Peer Review: Learning How to Give and Take

Photo of a traffic sign for "two way traffic" with two arrows, one pointing up and one pointing down. By Joe Pickett, OCW Publication Director

Peer review! Hardly are those words out than a writing instructor’s heart starts to stir—but with joy or trepidation?

Peer review! That activity in which students review each other’s work and give each other feedback. It’s an essential writing skill, after all, being able to assess a piece of writing critically and offer suggestions for making it more effective without sending the author into a tailspin of despair.

It’s what every good editor does.

Writing is an art, like playing a musical instrument, and to learn how to do it well, you have to practice, so students in writing courses have to write a lot if they are going to improve. But even the most conscientious writing instructor can’t analyze everything the students in a class produce, and it’s often helpful to get more than one perspective on a piece of writing, so peer review offers an attractive solution on more than one front. It can also allow an instructor the breathing space to focus on higher-level things, like getting the students to think like writers.

Not Sweating the Small Stuff

Running a peer-review workshop is not easy, as anyone who’s tried it knows. Great advice from a veteran of many workshops is offered by Jared David Berezin, whose 21W.035 Science Writing and New Media: Communicating Science to the Public appeared this month on OCW.

Rather than just throwing the students into the workshop environment, he begins by holding a discussion, where he shares his own experience on the best and worst of workshopping and gets students’ thinking “about the value of peer-review in the workplace, and ways to solicit peer feedback in a professional, non-classroom setting.”

In the workshops, he wants students “to focus on the larger, global issues in the drafts, rather than editing sentences.” How come? “For many readers, it’s easier to focus on the little things, because they can be commented on with confidence and fixed quickly. Instead, I’d rather students use the precious time in the classroom to discuss the more difficult and nebulous issues within a text.”

Paraphrase as a Passport to Understanding

Nonetheless, he asks students “to provide evidence for all comments by referring directly to the text. Referencing single moments in the text can allow readers and authors to engage in a concrete discussion of ways to improve the overall draft, rather than speaking in vague abstractions.”

Students are required to take notes on each other’s work and to ask others to paraphrase what they have written. This “allows the author to assess whether the reader’s understanding aligns with the intent and desired meaning.”

Active Experiments

Aside from these and many other practical tips for making peer-review workshops a success, the course site has a gold mine of detailed assignments, in-class exercises, and “communication experiments” designed to foster creativity and versatility (Berezin shares his reflections on these experiments, peer review, and other facets of his teaching in his Instructor Insights). Most experiments, like “reverse-engineering metaphors” and descriptions of a green space from assigned perspectives, involve group work as well as individual writing. In this class, isolation is not an option.

If you are a writing teacher, or an aspiring writer hoping to make your mark, you’ll want to take a look at 21W.035. It has a lot to offer, both to you and to your peers.

The Once and Future City

“A cloudy evening on the bridge between Boston and Cambridge. In 2015, this course focused on the 100th anniversary of MIT’s move across the Charles River, from Boston to Cambridge. (Courtesy of nd-nʎ on Flickr. CC BY-NC-SA.)”

By Joe Pickett, OCW Publication Director

Walk around a neighborhood in your city or town, and you might notice the different styles of buildings, the width of the streets, the kinds of trees or other plants, the open spaces, the way the wind whistles. Taking it all in, you might feel caught up in the moment. Ah!

But maybe you’re just trapped in the present.

Stretching your time frame is a major focus of 11.016J The Once and Future City, just published on OCW as taught by Professor Anne Whiston Spirn in Spring 2015.

 

Identifying the Pieces

“Cities are the products of the actions of millions of people and countless decisions, public and private,” Professor Spirn notes in one of her three videos that kick off the assignments. “How do all the pieces, styles, and times fit together?”

Early in the class students investigate maps of Boston, discovering how the city has changed over the centuries. “Who has the power to erase roads, to consolidate hundreds of properties?” a second video asks. “Why do some things persist and others disappear?”

