the use of computational software to analyze biological problems and models. Achieving an appropriate balance of mathematical rigor and biological applications is an important goal for such a course sequence. In this presentation, we address the course syllabus, highlight several of the computer laboratory projects used in the courses, and discuss student success in the course sequence. We also discuss how the course sequence has evolved since its initial implementation, how biological content has been incorporated into other lower level mathematics courses, and challenges for implementing our biocalculus courses as well as other models for integrating mathematics and biology.
Merit Program for Emerging Scholars: How to Retain and Recruit Students in STEM Disciplines sssss ssTracey Hickox, University of Illinois at Urbana-Champaign
The Merit Program at the University of Illinois directly responds to the challenge of having enough trained citizens in the science and technology sectors. The main objective of the program is to recruit and retain students in STEM fields. Special importance is placed on recruiting underrepresented minorities, women, and students from small high schools who have to take first-year general chemistry, biology, and/or mathematics. It is designed to support and encourage students in their studies of these subjects by utilizing Dr. Uri Treisman’s model of collaborative instruction methods. Because of the program’s demonstrated success, we received an NSF grant to expand our student base to students that have not yet declared a major, with the hope that they will choose a career in a math, science, or engineering field. I will briefly give an overview of the program, discuss the results of our qualitative and quantitative studies, and how we involve/recruit students that are interested in teaching as a STEM career. This program can be easily adapted to the community college and high school levels.
In addition, I will demonstrate how I use MasteringBiology™ to enhance my learning goals in the Merit Workshops in Integrative Biology. MasteringBiology is the most advanced science tutorial and homework system available. It is the first to tutor students by responding with answer-specific feedback and optional hints and simpler questions when they get stuck. By tracking all student interaction with the program, MasteringBiology provides instructors with detailed individual and collective student work, allowing one-click insight into their students' learning.
May 1 Plenary Talks
Opening plenary session
Beyond Words: Language(s) and Learning Mathematics
Judit Moschkovich, University of California, Santa Cruz
Language is an important aspect of learning in mathematics classrooms. Whether students are speaking one language or two, learning and teaching involve communication. While questions about language and learning mathematics are particularly important to consider for students who are bilingual or learning English, they are also relevant to all mathematics learners. Research in mathematics education has explored how learners participate in mathematical discourse and research in sociolinguistics has examined how bilingual learners use two languages. This talk summarizes what this research says about how students communicate mathematically and how students use two languages. Drawing on reviews of the research literature, analyses of classroom data, and video clips as examples, I address questions about language(s), discourse, and learning mathematics relevant to research and practice:
- What are mathematical discourse practices? How is mathematical discourse more than words?
- What are common language practices in mathematics classrooms among students who are bilingual or learning English?
- What resources do students use to communicate mathematically? How can instruction build on these resources?
Closing plenary session
Separating Facts From Fads: The Evidence That Educators Need for Effective Science Instruction and Policy Decisions
Philip Sadler, Harvard-Smithsonian Center for Astrophysics
U.S. schools are unique in the variety of teaching methods and curricula used for teaching science. Freedom to choose pedagogies and materials are most often vested with the classroom teacher. Because of this natural variation, we have utilized epidemiological methods to mine the backgrounds of college students taking introductory science courses for predictors of performance and persistence while controlling for demographic differences. In surveying thousands of students in randomly selected introductory college biology, chemistry, and physics courses, we have put to the test educators' cherished beliefs about the kinds of preparatory experiences and key resources that predict successful performance in college . I will report on our findings on the value of lab experience, technology, demonstrations, content coverage, block scheduling, class size, Advanced Placement courses, Physics First, project work, and mathematics preparation. We have also examined the role of teacher subject matter knowledge and pedagogical content knowledge on student gains. Of particular interest is teacher awareness of common student misconceptions as a predictor of student gains.
May 1 Breakout Sessions
Breakout abstracts schedules are subject to change.
A complete schedule and abstracts will be provided at the sympoisum.
Session I
Assessing Conceptual Understanding in Science with Misconception-Based Tests
Philip Sadler, Harvard-Smithsonian Center for Astrophysics
Our team uses research studies of student conceptions in order to generate specialized assessments that measure the degree to which both teachers and their students hold the accepted scientific view represented by each of the K-12 National Content Standards Science. Learn how we use psychometric models that are aligned with cognitive research findings to establish scales and subtests that accurately gauge the scientific understanding needed for teachers to be effective. We will use several examples of powerful test items. Participants will learn how to gain free access to tests in their fields and how to use them for formative assessment purposes.
Convincing prospective secondary teachers that proofs are convincing:
Identifying and addressing the purpose of advanced mathematics topics courses for teachers.
Tanya Cofer, Northeastern Illinois University.
