Saturday, September 9, 2023

IBL Teaching Podcast on YouTube

I'm launching a new podcast on YouTube to share stories and useful tips about IBL Teaching. The podcast will focus on a range of topics from interviewing faculty about IBL to specific skills or practices in IBL. We talk about math in higher education, but will expand beyond.  The plan is to drop an episode about once a month, hopefully more frequently if my role as undergrad chair doesn't take up too much time.

The first three episodes are linked below. We start "at home" with two great people who have been working with me for more than a decade, and a short video about the IBL handout approach. 

Have a question or suggestion for a topic? Let me know at stan at math dot toronto dot edu.   

Matt Jones, CSU Dominguez Hills

Dana Ernst, Northern Arizona University

IBL Handout Approach

Tuesday, February 21, 2023

Email mentoring after a professional development workshop (for professional developers)

This primarily audience for this post is professional developers in higher education.

After a workshop in the early part of the summer, attendees go back home... and then the calendar unceremoniously flips to August.  Fall semester is approaching, and summer is ending. All of the ideas learned at the summer workshop have to intersect with reality. Real students are coming, the syllabus needs to be written, choices need to be made, and the LMS needs to be set up.  During this phase instructors new or newish to IBL can benefit from the community they worked with at the workshop.

Email mentoring doesn't sound exciting. It sounds like "having to mow the lawn after a long week."  I apologize for the unexciting, descriptive title. But in reality email mentoring is important for participants and truly rewarding and fun. 

What is email mentoring? Email mentoring is follow-up support after workshops, and is organized by workshop facilitators. Facilitators email the whole group every two or three weeks to check-in on the group, asking participants to share how planning or teaching is going. Participants have questions before the start of the term, and issues or questions might come up during the term, or they may have a success story to share with the group.  

A typical pattern is the facilitators send out a few emails to see how people are doing, and a few responses trickle in. But then eventually there are times when you get large threads. Someone has a question. Another participant chimes in. And then another chime. A facilitator thanks the people who chimed in, and asks for more thoughts. More people chime in, and it's a flurry of helpful, insightful, and supportive messages.

Activity ebbs and flows within a semester. Email mentoring starts a few weeks before the term and is heavily used during the parts of the first half of the term.  Activity tends to pick up again towards the end of the term, when facilitators encourage participants to share and reflect on the semester.  

Email mentoring is a type of follow-up support.  Follow-up support is a broad category of continuing professional development after the main workshop. Follow-up is the booster to the summer prime doses, and strengthens and enhances what was accomplished in the summer.

One common example of follow-up support is having monthly meetings, which is more common for professional development programs that take place in a specific region, such as a single campus or in the K-12 setting of a school or school district.  

Meeting regularly during the school year makes sense in cases where all the instructors are in the same geographic area. You can continue to support workshop participants as they are implementing their courses, get together over boxed lunches, and get folks outside of their environments. Video conference call is another option to do this for groups that are more spread out.

Email mentoring especially makes sense for undergraduate math instructors, because of the asynchronous nature of email. Everyone uses email, and access to the conversation fits into faculty work life.  Scheduling faculty meetings is also a big challenge, because finding a common time across multiple time zones with 20-30 faculty is nearly impossible. Hence, asynchronous email exchanges make sense in this context.

Email mentoring also does not require prep like the summer workshops. The main thing is being effective with timing and being kindly persistent and supportive. Thinking about this work as building community rather than "getting lots of chimes" is a more useful mindset.  

Why is follow-up support important? As mentioned above, learning about IBL, active learning, or any other topic during the summer is great for getting over the "activation energy" needed to start the change. But implementation in the real world requires steady work, and having a community of collaborators doing the same thing can make a difference in how much and how well someone implements new teaching changes (to them). In some instances, follow-up support can make or break an implementation attempt. I think of follow-up support as an important part of the workshop.

Some people are teaching in departments where they are the only one doing active learning. They feel isolated, and going to a workshop for a week is a refreshing change. Having their community still with them during the term via email mentoring gives folks working alone much needed support and camaraderie. 

How do you ping the groups?  We use low-entry, high-ceiling prompts. 

"Hi everyone,

Hope your week is off to a good start.  Please let us know how things are going with your teaching. Even if you don't have a lot of time, please feel free to click 'reply-all' and send us just a sentence or two. We want to know how you are doing.



