An Adventure in Standards Based Algebra

This semester I am teaching several sections of “Math 101: College Algebra”. One section uses an “emporium” method, where students work independently in a computer lab. Instructors are available for questions and we also hold mini-lessons as needed, during which small groups of students can work on a particular topic at the same time. The other two sections are “traditional” in format and I’ve designed a standards-based grading system for them.

I began by creating a list of 30 standards for our 16-week semester. These are grouped by textbook section. Each standard has one or more “I can…” statements associated with it. Here’s the complete list. I’m giving three midterm tests this semester and each test will have an assortment of problems. The exam I gave this week covered our first six standards and had fourteen problems. Not all standards had the same number of problems.

I graded each problem using a modified “ERMF Rubric” (see http://www.nctm.org/Publications/mathematics-teacher/2004/Vol97/Issue1/EMRF_-Everyday-Rubric-Grading/). If you aren’t familiar with ERMF, I’d suggest checking out this post by Taylor Belcher, or some examples of the ERMF Rubric used in a beginning physics course. I decided I didn’t like the baggage associated with an “F” so I made mine an “ERMN” rubric:

Basically, I’m implementing a “Pass/Fail” system — although I refer to those as “Proficient” and “Not Proficient.” Scores of “E” and “M” are passing scores, and scores of “R” and “N” are failing scores. If a student earns all “E”s and “M”s on problems from a particular standard, then they get a “Proficient”. If there’s a mixture of some “R”s or “N”s, I looked at those case-by-case to determine if the student had shown enough understanding of the relevant ideas to merit a “Proficient” or not.

Overall, grading the exams took about one minute per exam page. I have about 50 students and this exam contained 6 pages. I don’t think this is too far off what it would have taken, time-wise, to grade using a traditional points- or percentage-based system.

I’m allowing students to come to my office for re-assessments, so any standards that earned a score “Not Proficient” can be improved upon later. In an upcoming post, I’ll write about my “Policy for Re-Assessments” and outline my system. From past experience, one key factor I’ve found is limiting the number of standards that can be re-attempted to no more than one per week.

At the end of the semester, 50% of the course grades will come from how they perform on their midterm tests. I’m converting all these “Proficients” and “Not Proficients” into a numeric score using this formula: “Midterm Exam Grade = 25 + 75*(# Proficient)/(# Total)”. Basically, this is the percentage of standards ranked Proficient, plus a tiny bit. Now I have to run off to class to return exams to students and explain more about how this grading system works — and why I believe it is to their advantage.