tag:blogger.com,1999:blog-5416226109504306692020-02-29T03:55:50.660-05:00Online College Math TeacherJerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.comBlogger20125tag:blogger.com,1999:blog-541622610950430669.post-64548519764121232102018-07-04T14:53:00.000-04:002018-07-04T14:53:07.594-04:00<bold>Math in the news</bold> <div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-0Y0YDwH-5jE/Wz0W2czQdoI/AAAAAAAAC2E/oFoMevWDYwg0kAyxK8LblCiyWSa78ueIgCLcBGAs/s1600/bobby_bonilla.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-0Y0YDwH-5jE/Wz0W2czQdoI/AAAAAAAAC2E/oFoMevWDYwg0kAyxK8LblCiyWSa78ueIgCLcBGAs/s320/bobby_bonilla.jpg" width="225" height="320" data-original-width="218" data-original-height="310" /></a></div> Every July 1 there will be something in the news on the New York Mets paying retired baseball player Bobby Bonilla $1.9 million per year, even though he last played for the Mets in 1999.<p> The Mets released him in 1999, but they still owed him $5.9 million in 2000 for the last year of a 5-year contract. The Mets and his agent negotiated a deal where the Mets would pay him 25 deferred payments of $1,193,248 per year starting in 2011 and ending in 2035. This was calculated at an 8% interest rate. The Mets were willing to do this because they thought they were earning 12% to 15% on investments with Bernie Madoff which turned out to be fictional.<p> From Bonilla’s viewpoint these 25 payments of $1,193,248 per year, deferred 10 years from 2001, has a present value equal to the $5.9 million he otherwise was due: (1/1.08^10) * 1193248 * (1 - 1.08^-25)/.08 equals 5.9 million, so at 8% interest this was a fair deal for him. At today’s low interest rates, 8% looks pretty high. From the Mets’ viewpoint, even if they only earned 10%, the present value is $4.2 million, which is lower than the $5.9 million they originally owed him. Of course the Mets did not earn 10% on their Madoff investment.<p> These formulas appear in many math and finance textbooks under the subject of math and finance. Accountants were no doubt involved in the negotiations. I just want to suggest that math and accounting are sometimes in the news.<p>Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com0tag:blogger.com,1999:blog-541622610950430669.post-44711988487842516992017-07-25T15:28:00.000-04:002017-07-25T15:28:35.163-04:00Hi. <div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-K3pNh2WC7bE/WXea3xCKIUI/AAAAAAAACVk/pvkmGu9SnDoW-e6MDbZRiEaIWRbtt201ACLcBGAs/s1600/Accounting.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-K3pNh2WC7bE/WXea3xCKIUI/AAAAAAAACVk/pvkmGu9SnDoW-e6MDbZRiEaIWRbtt201ACLcBGAs/s200/Accounting.JPG" width="192" height="200" data-original-width="405" data-original-height="422" /></a></div> <P><P> A high school Social Studies teacher may have a degree in History, but may be called upon to teach Economics, Business Law, Personal Finance, Sociology, Psychology, Criminal Science, or whatever subjects fall under Social Science, despite having little or zero background in that subject. We just assume the teacher will learn what he or she needs.<P><P> A high school or college Math teacher may have a degree in Math, but that doesn't mean he or she has taken every possible Math course. College Geometry? Finite Math? Statistics? Cryptography? A Math teacher may be called upon to teach one of these, despite having little or zero background in that subject. We just assume the teacher will learn what he or she needs.<P><P> So when a small college puts Accounting in its Math department, and decides that Accounting will fulfill a student's Math requirement, is it so surprising that the college will ask a Math teacher to teach Accounting? They did, and I am.<P><P> I did take a semester of college Accounting, decades ago. I have worked in my non-academic career with accountants. And trust me, Accounting 1 is not rocket science. So I am teaching Accounting.<P><P> The part that bothers me is that unlike the claim I make when I teach Math, I do not have a passion for Accounting.<P><P> Any comments? Would you agree to teach Accounting?<P><P> Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com1tag:blogger.com,1999:blog-541622610950430669.post-42365102707455910872017-01-02T16:36:00.004-05:002017-01-02T16:38:41.187-05:00Math is hard. Although so is putting on eyeliner - not that I've done a lot of that.<br /><br /><br /><div class="separator" style="clear: both; text-align: center;"> <a href="https://1.bp.blogspot.com/-1eLphWT_IQw/WGrE5CxQU1I/AAAAAAAACKI/qZ6zPHAvap44GGAe1kX9SnQQTKZ0H2tyQCLcB/s1600/art17.