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Ninth Annual Symposium Series on Excellence in Teaching Mathematics and Science: Research and Practice
ABSTRACTS for PLENARY AND BREAKOUT SESSIONS January 26 Plenary Talks Opening plenary session Developing assessment for learning with teacher learning communities (click for power point presentation) Dylan Wiliam, Deputy Director of the Institute of Education, University of London In this presentation, Dylan Wiliam will outline the research evidence that shows why we need to raise achievement in mathematics and science, why investing in teachers is the answer, and why supporting teachers to make greater use of evidence about student achievement to adjust their instruction should be the focus of that investment. The presentation will also show that in order to make that investment effective, it will be necessary to adopt different models of teacher professional development than have been common in the past, namely school- and college-based teacher-led learning communities. Closing plenary sessionAssessing Science Learning in 3 Part Harmony Richard Duschl, Professor of Science Education, Rutgers University New ‘science studies’ views about the nature of science focus on understanding the social, cognitive and epistemic processes taking place in the refinement and articulation of scientific theories and scientific models. New tools, theories and technologies are shaping the images of scientific inquiry. Recommendations from the NRC report “Taking Science to School: Learning and Teaching Science in Grades K-8” advocate similar refinement and articulation processes in young students science learning processes as they build theories and models. I will present a curriculum, instruction and assessment model based on Project SEPIA classroom research that seeks to develop epistemic (i.e., knowledge building) communities of practice. Two key features for building epistemic classroom communities will be presented; 1) employing the ‘Assessment Conversation’ instruction strategy to promote dialogic discourse processes; and 2) formative assessment strategies in 3 goal domains – conceptual goals, epistemic goals and social goals. Focusing on the scientific practices and argumentation discourse processes associated with theory-building and model-based reasoning has implications for the design of instruction sequences that promote learning progressions across grade bands.
January 26 Breakout Sessions Scheduling of the breakout sessions is subject to change.Session I 1:45 – 2:45 pmAssessment for learning with teacher learning communities: putting it into practiceDylan Wiliam, Institute of Education, LondonIn this breakout session, participants will learn about the five key strategies and the one big idea of assessment for learning. We will explore a range of techniques that teachers, in both schools and higher education institutions, have used in embedding these strategies into their own teaching. Participants will also learn about how to set up their own learning communities. What does it mean to "understand" science or math: a group discussionJoel Michael, Rush Medical CollegeWhen asked what they want their students to achieve, most faculty will volunteer that they want their students to "understand" their discipline (whether math or science). If pushed to define what they mean by "understand," faculty typically find it difficult to generate a useable (i.e. operational) definition. In this session will generate possible definitions for what it means to "understand" something and attempt to reach consensus on an operational definition. We will then discuss how this definition can be used by faculty in planning and delivering their course and then assessing their students. Sex Ratio: Misconceptions and ImplicationsOfra Peled, National-Louis University in ChicagoIn this breakout session we will discuss the importance of the human sex ratio (defined as the ratio of males to females in a given population) as a case study of dispelling misconceptions among students in secondary and post-secondary settings. The sex ratio is discussed in every General Biology course in the context of genetics, sex determination, and phenotypic ratio among offspring. We will discuss briefly how the sex ratio is determined biologically and how natural selection works to stabilize it. We will also discuss the extent to which human actions can affect sex ratios, for example is it possible to influence the sex of one’s children? And could demographic trends expressed as skewed sex ratios in India and China be associated with social practices of neglect and infanticide? In General Biology classes, we have found that students hold strikingly unbalanced beliefs regarding human sex ratios in their own communities. Our analysis of questionnaires suggests that most students perceive a huge proportion of females, both in the newborn and in the adult populations. Possible reasons for the misconception will be explored, and a teaching method that empowers students to dispel their own misconceptions by collaboration and discovery will be described and assessed.
Using History of Mathematics to Teach MathematicsSharon O’Donnell, Chicago State UniversityThe method of completing the square used to solve quadratic equations dates back to ancient geometric methods of solving quadratic equations. A more recent algorithm for extracting square roots has its “roots” in an ancient geometric Chinese algorithm. A modern algorithm for converting repeating decimals to fractions appears in an early 20th century arithmetic book. Although technology now does the work for us, exploring various methods fosters mathematical understanding. This session will look at algorithms such as these and how they can be incorporated into History of Mathematics courses as well as courses for pre-service mathematics teachers and others. Participants are encouraged to share other older and/or lesser known algorithms with which they are familiar. Handouts will be provided. Session II 3:15 – 4:15 pm
Building and Evaluating Science ArgumentsRichard A. Duschl, Rutgers UniversityIn Part 1 of the session, participants will complete a few activities from the “Earthquakes and Volcanos” SEPIA Unit in order to develop a sense of the conceptual, epistemic and social goals of the unit. In Part 2 we will turn our focus to the examination and assessment of student work samples. Through discussions of student work we shall deepen our thinking and understanding about how to progress students’ toward the goal of building a scientific argument.
