The presenter will reflect on his own evolution as a teacher using IBL principles as the primary basis for instruction.  In particular, he will emphasize the notion of “appropriate level of rigor” as it relates to the different levels of expected preparation of students populating target courses.  In addition, he will discuss what his experience suggests are enhanced opportunities afforded by IBL in the contexts of grading and student engagement and what his experience suggests are possible social challenges should one choose to use IBL at an institution at which the benefits of IBL are not clearly understood.

For more than twenty years, Harry Lucas and the Educational Advancement Foundation (EAF) have fostered the development and resurgence of the use of IBL approaches to the teaching of mathematics, particularly at the undergraduate level.
     For a variety of reasons, some related to a sense that progress may have slowed, changes to current approaches are being considered. Reasons for the strategic review also include the need to expand the participation of younger IBL practitioners and to raise funds beyond the limited resources of EAF.  The Strategic Planning Committee members will provide more details and summarize current approaches under consideration.
     Discussion, questions and comments will be welcomed during the session and throughout the legacy conference.  Feedback from the IBL community remains critical to the formation of a strategic plan that helps advance inquiry-based learning nationally

From Socrates through Seymour Cray: breakthroughs in mathematics, the sciences and computing are achieved by brave persons doing independent original research. To attack something new one must believe the attack has a chance of success.  That belief is based on careful and imaginative thinking and is founded on past experience.  A purpose of the Moore Method is to produce confident independent thinkers.  This talk will trace the history of some heroic mathematicians and explore their powerful influence on the advancement of next generation high-performance computing.

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.

Carol Mead, University of Texas at Austin
Randy Cone, Virginia Military Institute
Rob Kirby, University of California, Berkeley
Steve Armentrout, Penn State University
Mary Armentrout
Tatiana Shubin, San Jose State University
Sarah-Marie Belcastro, Sarah Lawrence College

MAA's Committee on the Undergraduate Program in Mathematics (CUPM) is writing recommendations for the curriculum for mathematics majors.  Special consideration is being given to the pre-service education of secondary school teachers.  The panel will discuss the ways in which departments might modernize with consideration of incorporating the Common Core Standards and IBL.

Panelists:  Angie Hodge (University of Nebraska Omaha) is a member of MAA’s Committee on the Mathematical Education of Teachers (COMET), Michael Pearson (Executive Director of the MAA) is working with James Tanton on the development of teacher professional development materials based on high-quality content from the MAA American Mathematics Competitions, and Diana White (University of Colorado Denver) is a member of CUPM’s Course Area Study Group in Abstract Algebra.

Steve Armentrout, Penn State University
Tom Hull, Western New England University
Brian Katz, Augustana College
Carol Seaquist, Texas Tech Uniiversity
Inga Johnson, San Jose State University
Andrew Perry, Springfield College

Brian Katz, Teaching Mathematical Maturity through IBL Axiomatic Geometry

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.

Stan Yoshinobu, Using IBL in Courses for Future Elementary Teachers: Doing Math, Video Lesson Study, and Addressing Beliefs

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.

Ali Shaqlaih, Inquiry Based Learning in Math for Elementary Teachers Courses  

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.

Michael Matthews, Engaging Teachers in a History of Mathematics Class using IBL: A Skeptic’s Experience

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.

Anna Spice, Success and Failure in Intro-to-Proof

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.

Steven Schlicker, Abstract Algebra: An Inquiry-Based Approach

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.

Andy Schultz, Cross-institutional refereeing in two IBL Number Theory Classes

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.

Dana Ernst, Implementing IBL in an introduction to proof course

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.

Anne Cawley, Resource Use of Preservice Elementary Teachers in an Inquiry-Based Learning Mathematics Content Course

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.

Nina White, How pre-service teachers in an IBL content course revise their mathematical communication

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.

Kelly Bubp, An Evaluation of Selected Notes from the Journal of Inquiry-Based Learning in Mathematics With Regard to Proof and Proving at the Undergraduate Level

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.

Sandra Laursen and Chuck Hayward, Building Momentum in a Movement:  A Community Snapshot of IBL and Predictions for the Future

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.

John Neuberger, Calculus and IBL

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

Janice Rech and Angie Hodge, Getting Everyone Involved in Calculus: IBL-Style!

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.

Ed Parker, Finding a Proper Platform for Appropriate Rigor

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.

Larissa Schroeder, Flipping Calculus to Enhance Student Engagement

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.

Patrick Rault, Daily e-feedback of informal e-homework 

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.

Elizabeth Thoren, WikiLogs: Students Reporting on Pre-Work

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.

PJ Couch, A Foray into College Algebra via IBL

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.

Amy Ksir, Inquiry-Based Calculus III at the U.S. Naval Academy

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.

Tatiana Shubin and Diana White, Math Teachers Circles: Navajo Nation Math Circles Math Teachers Circles: Panel Discussion

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.

Emily Cilli-Turner, Collaborative Revision and its Effects on Undergraduate Proof Skills

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.

Julie Sutton and James Epperson, A Comparison of How Emerging Scholars Program and Non-Emerging Scholars Students Critique and Rate Effective Solutions to Calculus Exam Questions

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.

Thomas W. Judson (co-authors: Lesa L. Beverly, Kimberly M. Childs, Deborah A. Pace),The Role of Inquiry-Based Learning in Developing Teacher-Leaders

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.

Cornelius Stallman, Bernd Rossa, A Tribute to Bill Mahavier

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.

Suzanne Doree, Teaching Conjecturing

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.

Julian Fleron, Phil Hotchkiss (Westfield State University), Workshop:  Mathematical Inquiry in the Liberal Arts

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.

Ron Douglas and center directors, Almost a decade ago EAF started funding large-scale IBL activities at Chicago, Harvard, Michigan, Santa Barbara and Texas.

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.

First, I see a vicious cycle: Students don't read the textbook because they know we will lecture on it, and we lecture on the textbook because we know they haven't read it, despite our exhortations.  What a waste of precious classroom time! Couldn't students be actively engaged in higher level work in the classroom, rather than merely in passive first contact with new material?  But how to cut the cycle? I will show how one can beat this trap: Surprise, my students CAN learn a lot from reading, writing, and other preparation, always before first classroom contact with new material, and I can find alternatives to lecturing, but only if I design the process right! Second, I will discuss why one might also jettison a standard textbook, and replace it with inquiry-based approaches such as primary historical sources, guided discovery, and 'only when needed', which can put students in the driver's seat as explorers.  I will describe a course taught by melding all these approaches.

Leon Woodson, Morgan State University
Paul Kapitza, Georgia Highlands College
Jane Cushman, Buffalo State University
Banning Lary, Walden University
Justin Lanier, Saint Ann's School
Ben Woodruff, Brigham Young University
Linda May
Rob Kirby, University of California, Berkeley