Wednesday, November 30, 2011

Why Students Leave STEM Majors

A recent (11/3) article appeared in The New York Times called "Why Science Majors Change Their Minds"

Quoted from the article:
But as Mr. Moniz sat in his mechanics class in 2009, he realized he had already had enough. “I was trying to memorize equations, and engineering’s all about the application, which they really didn’t teach too well,” he says. “It was just like, ‘Do these practice problems, then you’re on your own.’ ” And as he looked ahead at the curriculum, he did not see much relief on the horizon.

This article is a micro version of the book "Talking About Leaving: Why Undergraduates Leave the Sciences" by Seymour and Hewitt.  It should be on your bookshelf if you are an educator in a STEM field.  The top four reasons why students leave STEM fields in undergraduate education are teaching and learning related.

The Top Four Reasons why undergraduates leave STEM majors:

  1. Lack or loss of interest
  2. Non STEM majors offer better education/learning experience
  3. Poor teaching by STEM faculty
  4. Curriculum overload, fast pace overwhelming.

Traditional explanation or "justification" of this is that we are "weeding out" the weak or morally inferior students.  The data presented by Seymour and Hewitt says otherwise.  One cannot predict based on academic measures such as GPA which students will switch out of STEM majors.

In short, we waste talent and turn away many strong, capable students.  In our rush to "get through all the material" our system has to a large degree lost sight of the big prizes.  We can, however, regain this by focusing on the learner and the learning experience.  We can be coaches and mentors rather than gate keepers, and departments across the nation should reconsider the definition of success.

What should success really mean for a Math program?

Wednesday, November 16, 2011

Nuts and Bolts: Assessment of Presentations

IBL courses deserve assessments that match what students are asked to do in class.  In most full IBL courses, presentations form a significant portion of the grade.  Grading breakdowns could be something like this:

30% Presentations
30% Final Exam
20% Midterm
10% Written work
10% Portfolio

In this post I'll focus on presentations, and discuss the other items in future posts.  Student presentations are one of the key components of an IBL course.  Students should present their work to their classmates to be vetted for correctness and clarity.  This process by itself is immensely valuable.  In fact, it lies at the heart of IBL.  Students work on hard problems at home.  They bring back their findings, get feedback and repeat, until a problem is solved.

Assessing presentations can take on many forms.  One way is to use a point scale.  Here's a rubric which can be adjusted to suit the style of an instructor.
10 Completely correct and clear
8 or 9 minor technical issues, but the proof is correct
5, 6 or 7 Proof is incorrect, has a significant gap(s)

Points don't tell the whole story.  Instructors should have in mind the overall qualities they want from students.  Below is a general guideline that can be adapted to match your own criteria and your institution's.  Students should be encouraged and rewarded for their intellectual contributions to the class.  Generally students should present regularly and also participate meaningfully in discussions in groups and in class.  Students who are able to prove major theorems and present regularly in class should earn an A for presentations.  They are capable of doing original (to them) mathematics.   Students who present regularly, but none of the harder problems typically earn a B for presentations.  Students who show up to class regularly and present only occasionally earn a C for presentations.  Students who miss a significant number of classes and/or do not present more than once typically would earn a D or F for their presentation grade.

*Some instructors also include some bonuses for creativity and ingenuity.  When a student does something that you have not seen before that shows real creative thinking, it should be rewarded in some way.  I take notes in class and write comments and jot down the creative idea.

The main message is that students have an incentive to

  • Show up to class having worked on problems
  • Participate and discuss mathematical ideas
  • Prove theorems on their own
  • Contribute to their own and their classmate's intellectual development
Are these not the qualities we want from our students?  Aligning incentives in positive ways to what society values in people is a something we should strive for.  Assessment is not merely a way to determine grades -- it's also a tool to encourage students to be young mathematicians!

Thursday, November 10, 2011

Nuts and Bolts: Getting Students to Ask Good Questions

By Matthew G. Jones, Cal State Dominguez Hills <>

One of the keys to making IBL work is to make sure that students really engage with the topic. There are lots of ways to do this, but I will focus on two ways to get a whole class discussion going. The first of these ways is to use question starters. I have done this in two ways. In the first case, I simply write a question on each of three or four index cards, and distribute them around the classroom while another student is presenting a solution. The index cards have a single question type, such as, "How did you know where to start?" "Could you explain how you went from ... to ...?" "Can you explain what the question is asking?" "Was this the first thing you tried?" The students are told that if they are given a card, they must pose a question, and they can use the one on the card if they wish. This way, those few students are thinking of a question to ask while the presenter is working. The presenter also knows to expect questions, and the class understands that discussion of the solution is the norm, rather than passive silence. The other way I have seeded questions is to hand out a sheet to the entire classroom, and to tell them that you will call on a few students to pose a question, and that they can use the handout to help them formulate a question.
n either scenario, if I call on a student who claims to have no questions, then I will ask the student to paraphrase a specific part of the presentation, such as, "Could you explain what you think the presenter means by this line?" or "What is the goal of this part of the solution?"