Creating Interactive Mathematics Web Pages The speaker is the creator of CaluMath, a free software package that facilitates the construction of interactive web pages involving mathematics. A user-friendly web interface easily enables mathematics instructors to create their own interactive web pages and modify pages created by others. CaluMath can be used in any grade level, from K-12 through university. Purdue Calumet is piloting CaluMath web pages in its College Algebra class. The first part of the session will focus on two topics: 1. An introduction to CaluMath and the creation of web pages using it. 2. A demonstration of CaluMath pages targeted at various grade levels, with particular attention paid to the College Algebra pages piloted at Purdue Calumet. The latter part of the session will be a discussion focusing on the types of pages and their use in the classroom that the session attendees envision, along with pedagogical issues they would like addressed. It is hoped that this discussion will begin a dialog leading to the modification of CaluMath College Algebra pages to the high school setting. The CaluMath College Algebra pages can be found here: http://ems.calumet.purdue.edu/mcss/psturbek/CaluMath/cas_college_algebra/MA153 home page.html The home page for the CaluMath project can be found at: http://ems.calumet.purdue.edu/mcss/psturbek/CaluMath/CaluMath_HomePage.html
No Adult Left Behind? How does a high school dropout or an immigrant get a high school diploma? Two small, unique, high school completion programs in Chicago graduate students in one year or less based on their academic work (evening classes) and credit for life experience. The St. Leonard’s Adult High School is in its sixth year serving mostly previously incarcerated persons. The Dorothy Stang Popular Education Adult High School is a bilingual program in its third year working with mostly immigrant Latino/as. Graduates from both programs have enrolled in baccalaureate programs. These programs are linked by their history and faculty (all volunteer) and are inspired by alternative high school programs in Chicago in the 1970s and by the ‘popular education’ practices of Paulo Freire and others. A unique feature of the programs is ‘group’ which builds community and integrates dialogue and reflection into the weekly experience of the students. This breakout session will be led by faculty from both programs and will engage the participants in a dialogue about the curriculum, especially ‘group’ and the math and science content of the programs.
Activities Which Support Student Leaning Sharon O’Donnell, Chicago State University In this session, the presenters will lead the participants in several activities, which the presenters have used, in their “math for liberal arts” classes. The students in these types of classes are not math majors and, in fact, many of them have a poor background in math and/or have “math phobia”. Therefore, in order to enable the students to have success in this math class, the material must be presented in new and interesting ways. One way to do this is by incorporating “hands on” activities in the class. The activities come from a survey course at Columbia College in which some algebra, geometry, trigonometry and exponential functions are taught. One of the activities that the participants will do will require that the participants understand the physical problem and then apply the right triangle trigonometry in order to solve it. Another activity involves the use of gears while in another the participants will prove the Pythagorean theorem using a puzzle. Depending on time, more activities may be used. After each activity, there will be a group discussion on how the activity enhances student learning and why activities should be incorporated into the math classroom. Tips will be given as to how to create your own activities for your classroom. This break out session will be a workshop in which participants will do some activities. All materials and equipment will be provided. After each activity, there will be a group discussion.
