When you have a chronic illness and a job, by definition you work when you are sick. Before I went on medical leave, I struggled every day to balance my desire to take care of myself with my desire to keep my job and do it well. Sometimes the balance felt impossible, and eventually it became so, but along the way I found some strategies that genuinely helped. I share some of them below.

Telling People about my Illness

Hiding my illness would have been very stressful and perhaps impossible, as I often looked sick and had colleagues who noticed. I did not share details with everyone, but most of the people I regularly interacted with knew something about my situation. Some of them would listen to my tales of drugs, doctors, and hospitals and remind me to slow down when they could see that I was getting worse.

On the first day of class, I told students that I had a chronic illness and was more likely to be absent than some of their other professors. I offered to call commuter students if I had to cancel class (although usually when I stayed home, I asked classes to meet without me).

Sometimes more details about my illness would emerge throughout the semester, sometimes not. We had conversations framed as biology lessons, as Q and A’s about whether stress causes or Crohn’s or whether taking vitamins helps, and as discussions of school bathroom policies and their effects on children with bowel diseases (a topic that was interesting because most of the students were planning to be elementary teachers). Many students talked to me privately about their own health issues or those of family members.

Clear Priorities

I polled some colleagues who had worked with me for years, asking what they thought I could do to reduce my stress at work. Their responses were consistent: I needed to prioritize better. I tried to do too many things, and too often when I got an idea, I’d start implementing it immediately, even if I had many other things to do. I would have had to grapple with this tendency eventually, but my illness made setting priorities a priority (sorry, couldn’t resist).

I chose teaching my classes and keeping the math program running as my main priorities. I stopped going to meetings that weren’t related to either of these two things. I sometimes felt guilty about missing meetings, but the culture at my college favors many large meetings, and going to them left me too exhausted to accomplish my priorities. I am not sure what I would have done if I’d gotten sick earlier in my career, but I’d had about a dozen years of regular attendance under my belt before I cut back.

I chose my battles in line with my priorities. I used to speak out on every injustice I saw at the college –from major to very minor — and I was proud of that, but again, I chose to conserve my energy to focus on priorities.

I gave up many things that I enjoyed. We had a thriving math club that met once a week in the evening, but it was too tiring for me to go to the club meetings and then teach the next day. I stopped going to senior seminar final presentations and to talks given by faculty and guest speakers. I stopped going to out of town conferences and to most in town ones too. I hope to be able to resume some of these activities when I return (although I’m less excited about more meetings).

Simple Boundaries on Work Time

If I’d had a less flexible job, I would have been fired, switched to part time work, or gone on disability. For better or worse, the flexibility of my job enabled me to keep working as long as I did, but it also was hard to manage, as I was inclined to work more than was good for my health.

I imposed some simple boundaries to constrain my workaholic tendencies. I kept a Sabbath: I didn’t do any work from Friday night until sometime on Sunday, and I kept the computer off. I stopped working by 4 p.m. on other days (I often started at 6 a.m., so this actually wasn’t that early) and turned the computer off by 7 p.m. I didn’t get a smart phone.

These simple rules were easy to communicate to others: colleagues knew I wasn’t available for Saturday accepted student lunches or for 4:00 meetings, but I might be free for summer advising on a Sunday. On occasion, I ignored my rules, but that was very different than not having them at all.

A Steady Schedule

Like many academics, I used to jam all of my classes into as few weekdays as possible, but I no longer had the stamina to work such grueling days. I changed my schedule so that I started teaching at 11:30 four or five days a week. My guts acted up the most in the morning, but they usually settled down before my commute. Prior to leaving for school, I planned classes, graded, and did administrative work – near my own bathroom. After teaching I usually stayed for a few hours to finish up and meet with students and colleagues, but I aimed to leave by my 4:00 limit and left earlier if I was especially tired or sick that day.

I emailed my advisees a few days before advising period started to set up appointments, and I got the new course schedule as soon as it was available. I scheduled no more than two or three students per day during the two week period, with a few days off.

As much as possible, I staggered tests and hard to grade assignments to avoid getting overwhelmed with grading at any given time. When I had long papers to grade, I read a few a day, rather than the “binge” grading I used to do.

Modifying my Schedule as Needed

I learned to gauge my energy levels and modify my plans for the day. I had many routes to and from work, and I could adjust the transportation mix of bus, subway, and walking to fit my energy level; occasionally when I was exhausted, I took a cab.

Once in a while I moved an activity that required me to be especially “on” to a day when I was more capable of it and did a quieter activity on a day when I was feeling worse. A strategically timed day off could prevent even more missed days.

Certain times of the semester, particularly during advising and near the beginning and end, were especially difficult for me, and I was careful to pace myself then. Sometimes I planned in advance to stay home for a day, as I knew that otherwise I would work too much.

A Private Time Clock

I had trouble setting limits on my administrative work, which follows a different rhythm than teaching. With teaching, sometimes the papers are graded, the next class is prepared, and the work is done for the moment, but administrative work just keeps rolling in.

For many years, my job as the math coordinator was, “do what needs to be done,” but the program was expanding and too much needed to be done. My dean and I negotiated a more specific job description, with an expectation of no more than ten hours a week of administrative work (generous, given the one course release compensation).

I made a spreadsheet with columns for various administrative tasks and kept track of how much time I spent on each, in fifteen minute increments. Soon I started keeping track of teaching time too. I found that when I got to ten hours of administrative work, I could leave the rest for the next week without feeling guilty. The numbers on the screen helped me notice when I was starting to work too much, while I still had some energy left to conserve. I also used these data to make a case for paying someone else to take over some of the administrative work.

It’s a bit ironic that I chose academia partly for its flexibility and then made my own time clock, but recording my working hours was one of the most helpful things I did.

Technology

There were a few times when my advisees were in practica and couldn’t meet until the evening. Sometimes I “met” with them from home via instant messaging (Skype would have been better, but I didn’t have it yet). These students were strapped for time too and often appreciated the remote option. These conferences took much longer than in-person meetings (I was surprised at how slow some of the students typed) and they felt less connecting, but they were adequate.

Yoga and Meditation

I started practicing yoga years before I was diagnosed, when I had back problems, but yoga also helped me get better at staying present and calm during difficult moments. I built in little breaks throughout my work day to stretch or to just sit for a minute or two and breathe and check in with myself. These were good times to assess my energy level and decide whether I needed to modify my original plans for the day.

Preparation

I kept an extra pair of jeans in my office, and I always carried extra underwear and pants in my knapsack, just in case I had an accident. Accidents often felt imminent, but I didn’t have that many. I never used the extra clothes at school, but was comforted that they were there.

I knew the location of many bathrooms along my various routes to work and at the college. I knew that even though a private bathroom was nicer, it was better to go to a multi-stall bathroom when it was urgent, as an available toilet was more likely. I kept containers of air freshener in my office and my bag to quickly grab and bring with me to the rest room.

I kept food in my office, as my diet often was too restricted for me to easily find a meal or snack. I kept some special, easy to digest high calorie, high protein shakes, as well as an immersion blender to mix them, and I could drink a shake when my energy was lagging.

Conclusion

When my sabbatical ends in the fall, I hope to return to work much healthier than I was when I developed these strategies. I am grateful that surgery ended my days of urgently running to the bathroom, and I also look forward to having more energy and being able to do more things. Some strategies will no longer be necessary, but others, such as setting boundaries and priorities, are just better ways of working.

I welcome comments, including sharing some of your own strategies.

I learned the circle definitions of sine and cosine in my junior year of high school, in the class that would now be called pre-calculus (it was called “Trig Senior Math”). Two years earlier, I’d learned the triangle definitions of sine, cosine, and tangent in geometry class. I don’t remember any of my teachers ever mentioning a circle definition of the tangent function.

The geometric definition of the tangent function, which predates the triangle definition, is the length of a segment tangent to the unit circle. The tangent really is a tangent! Just as for sine and cosine, this one-variable definition helps develop intuition. Here is the definition, followed by an applet to help you get a feel for it:

Let OA be a radius of the unit circle, let B = (1,0), and let \( \theta =\angle BOA\). Let C be the intersection of \(\overrightarrow{OA}\) and the line x=1, i.e. the tangent to the unit circle at B. Then \(\tan \theta\) is the y-coordinate of C, i.e. the signed length of segment BC.

Move the blue point below; the tangent is the length of the red segment. (If a label is getting in the way, right click and toggle “show label” from the menu).

The circle definition of the tangent function leads to geometric illustrations of many standard properties and identities. (If this were my class, I would stop here and tell you to explore on your own and with others).

Some things to notice:

\(\left| \tan \theta \right|\) gets big as \(\theta\) approaches \(\pm 90{}^\circ \).

\(\tan (\pm 90{}^\circ)\) is undefined, because at these angles, \(\overline{OA}\) is parallel to x=1, so the two lines don’t intersect, and point C doesn’t exist.

\(\tan 90{}^\circ\) tends toward \(+\infty\), \(\tan (-90{}^\circ)\) tends toward \(-\infty\).

\(\tan \theta\) is positive in the first and third quadrants, negative in the second and fourth quadrants.

\(\tan \theta\)=\(tan (\theta+180{}^\circ)\) — the angles \(\theta\) and \(\theta +180{}^\circ\) form the same line. Thus the period of the tangent function is \(180 {}^\circ = \pi\) radians.

\(\tan \theta\) = \(- \tan (-\theta)\). Moving from \(\theta\) to \(-\theta\) reflects \(OC\) about the x-axis.

\(\tan \theta\) is equal to the slope of OA (rise = \(\tan \theta\) , run =1), which is also equal to \(\dfrac{\sin\theta}{\cos\theta}\), as well as Opposite over Adjacent for angle \(\theta\) in right triangle CBO.

\(\tan (45{}^\circ)=1\). When \(\theta=45{}^\circ\), triangle CBO is a 45-45-90 triangle, and OB=1. Similarly, \(\tan (-45{}^\circ)=-1\), etc.

For small values of \(\theta\), \(\tan \theta\) is close to \(\sin \theta\), which is close to the arc length of AB, i.e. the measure of \(\theta\) in radians.

If we define \(\arctan \theta\) as the function whose input is the signed length of BC and whose output is the angle \(\theta\) corresponding to that tangent length, then the domain of that function is the reals, and it makes sense to define the range as \(-90 {}^\circ< \theta <90{}^\circ\) (in radians \(-\pi/2<\theta < \pi/2\) and arctan's output is an arc length). This range includes all the angles we need and avoids the discontinuity at \(\theta= \pm 90{}^\circ =\pm \pi/2\) radians.

For \(\left| \theta \right|\leq 45{}^\circ\), \(\left| \tan \theta \right|\leq 1\). Half of the input values of \(\tan \theta\) give outputs with absolute values less than or equal to 1, and the other half give values on the rest of the number line. This mapping also occurs with fractions and slopes, but there's something very compelling about seeing the lengths change dynamically. Applets like the one above could also help students develop intuition about slopes.

\(\tan (180{}^\circ-\theta) = -\tan \theta\). We reflect BC over the x-axis to form \(B{C}'\). Then \(\angle BO{C}'=\theta\) and \(\angle BOD =(180{}^\circ-\theta)\). \(B{C}'\) (the blue segment) is the tangent of \((180{}^\circ-\theta)\).

\(\tan (\theta \pm 90{}^\circ)\) = \(-1/\tan \theta\). The picture below illustrates the geometry of this identity when \(\theta\) is in the first quadrant.

The line formed at \(\theta + 90{}^\circ\) is perpendicular to OC and \(\triangle COB\sim \triangle ODB\). Thus \(\dfrac{BD}{OB}=\dfrac{OB}{BC}\), and with appropriate signs, \(\tan (\theta + 90{}^\circ)\) = \(-1/\tan \theta\). Since \(\tan \theta\)=\(\tan (\theta+180{}^\circ)\), \(\tan (\theta +90{}^\circ)=\tan(\theta-90{}^\circ)\).

The applet below shows the geometry in all quadrants, and it gives a dynamic sense of the relationship between \(\tan\theta\) and \(\tan(-\theta)\). Again, move the blue point:

Special Bonus: The Secant Function

The signed length of the segment OC is called the secant function, \(\sec\theta\).

Using similar triangles, we see that \(\sec \theta = \dfrac{1}{\cos \theta}\).

The Pythagorean Theorem applied to \(\triangle COB\) shows that \(\tan^2\theta+1=\sec^2 \theta\).

When the tangent function is big, so is the secant function, and when the tangent function is small, so is the secant function. Also \(\sec \theta\) is close to \(\pm 1\) when \(\theta\) is close to the x-axis and when \(\tan \theta\) is close to 0.

The graphs of the two functions look nice together:

Here is a very pretty graph of \(x^y=y^x\) with areas where \(x^y < y^x\) shaded in green and areas where \(x^y > y^x\) shaded in purple.

I am working on an article about some problems related to these equations, including The Biggest Product Problem. There’s a lot of interesting stuff here!

This is a great trigonometry assessment question.   Unfortunately, virtually none of my college students who haven’t used trig for a while can answer it (without a calculator).   For a lot of students, trig is one of those subjects that just didn’t stick very well.

So, we start trig functions all over, but this time with circle definitions and some “trigonometry yoga” (no trademark; I made up the name when I was thinking of a title for this post).

I introduce \((cos\theta,sin\theta)\) as the coordinates of the point on the circumference of a unit circle at angle \(\theta\).    I point out that cosine and sine, like x and y, are in alphabetical order, which is one way to remember which is which.

Everyone stands.

We practice: hands over the head, as high up as they can go, represents 1.   Hands at waist level represents 0.  Hands as low as they can go represents -1.

We start with sine yoga.  Hands start at waist level, 0.  I start at \(\theta\) = 0 degrees and move my finger counter-clockwise around the circle, while the students move their arms up, corresponding to the height of my finger — up to 1, then down to 0, then down to -1, then back to 0.  We go around a few more times.  They make waves.

I ask again, which is bigger, sine of 40\(^{\circ}\) or sine of 50\(^{\circ}\).   Now everyone can easily answer – their hands are moving up from 0 degrees to 90 degrees, obviously sine of 50\(^{\circ}\) is bigger.

We try some cosine yoga.  I start at 0, their hands start up at 1, and then down to 0, down to -1, back up to 0, and back to 1 again.  Cosine yoga is a little trickier, but they catch on easily.   After a few rounds, cosine looks, well, just like sine, except 90 degrees out of synch.

There’s much more trig yoga we can do – go around the circle twice as fast (or three times or half), go backwards, use a smaller circle (a bigger circle requires longer arms or a change of scale), start in different places, or move the furniture and try a yoga dance with students moving across the room at a constant rate as their arms move up and down (get out some paper and convert this last one to a graph!).

I haven’t actually tried all these trig yoga variations, but I’ll try some more next time I teach this topic.

Before the activity, here’s what most of the students remembered about trig functions: SohCahToa – Sine: Opposite over Hypotenuse; Cosine: Adjacent over Hypotenuse; Tangent: Opposite over Adjacent.

Here’s what they could do with this information: Take a right triangle where they know the sides and find the sine, cosine, and tangent.  Or take a right triangle where they know the angles and one side, and find the other two sides.

Here’s what the students who remembered a little more also remembered:  Sine and cosine are waves.   When you’re graphing a wave, you’re supposed to use radians for some reason, and radians have pi in them and there’s a formula for converting degrees to radians.   It’s not so clear what sine waves have to do with the SohCahToa right triangle business.

Students know that answering which is bigger, sine of 40\(^{\circ}\) or 50\(^{\circ}\) should be an easy question, but they haven’t internalized the meaning of trig functions beyond direct application of the memorized mnemonic.

I think the ratio definitions are a big part of the problem.  Opposite and Hypotenuse are two different lengths, and defining sine as their ratio means defining sine as a relationship between two variables.  Developing intuition about definitions involving ratios is much more difficult than developing intuition about one-variable definitions.  Fractions are harder than whole numbers; slopes are harder than distances.

Trigonometry yoga is different from anything my students have seen before, so it’s a way to revisit an old topic without seeming repetitive.   It’s silly and fun. Involving the whole body helps students literally get a feel for the definitions.   Certainly middle school kids could do trigonometry yoga (elementary kids too).   I wonder what it would be like to introduce sine and cosine for the first time this way and to save the SohCahToa for later (or better yet, skip it entirely).

It’s straightforward to derive the triangle definitions of sine and cosine from the circle ones:  dilate the unit circle so it has radius \(r\) (or radius \(h\) if you prefer).  Now the point on the circle at angle \(\theta\) has coordinates \((r cos\theta,r sin\theta)\).

Draw the right triangle with sides parallel to the axes and with hypotenuse the radius at angle \(\theta\), as shown above.   Using this triangle, it’s clear that \(sin\theta\) is equal to Opposite over Hypotenuse, and \(cos \theta\) is equal to Adjacent over Hypotenuse

The above representation shows a vector separated into vertical and horizontal components – another very useful way to look at sine and cosine.

The tangent can be defined as the slope of the line forming angle \(\theta\) with the x-axis, which is another ratio definition, but one that students have at least already seen when they studied slopes.  The tangent can also be defined with a geometric, one-variable definition; see my post, The Tangent is a Tangent!

In his excellent article, Historical Reflections on Teaching Trigonometry, David Bressoud writes that circle trigonometry preceded triangle trigonometry by a thousand years, and it wasn’t until the mid to late 1800’s that schools started emphasizing triangles over circles in teaching trigonometry.   The article discusses the astronomical calculations of chord lengths that motivated the development of circle trigonometry and the calculations of shadow lengths that later motivated the development of triangle trigonometry.   Bressoud advocates introducing trig functions first as lengths of segments in a circle with radius 1, as developed historically before the triangle definitions, and as we do in trigonometry yoga.

So, trigonometry yoga has some historical resonance , although trigonometry predates Cartesian Coordinates by many years, and I don’t think the ancient astronomers who developed it waved their hands up and down to mimic the sine function (but who knows?).

If you try trigonometry yoga with your students, please let me know how it goes.

The handout reinforces that there are a lot of different ways to solve a problem and also that a student’s idea can be worthwhile, even if there are mistakes and the final answer is wrong. It also helps students work on reading mathematics in a format that is friendlier than most text books. The handout includes a variety of representations of the problem.

This is one of those problems that I do every time in the math for teachers sequences, even though some students have seen it in high school (they don’t usually remember it that well). It is a good way to introduce important mathematics — recursive and explicit equations and triangle numbers — that we use throughout the course. It’s an engaging activity that works well. There’s a reason why it’s taught so frequently.

The eye condition – then diagnosed as pink eye, later found to be marginal keratitis — was one in a series of recent and terrifying complications of the Crohn’s disease I’d had for seven years officially, several more unofficially. The light hurt my eyes so much that I’d taken to calling myself “batgirl” and lying on the couch with a blanket over my head during the day; yet the energy of first-day-of-class-need-to-be-completely-on distracted me enough, and these were some of my best first classes ever. I knew most of the students from previous classes, and they jumped into making conjectures, looking for patterns, challenging their classmates. I was in a groove – I paused for just the right lengths of time, asked questions that engaged but did not overwhelm, knew when to talk and when to shut up.

For the second days of each class I triumphantly held up a tiny pink and white bottle of steroid eye drops, proclaimed, “Best. Drug. Ever.,” and taught without the hat and glasses. These classes were also terrific; I couldn’t remember ever starting a semester with four great classes in a row. Even though I was sick, I still had it: Batgirl could teach.

Then I had a day off, and beyond a few necessities, I couldn’t get myself out of bed until two p.m., when I had to leave for an appointment with my gastroenterologist. Dragging myself from the subway to his office, resting every half block or so, it dawned on me that I was really sick.

Long story short: my temperature was 104, my doctor put me in the hospital for what turned out to be ten days, and when I got out I found out that the substitute instructor I’d recommended had been hired to teach my classes until spring break. I’d never missed half a semester because of my illness, and that reality was the last straw that pushed me to agree to major surgery: I decided I’d rather lose my colon than my job. I went on medical leave. I was able to come back as a guest for final presentations, but I did not teach those two courses again.

In the midst of preparation, grading, frantic emails, broken projectors, long meetings, dashes to the copy center, addressing texting in class, and all the tasks that fill the teacher’s day, it’s easy to forget what a privilege it is to teach. Until the body stops cooperating and the privilege is revoked.

Surgery restored my health in a way I no longer had imagined possible: after being sick for years, it was easy to equate feeling better with feeling good. “Better” might have meant, “Only ten bathroom trips today, when I had fifteen yesterday; fell asleep at 8:00, not 6:00,” and one has to be pretty far gone to call that “feeling good.”

I am now on sabbatical, as well as two months into a life of mostly bed rest, due to unfortunately placed stitches from a second surgery to fix a complication from the first. I am not sick, and I have been reflecting on some of the ways – not all of them bad – that having a chronic illness has affected my teaching. I haven’t read much on this topic which surely affects many, many teachers and thus many more students.

No disease is truly glamorous, but mine is especially not – my main symptoms were diarrhea, urgency, and fatigue – nothing anyone wants to put on a poster or talk about over lunch. When I was first sick, I worried about having to run to the bathroom during class, and I worried even more about the one-person bathroom across the hall being in use and not being able to make it to another bathroom in time (several friends suggested I put an “Out of Order” sign on the bathroom door, but my colleagues can rest assured that I never did). Over time I developed coping strategies that mostly worked, until they didn’t.

In many ways, it was a blessing that I finally crashed, although I’ll always be sad that I didn’t get to teach those two classes.

This post is the first in a series. Ideas for future posts include entries about the day-to-day realities of teaching when I was sick all the time, but still able to work; thoughts about how attendance policies and other classroom structures can teach students to ignore their health; a teacher’s take on improving the educational component of doctor’s visits; reflections on my recent, mostly self-directed, mostly online crash course in learning to live with my new plumbing; and finally, how missing class a lot led me to stumble into some effective ways to promote student ownership of their classes and their learning.

If you are so inclined, please leave a comment. At the left, at the end of the sidebar text, there is a link to subscribe to a feed for just these posts and not the more math focused ones (of course, feel free to subscribe to everything if you’re interested in math!).

Next>> A Few Practical Strategies that Helped me Teach with a Chronic Illness

At some point a student or a few students will announce that they are done, and I tell them they aren’t done until everyone’s schedule is filled in. It’s an interesting question to figure out a good number of appointments to give them so that they will get stuck, but not overwhelmed; I usually go for a few more than half the number of students (12 for a class of 20).

Occasionally students are able to make a schedule just by switching around a few appointments, so then I ask them to do it again with a few more time slots, but usually they get stuck enough that they have to start over. I sit near the back to make it clear that students can use the board at will, and usually a few students go up to the board and take the lead; if not, I put the students in small groups to brainstorm, but either way, many students participate.

The first time I taught this activity, I happened to have sixteen students in class, and they broke themselves into two lines and made 8 appointments by shifting one line and writing down the person across from them. Then someone who had used a reform curriculum in high school suggested breaking the problem into a smaller one — a great strategy that doesn’t always work very well for this problem, but works perfectly with 16 students. I saw before they did that they were going to be able to get all 15 appointments that way, and then after they got there (the next class), we looked at using their algorithm with different numbers of people, which related to number theory concepts later int the course.

