Memories from MAAthfest 2018

0. At #MAAthfest this past August, Drew Lewis asked, “How can we make sure we are providing adequate opportunities for all our students to demonstrate mastery?

This year’s MAAthfest was held in Denver, Colorado from August 1st through August 4th. I went, I had a great time, and I want to tell you about some of the things I learned. While there, I presented twice: once as an invited panelist for Project NExT and then as a speaker in the Special Session on #MasteryGrading. Info about my talks is available here in my blog post called “MAAthfest 2018“.

Now I hope to give you a quick summary of some of the many great take-aways from the rest of the #MasteryGrading session.

1. Many of us noted that Mastery Grading reduces stress levels, both for the instructors and the students.

2. It’s hard to get by on a partial credit strategy. Mastery Grading holds students accountable for their own learning.

3. Many of us moved toward Mastery Grading after spending a long time really considering questions like “Why do we assign grades?” and “What do we want grades to tell us?”

4. I really like, respect, and enjoy these people.

We didn’t spend the entire time working. We also had shared some great meals:

5. Traditional Grading expects all students to learn material at the same pace, but Mastery Grading allows learners to find their own path.

6. Mastery Grading really changes the way you write questions. If your goal is for students to change how they answer questions, sometimes you have to change what you’re asking them.

7. In Traditional Grading, instructors give students points. In Mastery Grading, students have accountability for gaining and then displaying knowledge.

8. There are many different ways to implement Mastery Grading. The real challenge is  finding the one that works best for you, your courses, and your students.

I’m excited to read an upcoming issue of PRIMUS (Problems, Resources, and Issues in Mathematics Undergraduate Studies) devoted to Mastery Grading. Submissions are due October 15th, 2018 and more information is available here.

9. In all learning, there’s struggle. Mastery Grading supports and encourages students through the struggle.

Austin added, “Assessment should guide students toward productive struggle” and I really like this quote. On Deadlines, he also gave us two pieces of important advice:

 

10. Mastery Grading allows a path for improvement and success for all students, while still keeping clear, high expectations for learning.

 

Bevin Maultsby (NC State) shared with us course grade distributions for students in a course on Matlab, a computer programming language. Over 60% of her students earned As! So impressive.

11. Some adaptations of Mastery Grading work well in project-based courses, courses with proofs, etc.

Chad Wiley (Emporia State University) told us about his use of specifications grading, and I’m hoping to adapt some specs-style setup in my upcoming “Math for Teachers” course that starts in October.

If you’re wondering about the difference between standards-based grading and specifications-based grading, Joshua Bowman (Pepperdine University) really summed it up well:

12. Common benefits of Mastery Grading include sustained student effort, clearer learning objectives, and changes in conversations with students.

We had a great three-presenter talk about #SBG happening at three different institutions:

I really need to look back on this list of “14 Characteristics for Evaluating Grading Systems” by Linda Nilson.

13. The Mastery Grading community has begun gathering powerful data about student learning, and we’re seeing that Mastery Grading allows for students to be successful even with differentiated pacing of their learning.

Drew Lewis (South Alabama) had a really amazing slide called “A tale of two students” and I am committed to generating such graphs for my own students this semester:

Honestly, if I had to pick one slide that has stuck with me daily since MAAthfest, it’s Drew’s graph of the learning trajectories of two different students. If we want all our students to have the opportunity to be successful, we must construct our courses that allows for differentiated learning trajectories. 

14. Most University grade systems are already built with Mastery vocabulary in their grading scales.

15. Occasionally I missed Tweeting great stuff.

There are several other talks I don’t have archived on Twitter. Joshua Bowman gave a great talk about his years of experience using standards-based grading. His work was what originally inspired me to make the Mastery Grading jump in my own courses in 2013-2014.

Steven Clontz gave some really great practical tips (and I was too busy taking notes to tweet them!). Thankfully, he did that part himself:

I wasn’t able to attend David Clark’s (from GVSU) presentation when he won the Alder Award, but here’s what the MAA tweeted:

16. Outside of Mastery Grading, I was inspired and found joy in several other places.

 Her slides are available here, courtesy of the MAA.

  • I went to Emily Riehl’s talk in the “Category Theory for All” session and her talk was amazing.


    I mentioned to a colleague here what I had learned about category theory and it turns out one of our graduate students at the College of Charleston is writing a masters thesis in this area. I was invited to join his thesis committee, so now I’m going to have the opportunity to learn a lot more. Emily’s talk reminded me of some of the things I love about universal algebra.

  • One of my best friends from childhood was able to fly to Denver to spend some time with me, and her company was the best gift. Also, this was my first trip away from my three children — ever! — and by the time she got there, I was hug-starved. So great to have someone to offer a hug (and a hundred laughs) each day.