Opening plenary session Researching K-16 Mathematics Classrooms: Kathryn B. Chval, Assistant Professor and Co-Director of the Missouri Center for Mathematics and Science Teacher Education at the University of Missouri-Columbia. The No Child Left Behind Act of 2001 (NCLB) elevates the importance of educational research and thereby provides opportunities for mathematics education researchers in its support for and funding of rigorous research studies and its requirement of effective, research-based practices. At the same time, by demanding more of overburdened teachers and administrators, NCLB may exacerbate a long-standing gulf between educational research and practice. In this session, Dr. Chval will discuss her recent experiences with conducting school-based and university-based research to illustrate how educational research can be impeded by the added demands of NCLB and other factors in the current climate. In addition, Dr. Chval will encourage researchers and practitioners to work together to capitalize on NCLB’s increased emphasis on educational research to create a systematic approach to bridging the research-practice gulf. Closing plenary sessionWho Can Do Math and Science? Danny Bernard Martin, Associate Professor of Mathematics Education and Mathematics and Department Chair of Curriculum and Instruction at the University of Illinois at Chicago. Embedded in recent mathematics education and science education reform movements are stated concerns for equity and diversity as evidenced by slogans such as Mathematics for All and Science for All. These concerns about equity and diversity are partly related to a desire to eliminate differences in achievement and participation among various subgroups of students. Researchers and policy makers have conceptualized these differences as racial achievement gaps. Additionally, concerns for equity and diversity in mathematics and science education have been fueled by a desire to maintain United States competitiveness in an increasingly technological world. Linking these concerns is the belief that more rigorous mathematics and science education for underrepresented students will provide a more diverse workforce and address shortages in many technical fields. In this presentation, I draw from my research and mathematics teaching experiences in middle school, high school, community college, and university contexts to offer a critique of this equity and diversity rhetoric, with a particular focus on the notion of a racial achievement gap. I bring to bear (a) critical perspectives on the purposes and goals of mathematics and science teaching and learning, (b) the power of research on the sociology of race, and (c) data gathered from African American mathematics and science learners. March 23 Breakout Sessions Scheduling of the breakout sessions is subject to change.Session IPreparing to Teach Mathematics: Considerations and Challenges Preparing undergraduates to teach mathematics using innovative and relevant methods is challenging. In this session, Dr. Chval will facilitate a discussion with undergraduates related to the teaching of mathematics. Other participants will have the opportunity to observe the discussion. The session will conclude with an opportunity for observers and undergraduates to pose questions. Developing Leaders Through Peer Facilitation in STEM Disciplines In this presentation we will describe the Gateway Science Workshop (GSW), a peer-led small-group learning program at Northwestern University, and the accompanying peer-leader training program. We will also present results of follow-up exploratory studies that evaluated the perceived long-term impact of the program on peer facilitators. The session will continue with an audience discussion about how this peer-leader program compares to similar programs at other, possibly quite different, institutions and how we can all learn from each other to continue to improve our training programs. Making Proof Meaningful Two-column proof is a common, but highly questioned, component of many high school geometry courses. In my own experiences as a teacher, I often felt that my students were able to write correct proofs without truly understanding the concept of proof. In order to combat this problem, I have chosen to teach the two-column proof format in a broader context of logical reasoning and proof in general. The break-out session will begin with an introduction to the way logical reasoning was discussed in my classes. I will then demonstrate how these ideas were connected to two-column, and other forms, of proof. The goal is for session participants to begin thinking about how to help students improve their reasoning, particularly in the context of a high school geometry course, but also hopefully in a broader context. Lively discussion – and challenging questions – will be encouraged.
Session IIBeyond the Rhetoric of Mathematics and Science for All: The goal of this seminar will be to encourage participants to reflect on their own teaching and research experiences in the context of concerns for equity. I will encourage participants to address fundamental questions such as (1) what do we mean by equity in mathematics and science education, (2) why should students learn mathematics and science, (3) how do students and teachers experience mathematics and science through racial, and other, social identities, (4) who should teach mathematics and science to underrepresented students of color, and (5) what are some successful strategies and conceptualizations of mathematics and science education that contribute to more equitable and meaningful experiences for underrepresented students of color? How can we help our students gain an "understanding" of science or math: Furthering the discussion When asked what they want their students to achieve, most faculty will volunteer that they want their students to "understand" their discipline (whether math or science). If pushed to define what they mean by "understand," faculty typically find it difficult to generate a useable (i.e. operational) definition. In this session will generate possible definitions for what it means to "understand" something and attempt to reach consensus on an operational definition. We will then discuss how this definition can be used by faculty in planning and delivering their course and then assessing their students. Clickers in the classroom Would you like to know how well your students can apply course material as you are presenting it to them? Would you like to have everyone answering 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? Student response systems (SRS) also known as clickers, allow faculty to ask questions, get immediate feedback and full student participation in classes of any size. In this session, clickers in hand, we will explore different types of effective questions, and explore different ways on using these systems to stimulate student engagement and provide immediate feedback about learning. Opening plenary session