Standards-Based Grading Example in an IBL Course

I'm sharing an outline of standards-based grading I've recently used in a course for future elementary school teachers, although much of this is generally applicable to other courses. I'll list the main features and then get into some of the details below.  Also this is just one example, so do not assume that what I am sharing is representative. It's really a form that works for the specific course.

Here are the main features:

1. Gateway exams
2. Reading assignments
3. Homework assignments
4. Productive failure
5. Class contributions and participation
6. Final project

How these fit together is that if a student earns a passing grade on all items, they earn a B in the course. Students can raise their grade to an A/A-/B+ with an excellent grade on the final project. Students earning one or more non-passing scores in any of the categories will earn a grade lower than a B, with specific grades reductions based on the nature and quantity of the unsatisfactory grades.

1. Gateway exams: These exams are based on the IBL units we work on regularly in class, and are based on the math being learned in the course. Students are required to pass all of the problems on the gateway exams (i.e. get the correct). For any problem that was not successfully passed, a student must retake that problem on the retake exam.  The retake exam is given about two weeks after the initial exam. Problem done correctly do not have to be retaken.  The first retake is done in class. Subsequent retakes are completed in office hours or alternatively completed in writing and submitted for review.  This past term, I gave 2 exams, and was limited by the quarter system (10 week terms) in how many retakes can be given in class.

Retakes can become a logistical challenge for large classes or in courses where there is a significant amount of material to cover. One has to weigh the costs and benefits of this and plan accordingly. The strategy I've taken is to start with a course that I thought would be relatively easier to manage, and then work my way to other courses where I feel I would be better off with more experience.

2 and 3. Reading assignments and homework assignments are graded for process and completeness. Accuracy feedback is given, however, the goal of these assignments are for students to think and reflect on math and math knowledge for teaching. Points are not taken off for mistakes or incorrect answers, and instead feedback is given when necessary and points are awarded for good process. For example, if a student gets a problem wrong, but writes questions or explains what they did and what they still need to work on, then they earn full credit for the problem. 

4. Each student is required to present one productive failure (i.e. #PF) per term (in a 10-week quarter) about a mistake or something the student was stuck on. The format is to discuss (1) the mistake or issue, and (2) to share what they learned from the process.  (In some courses the number of #PF presentations is 2.)

5. Student contributions to the class discourse is another component. Students work in groups and are expected to show up to every class, contribute to discussions, be effective group mates (i.e. be good at listening, supporting, and sharing), and present math ideas sometimes. More or less this is participation grade, but with stipulations about expected behavior. 

6. In lieu of a final exam, students must submit a final report. The report is based on 4 tracks related to mathematics teaching in the elementary school and the course content (in this case fractions for teachers).  Each track has a lead source (article or book). Students are required to do library research, branching out from the lead source, to find learning challenges (for children) established in the Math Ed literature. Lastly, students are required to create rich mathematical tasks that address the identified challenges that build from starter problems to middle problems to goal problems. 

I get asked if creating math tasks is pedagogy.  The answer is no. Creating math tasks to address specific math learning goals is a teaching specific math activity. Identifying the main math ideas, ordering and sequencing math problems, and building up from first principals is doing a math (applied to teaching children). 

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Some general comments.

Gateway exams require students to learn all the standards of the course. There's no partial credit for problems, and students are required to demonstrate they know the math they need as teachers. Students have multiple chances to make sure they get problem completely correct. The retakes can be logistically challenging, if you are not organized. Overall, the workload is about the same, because retakes eliminates the time needed to determine partial credit, and there's a tradeoff that more or less washes out (for me).

Further, the overall assessment structure aligns the class to the mathematical work of teachers and the philosophy of IBL. The focus is on learning, and guiding students to what they know well and what they need to work on further. What students need to work on is clear, and this I find one of the main benefits of standards-based grading.

The reading assignments, homework, productive failure, and class contributions, as an ensemble focuses on process and prospective teacher beliefs. The shift is away from "answer-getting" without deep understanding.

Final projects or final exams can be implemented in ways that work with standards-based grading. In this specific case, I decided on final projects, since it gives future teachers the opportunity to connect they math they are learning, the research literature, and connect that to the classroom. In other courses, I have used standards-based final exams. 

If you're thinking about trying standards-based grading, I highly recommend giving it a go.  If you have been using standards-based grading, please share what you do! 

Edit: Dr. Kate Owens published A Beginner's Guide to Standards-Based Grading the AMS Blog.