MIT Electronic Seminar on Mathematics Education
This is an online seminar centered on mathematics education at the university level. Talks will cover curriculum, pedagogy, inclusiveness, professional development, blended and flipped classrooms, and other topics of interest.
Past Talks
Click on the title of a talk to show the abstract and references (you should see a next to the title if the talk has a folder).

$\begingroup$$\begingroup $Ralf Spatzier, University of Michigan
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Academy of Inquiry Based Learning
The IBL Center at University of Michigan is happy to share their IBL course materials with other instructors worldwide. Please email spatzier@umich.edu.
In IBL, students learn through guided exploration with the help of experienced instructors. We engage the students and emphasize discovery, analysis, and investigation to deepen their understanding of the material and its applications. Students solve problems, conjecture, experiment, explore and create. These practices have been strongly supported by the CBMS, MAA, and the NRC. I will discuss inquiry based learning as we have introduced it over the last fifteen years at U Michigan, a bit about the history and the “struggle”, and their effect on both students and instructors. I will describe our training of instructors, especially postdoctoral fellows, assessment, the role undergraduates play as course assistants and our course materials.
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$\begingroup$$\begingroup $Mike Weimerskirch, University of Minnesota
Practicing basic computational skills and developing conceptual understand are two of the many things that happen in the math classroom. Using videos and online homework to 'flip the classroom' is a beginning, but more can be done to promote higher order thinking skills. The University of Minnesota is in its sixth year of a redesign of its PreCalculus curriculum that 'flips the formula'. Instead of the professor beginning with the generalization and passing the formula to students who solve specific cases, students now begin with specific cases and develop algorithms for general solutions
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$\begingroup$$\begingroup $Sanjoy Mahajan, Olin College of Engineering
A war is on in probability and statistics: between the objective approach, a.k.a. frequentist or orthodox statistics, and the subjective approach, a.k.a. Bayesian statistics. For my sins, I find myself fascinated by fields where the unorthodox view is correct, so I made and taught an undergraduate course on "Bayesian Inference and Reasoning." I will illustrate, with many examples, several hopefully transferrable aspects of the course.
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$\begingroup$$\begingroup $Philipp Hieronymi, University of Illinois at UrbanaChampaign
I will report on a still ongoing project to develop and improve the largest linear algebra course offered by the Department of Mathematics at Illinois. This course is a (nonproof based) first course in linear algebra taken by more than 1600 nonmath majors each year (the majority of these students are sophomores and juniors whose major is in engineering). The two main goals of this redesign are to increase the active learning component and to identify applications and develop activities that showcase the power of linear algebra. Discussing both successes and failures, I hope that the experiences I have to share, prove useful to others who are redesigning/reimagining large service courses at (large) universities.
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$\begingroup$$\begingroup $Annalisa Crannell, Franklin and Marshall College
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In this workshop/lecture, we’ll explore ways to structure inclass learning activities: how we might lead an IBL activity, or even an entire IBL course. In addition, we’ll learn how the speaker wound up using IBL to teach a class on isomorphisms of quotient groups in a bagel shop.
Interactive Engagement in the classroom can take many forms: Inquiry Based Learning, ThinkPairShare, Flipped classrooms, and more. And beyond being a totally trendy pedagogical innovation, interactive engagement increasingly has demonstrated improved outcomes in student learning and retention of mathematics and science. This workshop will attempt to help participants increase their ability to put theory into practice within their own courses.
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$\begingroup$$\begingroup $Gavin LaRose, University of Michigan
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Increasing the use of inclusive teaching strategies starts with building awareness in departments and among instructors. In this presentation we will describe a lowcost effort to create a community of instructors with interest in and knowledge of how mathematics classrooms may be inclusive (or not), whose members have thought about and developed a toolkit of teaching strategies they can implement in their own classrooms. Our group met six times over the course of a semester, with two additional meetings in the semester following, to discuss readings and how to implement teaching strategies that would promote inclusiveness. In this talk we will discuss the model for our community, the departmental context in which it was developed, its activities, what it accomplished, and how we are moving it forward.
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$\begingroup$$\begingroup $Susan Ruff, MIT
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In this seminar, we’ll discuss concepts that can guide the teaching of mathematical communication: writing to learn vs. learning to write; Anne Beaufort’s model of the prerequisites to effective disciplinary communication; the view of genres and genre systems as rhetorical actions; and Lave and Wenger’s observation that limited peripheral participation can be an effective means for entering a community of practice. Periodic questions will guide participants to consider how these concepts could be applied in their contexts, and examples of their application to curriculum design, instruction, assignment design, feedback, and assessment will be given from communicationintensive mathematics subjects offered by the MIT Department of Mathematics.