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="2" height="208" src="https://1.bp.blogspot.com/-1eLphWT_IQw/WGrE5CxQU1I/AAAAAAAACKI/qZ6zPHAvap44GGAe1kX9SnQQTKZ0H2tyQCLcB/s400/art17.JPG" width="400" /></a> </div><br /><br />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. <br /><br />Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com0tag:blogger.com,1999:blog-541622610950430669.post-6314023931492991662015-10-30T11:49:00.001-04:002015-10-30T11:49:56.474-04:00Why do I have to study math? “Why do I have to study math? I’ll never use it.”<br> 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.<br> 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.<br> 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.<br> 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.<br> 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.<br> 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.<br><br> Saunders, H. 1988. <I>When Are We Ever Gonna Have to Use This.</I> White Plains, NY: Dale Seymour Publications. Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com0tag:blogger.com,1999:blog-541622610950430669.post-21546228518485128322015-04-26T14:41:00.000-04:002015-04-26T14:41:30.072-04:00Math is math, except in social science<dl><dt><span style="color: white; font-family: Arial; font-size: small;">"So how are the eggs?"</span><span style="color: white; font-family: Arial; font-size: small;"> "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." </span></dt><dt><span style="color: white; font-family: Arial; font-size: small;"><p> So goes a Seinfeld dialog. Similarly</span><span style="font-size: small;"><span style="font-family: Arial;"> Sigmund Freud is alleged to have said, "Sometimes a cigar is just a cigar," although researchers question whether he really said it.</span></span></dt><dt><span style="color: white; font-family: Arial; font-size: small;"><p> <div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-fDVyA9SoqEo/VT0uuV09dpI/AAAAAAAAB6A/ZF9OzhriEoE/s1600/Sigmund_Freud_LIFE.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-fDVyA9SoqEo/VT0uuV09dpI/AAAAAAAAB6A/ZF9OzhriEoE/s320/Sigmund_Freud_LIFE.jpg" /></a></div> And by the same logic, math is math, whether it is taught in high school or college, a 2 year community college or a 4 year college, etc. Right? I found a counter-example of this in statistics.</span></dt><dt><span style="color: white; font-family: Arial; font-size: small;"><p> 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 S<sub>X</sub> with an N denominator while defining the sample standard deviation for inferential purposes as s<sub>X</sub> with an N-1 denominator. I found a second statistics book for behavioral sciences that agrees with this.</span></dt><dt><span style="color: white; font-family: Arial; font-size: small;">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.</span></dt><dt><span style="color: white; font-family: Arial; font-size: small;"><p> Why can't we all just get along?</span></dt></dl>Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com0tag:blogger.com,1999:blog-541622610950430669.post-24171643833080882812014-01-24T12:11:00.000-05:002015-07-27T19:00:02.767-04:00<div class="separator" style="clear: both; text-align: center;"><a name="Barbie"></a><a href="http://2.bp.blogspot.com/-8bHGFGGPgCs/UuKc2ZJS-GI/AAAAAAAAB48/Wz4NEYv2e-0/s1600/barbie.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-8bHGFGGPgCs/UuKc2ZJS-GI/AAAAAAAAB48/Wz4NEYv2e-0/s320/barbie.jpg" /></a></div><br><br> After decades of suffering from her poor attitude toward math with her "Math class is tough!" quote <a href="http://www.youtube.com/watch?v=NO0cvqT1tAE">http://www.youtube.com/watch?v=NO0cvqT1tAE</a> 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: <a href="http://www.aikenstandard.com/article/20140113/AIK0101/140119826/1007/AIK0101/brave-barbie-takes-leap-to-engage-algebra-students">http://www.aikenstandard.com/article/20140113/AIK0101/140119826/1007/AIK0101/brave-barbie-takes-leap-to-engage-algebra-students</a><br><br> 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.<br><br> NCTM has a lesson on this: <a href="http://illuminations.nctm.org/Lesson.aspx?id=2157">http://illuminations.nctm.org/Lesson.aspx?id=2157</a><br><br> I guess blondes do have more fun!Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com0tag:blogger.com,1999:blog-541622610950430669.post-72061502592217410192013-10-15T08:34:00.000-04:002013-10-15T08:49:32.754-04:00Homer Simpson disproves Fermat's Last Theorem<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-leuWCFeinYQ/Ul01wUmF7DI/AAAAAAAAAPY/95pc1UATshU/s1600/Homer.