A big part of the course is learning how to look, how to find “significant detail.” This process can be awkward for students accustomed to finding a right answer to a given question. The students are “not just taking a text and applying it, or critiquing something that already exists. They are developing visual thinking skills, and they have to make observations using their own eyes and mind. Many are not prepared for this.”

 

Stepping outside the Classroom Box

Professor Spirn helps them see for themselves by taking them on short field trips, where she asks provocative questions to get students thinking. As she explains in “Leading Productive Field Trips,” one of her Instructor Insights,

“The field trips are designed to give the students an introduction to methods of observation before they have to go out and perform field observations on their own at the sites they choose for their projects. We walk around and I show them how to look at things, how to find significant detail. But what is significant? Some students don’t see anything at all . . . Others see so many things that they can’t make sense out of what is significant and what is trivial. The field trip helps both kinds of students.”

 

Seeing Patterns Emerge

This form of teaching is very different from how Professor Spirn originally taught the course, back when she imparted knowledge through class lectures. Several years ago she decided to flip her classroom. Now instead of lecturing, she says

“I put together a series of images—mostly maps and photographs . . . Depending on the current assignment, the images emphasize different phenomena. But they always consist of puzzles . . . I’ll project an image on the screen and say, ‘What pattern do you see here?’ Sometimes nobody sees a pattern, so I say, ‘OK, do you see any anomalies? Does anything stick out or seem odd?’”

From the puzzles emerge patterns, and from the patterns, a hypothesis.

 

Opening the Mind’s Eye through Projects

The course site has extensive descriptions of the assignments, in which students select a site to explore, observe the natural processes at play in it, analyze its changes through time, and see what all of this bodes for the future.

Included on the site are examples of student projects from four different iterations of the course, among them papers on Coolidge Corner, The Bullfinch Triangle, and Boston’s West End.

11.016J turns the present into a portal for time travel. If it sounds fantastic, that’s because it is.

Courses from MIT’s 2017 MacVicar Fellows

Photos of three MIT professors

MIT professors Maria Yang (left), Caspar Hare (center), and Scott Hughes have been named 2017 MacVicar Fellows. (Photos by Bryce Vickmark (Yang), Patrick Gilooly (Hare), and Justin Knight.)

By Sarah Hansen, OCW Educator Project Manager

For the past 25 years, the MacVicar Faculty Fellows Program has honored several MIT professors each year who have made outstanding contributions to undergraduate teaching, educational innovation, and mentoring.

This year’s awardees are Professors Caspar Hare (philosophy), Scott A. Hughes (physics), and Maria Yang (mechanical engineering).

OCW is honored to share courses from two of this year’s Fellows.

Caspar Hare

24.06J/STS.006J Bioethics

Scott A. Hughes

8.962 General Relativity

Through the OCW Educator initiative, we have also collected teaching insights from several current and past MacVicar Fellows.

Arthur Bahr

21L.460 Medieval Literature: Legends of Arthur

21L.705 Major Authors: Old English and Beowulf

Wit Busza

Vibrations and Waves Problem Solving

Dennis M. Freeman

6.01SC Introduction to Electrical Engineering and Computer Science I

Lorna Gibson

3.054 Cellular Solids: Structure, Properties and Applications

Steven R. Hall

16.06 Principles of Automatic Control

Anne E. C. McCants

21H.134J Medieval Economic History in Comparative Perspective

21H.343J Making Books: The Renaissance and Today

21H.991 Theories and Methods in the Study of History

Haynes R. Miller

18.821 Project Laboratory in Mathematics

18.915 Graduate Topology Seminar: Kan Seminar

Hazel Sive

7.013 Introductory Biology (Spring 2013 version)

Insights on teaching Humanities, Arts, and Social Science at MIT

PHoto of several people around a wooden workbench.

