👓 Teaching With Emerging Technologies | Inside Higher Ed

Teaching With Emerging Technologies by Michelle Pacansky-Brock (Inside Higher Ed)
Michelle Pacansky-Brock says digital learning is reshaping the higher ed landscape, and suggests five things instructors need to succeed. As online and blended learning reshape the landscape of teaching and learning in higher education, the need increases to encourage and support faculty in moving from delivering passive, teacher-centered experiences to designing active, student-centered learning. Our new social era is rich with simple, free to low-cost emerging technologies that are increasing experimentation and discovery in the scholarship of teaching and learning. While the literature about Web 2.0 tools impacting teaching and learning is increasing, there is a lack of knowledge about how the adoption of these technologies is impacting the support needs of higher education faculty. This knowledge is essential to develop new, sustainable faculty support solutions.

This might make an outline for a nice book, but as an article it’s a bit wonkish and doesn’t get into the meat of much.

Syndicated copies to:

Twitter List from #Domains17

Twitter List from #Domains17 by Chris Aldrich (Twitter)
Teachers, educators, researchers, technologists using open technologies in education #openEd, #edTech, #DoOO, #indieweb

I’ve compiled a twitter list of people related to #openEd, #edTech, #DoOO, #indieweb, and related topics who tweeted about #domains17 in the past week. The list has multiple views including members and by tweets.

Feel free to either subscribe to the list (useful when adding streams to things like Tweetdeck), or for quickly scanning down the list and following people on a particular topic en-masse. Hopefully it will help people to remain connected following the conference. I’ve written about some other ideas about staying in touch here.

If you or someone you know is conspicuously missing, please let me know and I’m happy to add them. Hopefully this list will free others from spending the inordinate amount of time to create similar bulk lists from the week.

Syndicated copies to:

📺 Domains2017 Conference: Tuesday June 6, 3:00pm with the OU Crew | YouTube

Tuesday June 6, 3:00pm with the OU Crew from YouTube
For more information see the blog post for the event at http://virtuallyconnecting.org/blog/2017/05/31/domains17/

Indieweb for Education: Some thoughts after the Domains 17 Conference

There’s some interesting discussion of Indieweb-related principles in this live-streamed (and recorded) conversation (below) from the Domains 2017 conference for educators and technologists which covers a lot of what I’d consider to be Indieweb for Education applications.

In particular, some asked about alternate projects for basing education projects around which aren’t WordPress. Some suggested using WithKnown which is spectacular for its interaction model and flexibility. I suspect that many in the conversation haven’t heard of or added webmentions (for cross-site/cross-platform conversations or notifications) or micropub to their WordPress (or other) sites to add those pieces of functionality that Known comes with out of the box.

Another section of the conversation mentioned looking for ways to take disparate comments from students on their web presences and aggregating them in a more unified manner for easier consumption by the teacher and other students (as opposed to subscribing to each and every student’s RSS feed, a task which can be onerous in classrooms larger than 20 people). To me this sounded like the general concept of a planet, and there are a few simple ways of accomplishing this already, specifically using RSS.

I was also thrilled to hear the ideas of POSSE and PESOS mentioned in such a setting!

An Invitation to Attendees

I’d invite those in attendance at the Domains 17 conference to visit not only the Indieweb wiki, but to feel free to actively participate in the on-going daily discussions (via IRC/Slack/Matrix/Web). I suspect that if there’s enough need/desire that the community would create a dedicated #education channel to help spur the effort to continue to push the idea of owning one’s own domain and using it for educational purposes out into the mainstream. The wiki pages and the always-on chat could be useful tools to help keep many of the educators and technologists who attended Domains17 not only connected after the event, but allow them to continue to push the envelope and document their progress for the benefit of others.

I’ll admit that one of my favorite parts of the Indieweb wiki is that it aggregates the work of hundreds of others in an intuitive way so that if I’m interested in a particular subject I can usually see the attempts that others have made (or at least links to them), determine what worked and didn’t for them, and potentially find the best solution for my particular use case. (I suspect that this is some of what’s missing in the “Domains” community at the moment based on several conversations I heard over the past several days.)

If you’d like, please add yourself to the growing list of Indieweb related educators and technologists. If you need help connecting to any of the community resources and/or chat/IRC/Slack, etc. I’m more than happy to help. Just call, email, or contact me via your favorite channel.

Syndicated copies to:

JUMP Math, a teaching method that’s proving there’s no such thing as a bad math student | Quartz

A mathematician has created a teaching method that’s proving there’s no such thing as a bad math student by Jenny Anderson (Quartz)
"Mathematicians have big egos, so they haven’t told anyone that math is easy.”

Continue reading “JUMP Math, a teaching method that’s proving there’s no such thing as a bad math student | Quartz”

Just spent the last 25 minutes hanging out with Terry Tao talking about complex analysis, blogging, and math pedagogy

Just spent the last 25 minutes hanging out with Terry Tao talking about complex analysis, blogging, and math pedagogy

Just spent the last 25 minutes hanging out with Terry Tao talking about complex analysis, blogging, and math pedagogy

Instagram filter used: Normal

Photo taken at: UCLA Math Sciences Building

Dr. Tao is keeping a great set of complex analysis notes on his blog.

Syndicated copies to:

Why math? JHU mathematician on teaching, theory, and the value of math in a modern world | Hub

Why math? JHU mathematician on teaching, theory, and the value of math in a modern world (The Hub)

Great to see this interview with my friend and mathematician Richard Brown from Johns Hopkins Unviersity.  Psst: He’s got an interesting little blog, or you can follow some of his work on Facebook and Twitter.

Click through for the full interview: Q+A with Richard Brown, director of undergraduate studies in Johns Hopkins University’s Department of Mathematics

 

Syndicated copies to:

Popular Science Books on Information Theory, Biology, and Complexity

The beginning of a four part series in which I provide a gradation of books and texts that lie in the intersection of the application of information theory, physics, and engineering practice to the area of biology.

