10 Minutes of Thoughts on My SBG Linear Algebra Class

I’ve been meaning to write a post about my standards-based Linear Algebra course for months, but the hectic schedule of the semester has kept me away from this task until now. Today was my last “content” day of Linear Algebra — we have two more classes remaining, one for a test day and another for a re-assessment day. This seemed like a good time for me to take ten minutes to gather some thoughts about how the semester went.

Standards List for Linear Algebrahttps://www.overleaf.com/read/kycvnvzdvksw  (Availablle on Overleaf, which is awesome and I can’t recommend enough)

What Went Well: We ended up having 20 standards this semester. This is a little more than one per week (our semester has 16 instruction weeks). Overall, I think this was a good number of standards to have, and I’m happy with how they turned out. I tried to group them again by “Big Questions” to have a reference frame of what it is we’re trying to do in the course. Oddly, we tackled “Big Question 5” last (on inner product spaces), but I kept it numbered like that because of the textbook we are using. My basic idea was to come up with a Big Question for each chapter. For some stuff, this worked well (e.g., eigen-everything) but for other stuff we didn’t cover a whole lot (e.g., determinants).

I think I’m doing a better job of the sales-pitch aspect of a standards-based course. Many of my students expressed to me at various times that they really appreciated the ability to improve on past performance and that they were under less stress than in a traditional class. In a recent class meeting, a student wasn’t happy with the performance on the last quiz, and exclaimed, “Oh, thank goodness we have an exam on this soon!!!” [I asked the student for permission to share this quote.] I think this is one of the best things about my SBG courses — students really want to take an exam just to show what they know, whether that means showing mastery of current material, or showing mastery of material they struggled with earlier in the course.

My SBG approach definitely has some pros and also some cons, but the way it has shaped my interactions with students has always been a huge positive. Even with the sticky details that need to be cleaned up from this semester, I can’t imagine going back to a traditional grading scheme.

Room for Improvement: This semester was a little odd because we lost several days because of weather. Tropical Storm Hermine hit us, and we lost almost a week because of Hurricane Matthew. The re-shuffling of the academic calendar created a speed-bump that I never really recovered from. I hope next semester our calendar runs much more smoothly.

In particular, I am wondering about how I can improve in three areas. First, I want to expose my students to more applications of the material we are learning. I felt rushed all semester (related to shuffling of course calendar, maybe?) and so I didn’t ever feel like I had time to fit in cool applications, or videos on where people use this stuff “in the real world,” etc. A colleague teaching the same course required students to do group projects on applications of linear algebra & I believe the students presented them to the class at the end of the semester. This seems like a great idea, but I’m always nervous about assigning group projects because I remember how much I hated doing them as a student. It’s something I should consider more.

Second, all of my course standards are weighted equally. This has served me well in Calculus II and in other courses. But in Linear Algebra it became a little tricky, because part of what I was aiming to do was to have my students attempt to write proofs of mathematical statements. (The only mathematical background required for entry into my course is Calculus I, and that is for “mathematical maturity” as opposed to content reasons.) So some of my students were concurrently taking our “Introduction to Proofs” course, but others weren’t taking this course and won’t need it for their major. In general, my idea was to ask them to prove elementary results they had already seen in class. The problem I encountered is that a “write a proof” standard is really tough. How do I let them have multiple attempts? Is it okay if they end up never being able to prove stuff about, say, matrix inverses, but they can prove stuff about, say, subspaces of a vector space?

One idea I’ve had is to have the students keep a “Proof Portfolio” and grade it as either “complete” or “not” at the end of the semester. I’m sure there’s some specs-based approach I could implement for this, but I haven’t worked out what it would look like yet.

Third, trying to put together all my course materials on the fly is hard. All of the time, I was working on: Plans for class, writing exams, writing quiz questions, writing reassessment questions, putting together online homework, meeting with students for several hours a week outside of class, updating the list of standards regularly… I would admonish my summer-month self that I should do more of this “in my free time” before the term begins so I’m not under such a time crunch during the semester. But I am not great at this because I like building a course as it goes, as I see how the students are responding, as I see how the pace of the course unfolds, etc. Having to get all this done ahead of time would probably help me out a lot, but it’s tough to do. Thankfully some of my stuff from this semester can be re-used when I teach Linear Algebra next semester.

My ten minutes are done so I have to move on to the next task on my queue! I hope to add more later.