Bio
For more than a decade, Susan Ruff of MIT’s Writing, Rhetoric, and Professional Communication has been collaborating closely with mathematicians at MIT to teach mathematical communication in their communicationintensive mathematics subjects. Susan researches the reasoning of mathematics, mathematicians’ experiences writing and learning to write mathematics, and mathematical communication pedagogy. She is founding coeditor (with Haynes Miller and others) of MAA Mathematical Communication (mathcomm.org http://mathcomm.org), a resource for teachers who engage students in writing about mathematics. When she isn’t at MIT, she’s often rock climbing someplace remote.
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$\begingroup$$\begingroup $Alfonso GraciaSaz, University of Toronto
In an ideal world, when a student asks for help with a math problem, we do not answer directly. We help them realize what is confusing them and we help them solve the problem by themselves. From the perspective of a beginning instructor (or TA), this is easier said than done. How do you do it exactly? What if the student does not cooperate? What if they just answer "I do not know" to anything we ask? What if they grow impatient or resent me?
"Ask. Don't tell" is a training session we developed at the University of Toronto for our TAs. We use real student questions gathered from the online fora of our courses, and we see what actually happened, so nobody can argue that we are not being realistic.
I will demonstrate this session during the EMES seminar.
If at all possible, please make plans to attend this seminar with at least one other person in the same room. You will enjoy the seminar better, and you will get more out of it that way.
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 Natasha Speer: natasha.speer@maine.edu
 Jack Bookman: bookman@math.duke.edu
$\begingroup $Jack Bookman, DukeNatasha Speer, University of MainePresentation:
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Contact Info
Despite the important roles they play in undergraduate mathematics education, little attention has been focused on the preparation of graduate teaching assistants (TAs). In addition, faculty who wish to start or enhance a professional development program for TAs may find it challenging to locate instructional materials. The purpose of CoMInDS is to create an infrastructure, housed and supported by the MAA, to enhance the mathematics community’s ability to provide high quality, teachingrelated professional development to graduate students. We will provide background for our efforts, research findings relevant to these issues and we will engage participants in discussion about the need for and design of novice college mathematics instructor professional development. Because the history is short and the numbers are not yet large, this will include both quantitative and qualitative results. We will also share our thoughts on future developments as we seek continual improvement of our program, and to make it available to others.
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$\begingroup$$\begingroup $Catherine Snyder, Clarkson UniversityPete Turner, Clarkson UniversitySeema Rivera, Clarkson University
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It has been said that university faculty are perhaps the most highly qualified profession but with essentially no training for (the teaching part of) the job they are hired to do. This seminar will discuss our effort to change that, by including formal training in teaching for our Teaching Assistants – the future professoriate. The idea was born out of the merger of Clarkson with what is now our Capital Region Campus, formerly Union Graduate College, in Schenectady, NY. The talk will begin with a little background to set the scene and then discuss the implementation of our intensive training program for new TAs in the STEM disciplines. Of course, mathematics is at the heart of STEM as the common element in almost all STEM fields, and so mathematics TAs are perhaps especially important. Typically, new PhD student TAs arrive with misconceptions about their role, about how to teach, and about their audience and that audience’s base of knowledge and understanding. What worked for them as undergraduate learners is not a good model for all, and many are new to the US educational system, too. The program will be described and then we will share results from the research evaluating the program. Because the history is short and the numbers are not yet large, this will include both quantitative and qualitative results. We will also share our thoughts on future developments as we seek continual improvement of our program, and to make it available to others.
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 Active Calculus landing page
 PNAS metastudy on active learning
 Matthew Jones and Stan Yoshinobu on "coverage"
 Activities Workbooks
 Daily Prep Assignments
 WeBWorK sets (.def files)
 Geogebra labs
$\begingroup $Matt Boelkins, Grand Valley State UniversityPresentation:
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Ancillary materials for Active Calculus that are available upon request at boelkinm at gvsu dot edu:
Several recent ESME presentations have focused on active or inquirybased learning (such as those by Angie Hodge, Darryl Yong, Robin Pemantle, David Pengelley).Indeed, it is wellestablished that active learning offers, on average, significant benefits to students.At the same time, implementing active pedagogy effectively is challenging on several levels, including achieving student buyin, developing engaging investigations for students, and addressing what Stan Yoshinobu and Matthew Jones have called “the coverage issue.”