History professor Jeff Ravel and students build a working printing press based on early modern European designs, in 21H.343J Making Books: The Renaissance and Today. (Photo by Jonathan Sachs / Jonathan Sachs Graphics, Inc.)

One of our favorite things at MIT OpenCourseWare is to shine a spotlight on fascinating subjects and great teachers that might otherwise escape notice. We’ve written before on the strength of MIT’s School of Humanities, Arts and Social Sciences (SHASS), both in their own right and in community with MIT’s more widely recognized STEM and business programs. OCW is pleased to freely share material from nearly 800 courses from across all SHASS disciplines.

Where to begin among all this free learning material? If you’re an educator (or just curious about teaching and learning process), you’re in luck!  OCW Educator project manager Sarah Hansen recently worked with SHASS colleagues to compile a list of OCW highlights, which we republish here. Each of these links goes to the course’s “This Course at MIT” section, where the instructor shares detailed insights about their teaching approach.

Anthropology

21A.445 Slavery and Human Trafficking in the 21st Century (Spring 2015), Mitali Thakor
Mitali Thakor describes how she uses non-traditional examples to broaden students’ understanding of human trafficking, how she thinks about students’ emotional responses to triggering topics, how she navigates teaching as a new instructor, and her thoughts on using writing assignments to encourage students to complete reading assignments.

Comparative Media Studies/Writing

21W.758 Genre Fiction Workshop (Spring 2013), Shariann Lewitt
Shariann Lewitt shares unique aspects of teaching fiction writing at MIT and discusses how she teaches students to challenge texts.

21W.747 Rhetoric (Spring 2015), Steven Strang
Steven Strang describes how he facilitates writing workshops and how he changes the course from year to year.

CMS.590J Computer Games and Simulations for Education and Exploration (Spring 2015), Eric Klopfer
Eric Klopfer describes the form and function of teamwork in this course. He also shares tips for facilitating project-based learning.

CMS.611J Creating Video Games (Fall 2014), Philip Tan, Sara Verrilli, Richard Eberhardt, and Andrew Haydn Grant
The instructors share their pedagogical approaches in 8 videos. Topics include: teaching students how to solve creative problems as teams; sequencing learning experiences; encouraging iteration, fostering diversity of voice in the course; assessing students’ projects; refining the course; advice for other educators; and their reflections on the collaboration between MIT and the Red Cross/Red Crescent Society during the course.  

CMS.608/CMS.864 Game Design (Spring 2014), Philip Tan and Richard Eberhardt
Philip Tan and Richard Eberhardt discuss how they prepare for the semester and class sessions, how they help students build game-playing experience, their assessment design, and factors, such as student background and feedback from students, that impact how they teach the course.

Global Studies and Languages

21G.101 Chinese I (Regular) (Fall 2014), Haohsiang Liao
In video interviews, recorded in both English and Chinese, Haohsiang Liao shares how the curriculum in this course helps students develop cultural competence. He also describes the daily grading system in the course, the importance of listening to audio files, reasons to prioritize speaking and listening before reading and writing, how he supports struggling students, how he creates an immersive classroom environment, and how he motivates students to engage in language study. 

21G.107 Chinese I (Streamlined) (Fall 2014), Min-Min Liang
In video interviews, recorded in both English and Chinese, Min-Min Liang shares her philosophical approach to language teaching, her insights about teaching heritage learners, her use of technology in this streamlined language course, her approach to assessment, and her hopes for incorporating more authentic texts into the curriculum in future iterations of the course.

21G.735 Advanced Topics in Hispanic Literature and Film: The Films of Luis Bunuel (1999-2013), Elizabeth Garrels
This course was taught at MIT seven times between 1999 and 2013. Elizabeth Garrels shares a history of the course, her film selections, and how she facilitated discussions in Spanish with students at different language proficiency levels.

RES.21G-001 The User-Friendly Classroom, A.C. Kemp
A.C. Kemp discusses the importance of focusing on International Teaching Assistants (ITAs), shares how user experience can be applied to ITA training, and ways to use the materials in this video training series.