The idea is to make participating easy and it can be a short update or something more involved.

Sometimes the facilitators send out informational emails, and they usually don't get many replies, although they can spark a thread on a topic usually not directly related to the original information being shared. Perhaps there is a good article worth sharing or a conference or workshop coming up. Those kinds of messages keep the community informed and in people's minds.

Repeatedly checking in the with group is necessary. Sometimes it takes a multiple tries to get a thread going. This is normal and fine. Not every email needs or should have a lengthy response from a large number of participants. The strategy is to gently check in regularly, because eventually someone will want or need to run something by the group, and you'll have primed people that chiming in is okay and welcome.

Emotional content is a key component of successful email mentoring.  What does emotional content mean in this context? Examples are thanking people for sharing, validating the struggle, and celebrating successes.  Here's an example.

"Hi ABC - thank you for sharing that story. I have been in that situation before several times, and you handled it better than I did the first time. Here's what I learned along the way...   Does anyone else have anything to share? Please chime in - it'd be great if we had more perspectives.  - SY"

Emotional content is often short and sweet.

  • (Participant) "Hi everyone! Just had a great day in class..."

  • (Another participant) "That's wonderful!..."

  • (Facilitator) "Thank you so much for sharing that story. Congrats!"

  • (More compliments...)

One thing to keep in mind is timing.  You want other participants to chime in, so facilitators need to carefully time their messages so they are not pouncing on all of the questions right away or letting big gaps of time go by.  Perhaps they can let a day or two go by and encourage someone to chime in. Facilitators can chime in with, "That's a great question. Does someone have something they'd like to share?" to amplify the question without answering. 

Why email and not slack/discord/teams? I personally would prefer to use something like Discord or a discussion board. But the reality is that you lose people from the group post workshop if you use slack/discord/teams/etc. Only a subset will take the extra step to login and check another platform that is not email.  This has been an consistent barrier for all the years I have run workshops.  Email is the one consistent way to reach everyone.There are definitely pros and cons to email, but in the end, the kicker is that email is the one universal platform out there that everyone already uses.

Email mentoring is fun and rewarding! Email mentoring is great, because you get to learn about what people are doing, help people with their questions, be part of a supportive community, learn new ideas, and celebrate successes. It's many of the good parts of being an educator rolled into one activity.

Email mentoring is a helpful and fun strategy to implement follow-up mentoring post workshop, especially when working with busy faculty schedules.  One way to think about it is that you already spent all that effort planning and running your workshop, and you want it to stick. One way to help ensure students experience the benefits of high-impact practices like IBL is to help your attendees when they are implementing your workshop ideas.

Want to learn more? Read Chuck and Sandra's paper super-detailed analysis of what we did to create a supportive community using feedback loops, which helped us achieve high response rates. 

"This workshop for 35 college mathematics instructors used online and in-person communities to provide support to participants during the post-workshop period of “refreezing.” Almost all workshop attendees participated in “e-mentoring” (94%), primarily through a productive, engaging group email listserv. By combining qualitative coding of message content with the techniques of social network analysis, we reveal how facilitators and participants on the group listserv provided intellectual and emotional support, as well as positive reinforcement through feedback loops. The analysis also shows how the facilitators made this a helpful group and maintained participant engagement through frequent encouragement, deliberate community building, and thoughtfully timed responses."

Edit: One pitfall to avoid giving up too early. Sometimes you will send out an email and no one will respond. And then you try it again, and no one will respond.  Don't give up. Keep on asking nicely, perhaps send out some info, or share something from your class, and end with open invitations. 

Saturday, February 4, 2023


“Simplicity is an exact medium between too little and too much.“ - Joshua Reynold

One lesson I have learned from photography is the importance of simplicity. In photography, one point of view in composing a photo is the process of elimination. You eliminate objects in your frame until you feel like you have a compelling image.

Leaning Oak, Central Coast CA (copyright Stan Yoshinobu)

The next photo shows what the scene looks like. It was taken at a different time and day. An arrow is pointing to the tree in the first picture. 
A view of the larger scene

Wide angle views take in nearly everything in the scene. Wide angle lenses are "greedy" lenses and they include so many things.  This is useful in some cases, but in many cases including everything makes the scene less compelling. There is just too much in the scene, no story, a documentation of what is there in a literal sense. 