See you at MAAthfest 2019.

Reflection on Standards-Based Calculus

Our semester is wrapping up and we only have one more class meeting day after Thanksgiving. I’ve been teaching two sections of “Calculus II” using my standards-based grading system that I’ve mentioned before. I think I made several improvements this semester and I wanted to share them, along with a couple of things I’m still contemplating. But first, here are things I thought went well:

  • I really liked having my standards organized by Big Questions. This is probably something I could have implemented outside of my grading system. Somehow writing and organizing my list of standards gave me the motivation and time and priority to think about the take-aways I wanted my students to get from our course.
  • Last Spring, I had approximately 18 standards, meaning about one per week. They were large learning targets. Take, for example, the “Techniques of Integration” standard that encompassed a couple of weeks of class time spent talking about integration by parts, by trigonometric identities, by trigonometric substitution, by partial fractions, and so on. This semester, I wanted more standards that were more specific. I hit my goal of 30 standards for the semester and this number worked well. On the one hand, the standards were specific enough that students could focus on just one idea at a time. On the other hand, there weren’t an unreasonable number for me to assess. Roughly they correlated to one standard per textbook section, spanning about 1.5 classes per idea.
  • Originally, I had a “policy of replacement” where a score would be updated each time a problem was attempted. In some cases, this seemed to harsh, since prior good work was “erased” easily. In some cases, this seemed to lenient, because sometimes an easy problem would earn a high score, but replace more thoughtful work on a harder problem. This semester scores were defined as the average of the scores from the last two attempts. This also made picking problems for re-assessments easier on me since I wasn’t as concerned about having them all be exactly the same difficulty. It also means that a score of 4 means a student demonstrated a strong level of mastery on two problems of a particular type, and that seems to work well.
  • I limited the number of re-assessments to one re-assessment topic per week. For example, if a student were struggling with Taylor Polynomials, they could come in throughout the week and try re-assessments. In some cases, they would just solve one problem. In other cases, they might solve four or five problems, each time getting a little more of the correct solution. Previously I let them do 2 standards per week but I found two problems with this: First, some students would just always pick their lowest two scores and try them, without really ever focusing on a single idea and working toward mastering it. Second, having multiple re-assessments on multiple topics times multiple students meant my grading workload was higher. So, one per weeks seems like a more manageable number for them to work on and it makes my grading workload lighter. Lastly, since we had 30 standards (but only 16 weeks) this policy pushed them to demonstrate mastery on in-class assignments (quizzes, exams) without just punting them to re-assess in my office later on.

Two things I don’t have data on yet:

  1. This semester I tried assigning online homework, with the homework contributing 5% to the overall course grade. I found assigning just textbook problems (and not grading them) did not work well. Perhaps I was not very good at motivating students to solve more problems on their own? I haven’t taken a detailed look at homework scores compared with course standing, so I am not sure if homework correlated with success on in-class assignments or not. I also feel a bit “icky” about assigning and grading homework, given some of the research I’ve seen.
  2. The other change I made was I separated “during semester scores” from “final exam scores.” So 70% of course grades will come from a letter grade assigned based on the scores on standards that were accumulated during the semester and 25% of course grades will come from a letter grade assigned based on scores on standards that will be accumulated on the final exam. This breakdown was in response to some conversations with students from last semester who felt that the old policy (“average of semester score and final exam score”) was too strict. We will see how this works out and if there is much movement in pre-final letter grades to post-final letter grades.

I’m teaching calculus II again in Spring 2015 and I plan to continue using this system. I am still entirely undecided about trying it in Pre-Calculus. I have several worries about trying it in that course.

Postscript: Here are some links to some older blog posts about my SBG Calculus adventure:

https://blogs.charleston.edu/owensks/2014/10/09/big-questions/

https://blogs.charleston.edu/owensks/2014/08/18/list-reboot/

https://blogs.charleston.edu/owensks/2014/02/25/on-the-purpose-of-examinations/

https://blogs.charleston.edu/owensks/2014/01/09/sbg-faq/

Some Thoughts for My Students

I spent some time over the last several days trying to track down documentation about SBG/SBL. I wanted to find something to pass along to my students to address some of their questions or concerns, like, “What’s this SBG thing?” or “How will this work in our course?” or “How is this going to be beneficial?”

Thankfully, Joshua Bowman came to the rescue and sent me something he gives out to his students. It addressed some of his students’ frequently asked questions and it was a great launchpad to write my own. I’ll post it below. I kept stole his format and questions, but re-wrote (most of?) the answers as the apply to my own course.

Introduction to Standards-Based Grading

How is standards-based grading different from traditional grading?