History

21H.134J Medieval Economic History in Comparative Perspective (Spring 2012), Anne McCants
Anne McCants shares insights about using a survey at the beginning of a course to understand students’ needs and backgrounds, to help students see that different students have different needs, and to encourage students to get into the habit of writing. She also discusses how she frames the humanities as problem solving endeavors and how she infuses the course with current events. Other topics include: teaching communication, the intersection of research and teaching, and adapting the course from year to year.

21H.343J Making Books: The Renaissance and Today (Spring 2016), Anne McCants, Jeffrey Ravel and Ken Stone
The instructors of this course, in which students built a printing press, discuss using archival experiences to ground readings and allay educators’ skepticism about facilitating a hands-on course in the humanities.

21H.991 Theories and Methods in the Study of History (Fall 2014), Anne McCants
Anne McCants shares how she engages students in archive-based research, how she infuses the course with multiple voices, and how she helps students develop professional competencies.

Literature

21L.011 The Film Experience (Fall 2013), David Thorburn
David Thorburn shares his pedagogical approach to teaching film in seven videos. Topics include his approach to lecturing, how he views the course as literary in nature, how the course has changed over the 30 years that he has taught it, the role of video lectures, and the themes structuring course.

21L.315 Prizewinners: Nobelistas (Spring 2015), Wyn Kelley
Wyn Kelley shares how she selects Nobelistas to spotlight in the course, how she facilitates discussions, and her approach to teaching novices.

21L.460 Medieval Literature: Legends of Arthur (Fall 2013), Arthur Bahr
Arthur Bahr describes how he sets the stage for the study of Arthurian literature with a key question, how he encourages participation during classroom discussions, and his ideas for alternative assessment strategies in the course.

21L.501 The American Novel: Stranger and Stranger (Spring 2013), Wyn Kelley
Wyn Kelley describes her motivation for developing the course and how she organizes it. She also describes her text selection, the digital tools she uses in the course, workshops, and unique aspects of teaching literature at MIT.

21L.705 Major Authors: Old English (Spring 2014), Arthur Bahr
Arthur Bahr describes the curricular scope and sequence of the course, his textbook choice, how he assesses student learning, and how he develops rapport with students.

Linguistics and Philosophy

24.191 Ethics in Your Life: Being, Thinking, Doing (or Not?) (Spring 2015), Sally Haslanger, Patricia-Maria Weinmann, Brendan de Kennessy
Patricia-Maria Weinmann and Brendan de Kenessey share the history and design of this course, how they cultivated a classroom culture conducive to honest discussions, and how they experimented with a new discussion format.

Music and Theater Arts

21M.065 Introduction to Musical Composition (Spring 2014), Keeril Makan 
Keeril Makan describes his pedagogical goals in the course, which include helping students develop different ways of listening to music and to their environments and providing students with a hands-on introduction to music. He also shares pedagogical strategies, such as emphasizing student performance, using paper and pencil before employing software to complete projects, and engaging students in composer forums and concerts.

21M.380 Music and Technology: Sound Design (Spring 2016), Florian Hollerweger 
Florian Hollerweger discusses course design, teaching with technology (and without), learning actively in groups, using surveys to get to know students, assessing student learning in creative contexts, and engaging students deeply in the design process.

Political Science

17.445/17.446 International Relations Theory in the Cyber Age (Fall 2015), Nazli Choucri
Nazli Choucri comments on the importance of active participation during seminars and shares how she uses questions to promote engagement.

Science, Technology, and Society

STS.080/11.151 Youth Political Participation (Spring 2016), Jennifer Light
tudents take an active role in this course. They help the instructor, Jennifer Light, write the exam questions, lead presentations, and examine primary sources at the MIT Museum. In addition to instructor insights, visitors to the OCW course will find student perspectives about the pedagogical strategies shaping the learning experiences in this class.

