Monday, January 2, 2017
Hi. Something not discussed in my various teacher trainings is normalizing the difficulty of an exam. In teaching a course for the first time, I borrow another teacher's exams, and then I try to create mine that seem about equal in difficulty. But how difficult is my exam, and is it the appropriate level of difficulty? For a gen ed community college math course, I sort of think the very best student should get close to 100, and the class average ought to be about 75. Of course this assumes students attend nearly every class, pay attention in class, take notes in class, do the assigned homework, etc.; assumptions that have not been exactly true in my classes. Maybe this also assumes I am a decent teacher. I have been curving my exams about 15 points to account for the fact that maybe my exams were too hard, and I was perhaps not the most effective teacher. Hopefully I will improve my exam creation with experience and curve less in the future.
Friday, October 30, 2015
I’m sure every math teacher has heard this question. It’s not easy to answer. I have heard several possible answers, but I’m not completely satisfied with any of them. I have a somewhat different reply, which I learned from - of all people - an English teacher.
One possible answer is how important math is in the real world. Each of us has our favorite real world problems that illustrate the importance of math. But these problems seem contrived, and are not the problems ordinary people encounter. The book When Are We Ever Gonna Have to Use This contains math examples from nearly 100 occupations, but most of these merely use arithmetic or pre-algebra.
Another possible answer is that many occupations require math, and a student limits his future options by avoiding math. My reply is that most students are not going to choose such occupations. A third possible answer is that math helps us to think logically. But many people who are quite logical thinkers and good problem solvers know minimal math. If the purpose is to teach logical thinking, maybe we should teach logic.
Here is my reply, which I discovered during a team project in an education course. I was teamed with an English teacher, and we were trying to find some common ground between us. To my surprise, she explained that when she analyzes a poem, she searches for various patterns in the poem.
Searching for patterns? As the math person, I thought I had exclusive rights on searching for patterns. But then I came to an epiphany: We’re all searching for patterns. The toddler who tries to learn which behaviors will elicit attention. The physician who tries to investigate the cause of an illness (think of the TV show “House”), who is similar to the police detective who tries to solve a series of crimes. The art critic and the movie critic. (I once heard a movie critic explain that when the major character travels across a bridge, there is about to be a personality change.) The plumber who searches for the leak. I’m sure you can think of many others.
We are all searching for patterns in life, and we do this with our own unique lens on we how we view the world. As math people we look for quantitative patterns. It seems to me that the more tools we have to discover patterns, the richer our lives are. I think students should study math to give them one more tool in their toolbox to discover life’s patterns.
Saunders, H. 1988. When Are We Ever Gonna Have to Use This. White Plains, NY: Dale Seymour Publications.
Sunday, April 26, 2015
- "So how are the eggs?" "Eggs are eggs." "Eggs are eggs. That is very profound. By the same token, couldn't you say fish is fish? I don't think so."
So goes a Seinfeld dialog. SimilarlySigmund Freud is alleged to have said, "Sometimes a cigar is just a cigar," although researchers question whether he really said it.
I recently taught an intro to statistics class in a psychology department using a statistics book for the behavioral sciences. This book defines the sample standard deviation for descriptive purposes as SX with an N denominator while defining the sample standard deviation for inferential purposes as sX with an N-1 denominator. I found a second statistics book for behavioral sciences that agrees with this.
- Is there a recent textbook in the math or statistics world that defines the sample standard deviation with an N denominator? I haven't seen it. And not only will the student of this psychology class find this definition conflicts with the math world, but she will also find (and did find) it conflicts with the Excel world, not only for the Excel standard deviation function but for the Excel statistics Data Analysis add-in functions.
Why can't we all just get along?
Friday, January 24, 2014
After decades of suffering from her poor attitude toward math with her "Math class is tough!" quote http://www.youtube.com/watch?v=NO0cvqT1tAE which ironically was misreported by the press as "math is hard," Barbie is apparently putting her life on the line in Barbie Bungie Jumping to help students learn algebra and statistics: http://www.aikenstandard.com/article/20140113/AIK0101/140119826/1007/AIK0101/brave-barbie-takes-leap-to-engage-algebra-students
This appears to be an experiment relating the distance of a jump to the number of rubber bands used, and then estimating the line of best fit.
NCTM has a lesson on this: http://illuminations.nctm.org/Lesson.aspx?id=2157
I guess blondes do have more fun!
Tuesday, October 15, 2013
Simpsons fans know that Lisa seems to know a lot of math for someone her age but Homer can also surprise us, and higher math often sneaks its way into the show. Two university professors give some references to some of the math that has been used on the show in their site Simpsonsmath.com, and they also link to another of their pages on the quite significant mathematical backgrounds of the Simpsons' writers.
I recently learned from another article that discusses math on the Simpsons that the writers once sneaked into an episode a counterexample to Fermat's Last Theorem. This theorem is a famous problem in the history of mathematics and states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n > 2. The theorem was conjectured in 1637 and not proven until 1995, yet Homer writes on a blackboard a counterexample 398712 + 436512 = 447212.
Try Homer's counterexample on your calculator or spreadsheet. Read Simon Singh's article for more on the counterexample.
Friday, June 21, 2013
I don't know how popular the television show "The Big Bang Theory" is among young women - probably not very - and while that show does have a pretty but somewhat dumb blonde, it also has several actresses portraying women with doctorates in science.
Melissa Rauch portrays Howard's wife Bernadette, a doctorate level microbiologist with a well-paying job.
Mayim Bialik, who portrayed Blossom in the 90's, portrays neurobiologist Amy Farrah Fowler. In real life Mayim has a Ph.D. in neuroscience from UCLA. She speaks on a variety of topics besides acting, including to scientific and mathematical groups.
Sara Gilbert portrays the very sharp-tongued Dr. Leslie Winkle, a physicist.
Christine Baranaski, currently a regular on "The Good Wife", portrays Dr. Beverly Hofstadter, Leonard's mother. She plays a neuroscientist and a psychiatrist. I think she is hilarious.
These women are all brilliant, witty and funny, and are not the social misfits that the male characters are. So I think these are pretty good role models for women in STEM (Science, Technology, Engineering and Math).
Tuesday, May 28, 2013
So let's enroll in one of these MOOCs, for the fun of it. I chose Stanford University's EDUC115N: How to Learn Math, which starts July 15, 2013.
I'm expecting an exceptional teacher, from a university I could never get into, zero one-to-one interaction with this teacher, an enormous number of fellow students, but a group of fellow students who will try to answer each other's questions. And I'm expecting to learn something I probably wouldn't learn somewhere else.
Why not join me, and see what a MOOC is like?