Previously, I had made a large and somewhat random list of books which lie in the intersection of the application of information theory, physics, and engineering practice to the area of biology.  Below I’ll begin to do a somewhat better job of providing a finer gradation of technical level for both the hobbyist or the aspiring student who wishes to bring themselves to a higher level of understanding of these areas.  In future posts, I’ll try to begin classifying other texts into graduated strata as well.  The final list will be maintained here: Books at the Intersection of Information Theory and Biology.

Introductory / General Readership / Popular Science Books

These books are written on a generally non-technical level and give a broad overview of their topics with occasional forays into interesting or intriguing subtopics. They include little, if any, mathematical equations or conceptualization. Typically, any high school student should be able to read, follow, and understand the broad concepts behind these books.  Though often non-technical, these texts can give some useful insight into the topics at hand, even for the most advanced researchers.

Complexity: A Guided Tour by Melanie Mitchell (review)

Possibly one of the best places to start, this text gives a great overview of most of the major areas of study related to these fields.

Entropy Demystified: The Second Law Reduced to Plain Common Sense by Arieh Ben-Naim

One of the best books on the concept of entropy out there.  It can be read even by middle school students with no exposure to algebra and does a fantastic job of laying out the conceptualization of how entropy underlies large areas of the broader subject. Even those with Ph.D.’s in statistical thermodynamics can gain something useful from this lovely volume.

The Information: A History, a Theory, a Flood by James Gleick (review)

A relatively recent popular science volume covering various conceptualizations of what information is and how it’s been dealt with in science and engineering.  Though it has its flaws, its certainly a good introduction to the beginner, particularly with regard to history.

The Origin of Species by Charles Darwin

One of the most influential pieces of writing known to man, this classical text is the basis from which major strides in biology have been made as a result. A must read for everyone on the planet.

Information, Entropy, Life and the Universe: What We Know and What We Do Not Know by Arieh Ben-Naim

Information Theory and Evolution by John Avery

The Touchstone of Life: Molecular Information, Cell Communication, and the Foundations of Life by Werner R. Loewenstein (review)

Information Theory, Evolution, and the Origin of Life by Hubert P. Yockey

The four books above have a significant amount of overlap. Though one could read all of them, I recommend that those pressed for time choose Ben-Naim first. As I write this I’ll note that Ben-Naim’s book is scheduled for release on May 30, 2015, but he’s been kind enough to allow me to read an advance copy while it was in process; it gets my highest recommendation in its class. Loewenstein covers a bit more than Avery who also has a more basic presentation. Most who continue with the subject will later come across Yockey’s Information Theory and Molecular Biology which is similar to his text here but written at a slightly higher level of sophistication. Those who finish at this level of sophistication might want to try Yockey third instead.

The Red Queen: Sex and the Evolution of Human Nature by Matt Ridley

Grammatical Man: Information, Entropy, Language, and Life  by Jeremy Campbell

Life’s Ratchet: How Molecular Machines Extract Order from Chaos by Peter M. Hoffmann

Complexity: The Emerging Science at the Edge of Order and Chaos by M. Mitchell Waldrop

The Big Picture: On the Origins of Life, Meaning, and the Universe Itself (Dutton, May 10, 2016) 

In the coming weeks/months, I’ll try to continue putting recommended books on the remainder of the rest of the spectrum, the balance of which follows in outline form below. As always, I welcome suggestions and recommendations based on others’ experiences as well. If you’d like to suggest additional resources in any of the sections below, please do so via our suggestion box. For those interested in additional resources, please take a look at the ITBio Resources page which includes information about related research groups; references and journal articles; academic, research institutes, societies, groups, and organizations; and conferences, workshops, and symposia.

Lower Level Undergraduate

These books are written at a level that can be grasped and understood by most with a freshmen or sophomore university level. Coursework in math, science, and engineering will usually presume knowledge of calculus, basic probability theory, introductory physics, chemistry, and basic biology.

Upper Level Undergraduate

These books are written at a level that can be grasped and understood by those at a junior or senor university level. Coursework in math, science, and engineering may presume knowledge of probability theory, differential equations, linear algebra, complex analysis, abstract algebra, signal processing, organic chemistry, molecular biology, evolutionary theory, thermodynamics, advanced physics, and basic information theory.

Graduate Level

These books are written at a level that can be grasped and understood by most working at the level of a master’s level at most universities.  Coursework presumes all the previously mentioned classes, though may require a higher level of sub-specialization in one or more areas of mathematics, physics, biology, or engineering practice.  Because of the depth and breadth of disciplines covered here, many may feel the need to delve into areas outside of their particular specialization.

Syndicated copies to:

Why Aren’t Math Textbooks More Straightforward?

Math textbooks often seem difficult, obtuse, and often incomprehensible. Here are some hints and tips for making the situation better for all students.

Some General Advice for Math Students of All Ages

I recently saw the question “Why aren’t math textbooks more straightforward?” on Quora.

In fact, I would argue that most math textbooks are very straightforward!

The real issue most students are experiencing is one of relativity and experience.  Mathematics is an increasingly sophisticated, cumulative, and more complicated topic the longer you study it. Fortunately, over time, it also becomes easier, more interesting, and intriguingly more beautiful.

As an example of what we’re looking at and what most students are up against, let’s take the topic of algebra. Typically in the United States one might take introductory algebra in eighth grade before taking algebra II in ninth or tenth grade. (For our immediate purposes, here I’m discounting the potential existence of a common pre-algebra course that some middle schools, high schools, and even colleges offer.)  Later on in college, one will exercise one’s algebra muscles in calculus and may eventually get to a course called abstract algebra as an upper-level undergraduate (in their junior or senior years).  Most standard undergraduate abstract algebra textbooks will cover ALL of the material that was in your basic algebra I and algebra II texts in about four pages and simply assume you just know the rest! Naturally, if you started out with the abstract algebra textbook in eighth grade, you’d very likely be COMPLETELY lost. This is because the abstract algebra textbook is assuming that you’ve got some significant prior background in mathematics (what is often referred to in the introduction to far more than one mathematics textbook as “mathematical sophistication”, though this phrase also implicitly assumes knowledge of what a proof is, what it entails, how it works, and how to actually write one).