You are probably accustomed to the following system: You do an assignment (like for homework, a quiz, or a test) and give it to your instructor to grade. After grading, it is returned to you with a score like “14/15” or “93%”. In our course, I won’t keep track of how you do on particular assignments; instead, I will keep track of how well you master specific mathematical tasks or concepts that are called standards. Once I see your work, my goal is to give you meaningful feedback: I want my feedback to tell you what you have mastered, what you should practice, and how what you have mastered relates to the goals of our course.

There are three major advantages to this system:

  • First, it rewards mastery instead of a “hunt for partial-credit” strategy. On an assignment with five problems, I believe it is better to do three problems extremely well (and leave two problems blank) than to just write stuff down on every page hoping you’ll earn enough points.
  • Second, I hope that it will allow you to see how to improve your knowledge of our course material. This system will allow us to track what topics you understand well, and also what topics you should spend more time working on. This way, if you seek additional help, you will know exactly what you need help with! Since your grade on a standard is not a fixed number — it changes over time — it is always advantageous to go back and fill in any gaps in your knowledge.
  • Third, it allows us to be clear about what the expectations of the course are (namely, demonstrating an understanding of topics in Calculus II) and how well you are meeting (or exceeding!) those expectations.

How will I know how well I did on a test?

Each assignment will probably look similar to those you have seen in prior courses. When I return them to you, you will be provided with a rubric. The rubric will give you two kinds of information. First, it will outline what standards correspond to each problem you solved. Second, it will outline the level of mastery you demonstrated on that problem, using a scale of 0-4. Apart from the rubric, my hope is to offer additional feedback on your solutions that will help you toward your goal of continued mastery.

How do I know which standards will be tested?

On each quiz, you can expect to see material we covered in the previous week. However, as you know, mathematics tends to build on itself. So although maybe we didn’t talk about the Quotient Rule last week, you will probably still have to know how to use it this week! Before each test, I will provide a list of all of the standards the test will cover. Since our course is cumulative, although a particular test might focus on recent standards, you might encounter problems that require knowledge of previous standards from earlier in our semester — or even prior mathematics courses.

How often will each standard be assessed?

It will depend on the particular standard. Standards that appear early in our course will be assessed multiple times, since we will be using them (either implicitly or explicitly) to solve problems later on. Toward the end of our course, you might only encounter a particular standard once or twice.

Why can my score on a standard go down?

It’s important that your score shows your current level of mastery. Your score on a standard may go down because you’ve forgotten some of the material, or you were unable to apply earlier techniques in solving problems later on.

In addition, some of our standards are quite broad: For instance, one of them deals with “techniques of integration.” We will see many of these techniques in our course. So your score may go down if you show mastery of the earlier techniques, but aren’t comfortable with techniques that show up later on.

How can I raise my score on a standard?

There are two ways to have a score on a standard raised.

First, you can wait for that standard to be re-assessed later on. For example, some standards assessed on quiz questions will be re-assessed on test problems. Especially early in the course, when there will be many opportunities to reassess standards, this may be the easiest way to raise your scores.

Second, it will be possible to “retest” a particular standard by making an appointment to meet with me. At this meeting, you will demonstrate your understanding by trying new problems and then answering questions I pose to you. You can make appointments to retest up to two standards each week. You choose which standards you would like to retest and when. You can retest any given standard more than once, as long as you only retest up to two each week. Each “retest” will take 10-15 minutes. Please request an appointment for re-assessment at least one class day in advance; this will allow me to prepare materials for you. You can request an appointment simply by e-mailing me and letting me know which standard you have chosen.

How many times can I ask for a standard to be reassessed?

You can ask for any standard to be reassessed as many times as you want, subject to the limitation that you may only retest two standards each week. If you require multiple attempts on a particular standard, I might ask you to work on some additional problems first (potentially with my help) so we can clear up any knowledge gap more quickly.

What about the final exam?

Our final exam will be cumulative and will have problems reflecting standards we have encountered throughout the course. Not every standard will be directly assessed on the final exam (after all, we don’t want to make it too lengthy!). Also, by the nature of final exams, you cannot re-assess any standard after the final exam. Your course score on each standard will be decided as follows:

  • If a standard does not appear on the final exam, your course score for that standard will be your score as of Reading Day. For Spring 2014, the date is Thursday, April 24th.
  • If a standard does appear on the final exam, your course score for that standard will be the average of [your score as of Reading Day] and [your score for that standard on the final exam].

How will my final grade be computed from my scores?

Your midterm grade and course grade will be the usual sorts of letter grades you are accustomed to. Here is how I will convert your mastery of the course standards into letter grades:

  • In order to guarantee a grade of A, you should attain 4s (or 5s) on 85% of course standards and have no scores below 3.
  • In order to guarantee a grade of B, you should attain 3s on 85% of course standards and have no scores below 2.
  • In order to guarantee a grade of C, you should attain 2s on at least 85% of course standards.

