Category Archives: Teaching

Friendship Policy

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I have my first course meetings this morning. Right now I’m enjoying a one-hour break between classes in what will become my Office Hours once students figure out what Office Hours are for. I thought I’d take the time to write about an important topic I covered during today’s PreCalculus class.

A Very Important Course Policy:

One of the notable policies I have on my syllabus is called my Friendship Policy: Students in my courses are required to make two friends from class. For those of you who, like me, haven’t been a college student in a number of years, this policy may seem very silly and totally unnecessary! However, the policy has an important function at fixing a “problem” I noticed a few semesters ago.

Before class, I would find students sitting on benches in the hallway for several minutes waiting for the previous class to end. There would be, say, ten or twelve students all from the same course, standing in the same hallway, and it was library silent. No person was talking to any other person! Instead, every single one of them was texting someone on their phone, checking Facebook on their iPad, playing a game on their laptop, etc. Eventually they would all enter the same classroom and continue their technologically dependent anti-social activities.

When I pointed this out to my students, they had never noticed this phenomenon and they didn’t understand why I thought it was weird!

“Back in my day,” says the professor…

There were no cell phones. In order to fill the awkward silence, students in my classes would talk to each other, real-time, face-to-face. Sure, we would talk about course-related things like homework or exam studying, but we would also talk about social activities or sporting events or movies or whatever. This is how we made new friends.

I realize that students in my class have lots of friends. (Otherwise, who would they be constantly texting?) But I still have not figured out how they make new friends. Hence the birth of my Friendship Policy:

Friendship Policy:

You are required to make friends with students in this class. If you are absent from class, your friends will be very happy to lend you their notes to copy! In fact, I think cooperative learning is so important I am going to leave blank space on this syllabus for you to write down the names of two of your class friends and their contact information.

After explaining all this to the students, they usually look at me with confused faces until I say something along the lines of, “Friendship Time: Commence!” and then stare at my wristwatch expectantly. Within seconds, the room explodes in conversation. Occasionally, I have to nudge some of the shy students in the right direction.

Results and Analysis

After several classes over several semesters, this policy seems to make a big difference. First, no one sits before class in techno-quiet. They talk to each other, get to know each other, and occasionally I have caught them teaching each other how to do math problems. Second, I no longer get e-mails asking, “What did you cover in class yesterday?” Third, I learn a lot from my students by participating in before class conversations. For example, in this morning’s class, one student is here on a golf scholarship from Sweden! (How awesome is that!)

I still have two more classes this morning. We’ll see how those groups take to forced friendship-making time.

Project Based Learning

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Our classes for the Fall 2012 semester start today. Thankfully, my teaching schedule doesn’t include Tuesdays, so I don’t start until tomorrow! I’m hoping to use Tuesdays this semester to work on several other projects, including adding more blog postings. Wish me luck.

This semester I’ll be teaching two sections (Section 05 and 17) of our Pre-Calculus class (Math 111) and one section (Section 05) of our Calculus I class (Math 120). Each class meets for 50-minutes per day on Mondays, Wednesdays, and Fridays, and an additional 75-minutes on Thursdays. The longer meetings on Thursdays will be useful in my current quest to incorporate Project Based Learning (“PBL”) into my classes.

I’ve begun the task of designing “Lab assignments” for students to work on, in small groups, during our Thursday meetings. Ideally they would be assignments that require no pre-lecture and ask the students to draw from their course content knowledge to form connections between ideas. By working together in a group, the students could collaborate (hopefully allowing for some peer instruction), ask questions, have a discussion, and digest what we’ve talked about during our other class meetings. According to my calendar, the students will have ten lab assignments over the course of the semester.

Yesterday I began working on the third lab assignment for Calculus. The topics covered earlier that week will be limits at infinity; asymptotic behavior; and continuity. I found an activity called “Carousel Game” from the NCTM‘s Illuminations series and modified it for my class. Here’s a brief overview of this lab:

  • Topic: Graphing rational functions
  • Goal: To correctly determine the equation that corresponds to the problem situation or graph
  • Technology Required: None allowed!
  • Warm-up: Vocabulary assessment, including: asymptote,  rational function, exponential function, end behavior, domain, range
  • Activity: Students will use a description or a graph to find the equation for twelve functions
  • Assessment: After finding the functions, students will find domain, range, vertical asymptotes, horizontal asymptotes, and all intercepts. This will be turned in and graded.