Following the undergraduate abstract algebra textbook there’s even an additional graduate level course (or four) on abstract algebra (or advanced subtopics like group theory, ring theory, field theory, and Galois theory) that goes into even more depth and subtlety than the undergraduate course; the book for this presumes you’ve mastered the undergraduate text and goes on faster and further.

A Weightlifting Analogy

To analogize things to something more common, suppose you wanted to become an Olympic level weightlifter.  You’re not going to go into the gym on day one and snatch and then clean & jerk 473kg! You’re going to start out with a tiny fraction of that weight and practice repeatedly for years slowly building up your ability to lift bigger and bigger weights. More likely than not, you’ll also very likely do some cross-training by running, swimming, and even lifting other weights to strengthen your legs, shoulder, stomach, and back.  All of this work may eventually lead you to to win the gold medal in the Olympics, but sooner or later someone will come along and break your world record.

Mathematics is certainly no different: one starts out small and with lots of work and practice over time, one slowly but surely ascends the rigors of problems put before them to become better mathematicians. Often one takes other courses like physics, biology, and even engineering courses that provide “cross-training.”  Usually when one is having issues in a math class it’s because they’re either somehow missing something that should have come before or because they didn’t practice enough in their prior classwork to really understand all the concepts and their subtleties.  As an example, the new material in common calculus textbooks is actually very minimal – the first step in most problems is the only actual calculus and the following 10 steps are just practicing one’s algebra skills. It’s usually in carrying out the algebra that one makes more mistakes than in the actual calculus.

Often at the lower levels of grade-school mathematics, some students can manage to just read a few examples and just seem to “get” the answers without really doing a real “work out.” Eventually they’ll come to a point at which they hit a wall or begin having trouble, and usually it comes as the result of not actually practicing their craft.  One couldn’t become an Olympic weightlifter by reading books about weightlifting, they need to actually get in the gym and workout/practice. (Of course, one of the places this analogy breaks down is that weightlifting training is very linear and doesn’t allow one to “skip around” the way one could potentially in a mathematics curriculum.)

I’m reminded of a quote by mathematician Pierre Anton Grillet: “…algebra is like French pastry: wonderful, but cannot be learned without putting one’s hands to the dough.” It is one of the most beautiful expressions of the recurring sentiment written by almost every author into the preface of nearly every mathematics text at or above the level of calculus. They all exhort their students to actually put pencil to paper and work through the logic of their arguments and the exercises to learn the material and gain some valuable experience.  I’m sure that most mathematics professors will assure you that in the end, only a tiny fraction of their students actually do so. Some of the issue is that these exhortations only come in textbooks traditionally read at the advanced undergraduate level, when they should begin in the second grade.

Patissiere puts their hands to a pie crust in a rustic kitchen
“Algebra is like French Pastry: wonderful, but cannot be learned without putting one’s hands to the dough.” -Pierre Anton Grillet

“It’s Easy to See”

A common phrase in almost every advanced math textbook on the planet is the justification, “It’s easy to see.” The phrase, and those like it, should be a watchword for students to immediately be on their guard!  The phrase is commonly used in proofs, discussions, conversations, and lectures in which an author or teacher may skip one or more steps which she feels should be obvious to her audience, but which, in fact, are far more commonly not obvious.

It’s become so cliche that some authors actually mention specifically in their prefaces that they vow not to use the phrase, but if they do so, they usually let slip some other euphemism that is its equivalent.

The problem with the phrase is that everyone, by force of their own circumstances and history, will view it completely differently.  A step that is easy for someone with a Ph.D. who specialized in field theory to “see” may be totally incomprehensible for a beginning student of algebra I in the same way that steps that were easy for Girgory Perelman to see in his proof of the Poincaré conjecture were likewise completely incomprehensible for teams of multiple tenured research professors of mathematics to see. (cross reference: The Poincaré Conjecture: In Search of the Shape of the Universe by Donal O’Shea (Walker & Co., 2007))

How to Actively Read a Math Text

The Problem

So how are students to proceed? It will certainly help to see a broader road map of what lies ahead and what the expected changes in terrain will look like. It will also help greatly if students have a better idea how to approach mathematics for themselves and even by themselves in many cases.

In my opinion, the most common disconnect occurs somewhere between high school mathematics and early college mathematics (usually a calculus sequence, linear algebra) and then again between linear algebra/differential equations (areas which usually have discussion followed by examples and then crank-out problems) and higher abstract mathematical areas like analysis, abstract algebra, topology (areas in which the definition-theorem-proof cycle of writing is more common and seemingly more incomprehensible to many).

The first big issue in early college mathematics is the increased speed at which college courses move. Students used to a slower high school pace where the teachers are usually teaching to the middle or lower end of the class get caught unaware as their college professors teach to the higher ability students and aren’t as afraid to leave the lower end of the spectrum behind. Just like high school athletes are expected to step up their game when they make the transition to college and similarly college athletes who go pro, mathematics students should realize they’re expected to step up their game at the appropriate times.

Often math students (and really any student of any subject) relies on the teacher assigning readings or problems from their book rather than excersizing their curiosity to more avidly and broadly explore the material on their own.  If they can take the guidance of their teacher as well as that of the individual authors of books, they may make it much further on their own.  High school teachers often skip sections of textbooks for time, but students should realize that there is profitable and interesting material that they’re skipping.  Why not go and read it on their own?

Earlier I mentioned that an average undergraduate abstract algebra textbook might cover the totality of a high school algebra textbook in about three pages.  What does this mean for upper level mathematics students?  It almost always means that the density of material in these books is far greater than that of their earlier textbooks.  How is this density arrived at?  Authors of advanced textbooks leave out far more than they’re able to put in, otherwise their 300 page textbooks, if written at the same basic level as those that came before would be much more ponderous 1000+ page textbooks.  What are they leaving out?  Often they’re leaving out lots of what might be useful discussion, but more often, they’re leaving out lots of worked out examples. For example, a high school text will present a definition or concept and then give three or more illustrations or examples of problems relating to the concept.  The exercises will then give dozens of additional drill problems to beat the concept to death.  This type of presentation usually continues up to the level of calculus where one often sees massive tomes in the 800+ page length. Math texts after this point generally don’t go much over 300 pages as a rule, and it’s primarily because they’re leaving the examples out of the proverbial equation.

