# A Failure: Indifference to Building Student Anxiety

I had an up-and-down day in classes today. I am still thinking about how linear algebra went early this afternoon.

We are now in the fifth week of the semester here at UNI, and my linear algebra class has been doing lots of tasks about the geometry of R2 and R3, especially those things that help us understand how to think about vectors, lines, planes, and the dot product in situations where we have a chance to draw the picture. Things have been getting steadily more challenging, and the tasks for this week are hard for them. For example, a task that made everyone unhappy today was this:

Consider the line in R3 given by the parametric equation
t → (-6,-2,1) + t(3, -1/2, 1).
Find the point on this line which is closest to T = (1,1,1).

That uses everything we have learned so far, and requires a little bit of thinking about the geometry. It is a great task. It was one of seven I asked them to do for today. (It was probably the hardest one.)

But Friday is the first exam.

I should have thought a little more carefully about this. I have lots of young students, and I have actually set things up in a way to make them more anxious than need be just before the exam. I set a trap for all of us, and then led the whole class into it with a big grin on my face.

Also, I am writing all of the materials myself. This means that if the students feel anxious and are having trouble with the text, that is my fault, too. There is no faceless textbook author to be grouchy at. I can’t be the friendly guy who saves them from the confusing writing.

We had a short chat in class, and I sent them a longer message by email after I had a chance to reflect. I HOPE that I have helped calm their fears a bit. Time will tell.

I am going to have to think more carefully about how I structure things when I edit and revise for next term.

# About Linear Algebra This Term

I am having trouble writing this morning, so I hope that blogging here will loosen my brain and thoughts will start to spill out properly.

I am working on my linear algebra books. “What’s that?”, you say, “You are writing books, plural, for a course?” Yes. I have taught linear algebra many times in the last few years, and I finally felt dissatisfied enough with my old materials and prepared enough with my ideas about the course to write everything from scratch. So, I am writing these:

• A primer, or reader, which discusses the basics of linear algebra but sticks entirely to the plane and 3-space.
• A workbook, which has a sequence of tasks I can use to run an IBL course.

My basic model for this is how I run my Euclidean Geometry course. I have the students read Euclid’s The Elements Books I-IV, and I have designed a sequence of tasks to go with that. The idea is to treat The Elements as the existing research literature, and then pose ‘research questions’ which drive the students to understand the material and learn to do math on their own. In geometry, we are working on proof-writing, definition-making, and conjecturing. This works great.

I want to copy the model for linear algebra, so I need something to replace The Elements. So I am writing it. I am trying to use the old-fashioned, discursive style that you would find in math texts pre-WWII, too. The text is much more a narrative, and avoids the now-standard “Defn-Thm-Proof” setup. Definitions and results pop up as we find them.

So, now I am about 75% of the way through writing chapter one, and I am past deadline for getting this to my students. They have the first half of the chapter, which got us through yesterday. I had hoped to give them the second half to read last night… and I failed.

My current sticking point is making a transition from talking about norms, angles, and the dot product in the plane, to talking about the equation of a line through the origin. I have written the start of three different versions today, and been happy with none of them. So, I am going to take a break and start again in about an hour.

Maybe I’ll read the copy of Math Horizons that just arrived.

ps. If you want to follow along with my crazy experiment, I use github. The files are here.

# New Course Page and Syllabus: Differential Equations

I have just finished putting together the course web page and syllabus for my third course of the fall term: Math3425/5425 Differential Equations. The course is cross-listed as an undergraduate and a graduate class, so there is a little wrinkle to this. Basically, the grad students have to do two longer-term, larger projects.

If you are curious for details, you can find the pages here:

Now that this course and geometry are ready to go for a few weeks, I will move back to preparing materials for linear algebra. I still have a lot of stuff to  write.

Here is a lesson I learned the hard way, which I present as a tip for newer faculty:

It pays to plan out your due dates for the entire term in advance. Spread the due dates around, so that that assignments from different classes come in at different times. Try to avoid having major assignments come it all at once.

I finally figured this out about two years ago (I am not that bright), and I have been conscious of it every term since. The “day to balance things” has become a regular part of my pre-term planning process. I just finished the plan for this term, and here it is, as a convenient Google Doc. I haven’t ever done it quite so formally as this table, but it feels natural now.

Note that I also have a column dedicated to what weekend commitments I have. That way, I can try to avoid having bad work vs family conflicts. This term, I have a weekend where my in-laws will visit, the Iowa Section of the MAA meeting to attend, and seven different travel days for my daughter’s soccer commitments. I don’t want a situation where I have a big stack of work to do when I have to drive the whole family to St Louis for the weekend to watch soccer games.

Of course, nothing is ever perfect. On September 22 I am collecting something big from two of my three courses right as family shows up. Sigh.

I am NOT worried about the big collection right before Thanksgiving. I get a whole week off, but my kids go to school on the next Monday and Tuesday. That means I have a few days of quiet office time.

If everything goes according to plan, I should be able to keep up with my grading work during the regular business day and still return papers either the next class meeting or the one after.

# Euclidean Geometry: New Course Web Page and Syllabus and…

I just finished prep work on my Euclidean Geometry course. This involved rewriting or rebuilding lots of fiddly little things, so even though it was the “easy” one with minimal changes, it still took a whole day to do. (8-10 hours?) You can find the course web page here:

Course Web Page for Euclidean Geometry

That has everything. All of the assignments are written. Even the exams are written, but I am not going to post those publicly. If you want to skip to the core of things, you can just look at the new syllabus and maybe the first assignment page.

Euclidean Geometry Syllabus for Fall 2017

I am feeling super cool, now, so I chose to decorate this post with a different version of Count Vertigo.

# Updated personal web site

One task that comes up every new semester: update the old web site.

So, I mostly did. Course pages (which will be of more interest to readers of this blog) will go up later this week.

TJ’s UNI web page

# New Syllabus for Linear Algebra

I last posted about how I was rethinking the content expectations for linear algebra, so that I could write my own text. I took another step towards getting class ready today: I finished my syllabus.

This was inspired by examples that Susan Hill, our CETL director, handed out at this summer’s Course Design Academy. She had several different syllabus pairs in a before/after set-up. I really liked the way that most of the redesigned and reworked documents looked, so I wanted to write my own, better, syllabus document.

Here it is. I guess you can comment, but I am done with this for now. I have other things to do.

My New Linear Algebra Syllabus

The primary changes for me are these:

• I am not doing SBG/SBAR this term, since I have so much else to manage.
• I have streamlined my list of outcomes into four “process goals” and five “Big Questions.”
• I am going to try out some peer grading for the first time.
• I am definitely going to use an IBL scheme which is “individual work at home; group discussion in class; solo presentation in class,” but I have not made a big deal of this on the syllabus as being an IBL environment.

Anyway, you can do this too. It just takes several years of flailing about and thinking hard, two weeks of digesting the University, Department, and MAA learning goals, and then about 12 hours of writing and editing over two days.