Standards-based Linear Algebra

This semester I’m teaching our introductory linear algebra course. As I did for Calculus II, I’ve implemented a standards-based assessment system. I’ve taken our course content and split it into “standards”, or little pieces of mathematics that I want my students to master. These standards are grouped together by what I call “Big Questions”. Here is what we’ve covered so far this semester:

  • Big Question #1: What are the tools for solving systems of linear equations?
    • 1.1: I can solve systems of linear equations using row operations. I can use Gaussian elimination with back-substitution to solve systems of linear equations. I can use Gauss-Jordan elimination to solve systems of linear equations.
    • 1.2: I can characterize the solutions to systems of linear equations using appropriate notation and vocabulary.
    • 1.3: I can use matrix inverses to solve systems of linear equations.
    • 1.4: I can find and use an LU-factorization of a matrix to solve a system of linear equations.
  • Big Question #2: What is the fundamental structure of the algebra of matrices?
    • 2.1: I can perform algebraic operations with matrices, including addition, subtraction, scalar multiplication, and matrix multiplication. I can compute the transpose of matrices.
    • 2.2: I can find the inverse of matrices using Gaussian elimination. I can find the inverse of matrices using a product of elementary matrices.
    • 2.3: I can demonstrate theoretical connections about properties in the algebra of matrices.
  • Big Question #3: How can we characterize invertible matrices?
    • 3.1: I can find determinants using cofactor expansion. I can find determinants using row or column operations.
    • 3.2: I can demonstrate theoretical connections between statements equivalent to “the matrix A is invertible.”
    • 3.3: I can demonstrate theoretical connections between matrix equations, vector equations, and systems of linear equations, and their properties and solutions.
  • Big Question #4: What are vector spaces & how can we describe them?
    • 4.1: I can prove whether an algebraic structure is a vector space (or not) using the vector space axioms. I can prove whether or not a subset W of a vector space V forms a subspace. I can determine and characterize subspaces of $\mathbb{R}^n$.
    • 4.2: I can write a proof showing whether a subset of vectors from a vector space forms a spanning set for the vector space (or not). I can write a proof to show whether a subset of vectors from a vector space is linearly independent (or not). I can determine whether a set of vectors forms a basis for a vector space. I can find the dimension of a vector space.
    • 4.3: I can find a basis for the row space, the column space, or the null space of a matrix. I can determine the rank and nullity of a matrix. Given a consistent system Ax=b, I can describe the general solution in the form x=xp+xh
    • 4.4: I can demonstrate knowledge of the theory of vector spaces by proving elementary results and theorems.

The remaining Big Questions are:

  • Big Question #5: What are inner product spaces and how can we describe them?
  • Big Question #6: What kinds of functions map one vector space into another while preserving vector space operations?
  • Big Question #7: What are eigenvalues and why are they useful?

Our first exam was last week, so today has been Re-Assessment Central in my office. I’ll hand back our exams tomorrow and I’m hoping to talk with my students more about standards-based grading and how they can improve their standing in the course.

Modeling Fun with Paper Fish

Kate Owens, 02/2016

Kate Owens, 02/2016

Back in early February, as part of my ongoing work with the Math & Science Partnership, I led a Saturday professional development workshop for STEM teachers on “Proportion, Decimals, and Percents (oh my!).” There were two major projects we worked on that day. First, I split the teachers into teams of two or three and they read over some “Always, Sometimes, Never” statements. Fawn Nguyen’s blog post has some great ideas to get you started on those. Second, we simulated determining a wildlife population. Since this is something I hadn’t seen blogged about before, I thought I’d tell you about how it worked.

I found the idea for this in a book called “Mathematical Modeling for the Secondary School Curriculum.” It’s based on an article called “Estimating the Size of Wildlife Populations” that appeared in the NCTM’s Mathematics Teacher back in 1981*. Here’s how it works. Suppose you have some closed ecosystem that has a population of animals — maybe a large lake containing a population of a certain species of fish. What if we want to know how many fish are in our lake? Can you think of ways we might approximate the number of fish?