Studying scientific inquiry close to the classroom Donald J. Wink Teaching scientific inquiry is part of the dynamic of science education throughout K-12, college, and in graduate school. This talk will present work that has been done to support student learning about inquiry in diverse classroom settings, unified by a theme of examining how classroom inquiry does, or does not, intersect with inquiry as it is done in authentic science settings. The talk will include references to theories about inquiry and how inquiry learning can support content learning. The potential of the pedagogy embedded in the Science Writing Heuristic method of laboratory work will be discussed with specific examples from college and high school classrooms. Closing plenary sessionPutting the Cart Before the Horse: An analogy for mathematics instruction Susan L. Forman Most mathematics textbooks and, hence, instructors, teach the tools of problem solving (filling students’ carts) before making brief, if any, reference to the kinds of authentic problems those skills can be used to solve. Our presentation will put forward the notion that in an applications-based course, the driving force (the horse) is an interesting, authentic problem that will motivate students to learn the skills needed to solve the problem. We will present examples of problems in mathematics and science that will challenge students and help them to understand the necessity of learning the requisite skills. Problems will be selected from both high school and college mathematics ranging from developmental mathematics through calculus and more advanced topics. May 4 Breakout Sessions Scheduling of the breakout sessions is subject to change.Session IExperiences of Disciplinary and Design Inquiry This session will include two activities that give participants experience with inquiry in two different dimensions: disciplinary and design. The activities have been chosen to allow participants to work through an experience that students might use. We then reflect on the nature of the science content that is associated with that particular experience, noting where prior knowledge, acting-with-intent, and reflection on results occurs. Steps that support the formation of new concepts will be noted. The activities will both be drawn from chemistry, but they will be accessible to non-chemists also. Proof in Geometry Why does it take a high school geometry text six lines to prove that if two line segments have the same length and equal line segments are taken away, the resulting segments have the same length? Contrast this with the first proposition of Euclid. Construct an equilateral triangle. Euclid has 5 postulates; this book has at least 25. Did Euclid miss that much? What did he miss and how did this lead to the current book? We have two theses: proof is a way to organize information; the choice of axioms fundamentally affects the ability of high school students to learn to prove. http://www.math.uic.edu/~jbaldwin/pub/loggeomfor.pdf Modeling with Quadratic Functions In order to understand quadratics, it is helpful to explore their behavior, their quirks, and their special needs. In this hands-on workshop, we will explore quadratics using multiple approaches (geometric, numeric and algebraic) to solidify the characteristics of quadratics. Teaching Science Integrating Technologies and Mathematics In this session we will present innovative approaches for integrating science and mathematics, community outreach and hands-on, inquiry-based learning, from our experiences working with Chicago middle school teachers. The work is a collaboration of three programs: • The Middle School Teacher Quality Enhancement (MSTQE) is collaboration with Northeastern University, Truman College, Wright College, and schools that prepares cohorts of pre-service math and science teachers thru math-science paired courses. • NASA’s Star Partners Pre-Service Institute in Puerto Rico. This program accepts approximately ten MSTQE pre-service teachers annually. • SciTech Hands-On Museum collaborates with both programs through outreach and student visits. Our presentation focuses on teaching environmental science by modeling a variety of instructional strategies used in these programs, and emphasizes the contribution of outside venues in science education. Discussants will present the goals, achievements, problems and model activities from their different perspectives: inviting audience participation and insight, and possible participation in future programs. This will be followed by a Q&A session focusing on the practical aspects of implementing an integrative science-math-technology approach in Chicago Middle Schools.
Session IITeaching prospective (and current) teachers of mathematics to use an applications-based approach to mathematics instruction We never know which of the students sitting in our classes will become teachers of mathematics, since those decisions are often not made until after students have completed some number of courses, including mathematics. This session will offer ideas for helping prospective (and inservice) teachers of mathematics to use an applications-based approach to instruction. We will include discussion of activity-based learning and present examples of the kinds of problems suitable for students at a wide range of levels of mathematics. How do we know if our students understand science or math? Understanding science or math means being able to apply what you know to solving problems (Simon, 2001). As teachers of science or math, what we need to do in our classrooms to help our students understand our disciplines is to provide hem with opportunities for active learning. The final question is how do we know if our students understand something? Participants will share their ideas about assessing student understanding, not just measuring how much material they have memorized. Classroom Supplements: Field Trips and Student Collaboration Research and experience converge on the importance of shifting from a passive lecture approach to an active approach facilitating student-student interactions. Nelson has presented a number of studies indicating that structured student-student learning is a powerful tool we have for increasing achievement. Chickering and Gamson concluded, “Good learning, like good work, is collaborative and social, not isolated.” This presentation discusses specific approaches to enhance student achievement by student-student collaboration outside the classroom. The author describes how field trip experiences can be used to achieve learning objectives in an environmental science course. Some successful approaches to enhance learning with student-student collaboration after class are also described. Strong and weak students in statistics and algebra courses have worked together to understand quiz errors. Audience members will be encouraged to share experiences that have enhanced learning outside of the classroom. |
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