What to do when you fall behind the expected pace in your MBT class

Our blog has been rather silent of late, in part because we have been working on a paper which we submitted this past summer. This paper outlines what mastery-based testing is and shares a bit of the data we collected from our first few years of implementing MBT into our classes.

I have been meaning write this blog post since Christmas break, but this post was always kept on the backburner. But today, I finally decided to go ahead and “eat the frog.” Today, I want to talk about something that I have been struggling with recently in some of my MBT courses which is what to do when you fall behind in a course. Here are some of the things I have done when I have gotten off-pace in a class:

  • Adjust the number of concepts
  • Adjust the number of exams or testing opportunities
  • Adjust the mastery concepts of the course
  • Streamline content in the course if you can (trim the fat)

Now, I think all of these are good ways to deal with falling behind as a teacher, but I want to warn you that making some of these adjustments may have unexpected results as well. Hopefully, my struggles will help you decide on the best course of action for your own situation if you fall behind.

 I consider myself to be a relatively “experienced” MBT-er. I have used mastery-based testing for four years in classes ranging from Calculus to Real Analysis. When I use mastery-based testing, I usually have 4 exams and a final with a total of 16-18 concepts. This structure has worked well for my 4-credit Calculus courses. It also worked well for my 3-credit Real Analysis course during my first two years using MBT. I was pleased with how these MBT courses went and my students were generally happy. But like all teachers, I was looking for ways to improve my courses. And the tweaks I made in my Real Analysis class over the past two years have yielded some unexpected consequences that I had to deal with in the middle of the semester.

During the summer of 2016, I went to an IBL workshop to help me incorporate more inquiry activities into my classes -specifically Real Analysis I. I have always tried to make my courses active (I use group work, ICE Sheets (In-Class-Exercises), clicker problems, and think-pair-share in my courses), but the IBL workshop challenged me to stretch my students more and I started adding more inquiry problems to my ICE-sheets. So I decided to do it and did a big overhaul with my Real Analysis class.

Oh my gosh, I am so behind!
Unfortunately, adding more IBL to my Real Analysis course changed the pacing. Instead of spending a day or day and a half on topics, we were spending over a week on some topics. Thus, I decided to delay our first MBT exam because we hadn’t gotten to all of the concepts I had planned to have on Exam 1. As I fell further and further off my planned schedule, it became clear we weren’t going to get to the 18 concepts I had mapped out for my class. Midway through the semester, I had to decide what to do to help with this pacing problem, so I made two quick adjustments. First I changed the number of exams from 4 to 3. Then I cut down the number of concepts from 18 to “however many we would get to.” Unfortunately, with only 3 exams, it didn’t really give my students enough time to retest, so I later had to make two more adjustments to my course. I added a testing week* between Exams 2 and 3 and changed the final exam to be a testing week as well.

How my pacing issues begot other pacing issues
These changes helped me give my students more chances, but they also caused a new problem with the pacing of the course. Because of the slower pace, instead of having exams placed more or less regularly throughout the semester, we ended up having Exam 2, the testing week, Exam 3, and the final testing week all within 4 weeks. It was very taxing on the students to be testing all the time. They were troopers and didn’t complain, but I could feel the extra stress. I vowed to do better next time.

This past fall, I tried to adjust and streamline some of the added inquiry activities, but I still had to delay exams and ran into similar problems. I am not sure if other MBTers have had this issue but now that it has happened twice I am going to try some of the following to help with this course in the fall.

  • I could change the concepts of the course. In general, a lot of the first part of Real Analysis isn’t broken down into many concepts. A lot of the start of the class is getting students used to writing proofs and how to construct well-written arguments. I could try to come up with some new “proof-writing” concepts which would allow me to keep Exam 1 earlier in the semester, but with new concepts included.
  • I could decrease the number of inquiry problems in some of the sections -especially those at the beginning. I could save some of these proofs for Real Analysis II or move the proofs to their homework to save time. This would allow me to get through more of the concepts for Exam 1.

Perhaps I will try a combination of these two options and of course if any of you wonderful readers have other suggestions, please share them in the comments! =) I plan to follow up on this topic after the fall to let you all know how it went.

One of the things I love most about teaching is that it is this great “unsolvable problem” that I always get to keep working on. This past year has thrown me some interesting situations that I hadn’t planned for which have required some adjustments to my MBT implementation. To close out this long-winded post, I will share some general advice on what I have learned from these mishaps:

  • Be willing to be flexible: I think this is an important quality for all educators. I remember David Kung, Director of Project NExT once said that even though you may be teaching the same subjects, each year you get to teach it to a new group of students which changes the dynamic and keeps it interesting. We need to be willing to make logical and fair adjustments to our plan when things don’t go as expected.
  • Don’t be afraid to be transparent with students: When the pacing became very off from our Real Analysis schedule, I talked to my students about why I was adding the inquiry activities and that because of this I didn’t know exactly where we would end up at the end of the semester. When I was debating different ideas to help with the MBT pacing, I asked for their input. At the end of the semester, after their oral exams (not MBT oral exams -just regular oral exams) I gave them another chance to give feedback about the class. I shared some of what I thought didn’t go as planned or as well as I had hoped (the pacing) and asked them for suggestions. In the end, even though I felt like I was struggling more with teaching this course than past semesters, I received the highest course evaluations I had gotten in this Real Analysis. I think this was in part because I was transparent with them throughout the semester.
  • Buy-in is important: I made sure to have my students understand why I was using MBT and thus, when the MBT schedule didn’t go as planned, they still understood why I was using MBT and why I was adding more IBL.
  • Forgive yourself: We aren’t perfect, it is ok when things don’t go how you want. Forgive yourself, learn from the situation, and let it go. You can try to do better next time. For goodness sakes you are a mathematician, we love problem-solving!

