Tag Archives: teaching

My teaching journey: there and back again

Today I gave the keynote talk for the spring New Educator’s Workshop for teaching assistants at UW-Madison. I’m posting my slides here. My talk was entitled, “My teaching journey: there and back again.”

Abstract. I will talk about my journey from a painfully shy TA to a professor who is comfortable in the classroom and when talking to the media about research on the evening news. I will talk about strategies I used to be effective in the classroom given my strengths (and weaknesses).  Topics include time management, active learning techniques, easy ways to teach with technology, tips for managing student expectations, and things I wish I knew when I was starting to teach.


Blog posts that inspired my presentation:


What I do for diversity and inclusion in the classroom

A series of incidents of hate and bias on the University of Wisconsin-Madison campus has prompted campus officials and my dean in the College of Engineering to send out a letter to faculty stating that the College of Engineering will embark on a multi-year process to provide implicit bias training for students, faculty, and staff. I applaud these efforts. I also recognize that most of the incidents are happening outside of the classroom where I cannot see them. Still, it’s imperative that administrators and professors lead on the issue of diversity and inclusion. Showing our students that we are committed to diversity and inclusion will play an important role in helping students feel welcome and safe on campus.

This is what I try to do for all students, with the intent that it may make more of a difference to marginalized students such as underrepresented minority (URMs), women students, students from disadvantaged backgrounds, or students with disabilities. I recognize that I am not perfect. I am always trying to learn and improve. Feedback is very welcome.

Note about myself: I am a women in engineering who has a lot of experience in diversity and inclusion efforts for women in engineering. When I was a student, I felt like a fraud, I felt marginalized at times, and I felt like I did not always have a voice. But I am not a diversity expert; I’m just a diversity fangirl. I try to do small things with great love and to continually improve what I do. My goal as a professor is to help all my students feel “welcome at the table” so to speak.

What I do in the classroom:

  1. I strive to treat all students the same. This means treating each student like an individual and responding to their individual needs. This will be a lifelong challenge because I am human and surely hold on to some stereotypes. I make it a goal to give all students the same opportunities as opposed to trying to “correct” for biases I may have (which can make things worse — see stereotype threat).
  2. I give a sense that my course is challenging but doable, with an emphasis on doable. I never only tell students how hard engineering is, because students who are marginalized in any way sometimes get the message that if they find something hard, it means they are inherently bad at it and will not be successful. Instead, I focus on the “doable” part. Recognizing that student abilities are malleable is a positive message that directly combats notions that a student is not welcome or is flawed.
  3. I do not use gender or names in any generic classroom examples (no “he” or “she” in classroom examples when referring to an engineer who is solving a problem about simulation).
  4. I am careful when “randomly” assigning student groups. I try to ensure that there isn’t only one woman student in a group, for example. I usually let students choose their own group so they are most comfortable.
  5. I strive to give all students a voice. I ask students what they think when talking with students doing group work in class. That way, I can “give” everyone a voice, which is particularly important for students from marginalized groups who do not feel like they have a voice.
  6. I touch base with students during active learning segments in class, even if they do not ask for help. Students who do not feel “welcome to the table” often do not ask for help because they feel like a fraud. Helping students clear small hurdles in class can build their confidence. Again, I like to focus on how engineering is “doable” and how skills can be learned.
  7. I talk about imposter syndrome in the classroom (this is not for everyone).
  8. I talk about stereotype threat in the classroom (this is really not for everyone).
  9. I give a class of students a positive affirmation before an exam. I remind my students about how much they have learned and how I believe they have come a long way. If they ask if the test is hard (and they always do), I say it’s tough but fair and doable. I keep the messages positive to counteract stereotype threat. In fact, this is one of the most effective ways for teachers to improve the test scores of marginalized students:
    • “One of the most powerful things teachers can do to offset the stereotype threat and bolster student performance is to prompt students to reflect on their talents, beliefs and values. These kinds of “affirmations” remind students of what’s important to them and can build a line of defense against stereotype threat.” [Reference]

What I do outside of the classroom aimed at improving student access to opportunities and achievement. Usually these things take place during office hours and advising:

  1. I ask students about their plans for the summer and encourage them to consider internships, co-ops, research experiences for undergraduates (REUs).
  2. I invite students to department events (colloquiums, receptions, reunions, etc.)
  3. I talk to students about graduate school. This is a big one. Graduate school is not on everyone’s radar, and telling a student they should think about graduate school because they have something to offer is sometimes a life-changing conversation for a marginalized student.
  4. I serve as a reference for students (if they ask me) and be even-handed in how I refer to students in the letters (see this word cloud of words used in letters for men and in letters for women).
  5. I tell a student that I believe in their abilities and know they will be successful as a future industrial engineer when they stop in for office hours, when the going gets tough, at the department graduation party, etc. Positive affirmations.
  6. I congratulate an underrepresented minority (URM) or women student for an achievement (internship, new job, award, etc.) and ensure that awards get publicized in the department and college.
  7. I nominate the student for a campus or department award and write a letter of recommendation for the student if one is needed.
  8. I publicize department opportunities in the classroom (for department scholarships, etc.) and personally recommend that students apply for a department scholarship award.
  9. I try to rid myself of stereotypes and biases I have by reading about biases when I can.

What I do with my colleagues:

  1. Add items to related to diversity and inclusion to the meeting agendas.
  2. Bring up issues of diversity and inclusion when discusses new classes, especially those for freshmen where inclusion should be a goal.
  3. Encourage inviting speakers from underrepresented groups to give department colloquiums.
  4. Ask colloquium speakers, especially those from underrepresented groups, to speak to graduate students when they visit.
  5. Encourage colleagues to ask candidates from underrepresented groups to apply for faculty positions (and do so myself).

I want to reiterate that I am not an expert. These tips are things that work for me, and I know I am leaving some top tips out. This list from Vanderbilt contains some additional recommendations and suggestions for learning more. What do you do in and out of the classroom? Help me improve.

Articles on bias:

XKCD comic called “How it works” because this is absolutely not how it should work.

Edits on 4/27 to include my tweets about this post:


Update on 7/15/16. I discovered this paper from PLoS called “Peer-Led Team Learning Helps Minority Students Succeed

Peer-Led Team Learning and active learning has been shown to reduce grade disparities between underrepresented minority students and students from more white and privileged backgrounds. Lecturing has the highest level of disparity. Other research out there done by education experts suggest that if you care about diversity, you should replace lecturing with active learning. I have some work to do, but it’s great to know how to target my teaching efforts.

Update on 3/29/18

Francis Edward Su wrote an article entitled “Mathematical Microaggressions” about creating a growth mindset in class to help a diverse set of students reach their potential.

Markus Brauer at UW-Madison has a handout with some suggestions for teaching in a diverse classroom. Here are some of his suggestions based on published evidence in the literature.

  1. Insist on the “utility value” of the material you are teaching in class. Explain clearly how the students will be able to use the knowledge they learn in your class later in life. Some studies suggest that this is beneficial for all students, but particularly for students from historically underrepresented populations.
  2. Ask all students to express what they value and why these values are important for them.
  3. Specify in your syllabus what tasks students will have to fulfill in your class and post your website ahead of time. This way, students can see if certain disabilities prevent them from having a positive learning experience in the class.
  4. Communicate that most students feel in the first semesters that they do not “belong” but that most of them tend to overcome these difficulties and end up feeling quite connected in later semesters.
  5. Build some flexibility in your assignment schedule. For example, allows students to have in 1 assignment up to 48 hours late with no penalty. This is essential for students with certain types of disabilities, such as mental illness.
  6. Be aware that you don’t have to call on the first student who raises their hand. Take the time to call on students who rarely talk in class to encourage everyone to give verbal and non-verbal feedback.
  7. When presenting empirical results, show pictures of the scientists who conducted the research. Do so especially when the researcher is a woman or a URM.
  8. Consider doing “low impact testing,” where students can take the quiz multiple times until they get all the answers right. These types of activities should account for <10% of the final grade. This type of activity tends to help pull up students with the lowest grades.
  9. Do not grade according to a curve. Instead, use an a priori grading scheme.
  10. When talking about groups, emphasize the groups’ heterogeneity and discuss the large within-group differences. Making salient that a stigmatized group is heterogeneous creates more positive feelings toward this group.

integer programming for locating ambulances

Last week I visited Oberlin College to deliver the Fuzzy Vance Lecture in Mathematics (see post here). In addition, I gave two lectures to Bob Bosch’s undergraduate optimization course. I will post my materials for both of my lectures on my blog. The first lecture was related to my evening talk and focused on ambulance location models and modeling integer programs.