The Solution

How does one combat this issue?  Students need to more actively think back to the math they’ve taken previously and come up with their own simple examples of problems, and work though them on their own.  Just because the book doesn’t give lots of examples doesn’t mean that they don’t exist.

In fact, many textbooks are actually presenting examples, they’re just hiding them with very subtle textual hints. Often in the presentation of a concept, the author will leave out one or more steps in a proof or example and hint to the student that they should work through the steps themselves. (Phrases like: “we leave it to the reader to verify” or “see example 2.”) Sometimes this hint comes in the form of that dreaded phrase, “It’s easy to see.” When presented with these hints, it is incumbent (or some students may prefer the word encumbering) on the student to think through the missing steps or provide the missing material themselves.

While reading mathematics, students should not only be reading the words and following the steps, but they should actively be working their way through all of the steps (missing or not) in each of the examples or proofs provided. They must read their math books with pencil and paper in hand instead of the usual format of reading their math book and then picking up paper and pencil to work out problems afterwards.  Most advanced math texts suggest half a dozen or more problems to work out within the text itself before presenting a dozen or more additional problems usually in a formal section entitled “Exercises”. Students have to train themselves to be thinking about and working out the “hidden” problems within the actual textual discussion sections.

Additionally, students need to consider themselves “researchers” or think of their work as discovery or play.  Can they come up with their own questions or exercises that relate the concepts they’ve read about to things they’ve done in the past? Often asking the open ended question, “What happens if I…” can be very useful.  One has to imagine that this is the type of “play” that early mathematicians like Euclid, Gauss, and Euler did, and I have to say, this is also the reason that they discovered so many interesting properties within mathematics.  (I always like to think that they were the beneficiaries of “picking the lowest hanging fruit” within mathematics – though certainly they discovered some things that took some time to puzzle out; we take some of our knowledge for granted as sitting on the shoulders of giants does allow us to see much further than we could before.)

As a result of this newly discovered rule, students will readily find that while they could read a dozen pages of their high school textbooks in just a few minutes, it may take them between a half an hour to two hours to properly read even a single page of an advanced math text. Without putting in this extra time and effort they’re going to quickly find themselves within the tall grass (or, more appropriately weeds).

Another trick of advanced textbooks is that, because they don’t have enough time or space within the primary text itself, authors often “hide” important concepts, definitions, and theorems within the “exercises” sections of their books.  Just because a concept doesn’t appear in the primary text doesn’t mean it isn’t generally important.  As a result, students should always go out of their way to at least read through all of the exercises in the text even if they don’t spend the time to work through them all.

One of the difficult things about advanced abstract mathematics is that it is most often very cumulative and even intertwined, so when one doesn’t understand the initial or early portions of a textbook, it doesn’t bode well for the later sections which require one to have mastered the previous work.  This is even worse when some courses build upon the work of earlier courses, so for example, doing well in calculus III requires that one completely mastered calculus I. At some of the highest levels like courses in Lie groups and Lie algebras requires that one mastered the material in multiple other prior courses like analysis, linear algebra, topology, and abstract algebra. Authors of textbooks like these will often state at the outset what material they expect students to have mastered to do well, and even then, they’ll often spend some time giving overviews of relevant material and even notation of these areas in appendices of their books.

As a result of this, we can take it as a general rule: “Don’t ever skip anything in a math textbook that you don’t understand.” Keep working on the concepts and examples until they become second nature to you.

Finally, more students should think of mathematics as a new language.  I’ve referenced the following Galileo quote before, but it bears repeating (emphasis is mine):

Philosophy is written in this grand book, the universe which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.

Galileo Galilee (1564–1642) in Il saggiatore (The assayer)

Though mathematical notation has changed drastically (for the better, in my opinion) since Galileo’s time, it certainly has its own jargon, definitions, and special notations.  Students should be sure to spend some time familiarizing themselves with current modern notation, and especially the notation in the book that they choose.  Often math textbooks will have a list of symbols and their meanings somewhere in the end-papers or the appendices. Authors usually go out of their way to introduce notation somewhere in either the introduction, preface, appendices, or often even in an introductory review chapter in which they assume most of their students are very familiar with, but they write it anyway to acclimate students to the particular notation they use in their text.  This notation can often seem excessive or even obtuse, but generally it’s very consistent across disciplines within mathematics, but it’s incredibly useful and necessary in making often complex concepts simple to think about and communicate to others. For those who are lost, or who want help delving into areas of math seemingly above their heads, I highly recommend the text Mathematical Notation: A Guide for Engineers and Scientists by my friend Edward R. Scheinerman as a useful guide.

A high school student may pick up a textbook on Lie Groups and be astounded at the incomprehensibility of the subject, but most of the disconnect is in knowing and understanding the actual language in which the text is written.  A neophyte student of Latin would no sooner pick up a copy of Cicero and expect to be able to revel in the beauty and joy of the words or their meaning without first spending some time studying the vocabulary, grammar, and syntax of the language.  Fortunately, like Latin, once one has learned a good bit of math, the notations and definitions are all very similar, so once you can read one text, you’ll be able to appreciate a broad variety of others.

Actively Reading a Mathematics Text Review:

  • Work through the steps of everything within the text
  • Come up with your own examples
  • Work through the exercises
  • Read through all the exercises, especially the ones that you don’t do
  • Don’t ever skip anything you don’t fully understand
  • Math is a language: spend some time learning (memorizing) notation

Exceptions

Naturally there are exceptions to the rule. Not all mathematics textbooks are great, good, or even passable.  There is certainly a spectrum of textbooks out there, and there are even more options at the simpler (more elementary) end, in part because of there is more demand.  For the most part, however, most textbooks are at least functional.  Still one can occasionally come across a very bad apple of a textbook.

