Nuts and bolts, part 1

This post is aimed at educators who are are considering taking the leap into mastery/standards/specifications-based assessment, but aren’t sure where to begin. My biggest question when I first heard about mastery-based testing (MBT) was: No points(!) — how does that work?

This post is part 1 of the ‘Nuts and bolts’ instructions for how to do points-free assessment with MBT. Part 1 deals with the logistics before the course begins — how should you write the syllabus and explain MBT to your students? Part 2 explains the specifics of writing exams and grading that you will be dealing with once the course starts.

Taking a mastery-based testing (MBT) approach to a course requires some advanced planning, but it is the type of planning that not only helps with the assessment but also with the long-term goals of the course. If you are nervous about trying a new assessment method like MBT or specification grading, you might consider starting it in a course you’ve taught before. I did this during the first year of my current job — I taught Calc 1 in the fall with a normal points system (100 point exams, 10 point quizzes, etc). The following semester I taught a section of the same course, but used an MBT approach to assessment.

Feeling comfortable with the content is important for laying the groundwork of mastery-based assessment because you’ll need a good idea of what it is the students should master in the course before you begin. You can think of it as writing the final exam before you write your syllabus. If you are the type of person who has already written your final for the course you’ll teach next semester — then congratulations, this will be easy for you! If instead you are like me and sometimes write the final exam during finals week, then I’m here to convince you that it’s still (mostly) easy to use MBT.

The first step is to create a list of the essential skills and topics that the course will cover. If you haven’t taught the course before, creating a list of learning outcomes is one of those recommended teaching techniques that (to be honest) I didn’t hear about until I had taught several courses on my own. [See, for example: Writing Student Learning Outcomes] In short, it is a good idea, even if you aren’t using MBT next semester. Your list might consist of both general skills like “students will engage in problem solving” and also subject-specific techniques like “students will be able to take the derivative of a composition of functions using the chain rule”. How you group the learning goals for assessment depends on the course and your own preference. For simplicity, you may initially try to limit yourself to 16 umbrella topics, and students can try to master each topic. For examples of lists like this, see the resources page.

I’ll talk more about choosing the list of skills, but now it’s time to write the syllabus!

Syllabus explanation of MBT

Your syllabus will look mostly the same as normal, except it should have some explanation of the mastery-testing method. Whether you put the list of topics on the syllabus is up to you — I did not put the list of topics the first time I used MBT because I was still figuring things out when the semester started. Now, however, I do try to put the list of topics on the syllabus because it helps to have the list easily accessible to students.

In the syllabus section where you would normally explain how many midterms there will be and whether the final will be cumulative, you will now have to explain how MBT works. I borrowed most of this directly from Austin’s syllabus, but this is just a starting point. In my class, I call the mid-terms “Quests”. The final exam is really just another Quest. Here is the MBT statement from my syllabus for Calc II.

Grading Policy

Grades in this course will be determined by an assessment system that relies on mastery of 16 sorts of problems. For each type of problem you will have multiple attempts to demonstrate mastery. The examinations (Quests and the final exam) will all be cumulative. The first Quest will have 5 problems, the second will have 5+4=9 problems (with 5 being variants of the ones occurring on the first quest), the third will have 9+4=13, and the fourth quest and the final exam will both have 16 problems. There may also be re-attempts periodically to allow for further attempts at each type of problem.

I record how well you do on each problem (an M for master level, an I for intermediate level, and an A for apprentice level) on each quest. After the final, I use the highest level of performance you achieved on each sort of problem and use this to determine your course grade.

If at some point during the semester you have displayed mastery of each of the 16 sorts of problems, then you are guaranteed at least a B+ (homework and Maple proficiency will determine higher grades). The grade of C can be earned by demonstrating mastery of at least 12 of the types of questions. If you master at least 8 of the types of problems you will earn a D-. A more detailed grading table is given below.

(See Jeb’s post on Nuts and Bolts: Part 2 for an example of a grading table.)

This method of arriving at a course grade is unusual. There are several advantages. Each person will have several chances to display mastery of almost all of the problems. Once you have displayed mastery of a problem, there is no need to do problems like it on later exams. It is possible that if you do well on Quests you may only have one or two types of problems to do on the final exam. It is also possible that a few students will not even have to take the final exam.