Women and Gender Studies

WGS.151 Gender, Health, and Society (Spring 2016), Brittany Charlton
Brittany Charlton shares teaching techniques she uses to engage students, her insights on teaching content rooted in real-world contexts, and her thoughts on teaching students with a broad range of background experiences. She also discusses students’ final projects.

Mind and Hand and Ears

Collage of a Pure Data patch, consisting of several labeled boxes connected by lines, overlaying a black-and-white photo of a steam locomotive with steam blowing up out of the whistle.

One of the sound design exercises in 21M.380 challenges students to synthesize a steam train drive-by, with each group working on a different sound related to that problem. (Steam train photo is in the public domain, from Flickr Commons.)

By Joe Pickett, OCW Publication Director

People love sound effects. They have for generations. Just think of the original King Kong’s roar, created for the 1933 film by weaving together lion and tiger roars and playing them backwards. What would the movie be without that signature sound?

Certain sound effects are so iconic they have legs, so to speak. Like that bird whose call tells you the setting is deep in the jungle, no matter the continent. Or the scream of the guy who meets his doom by being attacked or falling from a cliff. That same scream has been used again and again in over 50 years of movies.

And what about those sounds that must be fully imagined? Like those space ships careering across the galaxy? The sound of the engines is so compelling the audience is happy to forget that, in the vacuum of space, sound does not exist. How did that sound get made?

Actually, it was designed. Design is a key part of the MIT “mind and hand” education. The art and science of sound design is the subject of 21M.380 Music and Technology: Sound Design, the latest in a series of courses on sound and technology that OCW has up on its site.

This most recent publication reflects the teaching of Dr. Florian Hollerweger, a sound artist and sound technology researcher in MIT’s Department of Music and Theater Arts.

Teaching with Technology (and Without)

The course site has lecture notes, readings, assignments, and samples of student projects through multiple iterations, so you can see how the projects evolved. MIT students and OCW learners alike benefit from the course’s use of a free open-source program called Pure Data. Dr. Hollerweger’s extensive notes include linked audio samples and working examples of Pure Data code, creating a dynamic learning experience.

Dr. Hollerweger explains the central practice of the course in the Instructor Insights on his This Course at MIT page:

 . . . we take real-world sounds and try to understand how they work. We then recreate them from scratch without using any recordings. Instead we rely on oscillators, noise generators, and filters, which we control through computer programs that students learn to write as part of the course . . . The prospect of engaging with students in the process of aestheticizing everyday sound experiences was a major impetus for teaching the course.

Learning to Listen

Before creating sounds, students must first learn how to listen. Or, as Dr. Hollerweger puts it, “Your main tool for sound design is really your ears.”  The soundwalk assignment is where it all begins. The students

 . . . describe, in as minute detail as possible, their aural experience from a listening excursion that we conduct across the MIT campus together. This assignment teaches them to verbalize their sonic impressions and communicate them to others. It trains students’ ears to attend not only to individual sound sources, but also to flutter echoes, comb filters, and other subtle acoustics effects that are due to the abutting architecture.

In other Instructor Insights, Dr. Hollerweger explains how he uses surveys to get to know his students and to tap their various talents, how he gets them learning actively in groups (he employs only the shortest of lectures), how he teaches the iterative design process, and how he assesses and grades creative projects.

Offering Advice

A lot of the instruction takes place the old-fashioned way—meeting one on one during office hours:

A lot of the support I offer students during the design process occurs during office hours. This is because their projects are so individualized. Every student has to come up with their own idea. When a student gets stuck, we need to get together to identify the key challenges of their design through an open-ended discussion.

[Applause!]

21M.380 is but the latest course in which instruction in the iterative design process is represented on OCW. Some other recent examples are CMS.611J Creating Video Games, 6.811 Principles and Practice of Assistive Technology, and 20.219 Becoming the Next Bill Nye: Writing and Hosting the Educational Show.