Here are some ideas that might spring to mind:

  • If we knew something about the social personality of the fish — for instance, maybe they are really independent and territorial and don’t like hanging out together — then we might know that they prefer to have at least X cubic meters of space to themselves. If we knew how big the lake was, then this could give us a rough count on how many fish there are. Problem: Knowing how big a lake is, in terms of volume, can be tricky. The bottom of the lake might not be flat. The amount of water varies based on temperature and rainfall. And what if we don’t know if our fish are social swimmers or solo swimmers?
  • We could rope off (fence off? net off?) a portion of the lake and count how many fish are in our section. If we knew we’d roped off exactly 10% of the lake, maybe we could use this information to estimate the total number of fish. Unfortunately, this is also difficult. First, we don’t know the fish are uniformly distributed around the lake. Maybe we roped off a portion of the lake that’s very rich in food source so we have many more fish than we should. Second, it’s tough to know if we’ve gotten exactly 10% of the lake or not. (How do you measure the volume of a lake, anyway? I’m sure there’s some way to do this, but I have no idea how.)

You may have thought of some other ways, too. Leave them in the comments. Here’s the way proposed in the NCTM article. It’s known as a capture-recapture estimate. Let F represent the number of fish in our lake. First, we capture a large number N of fish and tag them in a way that isn’t harmful; then we toss them back. We wait a while. Once the fish have had a chance to do their fishy things, we go back to the lake. We then capture x fish — some are tagged(T for Tagged), some are not. Assuming the fish are randomly dispersed throughout the lake, we might conclude that the number tagged in our sample is proportional to the number of tagged in the entire lake: N/F = T/x.

For a quick example, suppose we capture and tag 1200 fish. When we return to the lake, we re-capture 200 fish and we find that 30 of them are tagged. Assuming that the number tagged (30) in our sample (200) is roughly proportional to the number tagged in the lake (1200), we conclude that 30/200=1200/F so F=8,000.

What could go wrong? Well, maybe our sample isn’t very indicative of the population. We throw back all of the fish and then take another sample of roughly the same size. If we take several different samples, we can use the additional information from further samples to get a better estimate of the fish population. (I’m not going to go into all of the statistics at work here.)

Modeling the Fish Population

I gave each group of teachers a box. A shoe box would work. Inside each box were about 200 squares of paper. I didn’t count the squares as I put them in, and I didn’t want any two boxes to have precisely the same number. Having ~200 isn’t necessary — you just want enough people can’t do a fast eyeball estimate, but not too many because eventually you’ll want to count them.

One teacher “went fishing” and “tagged” a handful of fish (a dozen or so) PDP-fishby marking those squares with a signature, symbol, smiley face, whatever. The fish were returned to the lake before they suffocated. The box was shaken up. Another teacher then took a sample of size larger than the tagged number — something along the lines of 20-25 fish, give or take. The number of tagged fish in each sample was counted. Fish were returned to the pond, the box was shaken, and like it says on your shampoo bottle, “Lather, rinse, repeat.” Assuming the captured sample was the same size, after taking 10 samples, we averaged the number of tagged fish. Using proportions, we found an estimate for the total number of fish in the pond. Lastly, each team counted the actual number of fish in their pond to see how close they were. Most groups were pretty close. As an extension, we discussed how we might modify the method if more than one species of fish were in the pond.

(I saved the boxes. If I do this experiment again, I need to remember to make sure there are lots of squares of paper. Students were easily “fishing” for 30+ fish at a time, and so sometimes they’d end up capturing all their tagged fish.)

The teachers enjoyed this activity & I hope they’ll try something similar with their own students. We had a lot of great conversations about ecology and how our method could be extended, what flaws it might have, and so on!

*Knill, George. “Estimating the Size of Wildlife Populations.” Mathematics Teacher 74 (October 1981): 548′ 571.

Fun with Paper Folding

Over the last several years, I’ve been able to work with teachers from local pythag-foldedschool districts as part of a grant-funded project called “The Math and Science Partnership Program” (MSP). Phase II of this program focuses on “Improving Math & Science Teaching through School Outreach.” We offer free professional development workshops for teachers, held on Saturdays, several times a year. Teachers who are part of our MSP Partner Schools can earn a $150 stipend from attending each workshop. All workshops are accepted for re-certification credit in the Berkeley & Charleston County School districts. Descriptions of our workshops dating back to 2014 are available online.


Christel and Kate

Last weekend, together with my co-Leader Christel Wohlafka, I held a Workshop called “Mathematical Fun with Paper Folding.” I was inspired to create this workshop as a direct result of Patrick Honner‘s “Scalene Triangle One-Cut Challenge,” which I think I learned about because of a mention of it by Evelyn Lamb. The “scalene triangle” puzzle stuck with me for several hours one day and I was almost unable to function in any capacity until I figured it out.


