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These visuals ae incorporated into the conference videos below
Thursday, 13 June 2013
— Welcome & Overview
— Some Reflections on Issues in Implementing Inquiry-Based Pedagogy in Mathematics
G. Edgar Parker, Visiting Professor, Guilford College and Professor Emeritus, James Madison University
— Future of the IBL Project at EAF
Strategic Planning Committee
— Parallel Sessions
Implementing IBL (coordinated by Dana Ernst)
A radically different course structure requires a different assessment regime. We discuss my attempts to use Standards-Based Assessment ideas to be more honest and forthcoming with my students in a (lightly) modified Moore method course.
In this talk, I will share some lessons learned having just implemented IBL in my introductory analysis course for the third time. I will outline specific classroom/course practices that I utilize, with rationale; my approach to assessment of student learning; and discusses successes and ongoing challenges.
I regularly teach at least three IBL courses. They include a second-year course in the Techniques of Proof and two fourth-year courses in Topology and Topics of Geometry. I am also experimenting with my Calculus III class using a technique that revolves around daily presentations by the students rather than around lectures. My version of IBL, except for the Calculus III classes, is modeled after the "Texas" or "Modified Moore" classes that I had as a graduate student at the University of North Texas and Oklahoma State University. It is essential to actively engage every student in these IBL courses. I do this by requiring my students to present their independent work to their classmates in both formal written and oral presentations that everyone in the class understands and accepts. This can require rewrites of results before they are formally accepted. I stress the connection between creating mathematics and the careful use of language. An important aspect of this process often involves working independently outside of class for extended periods of time on difficult problems. The class acts collectively as a group in evaluating the work presented in class. In this brief talk, I will attempt to describe my method of engaging, assessing and grading my IBL students.
The small proportion of proof tasks that exists within high school mathematics textbooks can potentially limit the opportunity for students to engage in proofs, or can devalue the vitality of the process of proving in mathematics. Considering that textbooks are primary sources of the mathematical content to which students are exposed, and that textbooks provide minimal opportunities for students to engage in proofs, intentional actions by teachers can provide students’ an increase opportunity to engage with proofs during enacted lessons. Therefore, this presentation will highlight research findings about high school mathematics textbooks attention to proofs, and suggest strategies to increase opportunities for students to engage with proofs during enacted lessons. To address the shortcoming of textbooks, relative to the amount and nature of proofs posed, teachers can make modification to tasks and carefully plan lessons in order to provide greater opportunities for students to engage with proofs. The selection of proofs and deciding how to unpack them during enacted lessons require considerable thought. Hence, this presentation will seek to identify elements within lessons teachers ought to attend to during their planning and subsequent enactment of proofs.
Around 1996 I began to require class participation as part of the course grade.(I got a little prodding from a provost.)Now I give points for speaking, for working problems at the board and even (lesser credit) for watching problems being worked.I get plenty of participation – from calculus down to algebra and trig! Here is an edited excerpt from my class syllabi:
Counting 5% each, discussion and board work are two pools of points that can transfer from student to student.Each pool is a zero-sum game.Points earned by one student are therefore lost by the other students, and vice-versa. … These pools would seem to be pure competition, but you can, and should, cooperate with each other at the board and in class. You can earn extra credit by getting points from the other students, or by inactivity you can lose points to those others.
Not every student likes what I do.But by respecting the class and valuing their actions (with conversation and course points), I have cultivated lively classes.
To better engage engineering physics students in the learning process, an inquiry-based learning approach to teaching the four semester engineering physics sequence at Victor Valley College has been adopted for the past three years. This presentation discusses the pedagogical approaches, assessment practices, student learning outcome assessments and student reactions.
Joseph Malkevitch, A Sample of Fairness and Equity Mathematical Modeling Situations
Video not available.
Students invariably find questions that involve fairness and equity interesting but are rarely aware of the insights that a mathematical approach to these problems offers. This talk will survey a variety of fairness and equity problems that can be used in Inquiry-Based Learning classes at various levels. Problems explored will include bankruptcy, elections and voting, and apportionment.
In this presentation, I’ll outline an IBL course taught on the theory of combinatorial games.We’ll examine some of the content of the course and I will cite particular aspects which made it successful.This may be of particular interest to those who are looking to teach IBL courses to non-math majors, those whose students aren’t the most intellectually curious, or those interested in another example of IBL in action.Finally, I’ll extend game-playing as a metaphor I have taken to other courses, both IBL and otherwise.