Person-to-Person in Urban Sociology

Photo of urban street scene, with brightly painted front of an auto muffler shop.

A neighborhood in the Bronx, New York City. Part of this course focuses on the changing concept of “community” and the effects of neighborhood characteristics on individuals. (Courtesy of Axel Drainville on Flickr. CC BY-NC.)

By Joe Pickett, OCW Publication Director

Teaching at the college level is often exciting and rewarding, but it is rarely easy, especially in discussion-based classes, where learning depends on student participation. Getting shy students to share their opinions in a classroom, and preventing the extroverts from dominating the conversation—these are perennial challenges for instructors. Students can have very different backgrounds, with different notions of forwardness and politeness, so establishing a civil dialogue can be a delicate matter.

That’s assuming the class is taking place on a college campus. How much more difficult would teaching be in a prison, with half the students as inmates and the other half as young eager beavers from a celebrated nearby college?

Professor Justin Steil and Teaching Assistant Aditi Mehta took on this challenge as instructors of 11.469 Urban Sociology in Theory and Practice, newly published on OCW. In Spring 2016 they taught this course at the Massachusetts Correctional Facility in Norfolk, MA, where about half the students were inmates participating in the Boston University Metropolitan College Prison Education Program.  In their Instructor Insights on their This Course at MIT page, Steil and Mehta explain their strategies for breaking the ice between these MIT and BU students to create a collaborative learning environment.

Opening Up Discussion through Collaborative Assignments

One way to get people talking is to have at least one student from each group working together on assignments.  The task can be simple, such as handing out to each group identical images of urban life, and then having the students with matching images join up and generate some observations about what they see.  Other assignments, such as presentations on the Spring 2016 readings, required similar cross-group collaboration. The challenge for the students was compounded by the fact that they could not communicate outside of class because of prison rules. That meant that all of their presentation’s insights and structure had to be developed during class breaks.

In this environment, discussions bloomed and interestingly showed some telling differences between groups. The MIT students tended to focus on “the oppressive power of larger socio-economic structures,” while the BU students felt that this viewpoint was too limiting and “found more dignity in recognizing the significance of personal choice and agency.” As the instructors saw it, “The micro ‘personal stories’ and macro ‘abstract analysis’ were different and valuable ways of making sense of and engaging the same material.”

Unleashing the Power of Low Tech

The BU students had no access to the Internet, email, word processing, or printers, so Steil and Mehta had to prepare everything in paper form before class. This forced them to be more organized than they would otherwise have been. They believe that it improved the dynamics of the class as well:

“Simply making eye contact with someone when they speak instead of typing on your computer actually builds trust.  Students were really listening to each other, and distractions were not a problem in this class.  And as instructors, lecturing or teaching without A/V aids forced us to internalize and embrace the material and communicate it clearly. We could not hide behind a pretty slide or bullet points. In our future teaching, we hope to continue embracing this way of facilitating and learning— simply person to person.”

Teaching Calculus, the Beautiful Language of Change

 

Move…accelerate…reach the peak…bottom out…transform…

So many ways to look at change, to talk about change. Change is inescapable. And change can be scary, especially when you don’t understand what’s happening. Yet change can also be an opportunity for growth, for progress, for new insights.

The same could be said of the millions of students who take calculus classes every year. As teachers know, it’s a rich opportunity for student growth and insight, and also scary as they’re getting started. More than a math subject, calculus is fundamentally the language of change. It’s a beautiful and powerful expression of this universal phenomenon, and a great way to tackle a wide range of real-world problems.