In this seminar, I will share some samples from my free and opensource text, Active Calculus, and demonstrate some of the features of the HTML version of the text. In addition, our practicefocused discussion will center on how I structure my calculus courses around active learning: daily preparation assignments, inclass activities, computer laboratory investigations, and outsideofclass WeBWorK and writing assignments.Seminar participants will be invited to share their experiences and questions regarding methods of interactive engagement in calculus and more. Following the seminar, I’ll be glad to share any of the discussed supporting materials upon request.
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$\begingroup$$\begingroup $Alissa Crans, Loyola Marymount UniversityDave Kung, St. Mary's College of Maryland
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Underrepresented minority students are more likely to drop out of college. Minority students and women are more likely to leak from the STEM pipeline at every stage from middle school on. Why do we need to address these issue? What can we do in our classrooms, departments, and institutions to ensure that everyone has an opportunity to succeed? When faced with a challenging situation, what will you do to make our world a more just place? In this session, we’ll dive into these issues  as an example of the kinds of professional development we provide to new mathematics faculty in MAA Project NExT.
Speakers:
Dave Kung teaches at St. Mary's College of Maryland and directs MAA Project NExT. After studying analysis, he switched to mathematics education, looking at instructor knowledge of student thinking. He has won his MAA section’s teaching and service awards, and he has passionately pushed to diversify mathematics. In his spare time, he runs, bikes, and plays violin  and coerces his daughter to join him.
Alissa Crans is a Professor of Mathematics at Loyola Marymount University and an Associate Director of MAA Project NExT. Her professional interests include higherdimensional and quantum algebra, relationships between math and music, and encouraging and supporting diversity and inclusivity in mathematics. She enjoys playing the clarinet, running, and baking (not cooking!).
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$\begingroup$$\begingroup $Angie Hodge, Northern Arizona University
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Calculus is often said to be the most difficult class in which to implement inquirybased learning (IBL) techniques. There are questions of class coverage, larger class sizes, and the mathematical maturity of the students taking calculus. Instead, IBL is historically known to be used in upperdivision mathematics courses where students are responsible for generating proofs with little to no help from the professor. In this seminar, I will discuss ways to successfully incorporate IBL into the calculus classroom. A variety of techniques will be discussed ranging from adding short active learning strategies into a lecture based classroom to a classroom where little to no lecture is given by the instructor.
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 Linear Algebra materials
 Abstract Algebra
 Support for use of these curricula, including summer workshops.
$\begingroup $Chris Rasmussen, San Diego State UniversityPresentation:
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Other Inquiry oriented initiatives:
Undergraduate mathematics education today faces a number of challenges and difficulties. One way to address these challenges is to build on promising theoretical advances and instructional approaches, even those not originally developed with undergraduate mathematics in mind. The Inquiry Oriented Differential Equations Project (IODE) is one such effort, which can serve as model for other undergraduate course innovations. In this presentation I describe central characteristics of the IODE approach, report on results of a comparison study, and provide an overview of the modeling sequence that leads to the emergence of a bifurcation diagram, a surprising and illustrative example of student reinvention. The overview and examples of student work tendered offers a fresh perspective on modeling and how an inquiryoriented sequence of tasks can lead to the reinvention of significant mathematics.
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$\begingroup$$\begingroup $David Bressoud, Macalester College
I've used history to motivate and organize introductory real analysis and Lebesgue integration. This talk will explain how it should be used to improve calculus instruction. The standard order of the four big ideas—limits then derivatives then integrals then series—is all wrong both historically and pedagogically. In addition, the standard models for derivatives and integrals, slopes of tangents lines and areas under curves, also throw obstacles in the path of many students. Drawing on history and recent research in undergraduate mathematics education, I'll make the case for calculus introduced first as problems of accumulation (integration), then ratios of change (differentiation), then sequences of partial sums (series), and finally the algebra of inequalities (limits).
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$\begingroup$$\begingroup $Andrew Tonge, Kent State University
In 1997, Virginia Tech dramatically changed how they taught lower division mathematics courses. They abandoned lectures and created a 500 seat “Mathematics Emporium” computer lab where students learned calculus and linear algebra assisted by software together with individualized input from teams of graduate students. Success rates soared and instructional costs plummeted. Other institutions soon adapted this model to their own needs with similar success. Emporiums, large and small, sprouted all over the country. They became popular for teaching remedial mathematics, often in highly modularized formats. A commonly reported outcome was a 25% increase in student success rates along with a 25% reduction in instructional costs. Most Emporiums were instructorcentered, driven by MyMathLab software, with students progressing through the curriculum lock step as a cohort. At Kent State we took a different, more studentcentered approach. In 2010, we created a 250 seat Emporium driven by adaptive, “artificially intelligent” ALEKS software. This builds and constantly updates an accurate representation of each student’s “knowledge space.” It allows students to choose individualized pathways through the curriculum and to advance efficiently, focusing their efforts primarily on learning what they don’t already know. We’ll discuss how and why we set up our ALEKS Emporium, describe a variety of positive outcomes, outline a recent radical metamorphosis, and situate everything within an emerging national agenda.
