Sometimes when I read or hear discussions of innovation or change in teaching mathematics or other STEM disciplines, whether it’s me or somebody else doing the discussing, inevitably there’s the following response:
What do we need all that change for? After all, calculus [or whatever] hasn’t changed that much in 400 years, has it?
I’m not a historian of mathematics, so I can’t say how much calculus has or hasn’t changed since the times of Newton and Leibniz or even Euler. But I can say that the context in which calculus is situated has changed – utterly. And it’s those changes that surround calculus that are forcing the teaching of calculus (any many other STEM subjects) to change –radically.
I’ve just started on a binge of screencast-making that will probably continue throughout the fall. Some of these screencasts will support one of my colleagues who is teaching Calculus III this semester; this is our first attempt at making the course MATLAB-centric, and most of the students are alums of the MATLAB course from the spring. So those screencasts will be on topics where MATLAB can be used in multivariable calculus. Other screencasts will be for my two sections of calculus and will focus both on technology training and on additional calculus examples that we don’t have time for in class. Still others will be just random topics that I would like to contribute for the greater good.
Here are the first two. It’s a two-part series on plotting two-variable functions in MATLAB. Each is about 10 minutes long.
Part of the reason I’m doing all this, too, is to force myself …
I was having a conversation recently with a colleague who might be teaching a section of our intro programming course this fall. In sharing my experiences about teaching programming from the MATLAB course, I mentioned that the thing that is really hard about teaching programming is that students often lack a conceptual framework for what they’re learning. That is, they lack a mental structure into which they can place the topics and concepts they’re learning and then see those ideas in their proper place and relationship to each other. Expert learners — like some students who are taking an intro programming course but have been coding since they were 6 years old — have this framework, and the course is a breeze. Others, possibly a large majority of…
I’ve made it to the end of another semester. Classes ended on Friday, and we have final exams this coming week. It’s been a long and full semester, as you can see by the relative lack of posting going on here since around October. How did things go?
Well, first of all I had a record course load this time around — four different courses, one of which was the MATLAB course that was brand new and outside my main discipline; plus an independent study that was more like an undergraduate research project, and so it required almost as much prep time from me as a regular course.
The Functions and Models class (formerly known as Pre-calculus) has been one of my favorites to teach here, and this class was no exception. We do precalculus a bit differently here, focusing on using functions as data modeling …
The calculus class took their third (and last) hour-long assessment yesterday. In the spirit of data analytics ala the previous post here, I made boxplots for the different sections of the test (Conceptual Knowledge (CK), Computation (C), and Problem Solving (PS)) as well as the overall scores. Here are the boxplots for this assessment — put side-by-side with the boxplots for the same sections on the previous assessments. “A2″ and “A3″ mean Assessments 2 and 3.
Obviously there is still a great deal of improvement to be had here — the fact that the class average is still below passing remains unacceptable to me — but there have been some definite gains, particularly in the conceptual knowledge department.
What changed between Assessment 2 and Assessment 3? At least three things:
The content changed. Assessment 2 was over derivative rules and applications; Assessment 3 covered…
I just graded my second hour-long assessment for the Calculus class (yes, I do teach other courses besides MATLAB). I break these assessments up into three sections: Concept Knowledge, where students have to reason from verbal, graphical, or numerical information (24/100 points); Computations, where students do basic context-free symbol-crunching (26/100 points); and Problem Solving, consisting of problems that combine conceptual knowledge and computation (50/100 points). Here’s the Assessment itself. (There was a problem with the very last item — the function doesn’t have an inflection point — but we fixed it and students got extra time because of it.)
Unfortunately the students as a whole did quite poorly. The class average was around a 51%. As has been my practice this semester, I turn to data analysis whenever things go really badly to try and find out what might have happened. I …
One of the fringe benefits of having immersed myself in MATLAB for the last year (in preparation for teaching the Computer Tools for Problem Solving course) is that I’ve learned that MATLAB is an excellent all-purpose tool for preparing materials for my math classes. Here’s an example of something I just finished for a class tomorrow that I’m really pleased with.
I was needing to create a sequence of scatterplots of data for a handout in my Functions and Models class. The data are supposed to have varying degrees of linearity — some perfect/almost perfectly linear, some less so, some totally nonlinear — and having different directions, and the students are supposed to look at the data and rank the correlation coefficients in order of smallest to largest. (This is a standard activity in a statistics class as well.)
I could have just made up data with the right shape on Excel or…
There’s a discussion going on right now in the Project NExT email list about calculus textbooks, the merits/demerits of the Stewart Calculus textbook, and where — if anywhere — the “next wave” of calculus reform is going to come from. I wrote the following post to the group, and I thought it would serve double-duty fairly well as a blog post. So… here it is:
I’d like to add my $0.02 worth to this discussion just because (1) I’m a longtime Stewart Calculus user, having used the first edition (!) when I was an undergrad and having taught out of it for my entire career, and (2) I’m also a fairly consistent critic of Stewart’s calculus and of textbooks in general.
I try to see textbooks from the viewpoints of my students. From that vantage point, I unfortunately find very little to say in favor of Stewart’s franchise of books, including the current edition, all of the…
It’s a beautiful day here on the shores of Lake Michigan as the ICTCM gets underway. It’s a busy day and — to my never-ending annoyance — there is no wireless internet in the hotel. So I won’t be blogging/tweeting as much as I’d like. But here’s my schedule for the day.
8:30 – Keynote address.
9:30 – Exhibits and final preparations for my 11:30 talk.
10:30 – “Developing Online Video Lectures for Online and Hybrid Algebra Courses”, talk by Scott Franklin of Natural Blogarithms.
11:10 – “Conjecturing with GeoGebra Animations”, talk by Garry Johns and Tom Zerger.
11:30 – My talk on using spreadsheets, Winplot, and Wolfram|Alpha|Alpha in a liberal arts calculus class, with my colleague Justin Gash.
12:30 – My “solo” talk on teaching MATLAB to a general audience.
12:50 – “Programming for Understanding: A Case Study in Linear Algebra”, talk by Daniel Jordan.
I learned the following trick for memorizing the value of e from my colleague, Gene White. It never fails to impress calculus students (given a wide enough definition of “impress”).
Start by carefully looking at this picture:
That’s a 20 dollar bill, so memorize “2″ and put down the decimal point.
The picture on the bill is of Andrew Jackson. He was our seventh President, so put a “7″ after the decimal point to get 2.7.
Jackson was elected in 1828, so put down “1828″ next. Since there’s a 2 in front of the decimal place, put “1828″ a second time. We’re now up to 2.718281828.
Now look at the red square over Jackson’s face. The diagonal creates two congruent right triangles with angle measures 45, 90, and 45. So, add on 459045 to get 2.718281828459045. And that’s e to 15 places.
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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