Integrated Course Design for Euclidean Geometry, Part II

I continue the process of redesigning Math 3600 Euclidean Geometry using Fink’s Integrated Course Design Guide.

Step Three: Feedback and Assessment

This is where I am ready to do some tweaking. I have tried to use a “Standards-Based Assessment” mindset in this course lately, but it still doesn’t meet my needs. Also, I have been part of an on-going conversation about Linda Nilson’s new book on Specifications Grading. (Hop over to Google+ and look for Robert Talbert or Bret Benesh.)

Fink makes a distinction between “educative assessment” and “audit-ive assessment.” At first glance it feels like the distinction between formative and summative assessment. But Fink means more than just this.

In his terms, educative assessment has four crucial features:

  • It is forward-looking, in that it mimics the ways in which students will be required to use the knowledge or skills from the course after the course is over. His focus is on life after school, but I think it might reasonably apply to subsequent courses.
  • It has clear criteria and standards. By criteria, Fink means those features of quality work that you will seek in your students work. By standards, he means figuring out what counts as good enough and what counts as awesome.
  • There is opportunity for self-assessment and reflection.
  • It provides for high-quality feedback. His guide for “high-quality” involves an acronym: FIDeLity
    • F — frequent
    • I — immediate
    • D — discriminating
    • L — loving

To check myself against all of this, I started by making a list of all of the bits of feedback and assessment that happens in the course. Students have always done these things:

  • Presentations of their arguments in class
  • Writing for the class (scientific) journal
  • Refereeing for the class journal
  • Writing a Final Exam

Of those only the Final Exam counts as a summative assessment. For an active student, the other three things happen pretty frequently and give a lot of formative assessment and self-assessment opportunities, but only about the quality of the mathematics done. Early on, it became clear that students needed a “early warning system,” so I started using a

  • Midterm Exam

It is important to note that my midterm is purely a formative assessment and feedback mechanism. I do not record anything from this in my gradebook, but I comment on them as much as I can.

About a year-and-a-half ago, I realized I needed to put in something which more seriously focused on self-assessment (and self-regulated learning). So now I also have a sequence of

  • Three self-assessment interviews. I ask the students to write a short reflection and then meet with me to discuss it for 15 – 20 minutes.
The big problems

This leaves me with some issues. First, my only summative assessment is a single (week-long, take-home) final exam. Also, the process of self-assessment does not play into my final assessment at all. The whole thing gets dropped after the third one (usually in week 12). Finally, I have no summative assessment which covers the learning goal for oral communication.

My Adjustments
  1. Next term, I will ask students to complete a portfolio of their work. This should involve almost no extra work, they should simply bundle together the things they have already done together with their solutions to final exam questions. I think of this a bit like a tenure portfolio document.
  2. To bring the level up on meta-cognition and self-regulated learning, I will ask students to write three additional essays. These will be written sometime in the last half of class, I think. I don’t know exactly how I will handle the details, yet.
    • An essay on “productive failure” of some sort. Maybe My best mistake or something similar.
    • A “how it happened” essay on “my best paper.” I want some sort of introspection on process as it pertains to success.
    • An essay on “what it means to do mathematics.”

Each of these will be less than two pages, I think. Unlike the rest of our work, they should be personal narrative storytelling.

Step Four: Teaching and Learning Activities

This part is a longer section of Fink’s guide. He tries to push the reader to set up some sort of active learning course. Consider getting the students to do the subject; think about the cycle of work in class and between classes, etc. I don’t need this push.

The class is run as a (Modified) Moore Method course. Students will spend time between classes finding and constructing arguments for a carefully designed sequence of mathematical conjectures. During our meetings, students will present their work and critique the arguments of others. After a successful presentation (deemed by the students to be a theorem), the presenter will write a paper for the class journal and submit it. It will go through a peer-review process and eventually get published. The whole environment is structured to be a miniature version of the wider mathematics community. I serve as the benevolent dictator and direct traffic. Everything is meant to mimic the professional work of a mathematician as much as is feasible.

Step Five: Integration

Now Fink encourages us to check that things fit together.

Are the situational factors accounted for? I think so…

Do the learning goals and the feedback & assessment line up? Mostly. I still have a problem with the lack of summative assessment for oral communication. I don’t think I have anything extraneous that don’t serve one of my goals.

Do the learning goals align with the teaching and learning activities? Yes. Both are aligned with how a professional mathematician works.

Does the feedback and assessment loop help students deal with the teaching and learning activities? Well, the feedback part does. Most of the true assessment comes pretty late. But feedback happens at the point of contact.

Just to check, I made a little table of my learning goals vs. my assessment methods (which are just my learning activities by other names). I noted when formative assessment and feedback is happening and when summative assessment is happening. I won’t share it here, but I was happy with the result. The only missing bit is that summative assessment of oral communication.

With that, I have finished the initial design phase. Next up, the intermediate phase where things get “assembled.” I think I might get through that quickly.

2 thoughts on “Integrated Course Design for Euclidean Geometry, Part II

  1. My one tip about portfolios: in spite of the fact that it _seems_ like it shouldn’t be much work for students to put together a portfolio at the end, it might actually take a lot of time. I did portfolios for real analysis, and I heard that my students were skipping other professors’ mathematics classes to complete them at the end of the semester. This is in spite of me having a practice portfolio (feedback only) at midterm time.

    I don’t know exactly what I will do next time, but it might be something like having the students create a plan for themselves. Then I would help them stick to the plans, including any penalties that they want (but I would require neither deadlines nor penalties).

    I hope that your students do better, but you may want to plan ahead for students procrastinating.

  2. Thanks for the tip. I might ask them to bring draft copies to our self-assessment interviews. That would provide a few check-in points. I could even make it mandatory if you want to get a grade above C.

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