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 Illinois Geometry Lab
 Geometry Labs United
 GLU conference (August 2017, University of Washington)
 The IGL has a family resemblance to the MIT Math Lab
$\begingroup $Jeremy Tyson, UIUCPresentation:
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The Illinois Geometry Lab (IGL) was founded in 2011 to promote undergraduate research and community outreach in the Department of Mathematics at the University of Illinois. From modest origins, the IGL has grown substantially: Spring 2018 witnesses nineteen IGLsponsored research projects involving over 80 undergraduates and 23 graduate students. The IGL has also quickly become the premier departmental organization focusing on engagement with and outreach to community organizations and schools. I will discuss the IGL’s history and modus operandi, and the challenges and rewards of administering a largescale undergraduate research enterprise within a researchoriented public mathematics department. The IGL partners with a number of similar undergraduate research labs across the country as part of the umbrella organization Geometry Labs United (GLU). I will briefly describe GLU’s vision for a nationwide network of experimental research labs for undergraduates in the mathematical sciences.
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 References for the connection between active learning and more equitable student outcomes can be found here.
 Ed Prather has material on thinkpairshare in an astronomy classroom available here. Prather has a compelling presentation.
 Groupworthy material has been developed by Inquiryoriented Differential Equations. Chris Rasmussen will report on this project in EMES on May 1.
 A sobering study by Gerhard Sonnert, Philip Sadler, Samuel Sadler, and David Bressoud.
 Here are further references.
$\begingroup $Darryl Yong, Harvey Mudd CollegePresentation:
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Active learning has many documented benefits both for students and instructors. Moreover, there is increasing evidence that it disproportionately benefits women, students of color, and students who previously denied the same learning opportunities as others. However, the empirical evidence for this disproportionate benefit doesn't explain why it happens, nor does it guarantee that all students will benefit from active learning. In fact, my own experience with active learning is that it is difficult to do well and sometimes it can have detrimental effects on students if we're not careful. So, we should aim not just for active learning, but learning that is both active and inclusive. We'll discuss some principles and practical strategies for making active learning more inclusive. (If you are able to, please watch David Pengelley's EMES presentation on active learning before this session.)
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 Common Core State Standards for Mathematics
 Progression Documents for the Common Core Math Standards Institute for Mathematics and Education, University of Arizona
 Illustrative Mathematics
 Aleks, Assessment and LEarning in Knowledge Spaces is a Webbased, artificially intelligent assessment and learning system.
 Ohio Mathematics Initiative Two suggestions from Natasha Speer:
 Carnagie pathways project in quantitative reasoning and statistics
 Researchbased educational products
$\begingroup $Dev Sinha, University of OregonPresentation:
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We discuss a dozen years of experience in course development with an aim of changing students' perceptions of what mathematics is and what success in mathematics classes ought to entail. Key components are identifying important common student misunderstandings and designing activities, often inclass, to address those, and aiming for authenticity of student practice. We share groundup (re)design of three courses: introduction to proofs, math for preservice elementary school teachers, and mathematical modeling in preparation for college algebra, the latter of which has very positive though smallpopulation data which indicates some success. We end with discussion of the challenges presented to campuses in trying to strategically implement such practicefocussed courses.
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 College Mathematics Instructor Development Source (CoMInDS) Website. To join the CoMInDS listserve, email Emily Braley.
 CoMInDS program profiles:
$\begingroup $Robin Gottleib, HarvardEmily Braley, HarvardPresentation:
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Part of providing a valuable classroom experience for undergraduate students is supporting teachers so that they are well equipped to deliver high quality instruction. Graduate students at research universities often serve as teaching assistants (GTAs) and many serve as instructors of record in undergraduate courses. We will profile two well established graduate student professional development support programs, one at Harvard University and the other at Duke University. Then we will talk about the College Mathematics Instructor Development Source (CoMInDS) project of the MAA and how this program aims to support graduate students and professional development providers.
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 Active Learning at Penn
 Student paper article on active learning at Penn
 Teacher prep courses
 Active learning math courses:
 Calculus for business students: mock canvas, mock calendar, mock handouts, real course materials
 Active version of Calculus I
 Active version of Calculus II
$\begingroup $Robin Pemantle, University of PennsylvaniaPresentation:
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This is a mathcentric history of the active learning initiatives at Penn, starting in 2013 with our involvement in a project funded by the AAU.