The second way to get a whole class discussion going is to let a presenter complete his/her solution, and then to give the student observers 2 minutes to discuss the solution with a neighboring student in the room. Sometimes I will ask a pointed question to prompt the discussion, such as, "What kind of proof did the presenter use, and why do you think that was his/her choice?" and sometimes it is left open. Then, I open the whole class discussion by calling on students and asking, "What did you and your partner discuss?" This kind of question diffuses the pressure for students to report themselves as confused, because they often give replies like, "We were trying to figure out..." or "We weren't sure about..." The main idea is that students are more comfortable reporting on their actions in a partner discussion than identifying their personal confusion or misunderstanding.

Tuesday, November 1, 2011

Carol Schumacher, Kenyon College

This article originally appeared on the AIBL User Experiences website in 2010.  It has been reposted here on the IBL Blog, the new home of AIBL User Experiences.

By Carol Schumacher, Kenyon College
Inquiry-based learning (IBL) has been transformative for me as a student and as a teacher.  I was an undergraduate at Hendrix College in Conway, AR, where I was fortunate enough to have all of my upper level courses taught with an inquiry approach.  I had always liked math and had been good at it, enough to be pretty sure from an early age that I wanted to major in math in college.  But it was my first IBL course that really made me a mathematician.
For me, as a student, the inquiry-based approach was exciting and empowering.  For the first time, I had a real sense of “ownership” for the mathematics I was doing.  I was able to see that mathematics is not only a set of techniques and ideas that I could master, but a powerful way of thinking.  Moreover, my appreciation for the beauty of mathematics increased, and I came to crave the “high” that I got from solving a problem or proving a theorem on my own.  So the inquiry approach also made me thirst for more mathematics in a way previous courses had not.

When I went to graduate school, many of my fellow students “knew” more mathematics than I did.  But this was really no problem, because I knew how to prove theorems.  When a topic came up that I had never studied, I never had a problem learning it on my own.  And I was pretty much fearless in the face of the problems that were set before me.  At one point, I was flabbergasted to find out that some of my fellow graduate students just scoured the library for solutions to the assigned problems.  This approach would never have occurred to me.  My IBL training showed me that mathematics is something you do, rather than something you read about in books.

When I began teaching, I knew that I would use an inquiry-based approach in all of my upper level theory courses.  So you may wonder in what sense it has been “transformative” for my teaching.  There are a number of ways.  Inquiry-based teaching is perforce centered on students’ learning.   (The main question in our preparation as IBL teachers is not “what am I going to do in this class,” but “how shall I craft these materials so that the students can make headway in the mathematics?”)  This insight from inquiry-based teaching, has infused all of my classes.  I have improved as a teacher by thinking less about teaching and more about learning.  Because it is not what I do, but what happens to my students that is important.

I certainly do not teach all of my courses with a strict inquiry-based approach, but I do believe that engaging students actively in the business of doing mathematics is the key to fostering deep learning.  This is just as true for non-majors taking a liberal arts math course or a calculus course as it is for a graduate school bound math major.  And I have found that I can adapt inquiry ideas for use in classes of all kinds and at all levels.  Even in courses that are more traditionally “teacher centered,” I intersperse periods of lecture and discussion with opportunities for students to work through some ideas on their own.  And I am entrepreneurial in looking for ways of turning the class over to my students in the form of active learning and exploratory exercises.  I have found that when I can devise a good way to substitute something that the students do for something that I have previously tried to do for them, it is always a good idea. The learning is more profound and the knowledge longer lasting.  (I was told by a recent graduate who is now a graduate student that he remembers the content of my courses best, because he developed the subject himself.)

Inquiry-based learning is, also, transformative for many students.  An IBL course can completely change the outlook of mathematically talented students who have never before found it particularly interesting.  They come to see that mathematics is not just as a set of techniques for building the new and improved mouse traps of the 21st century, but is a powerful tool for understanding the world around them.  They learn to appreciate this tool and they learn to wield it by making it their own.  What more could we want?

Links to some IBL textbooks written by Carol Schumacher:
Chapter Zero
Closer and Closer