The purpose of the lecture was to work on modeling in integer programming. We focused on coverage models and worked through two of the three models that successively lift simplifying assumptions (in a 75 minute lecture). The “Integer Programming Bag of Tricks” on slide 18 contains a series of constraints for modeling conditional constraints (courtesy of Jeff Linderoth and Jim Luedtke). We use these tricks to assign at least L calls for service (demand) to stations–but only stations that are “open”–in the modeling exercise. Slides are below.

Related reading:

just write, damn it

I’ve had little time to write lately, so writing feels like a guilty pleasure when I have the time to do it. I am advising four PhD students who often ask me about the writing process. I’ve almost forgotten about how hard technical writing was for me back when I was in their shoes.

Roger Ebert’s memoir Life Itself  jarred my memory. This weekend, I was listening to the audiobook while working on on my yard. One passage about writing got my attention:

[Bill] Lyon watched as I ripped one sheet of copy paper after another out of my typewriter and finally gave me the most useful advice I have ever received as a writer: “One, don’t wait for inspiration, just start the damned thing. Two, once you begin, keep on until the end. How do you know how the story should begin until you find out where it’s going?” These rules saved me half a career’s worth of time and gained me a reputation as the fastest writer in town. I’m not faster. I spend less time not writing.

Part one is really great advice. I’m a firm believer in writing as you go. I’m not so sure about part two for students writing their first article or thesis. First, most of the time it is even feasible to write until you reach the end. Second, organization helps when writing a lengthy manuscript (lengthy here is relative to newspaper articles). It’s usually easier to write when you have an outline that lays out your ideas in a straightforward fashion. You should know where you’re going. But if organization paralyzes you, I recommend just starting the damned thing and reorganizing later. Students seem to struggle with writing sins of omission – the biggest mistake is not getting started. If you want to finish something, you need to start it first.

When searching for Roger Ebert’s comment on writing, I found similar advice from Matt Zoller Seitz about writing movie reviews on rogerebert.com:

Just write, damn it. I believe that ninety percent of writer’s block is not the fault of the writer. It’s the fault of the writer’s wrongheaded educational conditioning. We’re taught to write via a 20th century industrial model that’s boringly linear and predictable: What’s your topic sentence? What are your sections? What’s your conclusion? Nobody wants to read a piece that’s structured that way. Even if they did, the form would be more a hindrance than a help to the writing process, because it makes the writer settle on a thesis before he or she has had a chance to wade around in the ideas and inspect them. So to Hell with the outline. Just puke on the page, knowing that you can clean it up and make it structurally sound later. Your mind is a babbling lunatic. It’s Dennis Hopper, jumping all over the place, free associating, digressing, doubling back, exploding in profanity and absurdity and nonsense. Stop ordering it to calm down and speak clearly. Listen closely and take dictation. Be a stenographer for your subconscious. Then rewrite and edit.

This isn’t quite the right advice for writing a thesis, but students should hear this. Students know they are supposed to organize. They seem less familiar with the idea of puking on the page, knowing that they can clean it up and make it structurally sound later. The latter approach is how I start almost all of my blog posts (most get cleaned up later).

How do you write?


some students don’t learn a whole lot in college

A few years ago, researchers Richard Arum and Josipa Roksa released a book called “Academically Adrift” that claims that many students don’t leave college with new knowledge and new skills [Link to an article in the Chronicle]: Here is what they found:

Growing numbers of students are sent to college at increasingly higher costs, but for a large proportion of them the gains in critical thinking, complex reasoning, and written communication are either exceedingly small or empirically nonexistent. At least 45 percent of students in our sample did not demonstrate any statistically significant improvement in Collegiate Learning Assessment [CLA] performance during the first two years of college. [Further study has indicated that 36 percent of students did not show any significant improvement over four years.]

The CLA is a proxy measure for what students learned during college. This suggests that more than a third of college students do not demonstrate any improvement in critical thinking during college. This is a tragedy. College is expensive.