Because of the economics of textbook publishing, it is often very difficult for a textbook to even get published if it doesn’t at least meet a minimum threshold of quality. The track record of a publisher can be a good indicator of reasonable texts. Authors of well-vetted texts will often thank professors who have taught their books at other universities or even provide a list of universities and colleges that have adopted their texts. Naturally, just because 50 colleges have adopted a particular text doesn’t necessarily mean that that it is necessarily of high quality.

One of the major issues to watch out for is using the textbook written by one’s own professor.  While this may not be an issue if your professor is someone like Serge Lang, Gilbert Strang, James Munkres, Michael Spivak, or the late Walter Rudin, if your particular professor isn’t supremely well known in his or her field, is an adjunct or associate faculty member, or is a professor at a community college, then: caveat emptor.

Since mathematics is a subject about clear thinking, analysis, and application of knowledge, I recommend that students who feel they’re being sold a bill of goods in their required/recommended textbook(s), take the time to look at alternate textbooks and choose one that is right for themselves.  For those interested in more on this particular sub-topic I’ve written about it before: On Choosing Your own Textbooks.

Parting Advice

Often, even with the best intentions, some authors can get ahead of themselves or the area at hand is so advanced that it is difficult to find a way into it. As an example, we might consider Lie groups and algebras, which is a fascinating area to delve into. Unfortunately it can take several years of advanced work to get to a sufficient level to even make a small dent into any of the textbooks in the area, though some research will uncover a handful of four textbooks that will get one quite a way into the subject with a reasonable background in just analysis and linear algebra.

When one feels like they’ve hit a wall, but still want to struggle to succeed, I’m reminded of the advice of revered mathematical communicator Paul Halmos, whose book Measure Theory needed so much additional background material, that instead of beginning with the traditional Chapter 1, he felt it necessary to include a Chapter 0 (he actually called his chapters “sections” in the book) and even then it had enough issueshewas cornered into writing the statement:

…[the reader] should not be discouraged, if on first reading of section 0, he finds that he does not have the prerequisites for reading the prerequisites.

Paul Halmos in Measure Theory(1950)

This is essentially the mathematician’s equivalent of the colloquialism “Fake it ’til you make it.”

When all else fails, use this adage, and don’t become discouraged. You’ll get there eventually!

 

Syndicated copies to:

Algebra is Like Pastry: Wonderful!

Pierre Anton Grillet (1941 – ), algebraist
in preface to Abstract Algebra, Second Edition (Springer, 2007)

 

Syndicated copies to:

A Mathematical Symphony

Robert B. Ash, mathematician
in A Primer of Abstract Mathematics (The Mathematical Association of America, 1998)

 

A Primer of Abstract Mathematics by Robert B. Ash
A Primer of Abstract Mathematics by Robert B. Ash

 

Syndicated copies to:

The Teaching Company and The Great Courses versus MOOCs

Robert Greenberg recently wrote a Facebook post relating to a New York Times review article entitled “For This Class, Professors Pass Screen Test“. It’s substantively about The Teaching Company and their series The Great Courses (TGC); for convenience I’ll excerpt his comments in their entirety below:

A most interesting article on The Great Courses (TGC) appeared in the New York Times on Saturday. TGC has been featured in newspaper articles before: scads of articles, in fact, over the last 20-plus years. But those articles (at least the ones I’m aware of and I am aware of most of them) have always focused on the content of TGC offerings: that they are academic courses offered up on audio/video media. This article, written by the Times’ TV critic Neil Genzlinger, is different. It focuses on TGC as a video production company and on TGC courses as slick, professional, high-end television programs.

My goodness, how times have changed.

Long-time readers of this blog will recall my descriptions of TGC in its early days. I would rehash a bit of that if only to highlight the incredible evolution of the company from a startup to the polished gem it is today.

I made my first course back in May of 1993: the first edition of “How to Listen to and Understand Great Music”. We had no “set”; I worked in front of a blue screen (or a “traveling matte”). The halogen lighting created an unbelievable amount of heat and glare. The stage was only about 6 feet deep but about 20 feet wide. With my sheaf of yellow note paper clutched in my left hand, I roamed back-and-forth, in constant motion, teaching exactly the way I did in the classroom. I made no concessions to the medium; to tell the truth, it never occurred to me or my director at the time that we should do anything but reproduce what I did in the classroom. (My constant lateral movement did, however, cause great consternation among the camera people, who were accustomed to filming stationary pundits at CNN and gasbags at C-span. One of our camera-dudes, a bearded stoner who will remain nameless kept telling me “Man . . . I cannot follow you, man. Please, man, please!” He was a good guy though, and offered to “take my edge off” by lighting me up during our breaks. I wisely declined.)

We worked with a studio audience in those days: mostly retirees who were free to attend such recording sessions, many of whom fell asleep in their chairs after lunch or jingled change in their pockets or whose hearing aids started screaming sounds that they could not hear but I most certainly did. Most distracting were the white Styrofoam coffee cups; in the darkened studio their constant (if irregular) up-and-down motion reminded me of the “bouncing ball” from the musical cartoons of the 1930s, ‘40s, and ‘50s.

I could go on (and I will, at some other time), though the point is made: in its earliest days TGC was simply recording more-or-less what you would hear in a classroom or lecture hall. I am reminded of the early days of TV, during which pre-existing modes of entertainment – the variety show, theatrical productions, puppet shows – were simply filmed and broadcast. In its earliest permutation, the video medium did not create a new paradigm so much as record old ones. But this changed soon enough, and the same is true for TGC. Within a few years TGC became a genuine production company, in which style, look, and mode of delivery became as important as the content being delivered. And this is exactly as it should be. Audio and video media demand clarity and precision; the “ahs” and “ums” and garbled pronunciations and mismatched tenses that we tolerate in a live lecture are intolerable in media, because we are aware of the fact that in making media they can (and should) be corrected.

Enough. Read the article. Then buy another TGC course; preferably one of mine. And while watching and/or listening, let us be aware, as best as we can, of the tens-of-thousands of hours that go into making these courses – these productions – the little masterworks that they indeed are.