After that first class, I rushed to the library (it was pre-WWW) to study more about the problem, which in the literature is under round robin tournaments. There is a standard algorithm, which amazingly, a few of my classes have discovered. This algorithm gives a different role for one person, so students are a lot more likely to discover it when there are an odd number of people in the room, and they see my role as distinct.

One of my students said that she had done this activity in elementary school, and that’s where the “Clock Buddies,” name came from; they would meet with, say, their 3:00 buddy to be partners for science on a particular day. She did not recall any conflicts making the schedules (probably fewer appointments).

This activity is particularly rich in representations. Students use a variety of pictures, graphs, tables, and notations to describe their thinking. It’s a great way to introduce the notion of an algorithm in a context that’s totally separate from elementary arithmetic.

Homework after the first class is usually to make a complete schedule of five appointments for six people and to represent it in two different ways (and to extend the problem to eight or ten people if they can). The activity lasts from two to four classes, depending on how engaged students are and what their strategies are, and along the way I can introduce them to the goals of the class and such.

Every class has come up with a good solution to the initial problem. This handout (Doc version, pdf version) illustrates some of the strategies and representations students have used, along with good follow-up questions for each strategy.

When we finish up the problem, especially in a class where many students have gone out of their way to tell me how bad they are at math, I ask a few questions. Was this a hard problem or an easy problem? Clearly it’s hard. Is it math? Clearly yes. Did you solve it or did I solve it? I am careful to hang back on this problem; I only facilitate when there are communication problems, so students own that they solved it. Then I say that they are telling me they’re terrible at math, but I have seen no evidence, as they just solved a hard math problem by themselves.

In order to teach this activity, especially on the first day of class, you have to be very comfortable teaching an open-ended class where students might come up with something you’ve never seen before. I love this style of teaching, and I find that the beginning of the semester adrenaline flow helps make me more present. In a way it’s fool proof, in that it easily gets students talking and moving — worst case scenario they learn names and that the class is active, and that’s not bad for the first day (although they always get further).

Several years ago I worked on a Mathematica simulation to try to decide what is a good number of appointments to assign. There are some assumptions that have to be made to model how the students interact when they are shopping for appointments. My programming skills are not the best, and I moved on to other things, but if someone reading this is a good programmer (or can recruit one) and is interested in working with me on this question, let me know (and if you just want to work on it without me, please let me know what you find).

.

“Premature, general, and indiscriminate lecturing defeats the formation of the very habits on which successful lecturing presumes.”

Abraham Flexner 1908, The American College: A Criticism,” pp 195-196. I learned about Flexner here.
.

“If something is not worth doing, then it’s not worth doing well.”

Sydney J. Harris (this one I copied from a column in the Chicago Sun Times sometime in the 1970′s).
.

“Teach the students you have, not the ones you wish you had.”

(I am not sure who to attribute this quote to; it is very popular in the math ed community).
.

“Be Joyful, though you have considered all the facts”

Wendell Berry, “Manifesto: The Mad Farmer Liberation Front.”
.

“I was going to die, if not sooner then later, whether or not I had ever spoken myself. My silences had not protected me. Your silence will not protect you.”

Audre Lorde, “The Transformation of Silence into Language and Action,” Sister Outsider.
.

“Our strongest gifts are usually those we are barely aware of possessing.”

Parker Palmer, The Courage to Teach.
.

Learn More >>

Attached are 123 multiple-choice questions for the Mathematics Subtest of the Massachusetts Test for Educator Licensure General Curriculum Test (doc version, pdf version).  This is the test for elementary teachers and K-8 special education teachers, test 03; there are separate mathematics tests for elementary math specialists, middle and high school teachers.

I am working on an online interactive version of this test, where you will be able to get hints on questions you miss and get your scores emailed to you.

Please contact me if you find a mistake on the test. Instructors, feel free to use them or modify them for your students; see terms of use.

For more of my thoughts on this test, see this post.