Math in the Media: Math Food?

One of the more basic and interesting shapes (spaces) in mathematics is the torus.  We typically describe is as the surface of a doughnut or bagel.  That it is mathematically different from the surface of a ball is a good entry point for a lay explanation of some fun higher mathematics. 

Speaking of a bagel, here is an interesting video on a way to mathematically play with your food:

A Mathematically Correct Breakfast

Buon appetito!!!

A Find: In Praise of Lectures

Currently vogue in internal university discussions involving education is the idea that the standard lecture format for a course is not the most effective means to educate students.  We here at Hopkins are quite interested in understanding better how serve our entering students in the large-lecture courses we call Gateway Science courses (Our study of this issue here at Hopkins is appropriately called the Gateway Science Initiative.  Also, you can read a JHU-centric white paper on this issue).  I am on the Steering Committee studying this issue.  There is a lot of talk about active learning, and other alternatives to inspire students who do not benefit from the simple instructor-led lectures.

I definitely agree with the idea that the classroom experience could benefit from a purposeful study of how our students acquire knowledge and an active design approach to how we teach.  However, I was always a bit troubled by some of the criticism leveled at the standard lecture format.  I love lecturing, feel comfortable in leading a classroom this way, and see great value in the experience.

It turns out I am not alone.  Thomas Korner, a mathematician in Trinity College at Cambridge University, has written a defense of the lecture format:

In Praise of Lectures

 I find this essay particularly inspiring.  Give it a read.  It definitely says things that I strongly agree with.

Math in the Media: To save this math class, we must destroy it!

Words failed me (mostly) when I read this article today in the Washington Post:

At Virginia Tech,  Computers Help Solve a Math Class Problem

It is a common problem that the transition from high school mathematics courses to those at university can be quite difficult to make.  Even in courses whose content is basically the same, like Calculus AB in the AP system and what most universities call Calculus I, the treatment of that content is much different here at the university.  Of course, students sometimes do not do well.  And I am sure that sub-standard teaching from some of us up here may be a part of it.  We need very much to analyze how we teach and learn to do a better job!  And many of us are.  IN fact, here at Hopkins, we are devoting a LOT of resources precisely to this problem of how to better and more comprehensively educate our incoming students.

But to help cure the "problem" of not-high-enough passing rates by essentially removing instructor face-time from teaching!?!  That is patently absurd in my book.

Mathematics is absolutely NOT about learning a few techniques to apply to standard problems set up to test those techniques, which is exactly what many unit-based, worksheet driven, math courses seem to be like pre-college level.  Porting that type of course to the university level may in fact raise passing rates.  But without the ability to study nuanced mathematical ideas and relationships via discussion and debate (think Socrates), one never learns how to THINK mathematically.  Only to calculate.

Maybe that is what VTech is looking for.  I, for one, am not.  

Math in the Media: The Scale of the UNiverse 2.

A stunningly beautiful illustration of the scale of the universe, from its largest (it's estimated size) to its smallest (the size of the strings that make up our matter, according to string theory), all in a striking sliding scale video, set to music.

ABC News found this. You must take a look!

'The Scale of the Universe,' by Two Teenage Brothers

Simply amazing!!!

Math (not) in the Media: Girls in STEM?

A huge waste of amazing potential talent...!


Created by: Engineering Degree

Math in the Media: Flipping a Lecture???

Here at Hopkins, we are engaging in a project to better understand the general purpose and success of how the large-lecture, so-called, Gateway Science classes (the calculus, chemistry, physics, biology, etc.) in preparing students for the higher-level, specialized study of their future majors. It is a huge affair, and taken as a holistic, university-wide endeavor, has the potential to transform the general curriculum here at JHU in far reaching ways.

But more on that later. There is an interesting article in the Chronicle of Higher Education on turning the standard lecture-type model for university instruction into a much more interactive and enriching experience. The article

How 'Flipping' the Classroom Can Improve the Traditional Lecture

is a very good read. Eric Mazur, a physicist from Harvard, gave a talk here at Hopkins recently on his efforts to enliven the classroom experience. Engaging, he was, and his notion of peer-instruction, whereby students learn by active discussion with their peers while under the direction of the instructor, is just one aspect of the search for new models to engage students and promote a better, deeper sense of learning.

If you are here at Hopkins, you WILL see more of this in the years ahead. For now, give the article a good read.

Study tip for the day: Quality vs. Quantity

People often ask me how many hours one must spend outside of class per hour inside of class to succeed in a university-level math course. I hesitate to answer. The reason is that the question is ill-posed. To really understand the logical structure of mathematical ideas, how they work and fit together, why they exist and work the way they do, one must really spend the time to dig into every nuance of the idea. To do this on a research level, a mathematician understands that she must isolate herself from outside distractions for sufficient periods of time to fully explore the structure of a new idea. The isolation-booth manner is as vital to the process as deep, dreamless sleep is to the health of a person. I call the process of getting to the level where one can focus exclusively on the task at hand without distraction as "going deep". It is kind of a meditation-type thing, and only really works when one practices it regularly. It can be dangerous, though, as the day-to-day tasks tend to get neglected. But it is quality time for understanding complicated mathematics, and easily outdoes simple quantity time when the latter is filled with noise and attention-taking "shiny objects" (distractions).

It's loads more productive to spend an hour in an isolation booth environment focusing solely on your mathematics work instead of 3, 4, or 6+ hours poring over books and notes while checking your phone, listening to music or chatting with friends (or potential friends). Distractions keep you from "going deep" and really digging into the conceptual and logical structure of the math you are doing. And if you do not allow yourself to go deep to really get a concept or idea, you wind up simply memorizing facts and patterns. While this may work for problems just like the ones you have seen, the minute a problem of a different form comes up, you will be lost.

Hence, there are no good guidelines in the form of "6 hours of study per hour in lecture". Studying is a personal thing, and the studying environment matters. If you refuse to allow yourself NOT to fully understand a new concept, then any and all time spent in the pursuit of full understanding is worth the effort. To do it right, allow yourself the ability to "go deep". Then you minimize the time spent to only the quality time.

Some people brag about their ability to multi-task. To me, the ability to mono-task is the lost art in society.