I also uploaded a copy of the lab instructions to my public Dropbox. If you are interested in seeing the entire lab, check it out here: http://dl.dropbox.com/u/59433434/120-Lab2.pdf. (Notice that it’s 120-Lab2, even though I mentioned before it is really our third lab — I start numbering things with zero.)

I’m hoping to reuse this activity in Pre-Calculus later in the semester, once we cover material about rational functions.

Wordle

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Earlier today, Derek Bruff (@derekbruff) tweeted a link to a Wordle done by graduate student Jessica Riviere. Jessica blogged about her Wordle, so check out this link for what she had to say. Her Wordle contained data from her teaching evaluations and what her students had commented. This was clever and fun and it inspired me to make one as well.

I used my course evaluations done by College of Charleston students during the last academic year (Fall 2011 through Summer 2012). Altogether I have data from eight courses (covering several sections of Elementary Statistics, Pre-Calculus, and Linear Algebra) for a total of 114 evaluations. To make the data collection easier, I restricted my focus just to the “Comments on Instructor” and “Comments on Teaching” prompts. This meant ignoring data from sections called comments on “Organization,” “Assignments,” “Grading,” “Learning,” and “Course.”

The most frequently used words were: and, the, to, I, is, she, a, class, was, of, her, Owens, with, Dr. Several of these were removed by Wordle since I had chosen to “Remove common English words.”  I also removed my first name and corrected some misspellings (ex: “explaiend” to “explained”). I enjoyed the following word counts: awesome, 6; funny, 5; humor, 5; and enthusiastic, 9.

Wordle: Eval Cloud

E-Seminar on “Mathematics Teaching and Learning”

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In a previous post, I wrote about finding an E-Seminar from the NCTM (National Council of Teachers of Mathematics). A full list of available topics can be found here. One of them I mentioned before is called “Mathematics Teaching and Student Learning: What Does the Research Say?” Check out the description on their webpage. Today was our first day in my summer SMFT course. Since the students are all in-service math teachers I thought they would benefit from watching the seminar. I hope that they got something out of it, especially considering that it took up around 75-minutes of our limited class time. Here are the top three take-home messages I got from the re-watch:

  1. The idea that teaching is a cultural activity. In other words, we all learn how to teach in a process of cultural immersion during our school years. We get some ideas about what a classroom is “supposed” to look like, what a teacher is “supposed” to be doing during class, and what students are expected to do. Many educators are not taught effective teaching methods and it is easy to revert to teaching how we were taught instead of how we would like to teach (or, how the research says we ought to teach).
  2. The idea that effective teaching is learned. It is not an “innate talent” and it requires a lot of “hard, relentless work.” This is a freeing idea since it allows us to ask questions like, “How do I learn to become a better teacher?” and “What is effective teaching, anyway?”
  3. The idea that improving teaching is a process instead of a goal. Instead of focusing on a large (unattainable?) goal of becoming an effective teacher, instead we can aim for a concrete, step-by-step process of making tiny changes in our classrooms over a long period of time. The seminar suggests to begin “by designing a few lessons with great care” — maybe even just one or two — and after implementation, then gather evidence on the lesson’s effectiveness. A lot of important work should take place after the lesson is introduced when we can consider how to improve it next time.
With these things in mind, one of the major assignments in my SMFT course this summer is for my students to engage in this third item: They are each required to create two lessons for use in their own classrooms. Although they teach for hundreds of hours per year, by focusing a lot of energy and attention on just one or two lessons I hope that they begin to make those small changes. In the meantime, I hope to change the culture of our classroom and move away from being the “Lecturing Professor” character.

