Statistics Group Project

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

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

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

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.cofc.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)

Peer Instruction and IF-AT

Whys and Hows of Peer Instruction
I’ve been reading a lot recently about the “whys” and “hows” of peer instruction. Robert Talbert, a regular blogger for the Chronicle of Higher Education, has several blog posts about peer instruction with great information on why you might be interested in implementing it in the classroom. This month I’ve been teaching a four-week summer course in Elementary Statistics. This gave me a great opportunity to try to implement some peer instruction in my classroom.

A lot closer to home is John Peters, a colleague over in the College’s Biology Department. A few months ago he told me about IF-AT testing system. IF-AT stands for Immediate Feedback Assessment Technique. The basic idea of an IF-AT test form is a cross between an old style scantron form and a scratch-off lottery ticket. They have a cool demo you can click through to see how they work.

Basics of IF-AT Testing System
Basically, the students are given a multiple choice question. They answer the question and then scratch off their answer choice on the IF-AT form. If the answer is correct, a star will appear under their answer choice. If they are incorrect, they can re-attempt the question, choose a different answer, and try to find the star.

Now, as an instructor, you have to be a little clever when you write an IF-AT quiz. You have to make sure that the answer to Question 3 is where it is supposed to be, since you can’t move the stars around. There are many different IF-AT forms and they are all coded in a way that the instructor can figure out where the stars are when writing her quiz. The IF-AT folks have created test generation software to help (but I haven’t used it yet).

Why bother with the IF-AT?

  1. Students know immediately if their answer was correct.
  2. Students can get a second chance at a question, allowing for “partial credit” on a multiple choice test
  3. Instructors can also get immediate feedback about how students are doing

Peer Instruction with the IF-AT
Here’s how I introduced my statistics students to the IF-AT system: Two weeks ago, we had a “review day” before our first exam. I wrote three different 5-question quizzes covering various problems and topics related to the test material. I started by distributing the first 5-question quiz to the students. Each student finished the quiz individually. Once everyone was done, they were asked to find a partner and compare answers. If they agreed on an answer choice, great. If they found different answers for a question, they were asked to discuss and debate their answer choices until they found consensus. Once a  pair of students agreed on all five answers, they raised their hands and I gave them an appropriate IF-AT form. They worked together to scratch off their answers. If they found a star (i.e., got the correct answer) with their first try, they earned 5 points; on the second try, 2 points; on the third try, 1 point; and on the fourth try, 0 points. Scores were tallied.

After that, we continued with Rounds Two and Three: We went through the same process (individual / pair / consensus / IFAT) for the next two quizzes, but they were told they had to work with a different partner each time. At the end of the activity, each student had worked with three of their peers and had three scores for their quizzes. The top performing student earned 75 out of 75 points — impressive! As a reward, the student got a “late homework pass” entitling them to turn in homework 24 hours late (without the usual late penalty).

Cost-Benefit Analysis
The IF-AT forms cost about 25-cents each. I purchased 500 forms that are 25 questions with four answer choices (A,B,C,D) per question. Since I needed three 5-question quizzes, I took a few forms and then used the office paper-cutter to slice them into Questions 1-5, Questions 6-10, and Questions 11-15. Since the students were working in pairs, I only needed half as many forms (for a cost of $0.12/student). This is fairly inexpensive.

The students really loved this review activity. I don’t know much (any?) cognitive neuroscience, but I’m pretty sure that finding the star hit their brains’ dopamine reward center. After the first few minutes of the activity, when a pair of students would find a star, a very audible exclamation of joy usually followed. After we were done, we still had a bit of class time remaining and knowing which problems were the tough ones helped focus our time on reviewing material they struggled with the most.

I still had a bunch of “tail end” IF-AT forms (with questions 16-25) so on their test the next day, they found ten multiple choice questions. When I first started talking with colleagues about the IF-AT forms, someone mentioned they had used them in a testing situation and that it had gone poorly. They had given the IF-AT form along with the test sheet and some students would proceed like this:

Answer Question 1. Scratch off answer. Get it wrong the first time. Try again until correct.
Answer Question 2. Scratch off answer. Get it wrong the first time. Try again until correct.
Answer Question 3. Scratch off answer. Get it wrong the first time. Try again until correct.

But, as you might expect, having missed a few problems at the start of the exam, the students ended up feeling fairly crummy about their chances for the rest of the test and some “gave up”. Overall class performance was lower than expected.

To combat this issue, I made sure that the students had answered all questions before I gave them an IF-AT form. That way they wouldn’t become discouraged early on. After the test, all of the students reported that they were happy about the use of IF-AT on their test. They liked leaving knowing how they had performed on that portion of the test. They appreciated being able to have a second (or third!) try on some of the problems. I liked that half the test was graded before I left the classroom!

Future IF-AT Use
I’m hoping to use the IF-AT review strategy again before our last test, which happens next week. The IF-AT forms seem great for running a review session that is constructive. In the fall, I will be teaching both Pre-Calculus and Calculus I courses and I’m planning on using the IF-AT forms in both as part of an early diagnostic to catch any students who were placed into the wrong course.