Standards Based Assessment for a College Mathematics Course, First Draft

Originally Posted 07-09-2012

SBA for a College Course

I am actively preparing for an experiment in Standards Based Assessment (SBA) this coming fall. For the newcomers: I will try SBA in my Euclidean Geometry course. The course is designed for preservice teachers, mostly sophomores and juniors, and is run as an Inquiry Based Learning (Modified Moore Method) environment. The class runs anywhere from 12 students to 25 students in the last five years.

Basic Implementation Concerns

What are the basic features of a SBA implementation?

  1. Your list of standards is a well-chosen description of what you want students to learn. Some of these items are tied to specific content, some of them are proces-oriented. But the standards should encapsulate what you really want to measure. Care should be taken to get a set of standards which are not too broad (rendering them difficult to assess fairly), nor too narrow (a nightmare to administer).
  2. The list of standards should be public knowledge. Every stakeholder should be aware of what your standards are, and how you will go about assessing each. Each assessment instrument should have the associated standards explicitly tied to it.
  3. Each assessment instrument is a vehicle for timely, detailed feedback on how to improve. So assessments should happen often enough to be of use to students, but not so often to destroy the instructor’s will to teach.
  4. Students should have multiple tries to demonstrate proficiency in a standard. It is unreasonable to expect every student to excel at every thing the first time. Students need the opportunity to receive clear feedback, work for improvement and then be reassessed.
  5. Instructors need to see demonstrated proficiency multiple times to ensure real progress. A simple one-off assessment might catch a student on a bad day. True mastery is only demonstrated by consistent, repeated demonstration of proficiency.

I’ve heard more experienced practitioners use the words “reassessment and spiralling” to describe structuring assessments so that standards periodically recur on assessment instruments throughout the course of study. This helps with items 4 and 5 above.

It is also important to note that there are many ways to measure and report porgress on standards. I prefer the simplest approach: a binary “demonstrates proficiency” or “does not demonstrate proficiency” with appropriate feedback. The binary nature might be hard to stick to. I can already feel a building desire to use a ternary system with a “working on it” middle ground. But I worry that this will turn into a cop out. So, the binary system it is.

Where do my standards come from?

My primary sources for developing my set of standards are these.

Notice that I am using the state K–12 Standards for a college class. This follows the excellent suggestion of my colleague Megan Balong, because the majority of my students are in a program for pre-service teachers. I hope that this choice helps make things a bit more relevant (and transparent) for them.

My Design

The course in question is run as an Inquiry Based Learning Environment. In this instance that means that class runs this way:

  • I design a sequence of tasks, mostly theorems to prove, questions to answer, and conjectures to settle.
  • The students work hard to accomplish the tasks I set them. Sometimes in pairs or small groups, but often alone. With rare exceptions, this work is done apart from class time.
  • Class meetings are dominated by student presentations of their work. They share and defend their ideas. The rest of the class takes up the job of peer review. Arguments can be accepted by the class (then we move on), or rejected (then we attempt to pinpoint the difficulties and brainstorm how to proceed).
  • After a successful presentation, the student writes up their argument as a scholarly paper to be refereed, and rewritten until it is “publishable.”
  • Iterate.

That is basically it. I also give a midterm and a final exam, just to have a uniform assessment a few times, but class really runs like a semester long working seminar. I play the role of ringleader, psychologist, traffic cop and mentor.

This semester I plan on adding a few “reflection” papers. Students will be asked to choose a task on which they worked–sucessful or unsuccessful—and then detail and reflect on their working habits and methods of investigation. These will help with assessment of process standards.

One of the things that makes SBA feel like a natural fit for this course is that features 3, 4, and 5 from the list above all happen already: every student presentation is an assessment opportunity, they happend regularly, students have ample opportunity to participate repeatedly, and quality feedback happens on the spot.

This leaves me with two chores: (1) choosing a good set of standards, and (2) communicating the standards with the students. Well, there is one more chore: (3) finding an appropriate way to turn a table of demonstrated proficiencies into a grade that the registrar will accept.

I think I have item (3) handled. It needs a few tweaks, but I am adopting a “conversion” scheme that I heard (or read) about from someone more experienced. Pardon the lack of citation—I have simply forgot where I heard this.

Standards are split into two categories: Fundamental and Advanced.
One is deemed to have “mastered” a Fundamental Standard when one has demonstrated proficiency at least three consecutive times. (One of those times being in the last three weeks, maybe?) One is deemed to have “mastered” an Advanced Standard when one has demonstrated proficiency twice. (No time constraint.)
Then we use this handy conversion table:

  • Grade Earned: C means achieved mastery of all fundamental standards

  • Grade Earned: B means also achieved mastery of x % of advanced standards

  • Grade Earned: A means also achieved mastery of y % of advanced standards

Here x and y are numbers I still have to choose. Of course, x is less than y.

To explain the whole thing, I have written this draft document to share with the students.

To share the list of standards with students, I am working on this other draft document to share with students.

Finally, to help me with administering this whole thing, I am preparing yet another draft document to use as a more formal record of feedback. Currently, I plan to fill one out after each presentation and share it with the presenter. It is not feasible to do that during class because there is so much else to manage. Instead, I will fill them out immediately after class based on my notes, and then send a copy to the student via email.

Wrapping Up

And that is it. I still have some work to do on my formal list of standards. (Coming Soon!) Once that is done, it will be a simple matter to type up the remaining parts of the last two documents, and I will be ready to go.

I’d welcome comments (especially comments and suggestions).