Plus and minus grades will be given based on how closely your performance is to a full letter grade. (For example, if you earn 3s on only 80% of course standards, and 2s on the other 20% of course standards, a grade of “B-” may be more appropriate than a grade of “B.”)

If I don’t like this method of grading, can I tell you about it?

Please! This is my first time using standards-based grading, and there are bound to be hiccups. However, I truly believe it will provide more helpful feedback and give you a better chance to prove your mastery of the material, so I ask that you at least give it a try, even if it seems strange at first.

If I have questions about how I’m doing in the class, can I ask you about it?

Absolutely! One drawback of this system of assessment is that you may have questions about your performance in the class. If you have questions or concerns about this, feel free to come talk with me and I will try my best to give you an accurate picture of your progress with our course material.

An Adventure in Standards Based Calculus

Today was the first day of our new semester. This spring, I’ll be teaching two sections of “Calculus I” and one section of “Calculus II.” I feel like “Calculus I” is basically on autopilot; I’ve taught the class every semester for the last couple years and so I’m very comfortable with the course content. But this will be my first time teaching “Calculus II” in many years. (I think the last time I taught it was 2006 or so, at the University of South Carolina, using an entirely different textbook.) I’ve decided that I want to try something different & I am embarking on my first attempt at Standards Based Grading (SBG) — or as someone suggested today on twitter, maybe Standards Based Learning (SBL) is more appropriate?

Why Am I Doing This?
For the last few years, I’ve noticed a few things about traditional grading (TG) that I did not like. One thing that has bothered me is that a student can go the entire semester without ever solving a problem 100% correctly, yet still do very well in the course. For example, it is entirely possible to earn a “B+” grade, by performing pretty well on everything, but never really and truly mastering a single topic or problem type. I hope that Standards Based Grading helps me motivate my students to really try to master specific sorts of problems, rather than try to bounce around, hoping they can earn enough “partial credit” points to propel them to success. Really, I want to reward a student who gets four problems absolutely correct (and skips two problems) more than a student who just writes jumbled stuff down on every page. I think SBG will allow me to do this.

Another (related) thing that has bothered me: The point of calculus class is not to earn as many points as possible, doing the least effort possible. I will admit that I have used a TG scheme for years and years; I have no idea how many college-level courses I’ve taught. And I am pretty sure that I can look at a calculus quiz question, assign it a score between 0 and 10, and accurately give a number close to what my colleagues would give for that same problem. We might all agree, “Okay, this solution is worth 7 out of 10 points for these reasons.” But I think this gives the students the idea that the reason they should study is to earn points on the quiz — after all, 9 points is better than 7 points! Instead, I think the reason they should study is to understand the material deeper than they presently do now, and I think by assigning X points out of 100 sends them the wrong message.

Something that has really bothered me recently is that when a student is struggling with the course, I am never entirely sure what to tell them. I look up their grades in my gradebook; I see that they have an average of 62%; and then I try to give them advice. But what advice should I give? The 62% in my gradebook does not tell me very much: I do not know if this student is struggling because they need more practice in trigonometry. Or maybe they were doing very well, but bombed our last test because they got some bad news the night before. Or maybe they got L’Hopital’s Rule confused with the Quotient Rule. I want to be able to tell a student exactly what they can do to improve their understanding. By tracking each student’s mastery of particular standards, if a student comes to my office for extra help, I can tell that student, “Okay, it looks like you need extra help with [insert specific topic].”

Lastly, I would like to give students more low-stakes feedback about their understanding: That is, feedback without the worry that it will negatively affect their grade in the class. I will be giving a weekly quiz, and I will grade it, offer feedback, and return it to my students; then (eventually) their score on that standard can be replaced with a newer [hopefully better!] score. I will constantly replace their previous score on a standard with their current score on a standard. This way, if they are really struggling with (say) Taylor polynomials, I can communicate this to them early, they can seek extra help and resources, and then they can be re-assessed without penalty for their original lack of understanding.

What Worries Me?
I have lots of different things worrying me about this system! For example, since this is my first time teaching Calculus II in many years, I don’t know all the “common pitfalls” that my students will encounter, so I don’t feel like I’m going to see them coming until they’re already here. Also, I am worried that students will struggle to understand this method of assessment & won’t really “get it” about how they are doing in the course — or won’t take the opportunity to re-assess when they need it. Lastly, despite reading online that “before a course begins, start by making a list of what you want them to master (a.k.a, the standards)” I was unable to do this. I have the first half (or so), but I don’t know how good they are. Am I being too vague? Am I being too specific? Do I have too many? Too few? How difficult will they be to assess?

Some Resources
In my own course planning, here are links to resources I found helpful:

Wish me luck!