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-leuWCFeinYQ/Ul01wUmF7DI/AAAAAAAAAPY/95pc1UATshU/s320/Homer.jpg" /></a></div><p> 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 <a href="http://www.mathsci.appstate.edu/~sjg/simpsonsmath">Simpsonsmath.com</a>, and they also link to another of their pages on the quite significant mathematical backgrounds of the Simpsons' writers.<p> 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 a<sup>n</sup> + b<sup>n</sup> = c<sup>n</sup> 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 3987<sup>12</sup> + 4365<sup>12</sup> = 4472<sup>12</sup>.<p> Try Homer's counterexample on your calculator or spreadsheet. Read <a href="http://www.theguardian.com/tv-and-radio/2013/sep/22/the-simpsons-secret-formula-maths-simon-singh">Simon Singh</a>'s article for more on the counterexample.Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com2tag:blogger.com,1999:blog-541622610950430669.post-22954142121063766832013-06-21T21:38:00.000-04:002013-06-21T21:40:16.586-04:00Women in STEM on television Other than female physicians, there are not a lot of women on television drama and sitcoms in science and technology. <p>I don't know how popular the television show <a href="http://www.cbs.com/shows/big_bang_theory/">"The Big Bang Theory"</a> 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. <p>Melissa Rauch portrays Howard's wife Bernadette, a doctorate level microbiologist with a well-paying job. <p>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. <p>Sara Gilbert portrays the very sharp-tongued Dr. Leslie Winkle, a physicist. <p>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. <p>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).Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com0tag:blogger.com,1999:blog-541622610950430669.post-23006314134389605802013-05-28T23:09:00.000-04:002013-05-28T23:09:39.286-04:00MOOCsOK, we've all heard about MOOCs: Massive Open Online Courses. Very few of them are for college credit at the moment. But for those of us reading this blog - we probably don't need three more credits.<br /><br /><center><a href="http://4.bp.blogspot.com/-NpyyhufU2o0/UaVuvP3mqLI/AAAAAAAAAOo/8m2Yl9PJ6pQ/s1600/cow.jpg" imageanchor="1"><img border="1" height="232" src="http://4.bp.blogspot.com/-NpyyhufU2o0/UaVuvP3mqLI/AAAAAAAAAOo/8m2Yl9PJ6pQ/s320/cow.jpg" width="310" /></a></center><br /><br />So let's enroll in one of these MOOCs, for the fun of it. I chose <a href="https://class.stanford.edu/courses/Education/EDUC115N/How_to_Learn_Math/about">Stanford University's EDUC115N: How to Learn Math</a>, which starts July 15, 2013.<br /><br />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.<br /><br />Why not join me, and see what a MOOC is like?<br /><br />Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com0tag:blogger.com,1999:blog-541622610950430669.post-50787003691450534852013-04-24T12:10:00.000-04:002013-04-24T13:24:39.773-04:00Copyright and math teachingLately I have been intrigued with the subject of copyright and math teaching. <br><br> I have done some reading and concluded that the copyright law is intentionally vague to provide users with flexibility, and that there are two schools of thought on permissible use of copyrighted materials in teaching. <br><br> The first school of thought is to take a very conservative approach and not do anything that could potentially trigger a lawsuit. This school of thought adopts the <a href="http://www.copyright.gov/title17">Section 107</a> Fair Use statute literally, and adopts the so-called <a href="http://www.copyright.gov/circs/circ21.pdf">Guidelines</a>as rules to follow. This school would say that Section 107 does not apply to for-profit schools, period. It would also say under the Guidelines that you had better obey the brevity, spontaneity and cumulative effect guidelines. <br><br> The second school of thought is to take a more liberal approach, and that Section 107 requires an individual assessment of all four factors. For example, if a copyrighted work has no economic value, then the owner is not going to lose money if I use the work in a for-profit school. As another example, if I show before and after steroid use photos of a famous ballplayer in the context of measuring the probability of his post-steroids results, then this is a transformative use of