 

My response to his post with some thoughts of my own follows:

This is an interesting, but very germane, review. As someone who’s both worked in the entertainment industry and followed the MOOC (massively open online courseware) revolution over the past decade, I very often consider the physical production value of TGCs offerings and have been generally pleased at their steady improvement over time. Not only do they offer some generally excellent content, but they’re entertaining and pleasing to watch. From a multimedia perspective, I’m always amazed at what they offer and that generally the difference between the video versus the audio only versions isn’t as drastic as one might otherwise expect. Though there are times that I think that TGC might include some additional graphics, maps, etc. either in the course itself or in the booklets, I’m impressed that they still function exceptionally well without them.

Within the MOOC revolution, Sue Alcott’s Coursera course Archaeology’s Dirty Little Secrets is still by far the best produced multi-media course I’ve come across. It’s going to take a lot of serious effort for other courses to come up to this level of production however. It’s one of the few courses which I think rivals that of The Teaching Company’s offerings thus far. Unfortunately, the increased competition in the MOOC space is going to eventually encroach on the business model of TGC, and I’m curious to see how that will evolve and how it will benefit students. Will TGC be forced to offer online fora for students to interact with each other the way most MOOCs do? Will MOOCs be forced to drastically increase their production quality to the level of TGC? Will certificates or diplomas be offered for courseware? Will the subsequent models be free (like most MOOCs now), paid like TGC, or some mixture of the two?

One area which neither platform seems to be doing very well at present is offering more advanced coursework. Naturally the primary difficulty is in having enough audience to justify the production effort. The audience for a graduate level topology class is simply far smaller than introductory courses in history or music appreciation, but those types of courses will eventually have to exist to make the enterprises sustainable – in addition to the fact that they add real value to society. Another difficulty is that advanced coursework usually requires some significant work outside of the lecture environment – readings, homework, etc. MOOCs seem to have a slight upper hand here while TGC has generally relied on all of the significant material being offered in a lecture with the suggestion of reading their accompanying booklets and possibly offering supplementary bibliographies. When are we going to start seeing course work at the upper-level undergraduate or graduate level?

The nice part is that with evolving technology and capabilities, there are potentially new pedagogic methods that will allow easier teaching of some material that may not have been possible previously. (For some brief examples, see this post I wrote last week on Latin and the digital humanities.) In particular, I’m sure many of us have been astounded and pleased at how Dr. Greenberg managed the supreme gymnastics of offering of “Understanding the Fundamentals of Music” without delving into traditional music theory and written notation, but will he be able to actually offer that in new and exciting ways to increase our levels of understanding of music and then spawn off another 618 lectures that take us all further and deeper into his exciting world? Perhaps it comes in the form of a multimedia mobile app? We’re all waiting with bated breath, because regardless of how he pulls it off, we know it’s going to be educational, entertaining and truly awe inspiring.

Following my commentary, Scott Ableman, the Chief Marketing Officer for TGC, responded with the following, which I find very interesting:

Chris, all excellent observations (and I agree re Alcott’s course). I hope you’ll be please to learn that the impact of MOOCs, if any, on The Great Courses has been positive, in that there is a rapidly growing awareness and interest in the notion that lifelong learning is possible via digital media. As for differentiating vs. MOOCs, people who know about The Great Courses generally find the differences to be self-evident:

  1. Curation: TGC scours the globe to find the world’s greatest professors;
  2. Formats: The ability to enjoy a course in your car or at home on your TV or on your smartphone, etc.;
  3. Lack of pressure: Having no set schedule and doing things at your own pace with no homework or exams (to be sure, there are some for whom sitting at a keyboard at a scheduled time and taking tests and getting a certificate is quite valuable, but that’s a different audience).

The Great Courses once were the sole claimant to a fourth differentiator, which is depth. Obviously, the proliferation of fairly narrow MOOCs provides as much depth on many topics, and in some cases addresses your desire for higher level courses. Still TGC offers significant depth when compared to the alternatives on TV or audio books. I must say that I was disappointed that Genzlinger chose to focus on this notion that professors these days “don’t know how to lecture.” He suggests that TGC is in the business of teaching bad lecturers how to look good in front of a camera. This of course couldn’t be further from the truth. Anybody familiar with The Great Course knows that among its greatest strengths is its academic recruiting team, which finds professors like Robert Greenberg and introduces them to lifelong learners around the world.

 

Latin Pedagogy and the Digital Humanities

I’ve long been a student of the humanities (and particularly the classics) and have recently begun reviewing over my very old and decrepit knowledge of Latin.  It’s been two decades since I made a significant study of classical languages, and lately (as the result of conversations with friends like Dave Harris, Jim Houser, Larry Richardson, and John Kountouris) I’ve been drawn to reviewing them for reading a variety of classical texts in their original languages. Fortunately, in the intervening years, quite a lot has changed in the tools relating to pedagogy for language acquisition.

Jenny's Second Year Latin
A copy of Jenny’s Latin text which I had used 20 years ago and recently acquired a new copy for the pittance of $3.25.

Internet

The biggest change in the intervening time is the spread of the  internet which supplies a broad variety of related websites with not only interesting resources for things like basic reading and writing, but even audio sources apparently including listening to the nightly news in Latin. There are a variety of blogs on Latin as well as even online courseware, podcasts, pronunciation recordings, and even free textbooks. I’ve written briefly about the RapGenius platform before, but I feel compelled to mention it as a potentially powerful resource as well. (Julius Caesar, Seneca, Ovid, Cicero, et al.) There is a paucity of these sources in a general sense in comparison with other modern languages, but given the size of the niche, there is quite a lot out there, and certainly a mountain in comparison to what existed only twenty years ago.

Software

There has also been a spread of pedagogic aids like flashcard software including Anki and Mnemosyne with desktop, web-based, and even mobile-based versions making  learning available in almost any situation. The psychology and learning research behind these types of technologies has really come a long way toward assisting students to best make use of their time in learning and retaining what they’ve learned in long term memory.  Simple mobile applications like Duolingo exist for a variety of languages – though one doesn’t currently exist for classical Latin (yet).