This talk recounts my efforts to implement inquiry-based learning aspects in a junior-level Applied Statistics course primarily populated by upper-division Biology majors, for whom the course is required and is meant to teach them how to analyze their research data. Because of this, it is essentially a service course with a highly prescribed and lengthy syllabus of statistical tests and techniques that must be covered. Strapped for class time and facing a reluctant audience (most Biology majors dread this course), I used open-ended projects to be completed outside of class in an attempt to pique student interest and introduce inquiry-based learning aspects to the course. In this talk, I will present examples of such projects that I have assigned, assess to what extent they achieved these goals and the learning objectives of the course, and discuss how I revised them to better accomplish these goals and objectives. Participants will be invited to share their own experiences and suggestions for incorporating inquiry-based learning into projects and for confronting challenges such as those faced in this course.
Advanced Calculus at Slippery Rock University is a two-semester sequence. The person teaching the sequence had to take an emergency leave for the second half of the 2010-2011 AY and I was asked to take over. To my dismay, the book my colleague was lecturing from was lacking in both content and depth. However, since the students had purchased the book, the text could not just be abandoned. But its shortcomings needed to be addressed. Thus was born Presentation Friday. On Monday and Wednesday I lectured the students following the content of the book. On Friday the students had their turns at the board, presenting solutions to exercises I wrote for this class. In this talk, we will look at the how the problems the students solved enhanced their understanding of theorems from the text, and taught them about both pathological examples and how mathematicians generalize the ideas in the text. We will also talk about student reaction to “changing horses in mid-stream” and how they felt at the end about the Friday presentations.
— Mathematical Heroes:
The journey of independent thinkers and
the computer as a mathematical object
Coke Reed, Interactic Holdings, LLC, Austin, Texas; designer of the Data Vortex network; student of H.S. Wall and R.L. Moore.
Friday, 14 June 2013
The goal of the Legacy of RL Moore Conference is to bring the members of the IBL community together in conversation so that we can share experiences and expertise and trade techniques, triumphs, and tribulations. The RoundTable discussions are microcosms of this community, organized around particular course topics that we are teaching or hoping to teach. If you have participated in the RoundTables in the past, you will notice two exciting, new features this year. First, these discussions are scheduled right after breakfast and while no other sessions are running to allow our conversations to develop fully from introductions and anecdotes to sharing of resources and detailed course structures. Second, we will use the end of our session to share clever ideas between course topics, emphasizing the teaching-problems we have tried to solve. Think of this session as an IBL experience about IBL! This year’s RoundTable discussions will include the following topics: Liberal Arts Math, Math for Elementary Teachers, Linear Algebra, Calculus, Real Analysis, Abstract Algebra, and Graduate Courses, Etc.
Moderator: Martha Siegel (chair of the CUPM)
— Five Minute Talks, Session II
— Parallel Sessions
Mathematics for Education Majors
Mathematical maturity includes the skills to interpret results through the epistemologies of the discipline. I will describe an inquiry-based course structured around an axiomatic development of Geometry, and I will analyze student products for evidence of changes in the level of mathematical maturity. The evidence will include a comparison of concept maps about mathematical truth from before and after the course as well as student reflection writings about the axiomatic method.
IBL teaching methods have been used in courses for future elementary school teachers for more than a decade. In this talk, I will share a set of IBL notes, video resources, and other assignments/tasks with the objectives of developing pedagogical content knowledge, addressing negative attitudes and beliefs about mathematics, and encouraging future teachers to adopt IBL methods in their own teaching.
Hybrid Inquiry Based Learning (HIBL) is a modified version of the Inquiry Based Learning model (IBL). It integrates the traditional teaching approach with the Inquiry Based Learning approach.In this talk, I will present how I used HIBL to teach a Math course to elementary teachers. A practical realistic implementation of the HIBL in classroom settlings will be presented. A description of the HIBL approach, students’ engagement, the challenges, and the assessment methods will all be discussed.
An IBL-skeptic (and previous “expert” at teacher-centered classroom control) has chronicled his experience using IBL techniques in a history of mathematics course. The previous years of teaching the course had always left the instructor dissatisfied on several levels. Using IBL techniques required moderate or at times radical change for this instructor’s instincts of good teaching. But, having stuck through the process, the results have been powerful. The instructor will share and help others share (using IBL techniques and not just a lecture) their experiences, feelings, fears, hopes, joys, etc. as they learn to use IBL. The instructor (and audience) will also share IBL elements of a history of mathematics course that seem to really engage the teachers themselves.
In this talk, I will discuss my experience teaching Intro-to-Proof classes in Inquiry-BasedLearning style. I will talk about successes and failures from the perspective of a non-tenured faculty member at a university with no existing IBL culture among its students.