Now there are a few things to note. Most obviously, these results are averaged across all students in all majors at all universities. Your mileage may vary. I share this information with my students on the first day of class. I challenge my students, but I think they will get their money’s worth from my class and will leave with tangible improvements in critical thinking and complex reasoning (and sometimes written communication, but I could do more with writing).

Students who did the best didn’t always go to the best universities (but that helps). Students with high levels of learning:

  • studied alone (yeah for introverts!)
  • had professors with high academic expectations
  • studied traditional liberal arts and sciences (as compared to business, education and communications).

This suggests the only thing I can do as a professor is to have high expectations for students (and to give assignments that raise these expectations).

I realize that in the big picture, some programs are quite competitive and attract the types of students who like being challenged and as a result, are challenged. But I realize it’s more complicated than this: there is a push and pull between professors and students about expectations (see this article about a teaching assistant at Columbia who inflated grades because so many students complained and it’s been widely reported that college students study much less than they used to). In general, these researchers found that professors do not expect much of the students and assign almost no homework.

A follow up report is out [Link] called “Aspiring Adults Adrift.” The authors found that the same students who didn’t learn much in college continue to struggle with employment afterward. What they find is really interesting. The same students that didn’t do well on the CLA were more likely to be unemployed, under employed, employed in a job with low skill requirements, and laid off. In other words, employers are good at recognizing who developed more skills in college and who didn’t.

The research suggests that some students don’t want to be challenged or to learn; they just want a degree. It’s not fun to “teach” students who don’t want to learn anything.

Interestingly, the students themselves cannot tell if they’ve learned a lot in college. They all assume they’ve learned a lot! This is not good. It implies that students are not good consumers when it comes to investing in their educations, and don’t see implications of taking blow off courses or choosing easy programs. (Side note: this is a reason why students should not estimate how much they’ve learned in end of the semester teaching evaluations.) The article ends with an important point:

Yet those same students continue to believe they got a great education, even after two years of struggle [after graduation]. This suggests a fundamental failure in the higher education market — while employers can tell the difference between those who learned in college and those who were left academically adrift, the students themselves cannot.

Finally, correction at the end of the NY Times article made me cringe:

“An earlier version of this article incorrectly used a male courtesy title for Josipa Roksa. She is a woman.”

I am curious about how you challenge students in tough classes. I’ve been given a lot of teaching advice of the years, and most of it hasn’t been very useful or practical (“Just be an extroverted man with CEO hair and you’ll do great!”). Teaching is definitely all about managing expectations, and I’d like to do that without caving and giving everyone an A (I don’t!). I’m sure I have a lot to learn from my readers who I know teach a lot of “hard” courses.

do you have any material for teaching undergraduate simulation?

I am teaching an undergraduate simulation course in the spring to industrial engineering students. I have plenty of lecture notes from colleagues, but I am missing simple classroom demos (like an Excel spreadsheet), classroom modeling activities, and case studies. This is a bleg for additional material to enhance my teaching. Please email me with any material or post a link. Thank you in advance!

math is your superpower

Today was my last class of the semester before the final. In most of my courses, I give a fun talk about what professors really do outside of the classroom. I also go over my one (or seven) things that I want students to learn from me every semester. At the end of the talk, I tell students that while our world is becoming more complex and quantitative, math is often underused. Math is a superpower.

I once heard that the world runs on eighth grade math. I don’t think that is true for many industries (especially the ones that hire operations research graduates!), but a study compiled in a Northeastern University study shows that few Americans use advanced mathematics on the job [Link to the Jordan Weissman article in The Atlantic].

I remain optimistic about the need for advanced math. First, it’s possible that few workers use math because few workers are proficient in math. In fact, “Upper Blue Collar” workers are the most likely to use math. This should motivate us to teach math better, not to conclude that it isn’t needed. Second, it’s worth noting that the Northeastern study data is summarized across the workers surveyed (not across industries or companies). It’s certainly possible that nearly all companies perform statistics but that relatively few workers actually do the statistics (22% of upper white collar workers in the figure above) and that the average worker isn’t always aware of it.

The bottom line is that the survey suggests that relatively few workers do the hard number crunching, so there is a competitive advantage for those who are willing and able to do it. Math may not really be a super power, but it’s something that most workers do not get to enjoy on a regular basis.

finding optimal marriage pairings using the assignment problem

The topic of today’s blog post is about optimally finding a spouse using optimization models (HT Anna Nagurney). This post is based on a paper published in EJOR entitled, “Optimizing the Marriage Market: An Application of the Linear Assignment Model,” and in it, researchers apply the linear assignment problem to identify how to optimally match potential (heterosexual) couples to find a new social optimum. While matching the couples is a textbook exercise, the researchers used a longitudinal dataset in Switzerland to identify meaning weights to assign to each potential pairing. They find that the actual marriages are far from optimal.

The weights are based on logistic regression models for predicting the likelihood of divorce from a longitudinal data set. The weights are based on four types of socioeconomic variables of each person in the set:

  1. Age
  2. Previous divorce (or not)
  3. Education (high or low)
  4. Nationality (Swiss, Western, or non-Western)

The weights for each pairing are not symmetric. For example, a wife is much more likely to divorce from a husband five years her junior than five years her senior.

ScreenHunter_02 Feb. 13 10.13

The assignment problem is an integer programming model that produces the lowest cost one-to-one matching between two sets of items, such as individuals and jobs. Here, the two sets of items are men and women. The assignment problem is totally unimodular, and therefore, can be efficiently solved via the Hungarian algorithm.


  • W = set of women
  • M = set of men (with |W|=|M|)
  • x{ij} = 1 if woman i is matched to man j, i in W and j in M
  • c{ij} = the “cost” of matching woman i is to man j.

The optimization problem is:

ScreenHunter_01 Feb. 13 10.13

A solution to the assignment problem admits exactly m=|M| = |W| variables with value 1 (the rest of the variables are zero). The structure here is a bipartite graph: one set of nodes represents the women and the other set of nodes represents the men. Every women is connected to all the men (and none of the women) and vice versa. There are m! possible matchings (corresponding to some permutation of possible pairings), and the assignment polytope has m! extreme points.

The Hungarian algorithm works by finding the reduced cost matrix, by first subtracting the smallest value in each row from the entire row. This is repeated for each row, leaving a zero in each row. Then, this is repeated over the columns. The resulting reduced matrix will have a zero in every column and every row, and all of its entries will be nonnegative. The optimal solution is identified by covering the zeros by adding lines row-wise and column-wise in a multi-step procedure.

I put together a small Excel spreadsheet with 9 men and women [Link to my Excel file and to the instructions], where I solve the assignment program. Please download and use in an introductory LP class.

ScreenHunter_03 Feb. 13 10.16

The authors of the paper say that their method is an “innovative method of optimizing romantic partner allocation.” Of course, this is no way to find a partner for life.  However, the authors point out that they could substantially improve marriage survival by reallocating 68% of the pairings. They conclude that “current marriage markets are suboptimally organized.” My Valentine’s Day wish to my readers is that you optimally organize your love life with or without the use of optimization models.

a multiobjective decision analysis model to find the best restaurant in Richmond

I taught multiobjective decision analysis (MODA) this semester. It is a lot of fun to teach. I always learn a lot when I teach it. One of the most enjoyable parts of the class (for me at least!) is to run a class project that we chip away at during class over the course of the semester. Our project is to find the best restaurant for us to celebrate at the end of the semester. “Best” here is relative to the people in the class and the .

The project is a great way to teach about the MODA process. The process not only includes the modeling, but also the craft of working with decision makers and iteratively improving the model. It’s useful for students to be exposed to the entire analysis process. I don’t do this in my other classes.

On the first day of class, we came up with our objectives hierarchy. I did this by passing out about five Post It notes to each student. They each wrote one criteria for selecting a restaurant on each Post It note. They stuck their Post It notes to the wall. Together, we regrouped and organized our criteria into an objectives hierarchy.  Some of the objectives because “weed out criteria,” such as making sure that the restaurant could accommodate all of us and comply with dietary restrictions.

Our initial criteria were:

  1. Distance
  2. Quality of food
  3. Variety of food
  4. Service: Fast service
  5. Service: Waiting time for a table
  6. Service: Friendly service
  7. Atmosphere: Noise level
  8. Atmosphere: Cleanliness
  9. Cost

Our final criteria were as follows (from most to least important):

  1. Quality of food
  2. Cost (tie with #3)
  3. Distance
  4. Fast service (tie with #5)
  5. Noise level
  6. Cleanliness

We removed variety of food, waiting time, and friendly service because classroom discussions indicated that they weren’t important compared to the other criteria. Variety, for example, was less important if we were eating delicious food at an ethnic restaurant that had less “variety” (variety in quotes here, because it depends on you you measure it).

In the next few weeks, we worked on identifying how we would actually measure our criteria. Then, we came up with a list of our favorite restaurants. During this process, we removed objectives that no longer made sense.

We collaboratively scored each of the restaurants in each of the six categories by using a google docs spreadsheet.

  1. Quality of food = average score (1-5 scale)
  2. Cost (tie with #3) = cost of an entree, drink, tax, and tip
  3. Distance = distance from the class (in minutes walk/drive)
  4. Fast service (tie with #5) = three point scale based on fast service, OK service, or very slow service
  5. Noise level = four point scale based on yelp.com ratings
  6. Cleanliness: based on the last inspection. Score = # minor violations + 4*# major violations.

A real challenge was to come up with:

  • the single dimensional value functions that translated each restaurant score for an objective into a value between 0 and 1.
  • the weights that balanced our preferences across objectives using swing weight thinking. FYI, we used an additive model.

I won’t elaborate on these parts of the process further. Ask me about these if you are interested.

When we finished our model, the “best” decision was to forego a restaurant and do a potluck instead. No one was happy with this. We examined why this happened. This was great: ending up with a bad solution was a great opportunity for learning. We concluded that we didn’t account for the hidden costs associated with a potluck. Namely, it would entail either making a trip to the grocery store or cooking, approximately a 30 minute penalty. We decided that this was equivalent to driving to a distant restaurant, a 26 minute drive in our model.  It was also hard to evaluate cleanliness since the state do not inspect classrooms like they do restaurants. But since cleanliness didn’t account for much of our decision, we decided not to make adjustments there.

The final model is in a google docs spreadsheet.

We performed a sensitivity analysis on all of the weights. Regardless of what they were, most of the restaurants were dominated, meaning that they would not be optimal no matter what the weights were. The sensitivity was not in google docs, since we downloaded the document and performed sensitivity on our own. I show the sensitivity wrt to the weight for quality below. The base weight for quality is 0.3617. When the weight is zero and quality is not important, Chipotle would have been our most preferred restaurant. The Local would be preferred only across a tiny range.

We celebrated in Ipanema, a semi-vegetarian restaurant in Richmond. I think our model came up with a great restaurant. We all enjoyed a nice meal together. Interestingly, Mamma Zu scored almost identically to Ipanema (see the figure below).

I cannot claim credit for this fun class project. I shamelessly stole this idea from Dr. Don Buckshaw, who uses it in MODA short courses.  We use the Craig Kirkwood’s Strategic Decision Making as the textbook for the course. I also recommend Ralph Keeney’s Value Focused Thinking and John Hammond’s Smart Choices.

How do you choose a restaurant?

Sensitivity with respect to the weight for quality (0.3617 in the base case).

university offers zombie apocalypse course to teach students survival skills

Michigan State University plans to offer a zombie apocalypse course to teach students survival skills. The course will be offered by the School of Social Work. (Hat tip to Paul Rubin). The course won’t really teach students how to survive a zombie attack, rather, it uses a zombie apocalypse as a vehicle for teaching students about how to model catastrophic events and infectious diseases like pandemic flu.

The instructor talks about the course in the Youtube video below.

This has me convinced that I should develop a course on OR models for a zombie apocalypse.

I am planning to develop a similar course that teaches introductory OR modeling to undergraduates by way of applications in emergency preparedness and emergency response. I had envisioned covering more traditional disasters, such as hurricanes and earthquakes. Maybe I should think outside the box.

What topics would you offer in an OR course on the zombie apocalypse? I would start with population models using birth-death models and/or differential equations (see one of my previous posts on this topic) and then look at how to staff deputies or federal marshals to combat the zombie hoards.

I plan to talk about zombies, werewolves, and vampires in the stochastic processes course I am teaching this semester. Here is a previous exam question.