Christel Wohlafka College of Charleston Department of Mathematics

Our agenda for our “Paper Folding Workshop” is available online. Many of our activities were inspired by great things I’ve learned about on Twitter, and many are available online at their original sources:

  1. The “Scalene Triangle” puzzle is part of @MrHonner’s blog series, “Fun with Folding”: http://mrhonner.com/fun-with-folding. The “One Cut Challenge” activities came from his “Fun with One Cut!” Workshop that he gave at the 2013 TIME conference. He blogged about it here: http://mrhonner.com/archives/11863 His templates are available online as a PDF file here: http://mrhonner.com/wp-content/uploads/2014/01/TIME-2000-2013-Templates.pdfgroup-one-cut-challenges
  2. “Hole punch symmetry” was produced by Joel Hamkins (@JDHamkins). He wrote about it in a recent blog post: http://jdh.hamkins.org/math-for-nine-year-olds-fold-punch-cut/ The template itself is available online: https://drive.google.com/file/d/0Bw3BMDqKsMmXRXlXU2xqbXlFYms/view Joel has a whole set of blog posts devoted to “Math for Kids” — http://jdh.hamkins.org/category/math-for-kids/
  3. The “Fold & Cut Theorem – Numberphile” YouTube Video we watched is available here: https://www.youtube.com/watch?v=ZREp1mAPKTM The female mathematician featured in the video is Katie Steckles, who finished her Math Ph.D. in 2011 at the University of Manchester. Katie’s webpage: http://www.katiesteckles.co.uk/ or you can find her on Twitter: @stecks
  4. Christel’s handout on “Dividing a Square into Thirds” came from an activity on Illustrative Mathematics
  5. Christel’s handout on “Paper Folding Proof of the Pythagorean Theorem” came from this “Teachers of India” resource.pythag1



Frank Monterisi Jr. folds paper.

I had a lot of fun at this Workshop and I hope we will offer it again next academic year. Between now and then, I need to order more and better-quality hole-punchers. With some of Joel’s “One Punch” activities, the paper ends up folded over itself five or six times, and some of the “well-loved” hole punchers we had with us weren’t up to the task.

#TLTCon and Digital Collaboration

On Wednesday, March 9th I’ll be leading a Workshop called “Introducing Students to Collaboration Using Google Docs” as part of the “Teaching, Learning, and Technology Conference“. It will be available to on-site participants at #TLTCon and also over Google Hangouts. If you’re interested in joining us, please contact me at let me know.

Groceries and Gratitude

Outside of my life as a mathematician, I’m a mom of three kids under age 6. If you’ve ever done some parenting, you know how it is exhausting and joyful and amazing and frustrating and beautiful and impossible–and can be all of these things in a single five-minute window of time. I had a life event recently that impacted everything about my daily life, both in and out of the classroom, in both my roles as “mathematician” and as “mommy”. I want to tell you about it to then share a really uplifting story that will make you feel better about the world.

!!! Ouch !!!
Two weeks ago, I was hanging out with my kids and my husband in our garage and in our driveway. The kids were playing on their bikes and we were enjoying a burst of Spring-like weather. Between our kitchen and our garage, there is a one-stair step down.While carrying my 7-month-old into the garage, I stepped out on my left foot and I think I twisted my ankle. My immediate reaction was to throw my weight over to my right side, which I did. And then, as if in slow motion, I started falling to the ground, holding my baby.

We landed. Thankfully, my mommy instinct kicked in, and I enveloped him in my arms as we fell. On the ground, he didn’t seem to notice anything had happened. He didn’t cry, he wasn’t hurt, he was completely fine.

Unfortunately, I was not completely fine. I landed on my kneecap with the full force of my body weight (plus his). In the blink of an eye, I found myself getting orthopedic knee surgery less than 48-hours later. I went from full-time care-giver to full-time care-receiver. It was a hard transition and I’m still working on figuring out this “new normal” around my house. I was devastated to learn I won’t be able to return to campus for several more weeks, but thankfully I will be able to do some work from home, teach an online class, and continue interacting with, supporting, and helping my students whenever possible.

A Happy Story

The grocery store closest to my house is Harris Teeter. They offer an online shopping service called “Express Lane“, where you can order your groceries online & then go through a drive-thru lane at the store for pick-up. Their helpful employees bring your groceries out, load your car, and they have a digital, portable payment system if you want to pay with a credit card. You can pay for the service per-order, or per month, or they offer a 1-year subscription.