Microsoft Mathematics Add-In

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Apologia
I have a confession to make: All of my teaching documents are created in MS Word. Among professional mathematicians, this is heresy. Don’t get me wrong, I know and love and appreciate all the features of LaTeX. In fact, in graduate school, I took my laptop with me to classes and took lecture notes “real-time” in LaTeX, keeping a running, self-updating Index, Table of Contents, and Bibliography.

I even really like writing in LaTeX, I like coding graphics and figures in TikZ, and for a while my favorite hobby was writing the LaTeX code for a great out-of-print book called Algebras, Lattices, and Varieties:Vol I (by McKenzie, McNulty, Taylor, ISBN 0534076513). In fact, you can see the PDF output of my efforts on Ralph Freese‘s course homepage for his universal algebra class. So for stuff I want to look really “pretty” (like the paper I published or my PhD dissertation), I’m down with all the LaTeX fans.

The problem is that I generate a lot of teaching documents. I provide my students with complete lecture notes for my courses, and as they will happily complain, they end up with a three-inch binder of printed materials. So I need something that I can quickly create and edit from a variety of places. Getting WinEdt installed with all the LaTeX packages I use, on machines that I don’t own or Administrate, it is beyond my threshold for acceptable frustration. So, hello Microsoft Word, my dear old friend!

Mathematics in Microsoft Word
If you haven’t used the built-in Equation Editor in Microsoft Word in a while, you might be happily surprised with what it can do now. First, I can input an equation easily using [Alt]-[=], and they are WYSIWYG. No compile/view/re-compile process! Second, it has gotten a lot easier to save a Word document as a PDF file. (I should say that I’ve had some difficulty getting the PDF producer to “play nice” with parentheses, but in that case I can always revert to CutePDF.)

Third, and most important, the Equation Editor has learned some LaTeX. It knows the stuff you use most often: Things like “\ldots” and “\delta” and “\Int_0^2” all do exactly what you think they should. It even has some {align} or {eqnarray} environment functionality, where you can align a series of equations at an equals sign.

But none of this is as cool as the Mathematics Add-In.

Microsoft Mathematics Add-In
It’s a computational engine that will display graphs, solve equations, and do lots of things your favorite graphing calculator can do, too. It’s available free at http://www.microsoft.com/en-us/download/details.aspx?displaylang=en&id=17786.  

It will generate awesome graphs of multivariable functions easily:

Did I mention that it is free?!?

If you want some quick documentation on how to use the Add-In, check out these Dropbox files: docx format or pdf format.

If you want some longer documentation, Microsoft has a support webpage with even more information. I found out about the Mathematics Add-In from a brief article I read, I think in The Mathematics Teacher, that I can’t find now! It made me scream, “How come no one told me about this sooner?! It’s awesome!” So check it out.

Statistics Group Projects: In Progress

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The Elementary Statistics students in my course are wandering the streets of downtown Charleston gathering data for their group projects. There are five groups and here are the questions they are asking (along with their best guess as to what they will find):

  • Do you own a bike? Best guess: At least 30% “Yes” response rate
  • Do you have a passport? At most 40%
  • Are you on vacation? About 30%
  • Do you consume alcohol? At least 80%
  • Have you ever had a fake ID? Around 50%

I look forward to seeing their data!

Statistics Group Project

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Project Motivation
There are two class meetings left in my “Elementary Statistics” summer course. This class time will be devoted to students working together on a group project. Last semester when I taught this course for the first time I really wanted to implement some type of end-of-term project. I wanted the project to be collaborative in nature since both my own experiences and recent research in education have shown that students explaining concepts to each other is as important to their learning process as hearing their instructor’s explanations. I also wanted the project to be somewhat self-designed by the groups themselves. It was my hope that giving them some freedom in their projects would increase their interest level in what they were doing.

The topics we finished covering at the end of the course were about creating confidence intervals and performing hypothesis tests (sometimes called tests of significance). Because we discussed this material so recently, it seemed appropriate to have this be the jumping-off point for the projects.

Project Introduction
I wanted the students to have experience going out into the “real world” to gather data, so the project asks them to conduct interviews with people they find around campus. Since it’s only a week-long project (instead of over an entire semester), to make things easier each group has to agree on a single”Yes” or “No” question to ask their random sample. There are three rules for the question.