Digital Humanities

The other great change is the advancement of the digital humanities which allows for a lot of interesting applications of knowledge acquisition. One particular one that I ran across this week was the Dickinson College Commentaries (DCC). Specifically a handful of scholars have compiled and documented a list of the most common core vocabulary words in Latin (and in Greek) based on their frequency of appearance in extant works.  This very specific data is of interest to me in relation to my work in information theory, but it also becomes a tremendously handy tool when attempting to learn and master a language.  It is a truly impressive fact that, simply by knowing that if one can memorize and master about 250 words in Latin, it will allow them to read and understand 50% of most written Latin.  Further, knowledge of 1,500 Latin words will put one at the 80% level of vocabulary mastery for most texts.  Mastering even a very small list of vocabulary allows one to read a large variety of texts very comfortably.  I can only think about the old concept of a concordance (which was generally limited to heavily studied texts like the Bible or possibly Shakespeare) which has now been put on some serious steroids for entire cultures. Another half step and one arrives at the Google Ngram Viewer.

The best part is that one can, with very little technical knowledge, easily download the DCC Core Latin Vocabulary (itself a huge research undertaking) and upload and share it through the Anki platform, for example, to benefit a fairly large community of other scholars, learners, and teachers. With a variety of easy-to-use tools, shortly it may be even that much easier to learn a language like Latin – potentially to the point that it is no longer a dead language. For those interested, you can find my version of the shared DCC Core Latin Vocabulary for Anki online; the DCC’s Chris Francese has posted details and a version for Mnemosyne already.

[Editor’s note: Anki’s web service occasionally clears decks of cards from their servers, so if you find that the Anki link to the DCC Core Latin is not working, please leave a comment below, and we’ll re-upload the deck for shared use.]

What tools and tricks do you use for language study and pedagogy?

Syndicated copies to:

Rap Genius, a Textual Annotation Browser for Education, Digital Humanities, Science, and Publishing

Since the beginning of January, I’ve come back to regularly browsing and using the website Rap GeniusI’m sure that some of the education uses including poetry and annotations of classics had existed the last time I had visited, but I was very interested in seeing some of the scientific journal article uses which I hadn’t seen before. Very quickly browsing around opened up a wealth of ideas for using the platform within the digital humanities as well as for a variety of educational uses.

Rap Genius logo

Overview of Rap Genius

Briefly, the Rap Genius website was originally set up as an innovative lyrics service to allow users to not only upload song lyrics, but to mark them up with annotations as to the meanings of words, phrases, and provide information about the pop-culture references within the lyrics themselves.  (It’s not too terribly different from Google’s now-defunct Sidewicki or the impressive Highbrow, textual annotation browser, but has some subtle differences as well as improvements.)

Users can use not only text, but photos, video, and even audio to supplement the listings. Built-in functionality includes the ability to link the works to popular social media audio services SoundCloud, and Spotify as well as YouTube. Alternately one might think of it as VH1’s “Pop-up Video”, but for text on the Internet. Ultimately the site expanded to include the topics of rock, poetry, and news.  The rock section is fairly straightforward following the format of the rap section while the poetry section includes not only works of poetry (from The Rime of the Ancient Mariner to the King James version of The Bible), but also plays (the works of William Shakespeare) and complete novels (like F. Scott Fitzgerald’s The Great Gatsby.) News includes articles as well as cultural touchstones like the 2013 White House Correspondents’ Dinner Speech and the recent State of the Union. Ultimately all of the channels within Rap Genius platform share the same types of functionality, but are applied to slightly different categories to help differentiate the content and make things easier to find.  Eventually there may be a specific “Education Genius” (or other) landing page(s) to split out the content in the future depending on user needs.

On even its first blush, I can see this type of website functionality being used in a variety of educational settings including Open Access Journals, classroom use, for close readings, for MOOCs, publishing in general, and even for maintaining simple-to-use websites for classes. The best part is that the ecosystem is very actively growing and expanding with a recent release of an iPhone app and an announcement of a major deal with Universal to license music lyrics.

General Education Use

To begin with, Rap Genius’ YouTube channel includes an excellent short video on how Poetry Genius might be used in a classroom setting for facilitating close-readings. In addition to the ability to make annotations, the site can be used to maintain a class specific website (no need to use other blogging platforms like WordPress or Blogger for things like this anymore) along with nice additions like maintaining a class roster built right in.  Once material begins to be posted, students and teachers alike are given a broad set of tools to add content, make annotations, ask questions, and provide answers in an almost real-time setting.

Screen capture from Poetry Genius featuring The Great Gatsby

MOOC Use Cases

Given the rapid growth of the MOOC-revolution (massively open online courseware) over the past several years, one of the remaining difficulties in administering such a class can hinge not only on being able to easily provide audio visual content to students, but allow them a means of easily interacting with it and each other in the learning process.  Poetry Genius (aka Education Genius) has a very interesting view into solving both of these problems, and, in fact, I can easily see the current version of the platform being used to replace competing platforms like Coursera, EdX, Udacity and others in a whole cloth fashion.

Currently most MOOC’s provide some type of simple topic-based threaded fora in which students post comments and questions as well as answers.  In many MOOCs this format becomes ungainly because of the size of the class (10,000+ students) and the quality of the content which is being placed into it. Many students simply eschew the fora because the time commitment per amount of knowledge/value gained is simply not worth their while. Within the Poetry Genius platform, students can comment directly on the material or ask questions, or even propose improvements, and the administrators (the professor or teaching assistants in this case) can accept, reject or send feedback request to students to amend their work and add it to the larger annotated work.  Fellow classmates can also vote up or down individual comments.