The process of elimination is in many ways the opposite of teaching. Especially in courses like Calculus, we have included so many problems, so many techniques, and every class has to cover so much.  

Teaching is complex. Intricate concepts, big ideas, lots of students, assignments, deadlines, planning ahead, grading, random stuff that messes up your plans. 

And then there is the pressure to innovate in your teaching. Trying new things, different things, adding technology, updating assessments.... Don’t get me wrong. This is all good and we need to innovate and continue to find ways to improve the human experience of education.  

But there is a simple truth at the root of all this. It comes down to the students, their engagement with the ideas, and the instructor and the course structure supporting students. All the rest are mostly details, important details, but in the end those other things are either supports or requirements. 

Does it matter that we use IBL/active learning and focus on the details and carefully execute our plans? Yes, of course!  

So what is the point? We can go to far by adding too many layers or we have too many assignments and things for students to do.  

I’ve talked to instructors who out of enthusiasm and excitement have flipped classes, WebWork homework, Perusall assignments, recitation assignments, hours of videos to watch each week, practice problems, writing assignments, group assignments, midterms, practice midterms, and more. This overwhelms students and creates a course requiring double the work.  The question I get asked is why are my students not buying into my class?  You're asking them to do more than they can handle and the experience is more painful than enjoyable and fulfilling. 

There can be too much of a good thing, such as watching all your favorite movies in one sitting. At some point you aren’t enjoying it and neither are many of your students. In teaching, if you’re managing a wide range of course management tasks and students are running from one thing to another, then you may be including too many teaching element into your course.

"To truly cherish the things that are important to you, you must first discard those that have outlived their purpose." - Marie Kondo

What I try and do is mentally start with student engagement in class. I focus on what they need to learn in terms of content and dispositions. Then the math tasks (curriculum) are aimed at those things. The assignments and assessment layers are added aligning with the goals.  From there you finish with the logistics, etc. and you have your course.  That helps me see what to cut, what to exclude.  Then I go back to my over-engineered course and take out the things that are not needed or at the very least revise them down. 

This doesn't mean my classes are simple or bare bones. That's a risk, too - a course that merely shows the content and gives multiple choice tests. Simplicity is about finding the right balance between all the things you wish you could accomplish in your class and a real-world experience that is fulfilling for the instructor and students. It's focusing on making the best choices you can make for student learning and growth and letting go of trying to do everything.  The coverage issue is a real thing. We all struggle with it, and what helps me stay centered is focusing squarely on students, the math, their interaction with the math, and their long-term intellectual growth.  

In short, you gotta choose.  

Thursday, December 15, 2022

Presentation at AMATYC 2022: Equitable and Inclusive Teaching Practices

This blog post is an adaptation of a presentation I gave at AMATYC 2022, in Toronto, Ontario. Title of the presentation is “Equitable and Inclusive Teaching Practices”

The presentation is split into two parts. Part 1 is an outline of 4 lenses we can use to think about our teaching and more generally society. The second part is about teaching scenarios using the four lenses and our experiences.

First some caveats. There are more than four lenses. The four I chose are just viewpoints I chose that I find helpful in a workshop-like session. There are many other things to consider, which are beyond the scope of the presentation.

Lens 1: Math’s teeming shore

The first lens to use is about something I call the Math’s teeming shore.

"Give me your tired, your poor,

Your huddled masses yearning to breathe free,

The wretched refuse of your teeming shore.”

In Emma Lazarus’ sonnet is the idea of all the people who were left out, gathered on the teeming shore yearning for a better life.  In one subset of America, the ideal is to bring these people in and welcome them.  In a similar way, so many people in Math have been left out. How many times have you heard, “I am not a math person” or “I am not good at math”? 

Math education has left many on the outside, and this is a major problem for our society, because this damages our ability to be a more equitable and informed society. This brings us to the second lens...

Lens 2: math literacy as a civil right, implicit biases

From the seminal work of Bob Moses and the Algebra Project (, we have the idea that math literacy is a critical literacy. In fact, math literacy is a civil right. Without an ability to think and evaluate some issues quantitatively and scientifically a person cannot fully exercise their rights and be a full citizen or have equal opportunities in society.