  • First, each member of the group must agree with the group’s decision on the question. They have to discuss different ideas, vote on them, and eventually reach consensus.
  • Second, the question must be “interesting.” This is hard to define, but basically I want them to avoid boring questions like “Are you a human being?” or “Have you ever been to Mars?” that will result in boring data.
  • Third, the question must be “appropriate” — it has to be something each group member would feel comfortable asking a perfect stranger or their grandmother or their kid brother. (Hopefully they would know to avoid offensive or disrespectful or inappropriately personal questions, but who knows?)

Once they have chosen their question, each individual is asked to guess (to the nearest 10%) what proportion of interviewees will answer “Yes” to the question. After reaching an individual conclusion, the groups discuss what they expect as a group. I wrote a handout describing the “What” and “How” of prior probability distributions and each group works on creating [a very basic] one before they are allowed to leave to gather data.

Project Report
The groups have the rest of the class time to gather data together. I tried to avoid giving them much direction on who they should interview, or where they should find the people, or what types of people to ask. (For instance, do they want to focus on College of Charleston undergrads, or are tourists okay too?) I suggested to them that they need to keep in mind a lot of the ideas we discussed in the class, like:

  • What’s an appropriate sample size?
  • What sampling method should we use? (Convenience, cluster, stratified, systematic, etc.)
  • Should we expect bias in our data? If so, what types? (Sampling bias, response bias, nonresponse bias, etc.)
  • Can we do anything to eliminate bias?

Eventually the groups must produce a typed project report, outlining their process from how they decided on a question and constructed their prior to where they conducted their interviews. They must use the methods of inferential statistics that we learned in our class to create a confidence interval for the proportion of subjects who said “Yes” and give a correct interpretation of the confidence interval. They also have to perform a one-proportion hypothesis test. They are expected to use their prior probability distribution to formulate a claim to test. They are graded on both their data analysis and interpretation of results.

Project Grading
I created a grading rubric for the project. It’s available as a public Dropbox file: 104-project-rubric.pdf A colleague looked over it in the copy room and commented, “You sure are overly detailed with that thing!” This is probably a fair criticism, but mostly I was trying to avoid hearing lots of student questions that boiled down to, “What is the least I have to do in order to get an A?”

Something that comes up a lot in discussions about graded collaborative assignments is the “slacker problem”, i.e., How do you keep students from getting by doing zero work? I don’t have a good answer for this. I know that when I was a student, I was annoyed by free-loaders, so I have empathy for students who feel the same way. One of the categories on my grading rubric is “Teamwork Assessment.” Each student must individually send me a confidential e-mail discussing how their group functioned as a team and how they contributed to the overall project. They are asked to give their team a grade of how well they worked together. It was my hope that telling them on the project rubric that (a) they are responsible for their group functioning as a team and (b) they are also responsible for ensuring they contribute to the group that it would create a cultural pressure toward equal collaboration. I can’t say for sure how successful this was last semester, however I was happy that out of nearly 100 students, I only had one or two complain about slackers in their groups.

Looking Forward
This summer’s class has a strong group mentality, I think partly because we have been spending ten hours a week together in class. I hope that this will contribute to great collaborative effort toward these projects. I am also excited to see what questions they will ask and what their data will show. I’ll end this post with a few questions I remember from the class projects last spring:

  • Do you have a fake ID?
  • Do you own an iPhone?
  • Will you vote to re-elect Barack Obama?
  • Did you drink alcohol last weekend?
  • Do you have blue eyes?
  • Do you have a car on campus?

Science and Math for Teachers

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This week is the last week of our “Summer I” term and so my “Elementary Statistics” course is coming to an end. My next course begins on July 9th. It is part of a graduate here at CofC that offers a Master in Education in Science and Math for Teachers. My students will be participating in a professional development program called the Mathematics & Science Partnership.