After my knee injury, I was trying to figure out how things like my family’s grocery shopping would work. I can’t walk very well, I certainly can’t drive, and I even struggle to watch my three kids unless there’s someone else to help me. (For example, actively potty-training a two-year-old requires a hands-on approach by a very patient and mobile adult.) I decided I’d send an e-mail to Harris Teeter’s Customer Service Team and see if they could help me out.

I’ll admit, I wrote a pretty sappy message. I explained I’m a professor, a mom of three kids, a wife, and a grocery shopper. I told them I love their store (which I do!) and I love shopping there with my kids — They love “driving” the race-car shopping carts and the free cookie they get (but only if they listen to Mom the whole time!). I told Harris Teeter about my knee injury and surgery and I asked if they would consider extending me a free one-month subscription to the “Express Lane” online shopping for my family to use during my immediate recovery. This will allow me to shop online from home, and then send friends & neighbors to pick up my groceries. The worst part, I explained, was “I won’t get to visit all the members of my HT Family during my regular shopping trips.

The next day, my phone rang. It was the manager of my local Harris Teeter. He introduced himself and asked how my knee was doing. Before I could ask how his day was going, he said,

“Yes, this is the manager of your local Harris Teeter, and I am calling from your driveway.”

Completely shocked, I sent my parents out to meet him and invite him inside.


Gifts from Harris Teeter

The Harris Teeter manager brought with him an amazing bouquet of flowers, a giant gift basket of fresh organic fruit, and a touching “Get Well Card” that was signed, “We hope you get well soon, Your HT Family“.

They also extended us a free one-year subscription to their Express Lane online grocery ordering program.

About Gratitude

I was completely blown away by this. My colleagues, friends, neighbors, and family have been so amazing supportive, compassionate, and loving during my recovery. This chain of events has been incredibly tough for me — whether medically, physically, psychologically, mathematically… just NOT fun. I had no expectation that even my local grocery store manager would go so far out of his way to be supportive and do something just to make life easier and my day brighter. I was really, really touched by the gesture and I am very grateful.

As “corporate” and anonymous as modern life has become, it really inspires me that there are complete strangers who will go well above & beyond for someone they don’t even really know.

Even if you aren’t a Harris Teeter shopper, please consider contacting my local Harris Teeter to say “Thank You” on my behalf. I have told them this several times already, but I don’t think they can hear it too much.

Post Script

The flowers were delivered two weeks ago today and they still look amazing. The fruit was delicious (especially the kiwis!) and is long-gone, but I still wake up each morning to see my bouquet. It’s pretty impressive they look as good as they do given how many days they’ve been hanging out at my house.

An Adventure in Standards Based Algebra

This semester I am teaching several sections of “Math 101: College Algebra”. One section uses an “emporium” method, where students work independently in a computer lab. Instructors are available for questions and we also hold mini-lessons as needed, during which small groups of students can work on a particular topic at the same time. The other two sections are “traditional” in format and I’ve designed a standards-based grading system for them.

I began by creating a list of 30 standards for our 16-week semester. These are grouped by textbook section. Each standard has one or more “I can…” statements associated with it. Here’s the complete list. I’m giving three midterm tests this semester and each test will have an assortment of problems. The exam I gave this week covered our first six standards and had fourteen problems. Not all standards had the same number of problems.

I graded each problem using a modified “ERMF Rubric” (see http://www.nctm.org/Publications/mathematics-teacher/2004/Vol97/Issue1/EMRF_-Everyday-Rubric-Grading/). If you aren’t familiar with ERMF, I’d suggest checking out this post by Taylor Belcher, or some examples of the ERMF Rubric used in a beginning physics course. I decided I didn’t like the baggage associated with an “F” so I made mine an “ERMN” rubric:


Basically, I’m implementing a “Pass/Fail” system — although I refer to those as “Proficient” and “Not Proficient.” Scores of “E” and “M” are passing scores, and scores of “R” and “N” are failing scores. If a student earns all “E”s and “M”s on problems from a particular standard, then they get a “Proficient”. If there’s a mixture of some “R”s or “N”s, I looked at those case-by-case to determine if the student had shown enough understanding of the relevant ideas to merit a “Proficient” or not.

Overall, grading the exams took about one minute per exam page. I have about 50 students and this exam contained 6 pages. I don’t think this is too far off what it would have taken, time-wise, to grade using a traditional points- or percentage-based system.

I’m allowing students to come to my office for re-assessments, so any standards that earned a score “Not Proficient” can be improved upon later. In an upcoming post, I’ll write about my “Policy for Re-Assessments” and outline my system. From past experience, one key factor I’ve found is limiting the number of standards that can be re-attempted to no more than one per week.

