Integrated Course Design for Euclidean Geometry, III

Today I finished grades for all of my Fall 2014 courses, so it is time to get back to planning next term. As my last “pre-holiday” bit of work, I’ll finish the course design template for Euclidean Geometry following Fink. I previously did the initial design phase which consisted of “building strong primary components” in Steps 1-5.

Intermediate Phase: Assemble the Components into a Coherent Whole

Step 6: Create a Thematic Structure for the Course

Fink encourages us to find 4-7 segments of the course, each focusing on key concepts or topics. I think I have five, or maybe four. It depends on how you want to count them. The first one on this list might be two things.

  1. Polygons, and the axiomatic method, conjectures, and definitions. This is mostly about using triangles to study other polygons. But there is a little mini-unit on arguments with parallel lines mixed in here.
  2. Circles
  3. Straightedge and Compass Constructions (as an efficiency game!)
  4. Area and the regular pentagon

Segment 1 is really long, it can take half a semester. Then segments 2 and 3 are shorter. We almost never finish segment 4 completely, but the fastest class I had finished 4 and started another (bonus) segment!

Step 7: Instructional Strategy

I have no desire to make changes here. For ten iterations of this course I have used a flavor of Inquiry-Based Learning called a Modified Moore Method. Really, I have done something called The Extreme Moore Method (EMM), which I have written about before. Students will spend their time out of class finding and composing arguments for conjectures. We will spend class time presenting and critiquing this work. Then students that will write papers for the class journal. Oh, just go read the other post.

Step 8: The Overall Scheme of Learning Activities

Here Fink wants the instructor to think about the variety of activities the students should do, and when. Also, how does the sequence of tasks for before, during, and after class meetings mesh together? This is all pretty well decided with my EMM.

Final Design Phase

I won’t be able to finish all of this tonight in detail, but I can generally get through the rest of the guide.

Step 9: How are you going to grade?

Well, I have been thinking about this a lot lately. For years. Next term, I will try something called “Specifications Grading” following the work of Linda Nilson. I have been part of conversation about this for a few weeks now. Go find the work Robert Talbert has been doing in this direction for a list of places to start.

I will wrap up work on this and make a new post soon.

Step 10: What Could Go Wrong?

I have run this class often enough that I only have one worry: The new grading system is (a) not a solution to my problem, or (b) actively messes with the other parts of class which were working fine. I guess (a) isn’t too big a deal. I’ll just keep looking in that case. But I worry about (b). So far, the assigning of grades has been kinda vague, and this pushes students to keep working. (It is just like the real mathematics community.) And I want to make things more reliable and, I hope, more “fair.” But I don’t want students to start micro-managing publication counts instead of trying to solve more problems. For now, I need an experiment.

Step 11: Make a Plan for Communicating with Students

Fink writes this as if the big deal is to just write a syllabus. Well, yes, and no. I see these tasks ahead of me.

  1. Rewrite my syllabus
  2. Rework my first day handout (which is like a mini textbook)
  3. Update the course web page (which is like a digital syllabus and record of class).
  4. Flesh out the detailed specifications for the grading system. In particular, this means I will have to update

* The class journal style guide
* the instructions for referees
* my grading policy document
* specifications for the “non-mathematical” writing assignments (reflections and essays)

Step 12: Make a Plan to Assess your Teaching

This is a challenge. How many of us do this with such foresight? Well, my plan is this: I will use a simplified SALG instrument at final exam time to assess student satisfaction and understanding of the new grading system.

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Let’s go fly a kite!

Today my Euclidean Geometry class discussed the construction of a kite with a compass and straightedge. They had four different constructions, all of them different from the one I had in mind. And these constructions led us to interesting discussions and new questions. It was a truly glorious day. I love teaching this class so much.

Anyway, it made me think of this song, so I played it in class. I had forgotten the two lines of dialogue right before the song starts, but they are appropriate too. I hope I can get my students to this state of wonder and excitement. This particular course makes me feel this way a lot.

The leap of faith

This semester I am running all three of my classes as “modified Moore method” courses. (The amount of modification depends on the audience and aims of the course.)

During our first meetings, I worked hard to set the right tone and expectations. We even took time to practice what class would look like. But then I had to let them go with tasks to try.

Tomorrow morning I walk in to my classes with a lesson plan that starts and ends with, “Are there any volunteers?”

I have faith in myself that I can handle whatever happens. I will think quickly and I will adapt, probably.

But more importantly I have faith in my students. They will have worked hard, and, though nervous, they will have something to say.

So I step into the void. “Who has something to share?”

2014 Legacy of RL Moore Meeting

Registration is now open for the 2014 Legacy of RL Moore meeting. I am a program co-chair (along with Angie Hodge of University of Nebraska-Omaha).

The registration page is here:
http://events.signup4.com/rlmoore2014

More info about the program is available here on the call for papers:
http://legacyrlmoore.org/Reports/201406/call_papers.html

This meeting is an annual gathering of practitioners of Inquiry-Based learning. Most of the attendees are in mathematics, and most of them teach in a college or university setting. But that doesn’t describe everyone, and all are welcome.

Come join us!

A reminder to myself: Sell the process

Here is a short report on the big experiment for this term, and a related note on a realization from today with wider applicability. I expect that this will start well, and then ramble on as I fiddle with some ideas.

Continue reading

A reflection on “Assessment Interviews, Phase 2”

I have spent a large portion of today in one-on-one conversation with the students in my Euclidean Geometry course. To prepare the students for these meetings, I asked them to complete a one page reflection paper, with this prompt. If you don’t want to click through, I basically ask the students to read through the “standards for assessment,” which is just a fancy name for my student learning goals, and do a self-assessment. Then I want them to make a plan of action for improvement during the next three weeks.

The striking part is the strength of the negative correlation between student self-assessment and my assessments.

Students who I recognize as having developed strong skills come it with focused critiques and tight plans for how to improve.

Students who I recognize as having not yet demonstrated many of our foundational skills show up with some confidence that they are doing everything just fine, and weak plans for self-improvement.

(This relationship is not perfect. Some students were spot on, of course.)

I have enough experience that I expected this, but to watch in unfold all day was really something.

Opening Week for a Moore Method Course: Getting Comfortable

I am teaching iteration number ten of my Modified Moore Method Euclidean Geometry course. This semester I am making an effort to refocus on the basics: managing and mentoring the students as much as I can.

At this point, my theorem sequence is very stable. (I am no longer surprised much by what happens in this course.) This allows me to work on the other aspects of the course. I feel like I have started to let some important things go in the last year or so, and now I want to sharpen up. What has been lacking? I don’t think I have kept on top of the students to keep them engaged as well as I might. And I don’t think I have done a good job selling the method of instruction, either.

So, I was much more deliberate about introducing myself to each of my sixteen students on the first day. I have been very explicit about my expectations and my willingness to help them meet those expectations (which are rather high). And I will be making a conscious effort to check in with as many students as possible each day.

The first week was a rousing success, I think. Each day we got at least one theorem. We have already set the expectation for what counts as an argument. (Well, surely, there is still some work to be done.) The class has made two conjectures. We took some time to discuss some basic points of what acceptable writing will look like. I even successfully navigated our first potential difficult situation and found something positive in it. All in all, I am feeling pretty good about this.

I think our next test comes when we have to finish conjecture 1.1. They haven’t addressed the second statement in that, yet.

And sometime next week I will have to steal ten minutes to talk with them about my Standards Based Assessment experiment for the term.