There is a fundamental paradox in education. Teaching people to think and problem solve is a good thing in my opinion, but not everyone would agree. If we teach people to think, then they start to question the system they live in.  If we teach people to think, they start to become qualified for jobs they are not intended to have. In short that is why there exists Math’s teeming shore.

A brutal example from the past is The Native American Boarding Schools (  These schools designed to “assimilate” indigenous people via their children. Assimilate of course is a euphemism for genocide, and in 2021 the first of several discoveries of hundreds of remains of children at these schools were reported (Content Warning). 

When people opine of the dearth of Indigenous people in STEM, one false myth some people use about this is that Indigenous youth are not interested in STEM, or that it’s falsely not part of their culture. Crucially what is left out as a possible explanation is our actual history.  That in itself is an indictment.  Further when people talk about culture, they are actually not talking about culture. They are really talking about power. One group had the power and the other didn’t, and that is how we got here.

The problem isn’t the Indigenous students or the black students or the women or whatever group you want to focus on. The problem is our history and our collective ignorance of it. 

How do these things relate to teaching?  History lives with us in ways we may not be aware of. For example, false assumptions can affect our daily work.  If a student requests an extension for an assignment or doesn’t turn something in, then certain assumptions can be triggered depending on a student’s identity.   A source of implicit bias goes down deep to underlying assumptions, norms, and conditioning that have formed us. Implicit biases are rooted in our history, and that impacts how we solve (or don’t solve) our problems with math literacy.

Lens 3: the shokunin or artisan spirit

I’d like to think that there’s a way out. What I’ve latched onto is starting at the core of what teaching is.  A Shokunin is an artisan with great skill who also works for the benefit of their community. This idea applies to teaching.  One way to deal with our equity and inclusion issues is to adopt a Shokunin spirit or artisan spirit when we teach.

When I started my career, I didn’t have a diversity statement in my syllabus. I didn’t intentionally think about equity in the classroom. I did not use IBL with an equity lens.  These are things I have learned over time from people who have made the case that we need to do more. 

This is one way our profession has moved forward. Some people have done the work to improve their courses and come together to form coalitions to courageously make the case to others for equity and inclusion in Math.  From there new policies were adopted and more resources and attention are being directed to make progress. 

Have we done enough? No, obviously. We have a lot more work to do. But the point still stands that if we think of our teaching practices like an artisan, we can continually improve our craft for the good of society. By teaching practices, I don’t just mean what we do in the classroom, but more broadly the system surrounding it.   If enough of us do this work at different layers of the system, we can potentially make systemic change.

Lens 4: IBL methods 

IBL can help with equity and inclusion, but only if the instructor focuses on these things.  IBL methods are a pathway, not a panacea. 

The artisan spirit should be connected to tools and practices that work. There is a body of scientific work that establishes IBL methods as effective in learning and leveling the playing field.  Here’s a link to work by Laursen at al. I won't go into details of what IBL is or what the literature says, since these are well worn paths that have been talked about elsewhere.

Part 2: Scenarios

With these lenses in hand, we looked at a few scenarios at the session, and discussed what we could do. The second was a little more than half the session in terms of time, and participants offered good ideas for how we could move forward with their teaching.  We discussed the ideas at our tables and then shared with the whole group, which was about 50 people.

Scenario 1: The same 3 or 4 students raise their hands first when it’s time for student volunteers. What can you do to make sharing more equitable?

Scenario 2: What are the positives and some pitfalls of randomly assigning groups of 3 or 4 students to work on a problem?

Scenario 3: In this scenario, put on your “implicit bias” lens. How can implicit biases and social frames amplify the comments left on student work?  Compare the following two responses.

  1. “Good start to a solution. I noticed that you didn’t use the definition of… Consider using the definition…”

  2. “It’s obvious you didn’t do the reading or put in a good effort…”

Task 4: In the spirit of being like an artisan/shokunin with your teaching, consider how to improve/update…

  1. Syllabus statement, pronouns, resources for marginalized groups

  2. Course content

  3. Deadlines (hard vs. flexible)

  4. Assessment

  5. Small groups, pairs

  6. Students with disabilities/accessibility

  7. Department/college level


Even for large classes, like the ones I teach at the University of Toronto, we do something significant with respect to equity and inclusion. I coordinate a course with 1500 students, split into 8 lecture sections, and 35 tutorials/recitations.  We have 8 instructors, 24 TAs working together to provide an equitable and inclusive class.  Large class sizes are not an obstacle for equitable and inclusive teaching, see the list below where most of the items are orthogonal to class size.