This method stresses working out the problems in a completely correct way, since accumulating a bunch of Intermediate-level performances does not count for much. It pays to do one problem carefully and completely correct as opposed to getting four problems partially correct. Finally, this method allows you to easily see which parts of the course you are understanding and which need more attention.

If at any point during the semester you are uncertain about how you are doing in the class, I would be very happy to clarify.

[Aside: Another MBT enthusiast uses something like Padawan/Jedi/Knight instead of Apprentice/Intermediate/Master. Come up with your own names, you can.  Yes, hmmm.]

Writing a statement about MBT in the syllabus is a first step towards getting student buy-in. It is equally important  to have a prepared summary you can give on the first day or during the first week about what MBT assessment is and why you use it.

Selling the idea to students/first day comments

On the first day of class, I spend about 10 minutes explaining how my version of no-points assessment works, and why I choose to determine course grades in this way. My biggest selling point to students is that I want to give them more than one try to demonstrate that they understand the course material. It is helpful to emphasize that while the standard for mastery is high, every single person in the class has the chance to succeed with MBT.

Most students have not encountered a mastery-grading system before, but they are usually excited by the idea that they may not have to show up for the final exam if they master all of the topics during the mid-term assessments. (That is, if you choose to handle your course in this way — there are other models that require a cumulative final exam regardless of mastery levels during the semester.)

When explaining the system to my students, I use the syllabus explanation as a guide,  and I add in my own personal reasons for approaching assessment in this way — here are a few.

  • I find points arbitrary — what does it really mean to get a 7/10 on a quiz? It is also difficult keeping a “7/10” consistent throughout the semester, which is frustrating to students.
  • I think that real learning requires revisiting your previous work and addressing misconceptions. To be successful in an MBT course, you have to address (at least some of) your past mistakes.
  • Completing a math problem in its entirety is an important skill — it requires persistence and focus. Removing the notion of partial credit emphasizes this skill.
  • Giving students the list of topics and skills at the start of the semester allows them to see a path to success in the course. It also lays out exactly what the course goals are. This can help to remove some of the mystery surrounding the class and it also may help with math anxiety.

When presenting the MBT system in the first week, I try to be relentlessly positive. Usually it goes over well. Some students may wish to leave the class because it is different from what they are used to, and that’s ok too! On the whole, enrollment in my classes has been steady since I’ve started to use mastery grading.

Incorporating other graded components in the course 

It is easy to incorporate other components of the course that are not appropriate for an in-class assessment — for example, practice homework problems, projects, oral presentations, Maple projects, and so on. You can choose to grade these other components in the mastery style (M/I/A or K/J/P) or you can revert to a standard points system for these components. I’ll demonstrate with an example of how I incorporated homework into Calc I and II.

I used WebAssign (an online homework system) for daily homework in Calculus I and II. I gave students repeated attempts on the homework, just as I did on exams. In the case of homework, 6 attempts was the cutoff. In the final course grade, homework counted the same as two of the “mastery topics” — if a student got at least 70% of the homework problems correct (eventually), I treated it as one mastery. If they got at least 90% of the homework problems correct, I treated it as two mastery. Therefore, my 16 “topics” grew to 18 in the final course grade, and two of them aren’t really topics at all, they are dependant on homework. There are other ways to incorporate homework or presentations — see the resources page for more examples.

Deciding on the list of skills to master

I recommend drafting a final exam that you would give in a standard version of the course, and determining the skills list based on that exam. It’s a great way to see what you are hoping that students accomplish. Some problems may require multiple different skills, so those sorts of problem may become two different topics. Others might not merit an entire topic on their own, but they might be easily grouped with another type of problem. For example, I had a topic in Calc II called “Applications of Integration to Arc Length, Surface Area, or Probability”. That topic usually had a question with two unrelated parts — but both parts used integration to solve a problem.

It’s a process of trial and error, for sure! I have edited my list of topics from past classes, after discovering that some topics shouldn’t be given equal weight in the final course grade.

Jeb’s post continues with an in-depth view of choosing exam problems, dealing with quizzes, and grading.


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