Video not available.
Over the last several years two of my colleagues and I have been developing IBL materials for our two semester sequence in Abstract Algebra. Our goals are to actively involve our students in their own learning with materials that carefully introduce the ideas behind the definitions and theorems to help students develop intuition and understand the logic behind them. We will share several specific examples of our materials and welcome questions and discussion. The development of some of these materials was supported by a grant from the Academy of Inquiry-Based Learning.
Motivated by the blind refereeing process used to evaluate mathematics research publications, the instructors of two IBL-based number theory courses run in the spring of 2011 planned cross-institutional review assignments for the students in their classes. Students were given the same set of problems and asked to submit proofs that would then be sent to students in the other class for evaluation. In this talk we will discuss the procedure that the instructors followed, the ways in which the two classes were similar and different, and the perceived benefits and drawbacks of this exercise.
In this talk, the speaker will relay his approach to inquiry-based learning (BL) in an introduction to proof course.particular, we will discuss various nuts and bolts aspects of the course including general structure, content, theorem sequence, marketing to students, grading/assessment, and student presentations.the theme being centered around an introduction to proof course, this talk will be relevant to any proof-based course.
Mathematics Education Research
Students in mathematics content courses use resources both within and outside of the classroom. We examine how preservice elementary teachers in an inquiry-based mathematics content class use available resources for their learning. We also are interested in what impacts the ways students use these resources. We interviewed and observed three students from an inquiry-based mathematics content course for preservice elementary teachers to investigate the resources they used (e.g., family members, peers, small groups, poster presentations, instructor, readings, colored pens). By analyzing how and why students used these resources, we identified three main recurring themes, two about specific resources (individuals and small groups) and one about the rationale for using a variety of resources (motivation). In this session we discuss each of these themes in detail. We would like to hear from faculty in regard to the resources that their students use.
Math content courses aim to develop mathematical reasoning and communication skills in future teachers. Instructors often assign problems requiring in-depth written explanations to develop these skills. However, when a student’s conception is incorrect, does written feedback from the instructor create the cognitive dissonance necessary to effect realignment of the student’s understanding? These conceptions may be mathematical (“what is a fraction?”) or meta-mathematical (“what constitutes a justification?”). Assigning problem revisions theoretically creates space for cognitive dissonance by having students rethink their solutions. I investigate a revision assignment in an IBL course for future teachers to understand the nature of students’ revisions and the possible impetuses for these revisions. In particular, I find preliminary evidence that students’ revisions demonstrate changes in their language, mathematics, and use of examples and representations. Further, students’ adoption of new representations in their solutions are largely due to observing peers’ presentations in the IBL class format, rather than to instructor feedback.
Mathematicians understand that proof is an integral part of doing mathematics, yet many students neither appreciate the role of proof in mathematics nor easily develop facility in constructing proofs. Furthermore, one of the key goals of undergraduate mathematics education is to develop students’ skills and understandings of mathematical proof. Numerous authors suggest that modified Moore method instructional strategies have great potential to help students develop such desired competencies and conceptions. In this talk, I will use a set of standards that I developed for proof and proving at the undergraduate level as a framework for evaluating selected notes from the Journal of Inquiry-Based Learning in Mathematics on abstract algebra and real analysis. The standards address the full range of competencies needed to be successful provers in mathematics such as intuition, informal reasoning, conjecture, creativity, and rigor. I will discuss my evaluation of the selected modified Moore method instructional notes with regard to their ability to help students meet those standards and develop both creativity and rigor in proving.
Where and how is IBL now used? What might this picture tell us about the spread of IBL? We will answer these questions using results from a spring 2013 survey of the IBL mathematics community. Then we will place the results in context of past and present efforts by EAF and this community to share IBL methods and support colleagues in adopting them. What does it take to create a movement—and what more may be needed? Come peer with us into the crystal ball.
Even an experienced user of IBL might shy from trying IBL in a calculus course. A possible obstacle in using IBL in a calculus course might be the following: A traditional calculus course prominently uses 'differentials' in a number of ways. The difficulty here is that such 'entities' are not, in a sense can not, be defined or even accurately described. Students are generally indoctrinated or trained in the manipulations of symbols standing for 'differentials'. Such an indoctrination can and is accomplished in an authoritarian classroom, but a class in which students are asked to make discoveries and to present their work to their peers, such activity is fatally hindered by a notation incapable of definition. Notes given here offer an alternative which doesn't have this fatal hindrance. Actually the notes are straight from R. L. Moore's calculus class, with the addition of some of H. S. Wall's ideas. Website link: www.legacyrlmoore.org/calculus
In this interactive session, we will discuss how we have introduced inquiry-based learning (IBL) into the calculus series. Sample materials used and developed for Calculus I will be distributed and will be the focus of the discussion for the session. The use of these materials, in conjunction with the addition of “homework room,” has created an active, collaborative classroom environment where students are engaged in IBL. The additional time spent on calculus, outside of the regular time, has become an important part of the success of IBL in calculus courses and has impacted the performance of the students. A final part of the success of the courses that will be discussed is the importance of having a team of instructors to help prepare materials and work together.