Coursework in advanced mathematics topics such as abstract algebra is required in virtually all secondary mathematics certification programs for teachers. However, recent trends in educational research suggest that we must study how these connections are established and employed, if at all, by prospective teachers. I will share preliminary results from a recent study I conducted that point to the existence of a knowledge gap problem among prospective secondary mathematics teachers. Many of the participants in the study had done well in their advanced courses and were able to provide correct formal mathematical argument when it was clear that such a response was expected. However, in formulating mathematical explanations appropriate for a K-12 school context, participants often argued incorrectly on the basis of the superficial qualities of a given concrete context or they relied on gut feeling or intuition, even when the results competed with correct mathematical argument. As part of this session, I will present an analysis of several interview responses and offer them for group discussion. I will also invite participants to discuss concepts from a variety of advanced mathematics courses for teachers and how these concepts can be presented to help prospective teachers learn to trust and use proof to support their teaching practices.
Using Enacted Curricular Assessment To Align Illinois Middle School Math Standards
Ximena D. Recalde and Brent E. Wholeben, Northern Illinois University
The government has been providing monetary resources and infrastructure to prepare and update teachers’ knowledge and skills to achieve a new goal-- the increase of knowledge among students of mathematics and science. Therefore, the effort of the government with the collaboration of universities and colleges should focus on supplying the knowledge and skills that in-service and pre-service teachers need to accomplish the expected learning goals for the enacted curriculum. Despite all the initiatives from the Department of Education, test scores for mathematics and science have not reached the desired levels. Goals from the Illinois Learning Standards (ILS) were compared to the topics in the Survey Enacted Curriculum (SEC) grades K-8 for mathematics. The topics of the SEC were grouped and categorized based on the ILS goals. The results indicated that the state goals are partially met but need improvement to reach the ILS requirements.
In this session we will work towards an understanding of
• Middle school math classrooms learning activities.
• The alignment of middle school math classroom learning activities and the Illinois Learning Standards (ILS) by using enacted curricular assessment.
• Understanding implications of the lack of alignment between cognitive learning activities and the Illinois Learning Standards (ILS).
Participants will be prompted to share their experiences concerning achieving NCLB learning goals by using enacted curricular assessment. In addition, participants will be asked to discuss possible barriers that exist or may appear while implementing cognitive demand classroom activities at the school, district, and statewide levels.
Session II
Hearing and seeing mathematical discourse practices
Judit Moschkovich, University of California, Santa Cruz
Participants will work in small groups to examine a video case from a mathematics classroom. Through discussion of student contributions, participants will deepen their understanding of mathematical discourse practices. We will address the following questions:
· How are students communicating mathematically?
· What mathematical ideas are students talking about?
· What resources do students use to communicate mathematically?
· How is the teacher supporting student participation in a mathematical discussion?
Implementing, Sustaining, Enhancing, and Evaluating a State Wide Professional Development Program.
Kirsten Fleming and Alice Gabbard, Kentucky Center for Mathematics
The Kentucky Center for Mathematics (KCM) is a state-funded, statewide center housed at Northern Kentucky University. The goal of the KCM is to enhance the teaching and learning of mathematics at all levels. A major strategy used to achieve this goal is to provide research-based, on-going professional development for educators. This talk will cover the evolution of the KCM’s Primary Mathematics Intervention Program; a program now in its third year and one in with 113 schools throughout the Commonwealth participating. Details of the program implementation and results from the program evaluation will be given with an emphasis on how and why decisions about the program were made and lessons learned during will also be shared.
At the intersection of faculty development, program design, and teaching practice–collision or pot of gold?
Richard Kozoll and Steven Rogg, DePaul University
One useful discovery from TIMSS is a process of sustained teacher led professional development long practiced in Japan, called “jugyokenkyuu”, which translates to “lesson study” or “research lesson”. This collaborative practice has gained popularity inK-12 schools in the United States as an alternative to typical professional development, and is part of the more general Professional Learning Communities (PLC) trend. In this session, we will briefly describe two recent research lessons (one on electrical circuits and the other on Newton’s Second Law) conducted in a university setting among classes of preservice teachers. We will then discuss the relevance of this model for faculty development, peer review, instructional design, and teaching practice. Participants will be invited to respond to relevant questions, including: How is faculty development defined and applied at our respective institutions? What are its aims? In an ideal world, how would you prefer faculty development to be defined? How is it supported? In what characteristic ways does Lesson Study compare with current practices? Could Lesson Study serve as the basis for a more viable faculty development model at the university?
Coping with the knowledge explosion in biology in our classrooms: A conversation
Joel Michael, Rush Medical College
The knowledge explosion is alive and well in biology! The 1000+ pages of most introduction college biology textbooks is stark testimony to it. No one expects their students to learn everything in such a textbook. What, then, should we expect our students to learn? One suggestion is that we identify the “big ideas” or “core concepts” of biology and focus our attention on helping students master these ideas. In this session participants will discuss what those “big ideas” might be and how we can build a biology course around them.
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