these copyrighted photos from their original purpose, which is permissible. <br><br> I'd love some comments to help me think through this. <br><br>Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com0tag:blogger.com,1999:blog-541622610950430669.post-14318332622970933972013-04-16T11:35:00.002-04:002013-04-16T11:35:52.726-04:00New tech / old techHi. <br><br> So many people are saying teachers ought to be including more web 2.0 technologies in their classroom, so I dipped my toe in the water. I created several five minute videos (my college age son liked the idea of five minutes) to help my students visualize and save for later use some calculations. I wrote a script, and I used screenr.com (free) to record my screen. I asked my class to be gentle in their comments, and I said I don't think George Clooney needs to be worried about me taking his job. <br><br> So what happened? I got no student responses on the videos. But what I did get a favorable response on, is a handwritten diagram that I scanned and posted. So sometimes maybe old tech is the best.<br><br> Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com1tag:blogger.com,1999:blog-541622610950430669.post-89343459836942179712013-02-27T15:10:00.000-05:002013-02-27T15:53:41.766-05:00Mr. Finch and pi<meta http-equiv="content-type" content="text/html;charset=utf-8" />March 14, Pi Day, is coming up. Is there any more to be said about <math>π</math> that hasn’t been said?<br><br> <center><iframe width="560" height="315" src="http://www.youtube.com/embed/yGmYCfWyVAM" frameborder="0" allowfullscreen></iframe></center><br><br> In the January 3, 2013 episode of the TV show “Person of Interest” (“you are being watched ... ”), computer genius Mr. Finch says that since <math>π</math> is an infinite non-repeating decimal, “contained within this string of decimals is every single other number. Your birth date, combination to your locker, your social security number ...”<br><br> Really? I didn’t think that is necessarily so. Mr. Finch doesn’t explain why.<br><br> There is a site that lets you search for a specific string of digits within the first 200 million digits of <math>π</math>, <a href="http://www.angio.net/pi/piquery">http://www.angio.net/pi/piquery</a>, but of course just because your number doesn’t appear, doesn’t prove anything. 200 million is a long way from infinity.<br><br> Are the digits in <math>π</math> truly random? There is something called a normal number, which is a real number whose infinite sequence of digits is distributed uniformly. See <a href="http://en.wikipedia.org/wiki/Normal_number">http://en.wikipedia.org/wiki/Normal_number</a> which says it is believed that <math>π</math> is normal, but this has not been proven.<br><br> So we think Mr. Fitch was right, but we’re not 100% sure.<br><br>Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com0tag:blogger.com,1999:blog-541622610950430669.post-62776782275051901352013-02-26T20:36:00.000-05:002013-02-26T20:47:35.219-05:00Counting with my fingers<table><tr><td> </td><td><a href="http://1.bp.blogspot.com/-FAFLkwzdFk0/US1ft7wAAcI/AAAAAAAAAKs/-NkL2BYjJcI/s1067/count_with_fingers.jpg" imageanchor="1" ><img border="0" src="http://1.bp.blogspot.com/-FAFLkwzdFk0/US1ft7wAAcI/AAAAAAAAAKs/-NkL2BYjJcI/s213/count_with_fingers.jpg" /></a></td><td> </td><td><a href="http://3.bp.blogspot.com/-m62-q0fhZxs/US1ft4vxJoI/AAAAAAAAAKw/miH9TfQh43A/s1067/right_hand_rule.jpg" imageanchor="1" ><img border="0" src="http://3.bp.blogspot.com/-m62-q0fhZxs/US1ft4vxJoI/AAAAAAAAAKw/miH9TfQh43A/s213/right_hand_rule.jpg" /></a></td></tr></table><br><br> We just did matrix multiplication, and I shocked my class by telling them that I think that is the perfect place to count with your fingers. I put my left pointer finger on the first element of the appropriate row, I put my right pointer finger on the first element of the appropriate column, do the multiplication, and move one element right and one element down to the next multiplication. Of course you need to mentally, or some other way, add these products, so that <font size="3">c<sub>ij</sub> = ∑</font><font size="small"><sub>k</sub></font> <font size="3"> a<sub>ik</sub> * b<sub>kj</sub>.</font> The other time I count with my fingers is when I do modular arithmetic, such as determining what is 7 months after October. I don't teach physics or three dimensional vectors, but I guess another application is the Right Hand Rule.