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Calculus: An Implementation of Standards/Specifications Based Grading

By Dr. Matt Thomas and Dr. Megan Martinez

During the summer of 2016, the three instructors of Calculus 1 decided to investigate the way we were teaching calculus and redesign our course.

We wanted our students to focus on the conceptual ideas of mathematics, and be able to examine, and improve on, their own understanding of the concepts. Among the many changes we considered was an alteration to the traditional grading scheme in a mathematics course in order to better align with these goals.

In this post, we’ll discuss the changes we made to our grading, which will hopefully inspire others as they consider assessing their students.

Our system used a combination of Standards and Specifications Based Grading; there are some differences between Standards Based and Specifications Based Grading, though we won’t focus on those differences here. Interested parties can check the resources at the end of this post for more information on the differences. Since we blended both systems, we will use the abbreviation SBG to describe what we did.

What is SBG?

SBG is an alternative to “points-based” grades. In a point-based system, grades are typically given based on a number or percentage of a possible total achievable (e.g. 90% for an A), and may be divided between types of assessments (e.g. exams vs homework). SBG begins with an outline of what should be achieved at each grade level, rather than with a percentage. Practically speaking, it makes a lot of sense to begin by defining the criteria for a B or C, and work up and down from there. There are many ways to determine these criteria, from the number of assignments completed, to different levels of difficulty of projects, to a number of learning goals completed. In our case, we used a little of each.

What does SBG look like?

On our syllabus, we included the following table to illustrate how each grade could be achieved.

SBG Rubric.png

Thus, to reach a B, a student would need to master 9 learning goals, achieve 15 lab points, correctly complete 75% of the online WeBWorK problems, and complete 11/16 of the video watching and reflection assignments. Each category represents an important goal in our course. For example, learning goals, as we describe below, represent a student’s understanding of each of the different topics in the material. Lab points are more closely tied to a student’s ability to reason, problem solve, and communicate their results. In our syllabus, the expectations for each of these categories were carefully defined, so a student would understand exactly what they should do to achieve a particular grade.

Learning goals

The most unique column of this table is the “Learning goals” category. In order to measure mastery of the concepts in calculus, we began the semester with a list of the learning goals for the term . Our learning goals are fairly coarse, with only 16 throughout the entire term; within each learning goal, we describe a number of tasks or ideas that contribute to a complete understanding of the topic (this list is also provided to the students).

In SBG, there are a number of ways to measure whether a student has mastered a learning goal. In our first iteration of SBG, each problem on a problem set was assigned at least one learning goal, so that correctly and fully answering a question indicated evidence of mastery of all the learning goals associated with the problem (these problems were graded on a pass/no pass basis). When a learning goal had been demonstrated twice, that learning goal was considered “mastered.” A student no longer needed to complete problems associated with that learning goal. In our second iteration, to ensure students did not ignore topics once they were mastered, we provided a score measuring the student’s mastery of a learning goal based on their work in a particular problem, and used a weighting system to more heavily weight the most recent attempts at a learning goal. Obtaining a high enough score for a learning goal will result in mastery.

The key component of each of these methods is that students are given the opportunity to improve their understanding, and their grade will reflect this improvement. In our first iteration, students were allowed to rewrite problems. In our second, we ensure that learning goals appear on numerous homework and quiz assignments, so there are many chances to improve. In the resources at the end of this post, we provide links to other schemes that have been used. The sky’s the limit for how you plan to assess!

Why use SBG?

Using SBG has a few benefits that were particularly important for us.

  • SBG makes expectations in grading clear to the students. The exact expectations for what we expect of a “B” student are laid out from day 1.
  • SBG allows students to take control of the work they need to do the achieve the grade they want. If a student only needs/wants a C in a class, they can see how many assignments they need to complete in each category, and manage their time appropriately.
  • SBG rewards effort and competence. In our implementations, students are evaluated on their understanding of a topic, and are given chances to be reassessed on learning goals. This allowed for fewer conversations about how many points they received, and more conversations on how to improve their understanding of a particular topic.
  • SBG allows for credit to a student on a topic regardless of when the topic is mastered. Because there were no time-benchmarks for topics, a topic could be learned at any time during the semester. What mattered to us was that a student had mastered a topic, not that they had mastered a topic by a certain date.

What did we learn and what are we changing

Our original motivation for seeking out a new grading system was to improve our students’ conceptual learning of mathematics; we saw a marked difference in the conversations we had with our students. A student can examine the list of learning goals that remains unmastered, and focus on their understanding of those concepts. This difference was noticeable in office hours, when students were likely to point out particular learning goals where they were struggling, and initiate a conversation on the overarching ideas of that concept.

As with any change in structure to a class, there were a number of challenges. In our first implementation of the course, we expected an extremely high level of responsibility and time management from our students. Because the due dates became very flexible in our implementation, this required students to plan their work over longer periods of time. While some students appreciated this flexibility to work on their own schedules, this was problematic for some students, and our second implementation tightens the schedule for problem completion.

Another concern was how students “buy into” this grading system. Points grading is widely accepted as the grading system. From day one, we take time to have candid discussions with our students about the system, and how it can benefit their own learning of the mathematics, especially as we see SBG is more in line with the development of a growth-mindset. The biggest lesson we have learned is to be upfront with your students about the expectations and motivations for a nontraditional course design.

Despite the challenges connected with implementing a new system, we remain optimistic about the future of our redesign. We saw many students flourish under the new grading system: they asked insightful questions, reflected on their past work, and improved their knowledge as the term progressed. Their hard won successes were rewarded by a grade that respected the level to which they had climbed.



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