MIT’s John Bush, professor of applied mathematics (and a fabulous photographer of fluid phenomena), offers some great calculus teaching tips in the above video. We hope you can motivate students by demonstrating how to revel in the beauty of the language, and all the things it can do, before diving into the nitty-gritty grammar of deltas and epsilons. Professor Bush suggests:

  • Sharks hunt with calculus! They intuitively “follow the gradient” of scent, or the direction that gives the highest rate of increase, to take them toward their prey.
  • Introductory physics students will have learned Snell’s law as an equation about the angles of light paths through different media. But calculus can show that it’s fundamentally an optimization problem of light following the fastest route; just like how a smartphone GPS map calculates your fastest route home through tangled streets and busy traffic. (See this explanation of route-finding by mathematician and writer Steven Strogatz.)
  • Archimedes’ Principle is a great way to experience the concept and importance of volume, and also the way integrals work. (Again, see Steven Strogatz’s engaging explanation.)

As Professor Bush says, calculus “is a language that’s valuable in virtually all disciplines, from physics to biology, from finance to engineering.”  Motivate deeper student engagement by demonstrating how beautiful it can be to describe their ever-changing world with the poetics of mathematics.

Calculus on OCW

OCW has a wealth of inspiring calculus teaching materials, all free and licensed for you to re-use and remix in your classroom. You’ll find complete courses, online textbooks, videos, many sample problems with solutions, and more. Here are some highlights.

Complete Courses

These two courses, from the OCW Scholar series, provide the complete teaching materials comprising MIT’s undergraduate calculus requirement. They’re a great place to begin, and house some of OCW’s most popular calculus material.

These OCW sites include complete video lectures, selected problem solving videos by course teaching assistants, and problems and exams with solutions. You can start at the beginning and work through it all in sequence, or pick and choose your own topics of interest from the syllabus.

Online Textbooks

These open-licensed textbooks by respected authors are free to download and use in your classroom, and for your own learning and inspiration.

  • Calculus for Beginners and Artists, by Daniel Kleitman
    An overview of calculus in clear, easy to understand language designed for the non-mathematician.
  • Calculus, by Gilbert Strang
    In-depth treatment of single variable and multivariable calculus, with plenty of applications. Also has an online Instructor’s Manual and a student Study Guide.
  • Calculus with Applications, by Daniel Kleitman
    Detailed lecture notes (in the form of a textbook) that cover differential calculus in one and several dimensions.
  • Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving, by Sanjoy Mahajan
    From its MIT Press catalog description: “…an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.”

Videos

Use these videos to inspire your own approach to teaching. Students can watch them for in-depth and engaging explanations of key concepts, and to supplement their classroom instruction time.

  • Highlights of Calculus video series, by Gilbert Strang
    Five videos provide an overview of the key topics and ideas of calculus and how they apply to real-life situations and problems. There are summary slides and practice problems complete with an audio narration by Professor Strang. The resource also includes a series of 12 videos, with slides and practice problems, that dig more deeply into derivatives.
  • Single Variable Calculus lecture videos with PDF notes, by David Jerison
    This sequence of videos and accompanying notes (beginning with the first class session) covers differentiation, applications of differentiation, the definite integral and its applications, techniques of integration, and exploring the infinite.
  • Calculus Revisited: Single Variable Calculus, by Herb Gross
    A revered series of videos and related resources covering the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970, and has achieved something of a cult following in its second life on OCW and YouTube.
  • Get problem solving tips in the recitation videos by course teaching assistants in 18.01SC Single Variable Calculus and 18.02SC Multivariable Calculus. Start with these videos at the end of the first 18.01SC session “Introduction to Derivatives“:
    • Definition of Derivative, by Joel Lewis
    • Graphing a Derivative Function, by Christine Breiner

Problem Solving and Assessment

Use questions and accompanying solutions from OCW’s worked examples, problem sets and exams directly with your students, or as a basis for your own instruction. Begin your exploration with these examples:

AP Calculus Exam Study

With OCW Highlights for High School, you can search for OCW calculus materials by topic and subtopic, to help students prepare for their AP Calculus exams.

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These material highlights are just a tiny fraction of all of the calculus content on OCW. In the words of Professor John Bush, with calculus “the possibilities are endless!”