As I was noticing the interesting educational-related functionality of the Rap Genius platform, I ran across what is presumably the first MOOC attempting to integrate the platform into its pedagogical structure. Dr. Laura Nasrallah’s HarvardX course “Early Christianity: The Letters of Paul,” which started in January, asks students to also create Poetry Genius accounts to read and comment on the biblical texts which are a part of the course. The difficult portion of attempting to use Poetry Genius for this course is the thousands of “me-too” posters who are simply making what one might consider to be “throw-away” commentary rather than the intended “close reading” commentary for a more academic environment. (This type of posting is also seen in many of the fora-based online courses.) Not enough students are contributing substantial material, and when they are, it needs to be better and more quickly edited and curated into the main post to provide greater value to students as they’re reading along. Thus when 20,000 students jump into the fray, there’s too much initial chaos and the value that is being extracted out of it upon initial use is fairly limited – particularly if one is browsing through dozens of useless comments. It’s not until after-the-fact – once comments have been accepted/curated – that the real value will emerge. The course staff is going to have to spend more time doing this function in real time to provide greater value to the students in the class, particularly given the high number of people without intense scholarly training just jumping into the system and filling it with generally useless commentary. In internet parlance, the Poetry Genius site is experiencing the “Robert Scoble Effect” which changes the experience on it. (By way of explanation, Robert Scoble is a technology journalist/pundit/early-adopter with a massive follower base.  His power-user approach and his large following can drastically change his experience with web-based technology compared to the  common everyday user. It can also often bring down new services as was common in the early days of the social media movement.)

Typically with the average poem or rap song, the commentary grows slowly/organically and is edited along the way. In a MOOC setting with potentially hundreds of thousands of students, the commentary is like a massive fire-hose which makes it seemingly useless without immediate real-time editing. Poetry Genius may need a slightly different model for using their platform in larger MOOC-style courses versus the smaller classroom settings seen in high school or college (10-100 students). In the particular case for “The Letters of Paul,” if the course staff had gone into the platform first and seeded some of the readings with their own sample commentary to act as a model of what is expected, then the students would be a bit more accepting of what is expected. I understand Dr. Nasrallah and her teaching assistants are in the system and annotating as well, but it should also be more obvious which annotations are hers (or those of teaching assistants) to help better guide the “discussion” and act as a model. Certainly the materials generated on Poetry Genius will be much more useful for future students who take the course in future iterations. Naturally, Poetry Genius exists for the primary use of annotation, while I’m sure that the creators will be tweaking classroom-specific use as the platform grows and user needs/requirements change.

As a contrast to the HarvardX class, and for an additional example, one can also take a peek at Cathy Davidson’s Rap Genius presence for her Coursera class “The History and Future (Mostly) of Higher Education.”

Open Access Journal Use

In my mind, this type of platform can easily and usefully be used for publishing open access journal articles. In fact, one could use the platform to self-publish journal articles and leave them open to ongoing peer review. Sadly at present, there seems to be only a small handful of examples on the site, including a PLOS ONE article, which will give a reasonable example of some of the functionality which is possible.  Any author could annotate and footnote their own article as well as include a wealth of photos, graphs, and tables giving a much more multimedia view into their own work.  Following this any academic with an account could also annotate the text with questions, problems, suggestions and all of these can be voted up or down as well as be remedied within the text itself. Other articles can also have the ability to directly cross-reference specific sections of previously posted articles.

Individual labs or groups with “journal clubs” could certainly join in the larger public commentary and annotation on a particular article, but higher level administrative accounts within the system can also create a proverbial clean slate on an article and allow members to privately post up their thoughts and commentaries which are then closed to the group and not visible to the broader public. (This type of functionality can be useful for Mrs. Smith’s 10th grade class annotating The Great Gatsby so that they’re not too heavily influenced by the hundreds or possibly thousands of prior comments within a given text as they do their own personal close readings.) One may note that some of this type of functionality can already be seen in competitive services like Mendeley, but the Rap Genius platform seems to take the presentation and annotation functionalities to the next level. For those with an interest in these types of uses, I recommend Mendeley’s own group: Reinventing the Scientific Paper.

A Rap Genius representative indicated they were pursuing potential opportunities with JSTOR that might potentially expand on these types of opportunities.

Publishing

Like many social media related sites including platforms like WordPress, Tumblr, and Twitter, Rap Genius gives it’s users the ability to self-publish almost any type of content. I can see some excellent cross-promotional opportunities with large MOOC-type classes and the site. For example, professors/teachers who have written their own custom textbooks for MOOCs (eg. Keith Devlin’s Introduction to Mathematical Thinking course at Stanford via Coursera) could post up the entire text on the Poetry Genius site and use it not only to correct mistakes/typos and make improvements over time, but they can use it to discover things which aren’t clear to students who can make comments, ask questions, etc. There’s also the possibility that advanced students can actively help make portions clear themselves when there are 10,000+ students and just 1-2 professors along with 1-2 teaching assistants. Certainly either within or without the MOOC movement, this type of annotation set up may work well to allow authors to tentatively publish, edit, and modify their textbooks, novels, articles, journal articles, monographs, or even Ph.D. theses. I’m particularly reminded of Kathleen Fitzpatrick’s open writing/editing of her book Planned Obsolescence via Media Commons. Academics could certainly look at the Rap Genius platform as a simpler more user-friendly version of this type of process.

Other Uses

I’m personally interested in being able to annotate science and math related articles and have passed along some tips for the Rap Genius team to include functionality like mathjax to be able to utilize Tex/LaTeX related functionality for typesetting mathematics via the web in the future.

Naturally, there are a myriad of other functionalities that can be built into this type of platform – I’m personally waiting for a way to annotate episodes of “The Simpsons”, so I can explain all of the film references and in-jokes to friends who laugh at their jokes, but never seem to know why – but I can’t write all of them here myself.

Interested users can easily sign up for a general Rap Genius account and dig right into the interface.  Those interested in education-specific functionality can request to be granted an “Educator Account” within the Rap Genius system to play around with the additional functionality available to educators. Every page in the system has an “Education” link at the top for further information and details. There’s also an Educator’s Forum [requires free login] for discussions relating specifically to educational use of the site.

Are there particular (off-label) applications you think you might be able to use the Rap Genius platform for? Please add your comments and thoughts below.

Syndicated copies to:

“We didn’t cover much, but we sure did learn.”

Steve Mitchell, algebraic topologist
on learning mathematics in Steve Mitchell short biography

 

Stephen Mitchell

Syndicated copies to: