Want Some Free Red Pens?

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I’m about 75% through this round of midterm exam grading. Overall, I’m down to around 100 students in total, over three classes. I’ll give four midterm exams and a final exam at the end of the semester. This requires a lot of red ink.

A while ago, I read an inspiring article in the MAA FOCUS called “Abandon the Red Pen!” written by Maria H. Andersen. The article was about digital grading. Since I read it, digital grading has been a dream of mine. Ideally, here’s what I’d like to do with the pile of exams currently sitting on my dining room table:

  1. Students take exams in class, on paper, like usual.
  2. After students turn in exams, magic happens. I end up having a PDF file of each individual exam paper, titled something like “StudentLastName-Calculus-Exam2.pdf”
  3. I dump all of the PDF files into a Dropbox folder and then I do all of the exam grading on my iPad.
  4. Once I’m done, I save each file as “StudentLastName-Calculus-Exam2Graded.pdf” and then more magic happens, and each student gains access to their graded exam — perhaps over e-mail, or through the file server in our Learning Management System, or some other solution.

Overlooking the requisite magic requirements, let me explain why I’d prefer this to offline grading:

  • I wouldn’t have to carry 100 exams home, keep them away from my toddler, make sure I don’t lose any to black hole of my desk, try to avoid spilling coffee on them, etc.
  • I would have a complete digital record of a student’s work. Occasionally a student comes to me at the end of the course and says, “I just checked the online gradebook. It says I earned grade X%, but I am certain I earned grade (X+4)%.” Sometimes they are able to produce the test paper and the gradebook indeed has an error. Sometimes they aren’t able to produce the test paper, and I can’t do anything for the student. Having a digital PDF file of every graded exam would solve this issue immediately.
  • In the unfortunate case of dishonest work, I would have a clear record. (For instance, if a student modifies their test paper after it is graded and returned, and then asks for more credit on a problem. This has happened in the past.)

But the most important reason I’d love to switch to digital exam grading is that I could give better comments in less time. On the current test, all students had to solve a similar “Optimization” problem involving having a constrained amount of fencing to build a backyard of area A. For the most part, students fell into one of three categories: (A) Response entirely correct; (B) Response entirely incorrect or missing or blank; or (C) Response partially correct, but some errors were made. In category (C), there were only about three types of errors: That is, everyone who made a mistake made one of the same three mistakes.

Digital grading would allow me to type up a full response as to what the error was, why it was not correct, and how to fix it. I would only have to type the response once. I could save it as a JPG file. Then whenever a student made that particular error, I could just “drag and drop” the response onto their test paper.

Also, eventually I’d have JPG stamps for the big “Top 100 Algebra Errors”, things like sqrt(9+16) is not the same as sqrt(9)+sqrt(16). I would never have to write anything about this mistake again because I could just drag and drop the explanation JPG!

Now, the tricky part: How do I get the magic to happen? The photocopy machine in my department is quite happy to take 8 pages, scan them to a PDF, and e-mail them to me. So, for a particular student’s exam, I could undo the staple, run it through the copy machine, and I’d be done. Unfortunately, I don’t know how to do this en masse very efficiently.

Suppose I have 100 exam papers, each 8-10 pages. How do I remove all of the staples, run each one through the copy machine individually, and rename the files? This process seems very easy, but I estimate it would take about a minute per exam. At this point, I’d rather spend 100 minutes doing the grading than 100 minutes dealing with the paper shuffle. Hence I need magical elves. Or graduate students.

Since I haven’t figured out how to do this first step, I haven’t given much thought as to how to “hand back” the graded files. I’m sure there’s probably some easy way to do this in our LMS, so maybe it wouldn’t even require magic.

Do you have any ideas about how to do the first step (i.e., scan each individual exam paper to PDF) that doesn’t require magic, graduate students, or administrative assistants? I’m happy to send you all my red pens in trade for such information.

LaTeX and the iPad

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I’ve been lecturing on my iPad for a little over a year now. If you’d like some information about which apps I use during my class, check out my previous blog post on that topic. One of the projects I’ve been working on this semester is converting my lecture notes into LaTeX. This has been a time-consuming task; my Precalculus notes, for instance, compiled to over 150 typed pages.

Here’s a current version of my lecture notes for Stewart’s calculus book on “The Chain Rule”: https://www.dropbox.com/s/j12ie3tnooluiyd/120-ch3s04.pdf (This is what my students will print and bring to class. I project the blank PDF and write on my iPad with a stylus.)

One of the things I was interested in having was a way to create, edit, and compile LaTeX documents on the iPad itself. Our “Teaching, Learning, and Technology” division offers mini-grants for technology-related things that cost a small amount of money ($5-$200). Last semester I applied for and received a grant for an iPad keyboard ($85) and an app called TexWriter ($8.99).

I like the Logitech keyboard. I haven’t had any problems getting it to find its Bluetooth connection to my iPad. There are only two minor annoyances when it comes to writing in LaTeX with this keyboard: (1) The “Backspace” key is really tiny, and (2) the smallest key on the keyboard is “\”, practically the most commonly used non-letter key in any LaTeX document. Here’s a photograph of the keyboard to see what I mean:

In my office, I have used the collaborative, online LaTeX editor writeLaTeX (https://www.writelatex.com/) on my computer. One of the great things about it is that it automatically saves your document to the cloud, meaning it is easily accessible from anything with a live internet connection (like my iPad). It compiles fairly quickly and easily and doesn’t require downloading any software. Screenshot:

But it does need an internet connection. Since my iPad is only a “WiFi” model, there are lots of times I would like to be working when I might not have internet access (like on an airplane trip). Also, the site seems a bit touchy when it comes to my iPad keyboard. For instance, I couldn’t figure out a way to use the “Copy and Paste” iPad commands, and I had some difficulties with the keyboard’s arrow keys when it came to navigating documents.

Meanwhile, TeXWriter seems to work fine with my iPad keyboard. The files sync with Dropbox, although not as smoothly as other apps I’ve used. Files created in TeXWriter are synced to a particular Dropbox folder (something like Dropbox/Apps/TeXWriter/index/) and there isn’t an easy way to put this file in one folder and the next file in a different folder. Here’s what TeXWriter looks like:

 

So, in the end, I can’t give a glowing review of either LaTeX-on-iPad solution I’ve found. I had troubles compiling on both TeXWriter and writeLaTeX, probably because I was using lots of packages (tikz, multicol, fancybox, hyperref, …) and didn’t take the time to set either account up properly. In the end, it was just much faster to return to my comfortable office and WinEdt setup.

The time I did use TeXWriter for over an hour (give or take) was during some exam proctoring. I could edit a Dropbox-stored LaTeX document between laps around the classroom. I’m not sure I’d fork over $10 for the app, but it is useful.

It would be lovely if I could try out the other LaTeX apps in the iTunes store before making a purchase. This is the type of application that you really need to have a trial period to see if it will function the way you want! Several of the other LaTeX apps are “expensive” — given that I’m accustomed to most apps being $0.99, thinking about purchasing a $5.99 app “on a whim” seems like a giant financial investment!

Do you know of any great LaTeX/iPad solutions? I’d love to know about them.

Other Sources, Same Ideas

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Two interesting links crossed my digital landscape today. One contained the link to the infographic below, found originally at http://www.citytowninfo.com/infographics/women-in-science. TItle: Under the Microscope: Women in Science: The challenges and opportunities for women interested in scientific careers. At the bottom of the infographic, the question “How can we continue to attract more women to science careers?” They highlight three key points, two of which I pointed out in my post yesterday on Gender & Mathematics:

  • Create tenure policies that provide flexibility for parental leave. I would extend this to all of the college and university instructorship, not just the tenure-track lines. There are lots of female scientists who, like me, have devoted their careers to postsecondary teaching and scholarship who are not in tenure-track jobs and who are not looking for a tenure-track appointment.
  • Provide support for the work-life balance. One response I’ve received about my post yesterday is that it isn’t just mathematics or science or academia that needs better accountability for the work-life balance problem. This is clearly true and it was never my argument that every other career path is daffodils for working parents. Nevertheless, this argument amounts to, “Well, other careers can also be miserable for parents and families, so there’s really no reason for us to work to have better policies in academia.” It seems obvious that everyone should have family-friendly, people-friendly, parent-friendly policies at their workplace, no?

The second link that caught my attention was an article posted by the Center for Excellence in Education. Their stated goal is as follows:

The Center’s mission is to nurture high school and university scholars to careers of excellence and leadership in science, technology, engineering and mathematics, and to encourage collaboration between and among leaders in the global community.

The article they posted today was titled “How to Create an Undergraduate Physics Program in Which Women Can Excel.” It was written by Janice Hudgings, Physics Department Chair and Associate Dean of Faculty, Mount Holyoke College. The entire article is certainly worth reading to anyone invested in undergraduate degree programs in science and who wonders about how to attract more women to STEM careers. The following is one of Hudgings’s suggestions [emphasis mine]:

All faculty in the department should be committed teachers, using active teaching and learning techniques.  Replace the dry, boring lectures with classrooms full of students who are arguing in small groups, gesturing, laughing, and actively engaging with physics.

This is precisely the point I made yesterday: Our lecture-based classrooms select for students who are great at learning from a lecture. Those students become our majors, and the best of those we mold into the future crop of graduate students, and then some of those go on to become our professorship. And we end up with generation after generation of professors who learned via lecture, who teach via lecture, and who wonder why there’s a need to do anything differently. I’m an active proponent of a classroom that looks different from that tradition, not just because I think it would benefit a particular subgroup of students, but because I think it would benefit all of our students. We need students who are actively engaged with the material — both in and outside of the classroom.

I’ve heard the argument made, by people who have very good intentions, that they would love to have more female and minority math majors, but those types of people just aren’t as interested in the subject. As Hudgings points out,

It can be very difficult for underrepresented groups of students, including women, students of color, community college transfer students, and low income students among others, to hear even heartfelt messages of belonging against a broader societal backdrop that is saying the opposite.

This has certainly been my experience. While in many, many cases I’ve felt nothing but welcomed, I do notice that I’m in a minority group. In departmental meetings, it’s easy to count that there are over 30 attendees (but only six women). The small percentage of female math professors has been obvious in every math department I’ve visited, over many years, in many places. Since I know that women can and do excel in mathematics, the lack of women among the math professoriate makes me wonder where they all went. In 2007-2008, 27% of new doctorates in mathematics and computer science went to women. Yet I don’t think I’ve come across a math department where 27% of the tenured faculty members are women. (And I don’t think this is all explained by the “trickle upward” time.)

Where are the women going? When I noticed this discrepancy as an undergraduate student and as a graduate student, I wondered why there weren’t more female tenured math professors. The “brain drain of women from STEM careers”  has been a hot topic of recent research. See “Technical fault: The worrying brain drain of women from science and technology” or the Harvard Business Review’s “The Athena Factor: Reversing the Brain Drain in Science, Engineering, and Technology” or 24000 other scholarly articles. As Hudgings concludes,

But strong academics must be combined with a student-friendly department environment that reinforces a message of “you are welcome here.”  That message can be difficult for women to hear against a broader cultural backdrop of discouragement, so it must be repeated over and over.

Hudgings offers a number of suggestions for specific things a department could do, apart from the obvious one of making sure the faculty is diverse. I’d love to see my own department implement several of her suggestions.

Women in Science: Under the Microscope

Courtesy of: Citytowninfo.com

Gender and Mathematics

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This morning’s New York Times had a headline reading: “Girls Lead in Science Exam, but Not in the United States.” The article started with a rather fascinating graph showing country-by-country performance on the OECD test with a display of the percentage gap between male and female students. In the United States, the average scores were 509 for males and 495 for females; thus the males outperformed females by 14 points, or around 2.7%. Compare this with Japan’s data: Average scores of 534 for males and 545 for females gave the girls about a 2% lead.

Both the graph and accompany article interested me enough that a printed copy can now be found on my office door, along with my own editorial remark at the top. (See photographic proof.)

I found the Times article through my Twitter feed. Other interesting articles that hit my feed were a blog post by Hariett Hall (“Gender Differences and Why They Don’t Matter So Much“) and a 2005 article from Time magazine on “The Iceland Exception: A Land Where Girls Rule in Math.” [Michael Shermer linked to Hall’s article, and I shared the link about to the Iceland article.]

After I posted the Iceland article, John Wilson (@jwilson1812) asked for my opinions “about what this report from Iceland might suggest, what’s generalizable, what isn’t, and so on.” In this post I’m hoping to capture a longer response than what 140-characters would allow.

1. The United States has a gender discrepancy problem in mathematics.
To me, this point seems somewhat obvious. But given the headline from Hall’s article, and other comments, conversations, and feedback I’ve received over the last decade or two, it also seems clear that it isn’t obvious to everyone. I mean “problem” in the above statement as in, “Something we ought to be concerned with pondering and understanding, and (if possible) fixing.”

2. A partial fix could be fixing the educational and employment climate.
As the Times article points out,

Researchers say cultural forces keeping girls away from scientific careers are strong in the United States, Britain and Canada.

Hall’s article points out that men and women are different, and that their skills, interests, and aptitudes are shaped both by biology and by culture. Talking about how biological differences may (or may not) influence mathematical aptitude gets murky very quickly, and I am certainly not qualified to say anything one way or the other. On the other hand, talking about how cultural differences influence mathematical aptitude is a conversation we ought to have frequently.

3. How can we fix the problem?
The real answer to this question is, “I don’t know.” But I have a lot of hunches.

Hunch #1: We need more collaborative classrooms.
Somewhere a long time ago I read about a study done on middle school aged children playing soccer during recess or physical education classes. The students were separated by gender. In each group, researchers looked at what happened if a soccer player were injured during the game. With the boys’ game, an injury momentarily paused play; a spectator was swapped for the missing team member; the game quickly resumed. With the girls’ game, an injury stopped play. The girls (on both teams) decided they’d rather not play without their injured friend on the field, and so they took up to doing another activity altogether.

I think this parable fits with how I picture what happens in math classrooms. While I’ve taken lots and lots of math classes, I was never able to take a class that would fit any description other than “traditional, chalk-talk, lecture-style, definition-theorem-proof.” The math classes I saw as a student were like the boys’ soccer game: If one student fell behind, or got confused, or failed at mastering a concept, the class would pause, remove the “injured” participant, and continue moving forward. The aim of the class was the soccer game itself and not who was playing and who wasn’t. In my experiences, math classrooms are places where students practice an individual sport (like tennis) concurrently. They are not places of collaboration or conversation or team work. The coach is interested in keeping the game moving forward (even if dropping players is necessary).

I think this is bad for a few reasons. But the top reason is that I think it gives everyone (both women and men) the false impression that mathematics is an individual sport where the performance of the athlete is a solo endeavor. But real mathematics is nothing like this. As mathematicians, collaboration is essential. We publish papers together. We give weekly colloquium addresses to teach each other new ideas and to solicit help on tough problems. We travel to conferences to have conversations with others and work through problems as a team. Why do our classrooms give the opposite impression of how mathematics is done?

Showing the world (and girls especially) that mathematics is not done in isolation is crucial. I believe that marketing mathematics as a collaborative, socially-based adventure would attract more girls to become mathematicians and scientists of all types.

Hunch #2: Attract, hire, and retain more female math professors.
I did my undergraduate work at U.C. San Diego where I was a “Pure Mathematics” major. At the time I was there (early 2000s), the department had about 55 full-time tenured math faculty members. Of those, 5 were female. [See their department directory today for comparison.] One of the women professors mentioned that, at the time, among the “Top 25” math departments, U.C.S.D. had the highest percentage of tenured female math professors. What percent is 5/55? About 9%. This statistic was quoted with pride: “We are so great to have so many women! Among the math professors, only 90% of them are male here! Fantastic job!”

I think our cultural conception of what “Mathematics Professor” looks like needs to change. Yes, there are plenty of math professors I know who fit the stereotype exactly. But then there are those who look like me. The way we shift the stereotype is to disprove it. We need more minority math professors, we need more female math professors, we need more math professors who aren’t 60-year-old white males with chalk dust on their pants.

On keeping women in science: One thing obviously in need of repair in academics is promoting careers that allow for a work-life balance. Right now, I am expecting my second child. When I complained recently to colleagues about the “Leave Policy for New Faculty Parents,” one responded, “Well, when each of my five children were born, I was back at work the next week.”

I wish I could say this were not the norm. But it reminded me of a conversation I had 10+ years ago, when one of the women faculty at U.C.S.D. told me about giving birth on Thursday and being back teaching classes the following Monday.

I love my job, I love my co-workers, I love my students, I love being in the classroom. But my employer’s Leave Policy, combined with the remarkable and surprising lack of empathy from colleagues about said Leave Policy, has certainly made me consider jumping ship. Academia needs to wake up and offer a family-friendly, parent-friendly work environment where people are valued for being people first (and professors second).

Hunch #3: We need to teach teachers differently.
As an educator, it’s difficult to structure one’s classroom in a way dramatically different from the one you were in as a student. You think back, “How was I taught this idea?” and that’s the easiest answer to, “How will I teach this idea to my own students?” You can see this all over the math community as the traditional, blackboard-based, definition-theorem-proof machine chugs chugs chugs along. Thankfully, there’s been a giant movement in recent years toward changing the idea of what a classroom should look like. (See my earlier ideas about collaboration.)

Given that we are all inclined to teach the way we were taught, and given that for a very long time it was accepted dogma that boys always outperform girls in mathematics, it’s easy to see how this idea could still linger. Not that I think any particular person goes into their calculus classroom and says, “Sorry ladies, everyone knows you don’t have the skills to be really good at this.” But I do think (and I have seen ways) that this underlying stereotype has affected the way people teach.

My Conclusions
1. The gender imbalance in mathematics has some cultural factors.
2. We ought to be concerned with what those factors are, and how to change them.
3. Changing them is a process that will definitely take a lot of time and probably take a lot of money.
4. My best strategy at overcoming this problem is this: Become a female math prof who posts blog articles about the gender imbalance in mathematics. Unfortunately, this strategy is probably not widely implementable. It definitely takes a lot of time. An easier thing to do is to support and encourage those who are doing this or things similar to it.
5. My next best strategy for overcoming the problem is: Seek out like-minded people and work together to figure out how we can change the math culture. 

As I said at the beginning of this, I know there is a problem and I don’t know it’s solution. But I’d be happy to hear what you think it might be.

Student Assessment of Learning Gains

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The College of Charleston has recently moved to a paperless, online-only course instruction evaluation system. The obvious benefit of the new system is that instructors are not required to use class time for student evaluations, and no students are required to shuffle sealed envelopes from one building to another once the evaluations are complete. I’m a big proponent of technology-enhanced learning and while I appreciate the time (and environmental) savings of the new system, I find myself frustrated with it. One problem is that every semester, there are problems with a very low response rate. Any of our Math 104 (“Elementary Statistics”) students can tell you about the issues with a voluntary response sample.

But the low response rate isn’t my main problem with the evaluations. In an ideal world, the course evaluations would provide statistically meaningful data that is useful in helping me guide course design, structure, and content. Unfortunately, the evaluations don’t do this. For example, one question asks students to rate (using a Likert scale) the statement, “The instructor showed enthusiasm for teaching the subject.” Yes, I am enthusiastic in my classroom (both about teaching and about mathematics), and I am happy that my students notice and enjoy my enthusiasm. But this doesn’t help me teach the course better. I would prefer student feedback on statements like, “In this course I learned to work cooperatively with my peers to learn mathematical concepts.”

Overall, my issue with the evaluations is that the questions posed are teacher-centered instead of learner-centered. Example: Rate the statement “Overall this instructor is an effective teacher.” This statement removes the student’s responsibility for their own learning. Compare with the following: Rate the statement “Overall in this course I developed skills as an effective learner.” The biggest goal I have in a mathematics course is to provide students with problem solving skills that they can use beyond my classroom. If a professor often gives a fantastic lecture, then that’s great; but that may not be helpful to students five years from now. Instead I hope to give students skills, practice, and experience in critical thinking, problem solving, complex reasoning, etc. Rating whether or not they’ve learned these skills is more important than rating “Overall, the required textbook was useful.”

Of course, figuring out how students have grown academically or intellectually is difficult. In this semester’s Precalculus classes, I’m working together with another instructor on designing course content. One of the things we decided to do was to use something similar to the Student Assessment of their Learning Gains (SALG) tool in an attempt to gather data on student progress through the course. Initially, the students are asked to take a benchmark SALG survey and they will repeat a similar survey two to three times throughout this semester. We are hoping to gather meaningful data on the growth of their skills by tracking things like whether they are in the habit of “using systematic reasoning in the approach to problems” or “using a critical approach to analyze arguments in daily life.” Hopefully this data will prove useful as we continue to tweak the course moving forward.

Making Twitter Useful at Work

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Following the FTI last May, I focused my Twitter account on feeds relevant to my professional life. I am still trying to figure out exactly what “professional” in this context means — right now, basically it means, “Stuff I like reading on Twitter while I’m at work.” Here are some “people” I follow:

But the most useful part of Twitter has been connecting with other math professors and math educators. I’ve found out about really fantastic resources from them, and I have no idea how I’d ever learn about things without them.

Great things I learned about via Twitter:

  1. The open-source graphing plotter “Graph”: http://www.padowan.dk/
  2. This open-source, free, activity-based calculus book: http://opencalculus.wordpress.com/
  3. How to do Origami in Geogebra: http://www.geogebratube.org/material/show/id/883
  4. Why we need more women math majors: http://kinlin.com/blog/2012/09/why-we-need-more-women-math-majors/
  5. The Wolfram|Alpha Chrome extension: http://wolframalpha.tumblr.com/post/33907023300/download-the-wolfram-alpha-chrome-extension
  6. The QAMA Calculator that now sits on my desk: http://qamacalculator.com/
  7. Everything written in Casting Out 9s is fantastic: http://chronicle.com/blognetwork/castingoutnines/
  8. GVSU’s Screencast channel: http://www.youtube.com/user/GVSUmath/videos?view=1

IBL Self Check

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“Assessing your own teaching is significantly important.  A trait of an effective teacher is one, who is reflective and assessing oneself continuously.”  – Stan Yoshinobu

I found a great list of “IBL Self Check” questions for course and instructor [self-] evaluation here: http://theiblblog.blogspot.com/2012/11/ibl-self-check.html Now I’ll go through them and see where my courses stand.

1. Are student presenting/sharing ideas in class regularly? Can this be done more often in a way that benefits students?

By the end of the semester, my students will have had lots of practice working in groups. At the start of the semester, I was very focused on having at least one group problem every class. Now that has fallen off quite a bit — partly, I think, because the problems themselves have gotten longer so we haven’t had as much time at the end of class as we used to. Each course will have had eight Lab assignments — weekly, group-based problems. I need to get better about grading them and returning them faster. (Turn around time has been ~1 week.)

2. What percent of time is devoted to student-centered activities?

My classes meet for a total of 225 minutes. About 90 of these have been for labs and end-of-class group problems. So 40%. Not bad!

3. Are students deeply engaged in the tasks you have given them?  Can your problems/tasks be improved?

Sometimes yes, sometimes no. In December, I want to go back and make up a “Top Ten” list of topics students struggle with — maybe using final exam data — and see if I can change the Labs to more closely reflect those topics.

4. How many times per class period are you being supportive by giving encouragement, positive feedback, coaching, adjusting tasks to meet the needs of your students? and 5. Can you give more positive feedback?

This is tough. With a full classroom of 40 students, I don’t know how to “check in” with twelve or thirteen groups of students, especially in a very short (~8 minute) window.

6. Can you improve the problems/tasks given to students?  Are the problems too procedural in nature? Are there good concept questions?  Are the problems too difficult?

I need to look at this in December.

 

My Courses and the Levels of IBL

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I have six days of teaching left this year. I have finished the last round of midterm exam grading. Committees are meeting to talk about writing the common final examinations. At this point in the semester, I always take a look at grade data and try to figure out, “How can I do better next semester?” I’m hoping to write a few blog posts trying to figure this out. Here goes the first!

Current courses: Calculus 1 (using Stewart’s Early Transcendetal calculus book) and Precalculus. [Our Precalculus course has College Algebra as its prerequsite.]

Current course structure: Four in-class exams (75 minutes each). Two online homework assignments per week. Three lectures per week (40 minutes each) and one “Lab” day per week (75 minutes). On lecture days, end class with 5-10 minutes of “group problems” to have students think, discuss, and digest the day’s topic.