The class itself is called “Applications of Algebra for Teachers.” The prefix for the course is “SMFT” since it’s part of the “Science and Math for Teachers” program. This is a new course, both under the SMFT prefix and in the summer Partnership program itself. I’ve been working on course development since late March, starting with the course description:

Applications of Algebra for Teachers (SMFT 697) – A course designed for middle-level and secondary teachers to investigate applications of algebra in science and technology. Topics will include numeration systems and number theory; linear, quadratic, exponential, and logarithmic functions; and matrix algebra with linear programming. Investigative labs, collaborative learning, and active learning approaches will be fundamental to the course structure.

(Other course descriptions for this summer’s program can be found here.) Our official textbook is “Reason and Sense Making in Algebra“, published by the NCTM. I have also used “Real-World Math with Vernier” for inspiration, since I hope at least some of our labs will use their LabQuest devices. We will also be using current and back issues of The Mathematics Teacher.

E-Seminar from NCTM

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The NCTM (National Council of Teachers of Mathematics) has several E-Seminars available on the web. A full list of available topics can be found here. If you aren’t an NCTM member, the seminars are $79 — but if you are an NCTM member, they are free!

Each seminar includes a facilitator guide, a PDF of slide show handouts, and a video of the presentation. The videos are approximately 60-minutes long.

The E-Seminar I just watched is called “Mathematics Teaching and Student Learning: What Does the Research Say?” Check out the description on their webpage.

It was my plan to head home by now but this seminar video captured my interest, so here I am, still in my office!

iPad in the Classroom

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Introduction

Here at the College, one of the subgroups of the IT Department is TLT: “Teaching, Learning and Technology.” Check them out on Twitter: @TLTCofC! For a full list of their programs, check out their blog at http://blogs.charleston.edu/tlt/. One of their functions is to offer equipment check-out for staff and faculty at the College. Last semester (Spring 2012) I was able to check out an iPad 2 from early February through the end of final exams. I was teaching three sections of our 3-credit “Elementary Statistics” course (MATH104) and one section of our 3-credit “Linear Algebra” course (MATH203). I abandoned the use of chalk boards in favor of lecturing on the iPad.

My Pre-iPad Lectures

For the last few years, I moved to using ELMO-style document cameras instead of board-based lectures. Originally I made this swap because the particular classroom where I had been assigned had a only tiny blackboard and I realized I would spend half of the class time erasing the board. But after a couple weeks of ELMO use, I was a big fan. Instead of presenting material while facing away from the students, writing on blank paper using pens under the ELMO camera allowed me to face the students for the entire class period. Doing this enabled me to catch many “I’m confused!” facial expressions from students who may not have felt comfortable voicing their concerns. Also, I was able to keep track of exactly what we had completed in any given class period since every day I walked out of the classroom with a written record of what we had done. It turns out that the ELMO cameras are going out of favor. I think this is because of the cost versus use computation done by the people in charge of budget decisions (but I’m not entirely sure). The iPad was the natural place to end up.

What I Do Now

As my class prep, I produce PDF files of class lecture notes for all of my courses. I upload the PDF files to our learning management system (called OAKS at the College of Charleston). My students can access the files on a password protected site. I don’t require my students to print out the notes, but I’d say about 95% of my students do print the notes and bring them to class because they find them useful.

Meanwhile, I load the PDFs onto my iPad and then project them in the classroom. I use a stylus to annotate the notes and my students write on their printed copies. The best app I’ve found for this purpose is GoodNotes. Currently I am using a Bamboo Stylus, which isn’t perfect but works well enough.

I have found it useful to name my PDF files like this: 104-ch7s123.pdf The “104” designates the course and “ch7s123” means these notes cover Chapter 7, Sections 1, 2, and 3. Last semester when I was teaching three different sections of the same course, I made three copies of each PDF file in GoodNotes and named them 104-ch7s123-05.pdf, 104-ch7s123-12.pdf, and 104-ch7s123-14.pdf for sections 05, 12, and 14. This helped since sometimes the classes wouldn’t be on exactly the same problem and each class I could re-load exactly where we had been the day before.

I hope the information below will help!

