I wasn’t sure how students in the course would respond to the inverted classroom structure. On the one hand, by setting the course up so that students were getting time and support on the hardest tasks in the course and optimizing the cognitive load outside of class, this was going to make a problematic course very doable for students. On the other hand, students might be so wed to the traditional classroom setup that no amount of logic was going to prevail, and it would end up like my inverted MATLAB class did where a
As I wrote before, each 50-minute class meeting was split up into a 5-minute clicker quiz over the reading and the viewing followed by a Q&A session over whatever we needed to talk about. The material for the Q&A was a combination of student questions from the Guided Practice, trends of misconceptions that I noticed in the Guided Practice responses (whether or not students brought them up), quiz questions with…
In the last couple of posts on the inverted transition-to-proofs course, I talked about course design, and in the last post one of the prominent components of the course was an assignment type that I called Guided Practice. In my opinion Guided Practice is the glue that held the course together and the engine that drove it forward, and without it the course would have gone a little like this.
So, what is this Guided Practice of which I speak?
First let’s recall one of the most common questions asked by people learning about the inverted classroom. The inverted classroom places a high priority on students preparing for class through a combination of reading, videos, and other contact with information. The question that gets asked is — How do you make sure your students do the reading? Well, first of all I should say that the answer is that there really is no simple way to  
It’s been a while since I last wrote about the recently-completed inverted transition-to-proof course. In the last post, I wrote about some of the instructional design challenges inherent in that course. Here I want to write about the design itself and how I tried to address those challenges.
To review, the challenges in designing this course include:
An incredibly diverse set of instructional objectives, including mastery of a wide variety new mathematical content, improvement in student writing skills, and metacognitive objectives for success in subsequent proof-based courses.
The cultural shock encountered by many students when moving from a procedure-oriented approach to mathematics (Calculus) to a conceptual approach (proofs).
The need for strong mathematical rigor, so as to prepare students well for 300-level proof based courses, balanced with a concern for student…
When I see the first back-to-school sales, I know it’s time, like it or not, to start prepping classes for the fall. This fall I am teaching two courses: a second-semester discrete math course for computer science majors and then two sections of “Communicating in Mathematics” (MTH 210). I’ve written about MTH 210 before when I taught it last fall. This fall, it’s going to be rather different, because I’m designing my sections as inverted or “flipped” classes.
If you’ve read this blog for any length of time, you know I’ve worked with the inverted classroom before (here, here, here, etc.). But except for a few test cases, I haven’t done anything with this design since coming to GVSU. I decided to take a year off from doing anything inverted last year so I could get to know the students and the courses at GVSU and how everything fits together. But now that I have the lay of the land, I…
I haven’t given many updates lately about, well, anything, but especially about my Calculus 2 class. Freakishly, we are 2/3 of the way through the course now. First of all let me say that there’s something seriously wrong with having a midterm in a class after three weeks, and then a final exam three weeks later. Students should have more time to dread those things.
I kid, but actually the biggest adjustment I’ve made in the class — and teaching a class that’s as compressed as this one is all about paying close attention to everything that happens and being nimble about making adjustments — has been the testing scheme. I know that I posted earlier about my idea of having in-class assessments that were smaller than the usual test, more frequent, and which leveraged student collaboration and the real-life social network of the class. But after a couple of tries with this, I dropped it…
In the American drive to boost science and math education, it’s science that has all the kid-friendly sizzle: Robots and roller coasters, foaming chemical reactions, marshmallow air cannons.
Math has… well, numbers.
“America has a cultural problem with math. It’s the subject, more than any other, that we as a country love to hate,” said Glen Whitney, a passionate mathematician who worked for years developing algorithms for hedge funds. “We don’t see it as dynamic. It’s rote and boring and done by dead Greek guys a thousand years ago.”
The article goes on to talk about some efforts to spice up math, including MIT’s Labyrinth tournament, DimensionU‘s celebrity-driven “DU the Math”…
We’re about to start working with gradient vectors in Calculus 3, and this topic uses a curious mathematical symbol: the nabla, which looks like: \(\nabla\). This symbol has several mathematical uses, one of which is for gradients; if \( f  \) is a function of two or more variables then \( \nabla f \) is its gradient. But there does not appear to be a use for the symbol outside mathematics (and mathematical physics).
One of my students asked me about the origin of this symbol, and I had to confess I didn’t know. I always figured it was somehow related to the much more common capital Greek delta, \( \Delta \), but the real story is a lot more colorful than that.
The nabla is so-called because it looks like a harp; the Greek word for the Hebrew or Egyptian form of a harp is “nabla” . What does a harp have to do with mathematics? The image came up in relation to mathematics…
But I will posit that all students should learn programming, whether they plan to become programmers or not. Many universities already require students take composition in order to graduate. Perhaps it’s time for programming — “the new literacy” — to become a requirement too?
I don’t mean that every student needs to learn C++ or Python or Perl or Java or Ruby. But I do think everyone needs to know how the Web works — how search engines operate, for example, and what’s “server side” and what’s “client side” and why the difference matters. Everyone needs to know some HTML (a mark-up, not a programming, language I realize). And with the move towards the fifth revision of the HTML…
Last week’s installment on columnar transposition ciphers described a formula for the underlying permutation for a CTC. If we assume that the number of columns being used divides the length of the message, we get a nice, self-contained way of determining where the characters in the message go when enciphered. Now that we have the permutation fully specified, we’ll use it to learn a little about how the CTC permutation works — in particular, we’re going to learn about cycles in permutations and try to understand the cycle structure of a CTC.
First, what’s a cycle? Let’s go back to a simpler permutation to get the basic concept. Consider the bijective function \(p\) that maps the set \(\{0,1,2,3,4, 5\} \) onto itself by the rule
$$p(0) = 4 \quad p(1) = 5 \quad p(2) = 0 \quad p(3) = 3 \quad p(4) = 2 \quad p(5) = 1$$
If you look carefully at the numbers here, you’ll see that some of…
I am a mathematician and educator with interests in cryptology, computer science, and STEM education. I am affiliated with the Mathematics Department at Grand Valley State University in Allendale, Michigan. The views here are my own and are not necessarily shared by GVSU.
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