Have you had to deal with the challenge of falling off pace? What have you done? What have you learned?


About the Blogger: Amanda Harsy teaches at Lewis University, a private, Catholic, Lasallian university located in Romeoville, Illinois, 35 miles southwest of Chicago. Lewis has 6,500 undergraduate and graduate students with a 34 percent minority population. Lewis is a primary teaching university and most professors teach 4 classes a semester. During her four years at Lewis, she has used mastery-based testing in Calculus II, Calculus III, Applied Linear Algebra, and Real Analysis with class sizes of 10-50 students.  During this time, she has also completed a two-year study comparing MBT to traditional testing in her Calculus II courses. She is currently working on a follow-up to this study with Dr. Alyssa Hoofnagle from Wittenberg University.

* In my Calculus courses, I usually use 3-4 testing weeks between exams to give students extra opportunities to retest. Students can test any concept, but only once during a testing week. So for example, a student could retest concept 1 and 4 on Monday and concept 2 on Tuesday, but they couldn’t retest concept 1 again on Tuesday. Before this semester, I had never used testing weeks in Real Analysis.



Mastery-Based Testing with Core Concepts


Hi everyone, Amanda Harsy and Jessica OShaughnessy here to add a few thoughts on a variation of Mastery-Based Testing. Both of us have been using Mastery-based Testing in our courses over the last two years. Jessica uses MBT in Calculus I, Calculus II, and Introductory Statistics, while Amanda uses it in her Calculus II, III, and Real Analysis courses.

We usually have 16-18 concepts in our Mastery Exams and students can add to their exam grade by mastering these concepts.  Now we have a choice: should we treat all the concepts as equal? That is, can students master any of the concepts to build their grade? In some courses, it may make sense to let the students choose.

But what if you feel that not all concepts are created equally? That is, are there some concepts you really think students should have grasped after taking a class?

Both of us use a slight modification in our mastery-based grading to address this belief. For example, since Calculus II is a sequential course, there are certain concepts we think all Calculus II students should master in order to be successful in Calculus III. We want students to successfully be able to differentiate transcendental functions, calculate area, and use integration by parts. In order to enforce these concepts, we have introduced “Core Concepts.” In Amanda’s  Calculus II course, for example, these concepts include differentiation and integration of transcendental functions, L’Hopital’s Rule, Advanced Integration Techniques, Calculating Area, Calculating Volumes, and Interval of Convergence for Series.  Students must master these 7 concepts in order to earn at least a C for their exam grade. Similarly, Jessica breaks her Calculus I classes into 16 topics and 7 core/required concepts. The students must master these 7 before any other questions count. If they do only these required concepts, they will receive a 70% as their test grade.

We both have a love/hate relationship with core concepts, which we tell students are “required” concepts. We’ll start with the love:

  • First of all, it forces students to have “mastered” important concepts they will need to understand to be successful in the subsequent course. As much as we love related rates, our students can probably manage Calculus II without fully understanding the topic. However, the chain rule is absolutely critical. Previously, they could get a C by half understanding the chain rule and half understanding related rates. This way, they know they cannot move on to calculus II without a full grasp on the chain rule (and other required topics). They are better prepared to build on these topics.
  • It also helps students focus on particular topics for each exam. For our weaker students, we can direct them to these concepts to get started. We want them to focus on the calculus concepts that they really need.

The cons (we will use cons instead of hate since we think hate is really too strong):

  • This method for calculating the mastery exam grade is a little more complicated than treating all concepts equally.  For example, it requires students to keep working on some of the more complicated integration techniques until they master them.
  • What about when a student masters 14/16 concepts, but one of the two they didn’t master is a required concept? Like limits? Should they be allowed to pass the course when they understand so much of the material? Granted, we think this is an extreme case, but we all know these extreme cases happen so it is important to think about how to handle these situations.  Here is one way that Jessica has dealt with these cases.
    • “Occasionally I will have students with several required topics going into the final exam. This stresses the students because they feel like they will fail the course if they do not master those required topics. Although I do not tell them, I grade these in a different way on the final. Typically, they master or do not master. However, I write up those that are “close”. If they are close but have not fully mastered a question, then I will count it toward their passing grade, but I will not add it as an extra “mastered” question. For example, 7 mastered questions is a 70% for my test. If they mastered 7 questions: 6 required concepts and 1 non-required, this means they would have 1 required concept unmastered. If they are “close” I will go ahead and give them a 70% for the test grade.  I will allow up to two that are “close”. My definition of close may be a few algebraic mistakes or some minor conceptual mistakes. Students who have no idea how to do the chain rule do not obtain a ‘close.’”-Jessica
  • What should we do when students don’t try the required concepts? Unfortunately, we both have had students who haven’t attempted the core concepts. Then they complain that they had 7 questions mastered and they don’t understand why they received a D in the course. It is extremely important to emphasize that some concepts are required and to spell this out carefully in the syllabus. Of course, there will always be students who do not pay attention to this, but at least we have done our best.

Overall, we both really like core concepts. This way, we can make our derivative questions hard enough that students will really show us they have mastered the concept without the ability to skip that concept because it is “too hard”. It allows students to be better prepared for their sequential courses and encourages them to review their old material. If you worry that students will skip some important ideas that won’t necessarily show up in other concepts because of the mastery-based system, this may be a good variation for you!