If one commits to rigor in his or her mathematics courses, the first question “What is an appropriate meaning for validation of `and this is why’?” is essential to ask oneself before setting up a problem sequence to drive the course. This is particularly problematic when one teaches the calculus, where the curriculum typically proscribed is routinely more appropriate to two semesters of investigation than the one semester allotted. In this talk, the presenter will suggest a core dictionary that articulates basic principles that he considers adequate to both establish a platform from which to reason AND investigate the standard curriculum for Calculus I. He will reflect on his experiences in teaching from the dictionary.
The Department of Mathematics at the University of Hartford recently implemented a pilot study to investigate how flipping pedagogy might enhance student engagement in our Calculus I courses and increase time outside of class studying course content. Prior to every class, students watch faculty-produced videos which highlight key ideas of the assigned section. Class time is spent discussing and solving problems or engaging in inquiry-oriented activities of calculus concepts in small groups or as a whole class. In this session I will discuss our progress on this project, the lessons learned, and our plans for the future.
Presentation Days and other modified Moore Method techniques
Students in an IBL course benefit from brief chats with their professor, in office hours or in the hallways, to check-in about their thoughts about a problem. However, students cannot perpetually visit office hours and professors cannot perpetually be available in their offices. We will present a simulation of this “check-in” experience using modern technology, used in an Introduction to Mathematical Proof course and a Theory of Numbers course. Each evening after class, students submitted an informally written solution attempt electronically via the Dropbox program (using a Smartpen, LaTeX, scanned file, photograph, etc). By 5pm the next day, a professor or teaching assistant provided feedback on the student’s attempts, and assigned a grade of 1 point (full credit) provided the student made an honest attempt to piece together some axioms, definitions, or previous propositions. The most notable consequence was an increase in pace; this allowed for an increase in the number of problems completed by students and thus an increased depth of student learning.
IBL classrooms are especially sensitive to student preparation; so like many IBL instructors, I assign "pre-work" problems to be completed or attempted before class to help students prepare. spring my students reported on their pre-work through a personal wiki - which allowed me to assess their understanding before class began. exercise proved to be extremely helpful for managing class discussion and, more surprisingly, it helped me teach my students how to struggle productively.
This talk will focus on the details of runningclass, such as howmanage presentation days, grading and developing assignments.should be useful to anyone wanting to take their first steps into IBL instruction with any freshman level class.
This semester I taught, for the first time, a fully inquiry-based section of "Calculus III with Vector Fields" at the Naval Academy. It brought me joy every day. I had 16 students in one of 18 sections of the course. The other 17 sections were using Stewart, many of them were using WebAssign, and we had a common final exam including 20 machine-graded multiple choice questions. I will share what I learned about choosing and adapting a problem set, grading, selling students on the method and sharing my experiences with my colleagues.
Math Teachers Circles
Math Teachers' Circles (MTC) aim to foster a culture of problem solving among K-12 math teachers, with an emphasis on the middle-grade years. By engaging teachers in investigating easy-to-enter but mathematically rich problems, MTC participation leads not only to increases in teachers' content knowledge but also to their appreciationinquiry based learning and its power in educating their students.
Emerging Scholars Program
This study explores the effects of a teaching intervention using a process called collaborative revision in the context of an Emerging Scholars Program course on introduction to proof. Collaborative revision refers to the process in which students present a proof they have constructed to their classmates and the other students are encouraged to provide feedback to aid in the subsequent revision of the proof and is similar to IBL. A discussion of the context and content of the course will be given as well as results about impact of the course on students proof construction and validation skills. Preliminary results show that although collaborative revision may not impact the ability to identify valid proofs, it does affect the way that students gain conviction about the proof of a statement. Additionally, students were asked about their beliefs about the function of proof and results show that this course did have an impact on these beliefs. Preliminary results also show that although collaborative revision may not impact the ability to identify valid proofs, it does affect the way that students gain conviction about the proof of a statement.