Bret Benesh (or @bretbenesh) provided a great link to Stan Yoshinobu’s post about “the Levels of IBL.” It seems my class fits into Level 2:

The instructor lectures for most of the time, but intersperses some interactive engagement, where students are asked questions and given mathematical tasks that require thinking and making sense, such as “Think Pair Share”.  Interactive engagement may take up a few minutes to anywhere up to approximately a third of class time, which may vary day-to-day or be based on weeks (e.g. lecture MW, problems on F). A key feature is that lectures remain a significant component of the teaching system.  The instructor is the primary mathematical authority and validator of correctness.

Overall, I’m relatively comfortable with this level. It’s hard for me to picture how I could move to “Level 3” and lecture only 1/3 to 1/2 of the class time. My major concern is the time investment it would take. Maybe eventually I could move in this direction, but probably not before next semester.

Conclusion: I’ll plan to stay at “Level 2” for the time being, until I can iron out some issues and have more time to create (or find) more content for my students.

Faculty Technology Institute Homework

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Last May, I participated in the “Faculty Technology Institute” run by the Teaching, Learning, and Technology (TLT) department. We spent a week during summer learning about the “Hows and Whys” of using technology in teaching and research. Along with a stipend, the FTI supplied each participant with an iPad-3. By participating in the FTI, we were required to make a “1-1-1 Committment”:

The 1-1-1 Commitment:
Faculty agree to employ at least one (1) tool and/or strategy introduced in the 2011 Summer FTI into at least one (1) courses or research within one (1) year of completion of the FTI.

Faculty can report on the results in the form of a scholarly paper, series of blog posts, or a self-contained digital presentation, such as a video or a slideshow with voice-over.  The projects will be posted on the TLT blog and shared with the campus community.

I plan to write several more blog postings about my course changes since the FTI, and I’ll try to keep a running list here along with permalinks.

 

Rational Power Functions

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One of the topics our PreCalculus syllabus (Math 111) covers is “Rational Power Functions.” Since functions like f(x)=x^n are called power functions, the rational power functions would be those of the form f(x)= x^{p/q} (where p/q \in \mathbb{Q} ). Unfortunately, this topic isn’t covered in our textbook (Zill’s “Essentials of Precalculus with Calculus Previews“).

Tom Kunkle, on his Math111 Homepage, provides his students a nice summary of how these functions behave: See ratpowfunc.pdf. When thinking about this week’s Lab Assignment, my goal was to give students practice on drawing graphs of functions like

y = -(x-5)^{4/3}+1
Lab Description
I created nine cards, which I’m calling “Function Cards.” Each card is a half-page (printed on heavy-duty card stock). On one side, the card has a Graph of some translated rational power function. On the other side, the card has an Equation of a translated rational power function. However, the equation and the graph are not the same function!

Here are the directions I provided to students:

  1. When you get your Function Card, flip it to the Equation side. Make a note of the card number. Write down the equation.
  2. As a group, work together to sketch a graph of the equation. You may use the Rational Power Function handout (if you like). You may NOT use a calculator. Work together! Your sketch should clearly display & label all intercepts, any cusp points, any vertical asymptotes, any locations where the tangent line is vertical, and the parent function.
  3. Once your group has agreed upon what you think the graph looks like, draw your sketch on the Answer Sheet, along with the information listed in Step 2. Then go around to the other groups. Find the Function Card with the graph that matches your sketch. Ask nicely, then take it from that group.
  4. Return to Step 1.

The students will have the entire class period to create graphs of each of the nine Functions. Since they will track down the graph most closely matching theirs, they will have a chance to check their answers. Even once they see the answer (i.e., the graph), they are still asked to do some thinking since they have to provide information about the graph’s important features.

Hopefully this process will work. The only thing that concerns me is how long it will take them. I am really terrible at gauging how long it takes students to think about things. My best guess was that it would take about 4 minutes to sketch a quick graph, and then another 3 minutes to write down its important features. So, (7 minutes)x(9 Function Cards) should be a little over an hour.

I picked the nine functions from Tom’s “Homework Handout” on this Section, available here. If the weather complies, maybe we can do this activity outside. The only thing better than math class is math class in the sunshine.