<br><br> The class seemed shocked because it doesn't seem very sophisticated to count on your fingers. I can think of a few friends who would never lower themselves to do such a thing. That doesn't bother me. Let's just get the job done.<br><br> Does anyone have any other applications of using your fingers to count, or experiences in doing this?<br><br>Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com0tag:blogger.com,1999:blog-541622610950430669.post-62888689610162134852013-02-15T07:59:00.000-05:002013-02-15T12:11:54.191-05:00Let's stop making excuses for Aunt Sally<center><a href="http://4.bp.blogspot.com/-I_Js0TGN0Mw/UR4xmqI0vAI/AAAAAAAAAKM/iXwmNDFQMr0/s800/sally.jpg" imageanchor="1" ><img border="1" src="http://4.bp.blogspot.com/-I_Js0TGN0Mw/UR4xmqI0vAI/AAAAAAAAAKM/iXwmNDFQMr0/s160/sally.jpg" /></a></center> <br> Let's stop making excuses for dear Aunt Sally. You know who I mean: Please Excuse My Dear Aunt Sally. Many students can still remember the mnemonic PEMDAS for the rules of order of operations, but PEMDAS omits or confuses some situations. Most prominently, even my current college algebra textbook does not make it clear that in the M and D of PEMDAS multiplication and division are of equal priority, so a division is performed before a multiplication if the division appears to the left of the multiplication. <br><br> I like to invite my students to use all their calculators on expressions like 300 - 200/50*10 to see which calculators obey the rules of operations and which do not. I am always surprised when students first turn to the calculator on their cell phone to answer this. <br><br> PEMDAS doesn't address fraction bars, nor that with multiple grouping symbols you start with the innermost grouping symbols first. And I suppose it's too much to expect that PEMDAS address that in -3<sup>2</sup> the negation precedes the exponentiation; by the way, Excel disagrees with this. <br><br> Speaking of exponentiation, what do you do with x<sup> y<sup> z</sup></sup> ? Exponentiation is not associative. Johnny Lott in <i>A Problem Solving Approach to Mathematics </i>says exponentiation is done in order from right to left (page 276), although Excel disagrees with this one too. <br><br> So there's more to the rules of order of operation than PEMDAS. But if you are getting a little tired of Aunt Sally, why not switch to Please Email My Dad A Shark, by the authors of xkcd.com <br><br> Anyone have any good ideas on teaching order of operations? <br><br> <center><a href="http://1.bp.blogspot.com/-sx55dO3U-l4/UR4xcDj255I/AAAAAAAAAKE/2mO1YYJ9UrI/s1600/shark.jpg" imageanchor="1" ><img border="1" src="http://1.bp.blogspot.com/-sx55dO3U-l4/UR4xcDj255I/AAAAAAAAAKE/2mO1YYJ9UrI/s320/shark.jpg" /></a></center> <font small>GFU2TT2BG3ZC</font> Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com0tag:blogger.com,1999:blog-541622610950430669.post-77140515593096068912013-02-07T14:11:00.000-05:002013-02-09T11:52:16.798-05:00The color-challenged math student<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-kkIyENpofsU/URPxCwWYMTI/AAAAAAAAAIU/cRxY7NQbxq0/s1600/Color45.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-kkIyENpofsU/URPxCwWYMTI/AAAAAAAAAIU/cRxY7NQbxq0/s1600/Color45.jpg" /></a></div><br /><div><br /></div><div>If you are part of the 92% majority (that was not supposed to be a political comment), then you can see a number inside that circle. But I can't. The common description for my condition is being colorblind, although I prefer the more politically correct "color-challenged". I am not truly colorblind. I see some colors, just not as many as you see, and I get especially confused between red and green, shades of red and green, and colors containing either red or green (for example blue versus purple).</div><div><br /></div><div>I will stop my car for the top (or left) traffic light, but I don't really think it is red. I would wear a red tie with a green-striped shirt if no one stops me, so I try not to own shirts with green. Or to wear ties. I'm never quite sure if the meat is cooked enough. You won't see me choosing colors of house paint or women's makeup shades, and I won't be disabling colored wires for the police bomb squad. So generally I have learned to live with this minor inconvenience, and the accompanying jokes, which has not impeded my career choice.