I recently learned of the work of L. Dee Fink on course design for college instruction. I am still amazed that (a) this hasn’t existed for a lot longer, and (b) no one had mentioned it to me before in its ten years of existence. Anyway, I have grabbed a copy of A Self-Directed Guide to Designing Courses for Significant Learning, and I am trying to use it to “redesign” my course Math 3600 Euclidean Geometry. I put that in quotes because I don’t think the course really needs a redesign. In fact, this one course is easily the best work of my career and runs pretty well with almost no friction. But that doesn’t mean I can’t maybe tweak a little thing. And it definitely makes a reasonable subject for learning the process set out in Fink.

Currently, my only concern with the course is in my assessment structure, and I have been thinking about standards based grading and specifications grading lately. We’ll see how that plays out when they pop up.

This is going to be a long post. I am going to work until I can’t, and then pick up again with a fresh post in the morning.

## General Structure

The Guide is structured as a bundle of worksheets and reflection prompts for the instructor to complete. There are twelve steps bundled into three phases: an initial design phase where you “build strong primary components”; an intermediate phase where you “assemble the components into a coherent whole”; and a final phase where you “finish important remaining tasks.”

A nice feature of this is the sequencing. Fink guides us to work with a *backwards design* philosophy where we identify outcomes and a scheme for assessment before thinking about regular coursework. That seems like a good idea, but

I have so much of this course settled that I know I cannot reasonably claim to be thinking about outcomes and assessment first. So be it.

### Initial Design Phase: Build Strong Primary Components

#### Step One: Identify Situational Factors

##### Students

*Math 3600 Euclidean Geometry* typically has between 15 and 22 students. Students can take the course anytime after completing a first semester of calculus, though many take it much later, so a class is usually mixed from sophomores to seniors.

##### Physical Facilities

We meet face-to-face three times a week for 50 minutes. The classroom always has a large chalkboard, but only some semesters do we have a full set of presentation equipment. (There is always a projector, an ELMO, and a set of VGA hookups, but not every room has a computer in it.) Most often the classroom has long, narrow tables and movable chairs. Some classrooms have a pile of chairs with attached desks. Next term, I have a room without a computer and with the “attached desks.”

##### Nature of the Subject

The course is dedicated to the study of classical planar geometry: triangles, polygons, circles, constructions, and area. Really, the idea is to teach **How to work like a mathematician.** Students need to get involved in the processes of finding, making, and critiquing axiomatic arguments. So, the subject is HARD CORE MATHEMATICS on REALLY BASIC OBJECTS.

##### Characteristics of the Learners

The primary audience consists of preservice secondary teachers, but usually there are students in a standard mathematics major, too. I have encountered a wide variety of attitudes towards (1) geometry, and (2) argument-based mathematics. Most are a bit apprehensive about “proofs.” A fair number did not enjoy high school geometry.

##### Characteristics of the Teacher

Well, I am pretty awesome. I also have an unreasonably high level of confidence in my abilities in the classroom. And I am pretty humble. Don’t underestimate how humble I am. I am really good at that.

I am a convert to Inquiry-Based Learning. I believe that students learn best by doing. I really like coaching, mentoring, and playing cheerleader for my students. Students tell me that I am a little scary, but I can’t tell if that is because I have inherited an unfriendly face or because I expect students to do challenging things. I don’t really consider myself an expert in classical geometry, but I am a mathematician and I can certainly handle this material. I do enjoy geometry, and I enjoy watching students grow.

#### Step Two: Identify Learning Goals

I have written about this many times before, so I will be brief. The goals in this course are mostly about *process*. I have tried a standards-based assessment scheme (sorta), where the listed standards are bundled into groups like:

- Mathematical Investigative Process
- The Axiomatic Method
- Planar Geometry Content
- Oral Communication
- Written Communication

For this list, I have tried to pick out the behaviors a professional mathematician engages in when going about the job of making mathematics.

Now, Fink has a spiffy diagram of “A Taxonomy of Significant Learning” at this point. In this model, there are six sorts of learning (broadly stated) that one can do, and learning counts as *significant* if it involves more than one of them. I like to think that my course hits four out of the six:

- Application
- Foundational Knowledge
- Learning how to learn
- Caring

But I don’t think I hit these last two, at least not directly:

- Human dimension
- Integration

Okay. Now it is midnight. I am two steps in, with ten more to go. I’ll attempt to finish the initial design phase tomorrow morning.