At the end of the semester, 50% of the course grades will come from how they perform on their midterm tests. I’m converting all these “Proficients” and “Not Proficients” into a numeric score using this formula: “Midterm Exam Grade = 25 + 75*(# Proficient)/(# Total)”. Basically, this is the percentage of standards ranked Proficient, plus a tiny bit. Now I have to run off to class to return exams to students and explain more about how this grading system works — and why I believe it is to their advantage.


Documents related to SBG

This afternoon I’ll be presenting about standards based grading as part of Teaching, Learning and Technology‘s “Faculty Showcase.” I’ll be giving a similar talk at an upcoming conference. In case you’re interested, here are some documents related to my presentations:

A lot of my FAQ document was borrowed from Joshua Bowman (@Thalesdisciple). This semester, I didn’t actually give my students the FAQ document — It turned out that after three semesters of SBG, my explanation to students about how our grading system works & why I think it’s a good idea has gotten a lot better.

Actually, that point speaks to one of the great things I’ve gotten out of using SBG: Implementing my system forced me to give deep consideration to exactly what mathematical content I want my students to get out of the course. Instead of debating if homework should count 10% or 12% of the overall grade, or what I should do if a student misses a quiz for an undocumented reason, or other administrative policies like those, the SBG system made my entire course planning process focus on the math stuff I want to teach and assess — instead of worrying about policies unrelated to mathematics (compliance with the rules, attendance, percentage breakdowns, etc).

Two Upcoming Talks on Standards Based Grading

In the next month or so, I’ll be giving two talks on my implementation of standards based grading. (Okay, if you want to be really precise, that should say that I’m giving the same talk twice.) The first will be hosted by our “Teaching, Learning, and Technology” (@TLTCofC) division as part of their events for “Assessment Week”, and it will be on Wednesday, April 1st at 2pm. The second will be at SOCAMATYC  — the South Carolina Mathematical Association of Two-Year Colleges Annual Conference. They haven’t finalized their schedule yet, but the conference runs Friday 4/17 through Saturday 4/18. Thanks go to Frank Monterisi (@frank314) for letting me know about this opportunity.

Here’s a blurb about my talk:

In this presentation, we will give an overview of standards based grading (SBG) including helpful answers to questions of the form “What?”, “Why?” and “How?”. While an implementation specific to Calculus II will be discussed, the method outlined could be applied to courses in any discipline. If you’ve ever wondered about alternatives to traditional grading and how to avoid hearing the question, “What percent do I need to make on the final exam to get an 82% in the class?” then this is a great place to start.

Once I have put together my slides, I’m hoping to upload them here, along with some updated SBG documentation from my Calculus II course, like my current list of standards and the information provided to students about how the grading system works.

In a way, it feels a little strange to prepare a talk about standards based grading when I feel like the relative newbie to this topic. My entire system came about after many conversations and interactions with fellow educators on Twitter, and I am still indebted to them for all of their helpful support and guidance. In particular, I couldn’t have gotten my course running smoothly without inspiration from Frank Noschese (@fnoschese) and Joshua Bowman (@thalesdisciple). A quick google search just told me that Joshua gave a similar talk about his transition to SBG; I stumbled on his slides here.

A useful quote

At lunch today I spent a few minutes reading a recent edition of the AWM Newsletter. One article, written by Jackie Dewar, is called “Situated Studies of Teaching and Learning: The New Mainstream.” In it, she gave a great quote that I want to keep handy for later. The quote is from the keynote address at the 2013 ISSOTL Conference, given by Dr. Lee Shulman:

What advice did [Dr. Shulman] offer [Scholarship of Teaching and Learning] investigators? “Do not look for generalizations. Try to figure out what to do tomorrow because it matters.” (emphasis mine)

Whenever I think about my teaching approach and philosophy, I always stumble across the following problem: I have the tendency to think about what I want my classroom to look like, say, five or ten years down the road. I think about what I want the student experience to be and about big, radical changes I’d like to fully implement to get things there. Usually what happens at this point is I am jolted back to reality. I have so many different things pulling me in different directions that, in the end, I never feel like I’ve got momentum in the direction I’d like to go.

This is why I wanted to keep Dr. Shulman’s quote handy. Instead of thinking about big, long-term changes and projects, I really should spend my energy figuring out how to make class better tomorrow, or this week, or this semester. Hopefully small changes over time will have an additive result.