</div><div><br /></div><div>But the world of math is not as black and white as it used to be. A textbook author would never graph two curves in the same color. But if <font color="red">y = .5e<sup>x </sup></font>is in red and <font color="green">y = <span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><sup style="font-family: 'Times New Roman', serif;">2</sup><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"> </span></font>is in green, I am going to be confused as to which curve is greater in 1 < x < 3. I also get confused by multi-color pie charts where some of those colors start to blend together. And if you really want to lose me, just show me one of those colored maps with ten or so different colors representing ten different levels of the amount of rainfall.</div><div><br /></div><div>So if you are a teacher with control over such things, please be aware that some small percent of your students could be color-challenged and they may not even know it. The best thing you can do is provide labels in addition to different colors. Another possibility is to provide different kinds of patterns (see Excel's FORMAT, FILL, PATTERN STYLES). Lastly, choose among colors we are more likely to recognize, and especially avoid red AND green together.</div><div><br /></div><div>Have you had any difficulties in math with a color-challenged math student? <br /></div><div><br /></div><div><br /></div>Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com1tag:blogger.com,1999:blog-541622610950430669.post-66994799723331191142013-02-01T16:21:00.001-05:002013-02-01T16:21:43.583-05:00Beyond the scope of the courseHi. Occasionally a student will ask me a question, or will make a mistake, that leads to a topic that is beyond the scope of the course. Recently this occurred in college algebra where students confused algebraic functions and algebraic numbers. This entire subject is beyond the scope of this course - we don't prove a function is not algebraic, but we merely state it without proof; and we really don't care for this course whether a number is algebraic or not.<br /><br />My philosophy is that I always try to answer a student's question, or try to correct a mistake, even though this gets us outside the scope of the course. Students will not be tested on whether a particular function is algebraic or not. But I always have this nagging feeling that I'm providing more information than anyone really cares about.<br /><br />Thinking about this dates back to when one of my sons was in middle school and says he was taught that only rational numbers can be exponents. I then dashed off a letter to my son's teacher, reminding him that while logarithms were not part of the middle school curriculum, did he really want to teach the kids something that they would have to un-learn in a future class? I try not to teach something that a future teacher may have to correct; my son's teacher felt an irrational exponent was too much information for that grade level.<br /><br />Which of us is right?Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com1tag:blogger.com,1999:blog-541622610950430669.post-77823900938312552772013-01-29T08:37:00.000-05:002013-01-29T08:37:44.439-05:00An algebra problem students struggle withHi. I am amused when a student midway through the class will ask what grade he or she needs on the remaining material, so that the final grade will be say a B. My amusement is because either it is a student in my algebra class asking this question, or a student in my statistics class where algebra is the prerequisite. <br /><br />I should use this example as additional ammunition to the question, "Why do we have to take algebra? I'll never use it."Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com0tag:blogger.com,1999:blog-541622610950430669.post-35127568156714280442013-01-28T20:23:00.000-05:002013-01-28T20:23:49.945-05:00We do this in chapter 2; by chapter 8 students have forgottenEvery time I teach statistics, at least one student will ask me a question about chapter 8, whose answer is in chapter 2.<br /><br /><div class="MsoNormal">In chapter 2 we calculate the standard deviation of a sample. I invite the class to do one calculation of a sample of three numbers using each step of the formula: √ ∑(x<sub>i</sub> - ̅x)<sup>2</sup> / (n-1). Then I show them how to do it with a single Excel function, =STDEV. At the end of chapter 2, every student can do this in Excel. </div><br />We discuss standard deviations in the subsequent chapters, such as when we do Normal distributions, but we don’t calculate any.