What are we doing?

  • Diversity statement in the syllabus, and visible inclusion in class, in Canvas announcements.

  • TA training on equity at the start of the term.

  • Teaching using IBL with a focus on equity.

  • Online option with recordings for students with disabilities.

  • Grading for growth to the extent possible, with group reports with resubmissions without penalty.

  • Offer online office hours.

  • Collect weekly feedback to adapt to students’ needs and to uncover issues that we can address early in the term.

  • Eliminating biased problems and images from previous iterations of the course.

Those are some of the things we have implemented, and these are just the start. We need to improve each of these items and create norms and a department culture where students feel they truly belong.

Each of us has some power as instructors.  To the extent we have power, we should use it to do good in our classrooms and at our institutions. We should be the hope we want to see in the world.

Thursday, September 15, 2022

Interview: Professor Daniel Reinholz, San Diego State University, Gender Equity in Math Classes

It's a great pleasure to be able to interview of Professor Daniel Reinholz, San Diego State University about a vital issue, gender equity in the academy. As it happens, how we teach using active learning matters very much. This interview is based on a recent 2022 publication, When Active Learning is Inequitable: Women Participation Predicts Gender Inequities in Mathematical Performance, Journal for Research in Math Education, Volume 53, Issue 3.

The authors of this article are Daniel Reinholz,Estrella Johnson, Virginia Tech, Christine Andrews-Larson, Florida State University, Amelia Stone-Johnstone, California State University Fullteron, Jessica Smith, Florida State University, Brooke Mullins, The University of Virginia's College at Wise, Nicholas Fortune, Western Kentucky University, Karen Keene, Embry-Riddle Aeronautical University, Niral Shah, University of Washington-Seattle.

Wednesday, June 15, 2022

The great 8 pillars of IBL teaching and grading for growth

It's time to connect the pillars of IBL teaching and grading for growth (alternative grading). The idea here is that these two sets of pillars go together and help provide a holistic framework of teaching. The combo is better than the individual components.  Peanut butter & jelly. Peas & carrots. Mac & cheese. 

IBL pillars:

  1. Deep engagement in rich mathematics.
  2. Frequent opportunities for students to collaborate with peers and their instructor(s).
  3. Instructor inquiry into student thinking.
  4. Instructor focus on equity.
Alternative grading pillars:
  1. Clearly defined standards.
  2. Helpful feedback.
  3. Marks indicate progress.
  4. Reattempts without penalty.
Both IBL and grading for growth are frameworks or "big tents," within which are a set of tools for each. Instructors can select tools to address the needs and challenges in their teaching context.

When you are planning your next course, use the great 8 pillars

Disclaimer The number of pillars can change over time.  So this might be the fab five or the nine pillars someday. The number doesn't matter. The combination of IBL teaching and grading for growth is what matters.

Wednesday, June 1, 2022

Grading for growth in large classes: a first attempt

Here's the context. 1000 students are in first-year Linear Algebra, split into 7 lecture sections with 7 different instructors, and 14 TAs, who teach dozens of tutorials/recitations.  That's a lot of people!

We started the term online due to the omicron wave in winter 2022, and then taught the second half of the term with a mix of in-person and online. At the beginning of the term, we did not know when or if we would return to in-person learning, and had to setup the course in early January with the uncertainties of the pandemic. This post focuses on the assessments for the course and some initial thoughts.  

TL;DR You can implement grading for growth even in large, coordinated courses.

Here the assessment setup:

  1. First a major constraint... An in-person final is mandatory and "owned" by the Faculty of Arts and Sciences, and has to be at least 35% of the grade.  The other 65% of the grade was based on the items below.  Also note that in Canada, 80% is an A-, 70% is a B-, and so on.  So the weight of the final is not as immense as it would be in the U.S.  In the U.S. 25% is a rough conversion.
  2. I gave a two-part final. Part 1 tests core standards worth 25% of the course grade. Part 2 of the final had challenging problems worth 10% intended for students who want to improve their grade to an A or A+.  
  3. In lieu of midterms (which would have been online for at least one of them), students submitted 4 graded group reports. (Two additional assignments were reflective writing assignments for a total of 6 reports.) Group size was set at 2-3 students, and some groups were allowed to grow to 4 due to special circumstances (e.g. adding a student to a group). 
  4. Group reports (30%) were submitted online (Gradescope) and the TAs and instructors graded 2 or 3 of the 4 or 5 problems.  The ungraded problems were checked for completeness.  Problems that were graded, were graded with a rubric for mathematical correctness and presentation.  The entire assignment was out of 10 points, and written feedback was given to students.
  5. Students could resubmit group reports at least once.  For the early group assignments, we had the capacity to accept up to 3 resubmissions. The last group assignment, which was due near the end of the term, allowed us to accept one resubmission.
  6. Online homework (20%) was assigned on MathMatize, and the due date for all assignments was set for the end of term. Students were allowed to redo problems as many times as needed, and were given suggested completion dates that matched the pace of the course. 
  7. Because the course was a flipped, IBL course, students were required to do reading assignments (15%) before class. Reading assignments were done on Perusall, where they were graded using "threshold" grading with instant feedback.  If students made 3 or more comments they would get credit for the assignment.  Reading assignments had a hard due date, because we expected students to read the sections before we would do activities in lectures.  The 4 lowest scores were dropped, which allows students some flexibility. 
Lectures were centered on activities to support student learning of the core ideas. Tutorials were a mix of activities, practicing basics, and preparing students for their group reports.  I won't go into further details about how classes were organized, since the focus of this post is grading for growth.

Students could pass the course if they did all of groups reports, online homework, and reading assignments. Students would need to perform well enough on the final exam to earn an A or B.

The Whys? 
I wanted to accomplish a few things. One is to reset incentives towards learning and intrinsic values.  Another is to center honest, hard working students who want to learn, and reduce incentives for cheating.  A third is to avoid using creepy proctoring software (where students have to ask a proctor for permission to move if they need to vomit), which also use biased algorithms

One aspect of grading for growth that I appreciate is that the honest students, who do their own work and submit their mistakes are not penalized or behind, compared to people who lookup answers or pay for services that give them the answers.  Students who make mistakes receive feedback, and grow from the process.  These students appreciated being able to update their reports and fix issues.  Their grades aren't being negatively affected by those who cheat. The students who cheat will learn less and be less prepared for the final, future courses, their lives, and careers. Online cheating is a reality at the University of Toronto and sadly almost everywhere, when things are setup the old way with timed, rigid, high-stakes (online) tests as the bulk of the grade. 

The pandemic is a major factor still (and will be next year too, imo), and impacts students and their families. The gradient of risk also skews heavily towards the more vulnerable and marginalized.  Grading for growth with opportunities to resubmit work without penalty gives students more time to learn the material during the semester and crucially creates a more level playing field.  If students get sick or have to deal with a family emergency, flexibility is built into the course to help students get their work done during the term. It should not matter, if a student learned something in week 8 vs. week 10. 

Students who don't invest in the learning will not do as well on the final exam or in their future work (or life). The final exam is one of the ways that students are held accountable during the term.  More broadly, students need to learn the course material as well as learn how to learn, and the course philosophy is talked about with students. Students will need both the content knowledge and the improved thinking in their lives, and cheating/looking up answers won't help them become better and smarter.  

Group reports are focused on why questions or having students explain why things work the way they do. Sample questions on group reports:

Give examples of a plane in $\mathbb{R}^3$, using vector form, normal form, and standard/cartesian form. Explain the advantages and disadvantages of each representation.

The setting for this problem is $\mathbb{R}^3$.  Suppose you have a plane $P$ and two vectors $\vec a$ and $\vec b$ in $P$.  The task is about the general question, ``If you add two vectors in a plane, is the result still in the plane?''  More specifically, using examples, diagrams, and sentences, find characteristics of planes, $P$, such that $\vec a + \vec b \in P$.  Additionally, find characteristics of planes, $P$, such that $\vec a + \vec b \notin P$.

Some things I'd like to change  The reason why we have to have group reports vs. individual reports is due to TA hour limitations.  Without constraints I would have students submit individual reports and have all problems graded.  But that is way beyond the budget for TA time. 