Hardware and Classroom Requirements

Classroom requirements:

  • A digital projector and a screen
  • VGA-in connection
  • A desk

To bring to class:

  • An iPad. I am now using a college-owned iPad3.
  •  My stylus
  • A dongle — It connects the iPad to the VGA input for the projector

Useful Apps

  1. Dropbox (Free)iTunes Store: http://itunes.apple.com/app/dropbox/id327630330

    Website: https://www.dropbox.com/

    Dropbox makes it easy to sync files across different computers (and the iPad). They have a free desktop application that installs as a directory, something akin toC:\Documents and Settings\My Documents\Dropbox

    which allows for easy “drag and drop” functionality as well as the ability to save files directly to your Dropbox. You can also share your Dropbox (or just part of it) with other people by extending them an e‑mail invite. Good reasons to consider this would be sharing course materials among colleagues teaching the same class, or to store joint files produced during collaborative research. The “Basic” service is free and gives 2GB of space. You can upgrade Dropbox to 50GB ($99/year) or 100GB ($200/year).

  2. GoodNotes (Free; or Paid version $3.99)iTunes Store: http://itunes.apple.com/us/app/goodnotes-notes-pdf/id424587621

    Website: http://goodnotesapp.com/

    The best feature of GoodNotes is that it behaves well with the projector. The projector will display only the PDF file and not all of the annotation features. (That way, my students don’t see me messing around with choosing different pen colors or highlighter widths.)

    GoodNotes easily syncs with Dropbox, which makes moving files from where I produce my notes (my computer in my office) to where I need them (my iPad in the classroom) simple.Another feature that makes GoodNotes great is the little “write here” box at the bottom of the screen. This allows me to write using big lettering, but it appears as a normal size on the screen. Writing in 12pt font using a stylus can be a bit tricky. In essence, what the “write here” box allows you to do is to write in 48pt handwriting but have it appear like you’re writing in 12pt handwriting instead.

    As an aside, a recent version of GoodNotes had an unhappy bug where all files would appear blurry when projected. This was a bummer for my class that day! I contacted GoodNotes customer support and they got back to me in eight minutes! That was amazingly fast and I was impressed. They knew of the problem and fixed it within a couple of hours, and took the time to update me about how it was going. Thanks, @GoodNotesApp!

  3. CourseSmart (Free)

    iTunes Store: http://itunes.apple.com/us/app/etextbooks-for-the-ipad/id364903557

    Website:http://www.coursesmart.com/

    CourseSmart is an eBook subscription service. Digital textbooks can be rented for 180 days. As an instructor, you can get free subscriptions to most textbooks. You will need a CourseSmart account. If you have used any other digital Pearson product (e.g., MyMathLab, MyStatLab, MathXL) your same login information should work on CourseSmart. If not, you can register as an Instructor here. You need to register from a computer (not a mobile device). Once you register, you can add different books to your eBookshelf. Once books have been added, the CourseSmart iPad app will allow you to access them. You can browse through them, flip to a particular (printed) page, take digital notes in the margins, put a “sticky note” down on a page, etc.

    CourseSmart is a great tool to avoid bringing the textbook with you to class every day. I have found this app useful in cases where a student will ask during class about a particular homework problem, or in-text Example.

    I have many books in my eBookshelf. I have several “Elementary Statistics” textbooks to browse through when I need more example problems, project ideas, etc. This is the digital solution to having bookshelves in my office with thousands of pounds of textbooks I don’t need.

    The one downside of the CourseSmart app is you need a live internet connection. On the “Wireless only” iPads, this means you can only access the textbooks while you have a wireless internet connection. So if you were hoping to read the Linear Algebra textbook while on a flight, this won’t work.

    Students can download the CourseSmart app and purchase a digital textbook subscription. Here is a pricing comparision for “Elementary Statistics (11th ed.)” by Triola.

    MSRP:  $160.00 (new book)

    Amazon:  $125 (new book with MyMathLab), $115 (new book), $75(used book)

    CourseSmart:  $63.99                                   (eBook)

    MyStatLab with eBook:  $82.00               (eBook + online homework)