<br /><br />In chapter 8 we do hypothesis testing of two samples that are matched pairs, such as a husband’s data and a wife’s data. We take the difference between the two values in each pair, calculate the mean of the differences, and the standard deviation of the differences. And at least one student will ask how to do these standard deviations. The answer is: the same way we did them in chapter 2.<br /><br />Even if you don't teach statistics, I bet you have a similar experience. Comments? Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com1tag:blogger.com,1999:blog-541622610950430669.post-47102910982790854232013-01-19T17:25:00.003-05:002013-03-05T09:58:56.538-05:00Division by zeroHi. One topic I cover in week one of a college algebra course is division by zero. We are going to see this later on in the chapter on rational functions, so I think we ought to settle this issue sooner rather than later. Most people reading this blog are well-aware that division by zero is an undefined operation in the rules of real and complex number arithmetic. 3/0 = undefined.<br /><br />This is often quite a surprise to my students, who apparently never learned this anywhere in their K-12 educations. Truthfully, I can't remember learning it in my K-12 education either. I think my fourth grade teacher is on Facebook, and I'm going to ask her if she remembers teaching it.<br /><br />I invite my students to try 3/0 on as many calculators as they own. Sometimes the calculator will show "Error" (which is descriptive, but is not a correct answer), and sometimes it will show zero (which is worse). Students are even more surprised when I tell them both of these calculator results are incorrect. However, we also experiment on calculators with Order of Operations problems, so students discover that not every calculator follows those rules.<br /><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://3.bp.blogspot.com/-TWQCrkq5yiE/UP2JruHwKmI/AAAAAAAAAG0/PHLTYxCVqDU/s1600/Reverend_Jim.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" align="left" src="http://3.bp.blogspot.com/-TWQCrkq5yiE/UP2JruHwKmI/AAAAAAAAAG0/PHLTYxCVqDU/s1600/Reverend_Jim.jpg" /></a></div> I can picture Reverend Jim on the TV show Taxi: "3/0 = undefined? You're blowing my mind!" I'd love to hear from some K-8 teachers or some high school algebra teachers on whether they teach division by zero.Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com1tag:blogger.com,1999:blog-541622610950430669.post-5598737678510997482013-01-16T21:14:00.002-05:002013-01-19T11:59:10.996-05:00First post - please be gentleHi. It's probably about time that I join the blogging world. I have been teaching online college math for about four years. I started out with pre-algebra, worked my way up the math hierarchy, and now mostly teach college algebra and statistics. <br /><br />I teach for several for-profit colleges. Sometimes "for-profit" has a poor reputation. I am not involved in the recruiting, advising, and counseling end of education, and perhaps this poor reputation is not undeserved. But as an analogy, I never like dealing with car salesmen, but I still drive a car.<br /><br />The first question I asked during my first interview was how does an online school know its students are not cheating. Unless there is some in-person proctoring by a certified third-party (which is possible - I have taken online courses as a student that did this), an online school can not know. But plenty of cheating goes on in a brick and mortar school too, from paying someone to submit assignments and using cell phones or crib sheets during exams, so please don't be "holier than thou."<br /><br />I have two bases of comparison of my online courses at online schools versus the content of brick and mortar schools. The first is that my son who attends a state university took a very similar statistics course to the one I teach. Although my course is fewer weeks than his, my course seems to cover approximately the same topics. Second, I recently took an online liberal arts course as a student at a different state university, and I was decidedly unimpressed with how little my professor was involved in the class, how infrequently she communicated with students, and how she apparently didn't read the students' posts at all because she never commented on some of mine which clearly exceeded that scope of the course. So I have some confidence that my online students are not getting an inferior education.<br /><br />I look forward to sharing some of my online math experiences, discussing math and teaching, and learning from this vast blogging community.Jerryhttp://www.blogger.com/profile/09210401103314913746noreply@blogger.com2