Practically speaking, reducing the number of group reports to 2 per term could allow for individual reports, with 1 rewrite each.  The pros would be that there would be more individual feedback, and less incentive for students to divvy up group report problems and focus on fewer problems.  The downside of going down to 2 reports is that you have fewer topics covered and higher stakes per report.  There are other options such as 3 reports done in pairs or 3 reports done individually.   I'll have to sort this out this summer. One takeaway here is that there are options and tradeoffs.

Reading assignments and online assignments generally work as they are intended. They focus on basic skills and fundamental concepts.  The one issue that is specific to the University of Toronto is regarding Perusall and reading assignments. There are local tutoring services in Toronto that sell Perusall comments that customers can copy-paste into the system.  Some of these get flagged as "plagiarism" by the Perusall system, but students can make slight edits and work around the issue.  One way to get around this is to switch to reflective writing assignments submitted via Canvas and grade these for completeness. 

Tweaking the final into more sections to make clear what the standards are and what students are expected to know for the final is another area that will be worked on.  One idea is to have three parts to the final with specific themes. 
  1. Part 1: 10% of course grade is based on core skills (e.g. computing determinants, determining if a set of vectors is linearly independent.)
  2. Part 2: 10% of course grade on demonstrating conceptual understanding of core concepts (e.g. answering concept questions via short answer or sentences.)
  3. Part 3: 15% of course grade on applying ideas and skills to solve more challenging problems. (Prove why a given matrix is/is not diagonalizable.)
Students will be given a final exam guide with the details, sample problems, and a list of standards that will be covered on the exam.   Students who do all the term work would go into the final with 65% of their course grade in hand (or a course grade equal to a C).  Getting 80% of parts 1 and 2, will net 16% or a total score of 81% in the course, which is an A-.   Students who want an A or A+ will need to solve some or all of the Part 3 problems (or get 100% on parts 1 and 2 to get an A).

Setting aside the details of the scheme above, the main takeaway is that instructors can set percentages for the term work and final exam parts in ways to fit the assumptions and values of their institution.  What I did was try my best to think of something that would work and then I'll adjust as I learn and get feedback. 

Places to start A couple easy places to start with grading for growth is to make homework online with infinite attempts (WebWork, MathMatize, or whatever is bundled with your textbook) and setting up a standards-based final exam using.  I am unable to implement a standards-based (formerly called mastery-based) final at UofT due to policy restrictions. 

With standards-based finals what I did in the past is to write a Part 1 of the final with the core standards, where students need to earn 90% on it in order to keep their grade going into the final OR earn a C- (if the incoming grade is below a C-).  Students scoring less than 90% on Part 1 could have their grade go down on a sliding scale up to a whole letter grade.  Part 1 has core standards, such as basic skills and computations.  The theme of Part 1 is "If you pass this class with a C-, you should know these things."  (What is on Part 1 needs to be transparent to students with ample opportunities to practice.)

Part 2 of a standards-based final are challenging problems that are opportunities for students to demonstrate that they learned the material deeply and can raise their grade up to an A.  Part 2 problems can be proofs, explanations, or more challenging problem-solving questions.  

Again I could not implement this due to policy constraints, but standards-based finals are a way to start without having to change everything. Keeping all the other parts the same, and using a standards-based final is a reasonable starting place.   Once you get that down, then you can move onto other parts of the assessment scheme.

Final thoughts  I used grading for growth in small classes (enrollment 25-35) for many years, so the idea wasn't new to me.  Transitioning to coordinating large courses meant focusing on things like group reports, a "tiered" final exam, and then thinking about how to make things work within the TA hours constraints.  The smaller the class, the more options you have. 

One advantage of having a TA hours budget is that you have to think about what would work without spending all your time on grading.  It's not ideal or "excellent," whatever that means, but it's better.  And better is good.  More TA hours would also be good :)  

If you are teaching a small course and have no TAs, one idea is to think of your own budget in time. Set aside a number of hours you would spend marking per week or per term, and then figure out what could work in that time budget. 

I know that for many it is big step to use alternative grading, but there are major benefits to switching that needs to be emphasized again and again.  When you align assessment with learning and implement IBL or active learning, it's a much better experience for students and makes the entire course more aligned with the goals of education.  It brings us closer to our vision of humanistic math education. Thus, it is worth the effort to go down this route.

Resource Check out the Grading Conference group, their slack channel, and work with a community of educators working on this grading for growth. They are a fun, friendly group, and will help you get started.