Calculus is widely viewed as a gateway to science, technology, engineering, and mathematics (STEM) fields; however, success rates in calculus continue to be a nationwide problem. Students’ ability to produce or recognize correct, well-written, robust solutions to calculus problems directly affect the latter, yet little research exists that examines this. In this study, using sample student work on calculus exam questions, we created an instrumentrequiring participants to critique and rate the effectiveness of the solutions presented. UT-Arlington offers students pursuing degrees in STEM fields enrolled in first-semester calculus the opportunity to participate in the Arlington Emerging Scholars Program (A-ESP). This intervention program incorporates inquiry-based learning techniques as students work in groups on challenging calculus problems for four hours weekly in addition to regular lectures and labs associated with the course. Findings based on the responses of fourteen students participating in A-ESPand 34 non-A-ESP students from the same section of calculus suggest that students participating in A-ESP communicated their views in a more clear, concise manner and demonstrated stronger skills for providing feedback on peer work and correctness of solutions than their non-A-ESP counterparts.
Saturday, 15 June 2013
— Parallel Sessions
General contributed Papers
Developing teacher-leaders must learn to view their role in new ways, since their clients are no longer their students but rather the colleagues to whom they will be delivering professional development. Inquiry-based learning experiences may not only lead to an effective transformation to this new role but also allow teacher-leaders to become familiar with another model of teaching and learning in the mathematics classroom. We will describe how inquiry-based learning experiences are useful in developing effective mathematics teacher-leaders within high-needs districts across East Texas through the Texas Middle and Secondary Mathematics Project Leadership Initiative and Texas Leadership Initiative: Mathematics Instruction Transformed programs, two National Science Foundation sponsored programs conducted through the Stephen F. Austin State University Department of Mathematics and Statistics.
The power of a legacy derives in large part from its ability to adapt to changing times. Bill Mahavier had a special knack for adapting a method that he knew and understood so fundamentally that he made it work until just before he passed away in 2010. Although on the surface Bill’s classes differed a great deal from Moore’s, his ability to transform the lives of students was unsurpassed.
While Bill transformed his students’ lives in one way, we, Bernd Rossa and Cornelius Stallman, have had our lives transformed in a different way. Our talks are about that transformation, how Bill, through his generous and engaged mentoring, set each of us onto our paths towards teaching more effectively by “asking questions” rather than by “telling students”, and about how Bill continues to inspire us through a course of his that both of us have taught many times since we first met him.
Question, experiment, observe, conjecture, test, prove, extend, repeat.IBL courses are focused on proof and generalization, which certainly has its place. for our mathematics majors we have found great success in encouraging more students to major in mathematics, in developing students' ability to construct proofs, and in preparing students for undergraduate research by focusing our (required) "transition" course on conjecturing (and testing our conjectures) instead. this talk I'll share a few successful conjecture-motivating activities, describe a process of transforming "textbook" problems into conjecture-based activities, and show an example of how a course can be structured around conjecturing. along the way perhaps you'll see a little bit of new (discrete) mathematics.
Discovering the Art of Mathematics
Curious about how to empower general education mathematics students using inquiry-based learning?Are you ready to have non-majors report, “I have to admit, I have never had a class like this, where learning is the most important factor”?If so, please join us. This 90-minute, hands-on workshop is sponsored by Discovering the Art of Mathematics, a National Science Foundation and Harry Lucas funded project.Specific foci for the workshop include:
Experiencing what inquiry can feel like and look like in a mathematics for liberal arts course by working through selected mathematical topics from the project’s extensive library of free, inquiry-based curriculum materials;
Investigating the breadth of the curriculum library’s content areas (using the online Topic Index for the project) to find topics that resonate with your students and connect with your general education course missions,
Glimpsing the potential for transformative change through student journals and videos, survey data, students’ written work, original student artwork, and feedback from external beta-testers, and,
Reflecting on opportunities these resources provide for creating a classroom environment where productive, safe, and deep mathematical inquiry can take place.
Lessons from the IBL Centers Project
Almost a decade ago, EAF started funding large-scale IBL activities at Chicago, Harvard, Michigan, Santa Barbara and Texas. This session will begin with a short description of some of the activities carried out on these campuses. In particular, many IBL courses have been developed and taught under a variety of circumstances and by a variety of personnel. During the session, directors will answer questions and provide feedback on the experience gained.
— How to beat the lecture/textbook trap, and then throw them both away! Melding inquiry-based alternatives for both
David Pengelley, Professor, New Mexico State University
— Five Minute Talks, Session II
and Concluding Remarks and Thanks (Jacqueline Jensen-Vallin; Harry Lucas)