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$\begingroup$$\begingroup $Teena Gerhardt, Michigan State University
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Over the last three years I have led a transformation of the Survey of Calculus course at Michigan State University. This applied calculus course serves over 3600 students per year. I will discuss the new course design, as well as the challenges in transforming large courses. This course redesign is part of a push by the MSU math department to improve introductory math courses, as well as a broader effort across the university to improve STEM gateway classes. I will briefly discuss efforts and programs at the department and university level that have led to these changes in institutional teaching culture.
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 Mathematical Assocation of America MAA Instructional Practice Guide (draft)
 Conference Board of the Mathematical Sciences Active Learning in PostSecondary Mathematics Education
 MAA Committee on the Undergraduate Program in Mathematics Curriculum Guide
 American Statistical Association Guide for Assessment and Instruction in Statistics Education (GAISE) Report
 National Council of Teachers of Mathematics (NCTM) Principles to Actions
 Association of Mathematics Teacher Educators Standards for Preparing Teachers of Mathematics
$\begingroup $Beth Burroughs, Montana State UniversityPresentation:
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The MAA Instructional Practices Guide is a companion guide to the 2015 CUPM Guide to Undergraduate Programs in the Mathematical Sciences. The IP Guide focuses on three core practices: Classroom Practices, Assessment Practices, and Course Design Practices. The guide is in draft form, preparing for release in 2018. This seminar will describe the principles the author team used in creating the guide, will provide an overview of the contents of the guide, and will provide an opportunity to discuss some of its recommendations indepth. Anyone wishing to review the guide in advance can access it here.
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 Beating the LectureTextbook Trap with Active Learning and Rewards for All
 The Calculus Concept Inventory—Measurement of the Effect of Teaching Methodology in Mathematics
 Evaluation of the IBL Mathematics Project: Student and Instructor Outcomes of InquiryBased Learning in College Mathematics
 Active learning increases student performance in science, engineering, and mathematics
 Largescale comparison of science teaching methods sends clear message
 Enough with the lecturing
 MAA Instructional Practices Guide (December 20, 2017) accepting reviewer comments until December 1st.
$\begingroup $David Pengelley, Oregon State UniversityPresentation:
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What is active learning? What is the scientific evidence about it in the classroom? What is the lecturetextbook trap? What are the alternatives, and how difficult are they? What about issues such as "first contact", and linkages between before, during, and afterclass. Is there a motto about student reading? What are the rewards of active learning for both teachers and students? How much inertia is there? I will address these questions based on pedagogy developed in 17 distinct university courses at all levels over 20 years. And there will still be plenty of time left for discussion.
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$\begingroup$$\begingroup $Haynes Miller, MIT MathematicsJennifer French, MITx
Since about 2002 a team at MIT has been developing a suite of specialpurpose applets to support student understanding of mathematical concepts and operations. They have been used extensively as lecture demonstrations and in homework assignments. We will show some examples of these uses, discuss their design and reception, introduce the website mathlets.org, and end with a description of how they have been integrated into online courses.
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 Course materials
 Discussions and information on the educational decisions taken when designing and implementing the flipped version of 18.05 are available here.
$\begingroup $Jerry Orloff, MITJon Bloom, MITPresentation:
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Several years ago at MIT we decided to flip our introductory probability and statistics class. This involved the use of technology both in and out of class as well as a major revamping of the syllabus. We will discuss our experience: what worked well and not so well. At this point we expect many participants will have tried flipping a class, so we hope to generate a discussion of our various experiences.
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 MOOC on how to design and produce content from Stanford: Blended and Online Learning Design
 JovE: peerreviewed scientific journal that publishes experimental methods in video format
$\begingroup $Petra BonfertTaylor, DartmouthSarah Eichhorn, University of California at IrvineDavid Farmer, American Institute of MathematicsJim Fowler, Ohio State UniversityPresentation:
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CuratedCourses in Mathematics is a project to create, gather, curate, tag, review, organize and make available high quality online open educational mathematics resources. The project aims to coordinate work being done at multiple institutions on similar courses, enabling faculty to share resources they create or curate from other sources. By creating a system for curating and tagging resources our hope is that faculty can more easily find high quality materials to utilize in their classes and more broadly disseminate good resources they create.
We will describe the project itself, describe resources we have created for faculty about how to design and produce online mathematics content, describe our tagging system for content submitted to our site as well as present our future goals for the project.
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