tag:blogger.com,1999:blog-18695295939271521242017-04-16T06:52:30.221-04:00Trial by BloggingNachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.comBlogger22125tag:blogger.com,1999:blog-1869529593927152124.post-11875751202211469092014-02-16T15:05:00.003-05:002014-02-16T15:05:57.151-05:00How Did Your Math Courses Prepare You For Teaching?So I saw this today:<br /><blockquote class="twitter-tweet" lang="en">Will be giving a talk next month--need to know: How did your math courses/major prepare you for teaching? NB: Math specific, not Ed courses.<br />— Breedeen Murray (@btwnthenumbers) <a href="https://twitter.com/btwnthenumbers/statuses/434422816960552962">February 14, 2014</a></blockquote><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script> And it got me thinking...<br /><br />First, a bit of background. When I was in college, I ended up completing a Computer Science major along with a mathematics major. I entered college thinking I'd become a secondary teacher, but then never took a single education class since the combination of math and computer science courses filled up all my time! A couple years later, I found myself earning a masters (this time in education) and now I'm teaching (mathematics) at a four-year liberal arts college. <br /><br />So, I can easily discuss how my math major prepared me - and how that major compared to the education classes I've since taken.<br /><br />First, the majority of my math classes taught me <i>how not to teach</i>. Too much lecture. Too many book problems. Almost no interaction. On the other hand, my later education classes taught me that too much group work <i>is just as bad</i> if not worse. There's a fine line somewhere between those two extremes.<br /><br />My math major did have one useful course though in terms of teaching down the road: Math Colloquium. It was in colloquium that each math major was required to pick a faculty adviser and a topic. Over the course of the semester, we had to prepare a 40 minute talk, and then near the end of the semester we actually had to give our talk to our fellow students and all our professors. <br /><br />Colloquium was a stressful time, but once it was over I realized how much I learned about teaching. I had to make my first ever PowerPoint (for instruction purposes). I had to fit a lesson in a time frame. I had to realize what my audience did (and did not) know coming into the talk. I had to keep the professors attention while simultaneously not losing the students in the minutia of the mathematics of the topic. Finally, I also had to impress everyone because my grade hinged on doing well. <br /><br />I think that colloquium was truly the only class that prepared me to teach at all because it was the only class where I had to stand in the front of the room and actually teach. I look at teaching a lot like I look at mathematics: you can watch someone else do it all you want - and it might even make sense - but it isn't until you actually try it that you'll know whether or not you understand it. <br /><br />Looking at my own teaching from my students point of view, I hope they don't have a lot of the same complaints that I did when I was in their shoes. I try my best to incorporate more problem solving, less book work, and the occasional class activity. I attempt to refrain from lecturing for more than five or ten minutes at a time. I also try to relate the material at hand to true "real world" applications, not the "real world" you read about in textbooks (typically the final six or seven word problems in a chapter or section). <br /><br />I also think this question deserves a lot more time and thought on my end - but I don't have a lot of time since I have my own teaching to prepare for the upcoming week! I did, however, think it was worth jotting a few things down in response...and perhaps spark some sort of dialogue with other teachers out there!<br /><br />Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com1tag:blogger.com,1999:blog-1869529593927152124.post-10849442455770152502013-07-10T22:42:00.003-04:002013-07-10T22:42:34.771-04:00The (Hidden) Cost of Higher EducationAnyone who pays attention to politics or the news will have undoubtedly heard plenty about the rising costs of higher education. Tuition keeps going up, up, up and yet our students still struggle to land jobs upon graduation. Surely, that's a problem - why keep paying more for something that won't even ensure you have a job at the end to show for you hard spent cash? I suppose that is, in part, what has led to the rise of online classes (and more recently, <i>free</i> online classes). <br /><br />Now, the merits of tuition raises and college preparation for the job market can be (and have been) debated by plenty of others. Since I work at a small liberal arts college (and I have no say in terms of things like the college's budget), I like to focus on things that I can have some input on - namely, the hidden costs of higher education. <br /><br />What are the hidden costs? <br /><br /><ul><li>Books</li><li>Graphing calculators</li><li>Printing costs</li><li>Software costs</li></ul><br />And those are just to name a few - certainly the four biggest costs for a potential mathematics, physics, biology, or chemistry student. <br /><br />How do I help my students minimize their hidden costs? This coming fall I'll be teaching two sections of Calculus I and one section of The Mathematics of Games and Gambling. For the gambling class, I do require a textbook but it sells at the campus bookstore for about $40. Sure, that is still probably $20 too much but at least it's less than fifty bucks. <br /><br />For my Calculus class, I have decided to forgo a textbook entirely. On the first day of classes, I'm going to tell my students that they can get virtually any calculus book (late transcendentals) and it should (more or less) follow along with my lectures and homework. The downside for me is that I have to write all my own homework assignments (complete with answer keys and hints). Still, I consider that part of my job - and I have a feeling my students (and their parents) will appreciate all my work.<br /><br />As for the other hidden costs, well, they are a bit trickier. Actually, the second one isn't hard at all - not only do I not require a graphing calculator, I don't allow them to be used. I'd much rather have my students know how to graph y = (x + 2)^2 than use a graphing calculator to get the exact graph of y = (2.3x - 3.8)^2. Sure, in theory the students should be able to graph the second equation, but why? Keep it simple I say - it's more important to work on intuition, observation, and determination!<br /><br />My other beef with graphing calculators? Their costs haven't dropped.<br /><br />Why can get a Samsung Galaxy S3 (or even an S4) smart phone for under $100 but I can't get a TI-84 graphing calculator for that price? Why can I buy a brand new WiiU video game system for $299 but a calculator that's essentially over a decade old still costs me over a third of a new HD gaming system?<br /><br />One reason: College.<br /><br />It's a hidden cost. Each professor that requires a graphing calculator forces students to buy said devices. Since there are tons of classes that require TI-somethings, Texas Instruments gets to keep the costs of their device artificially high. For all the grief that textbook companies get, it hardly seems fair that Texas Instruments gets a free pass. They are clearly just as guilty.<br /><br />In the end, the only way for the cost of education to go down will be for more professors to take proactive steps to reduce hidden costs for their students. As more professors move to cheaper (or even free) options for their students, more and more schools will begin to follow suit. After all, if all a student's professors provide printed handouts (saving the students printing costs), the schools will eventually have to stop charging so much for printing fees (or else start charging professors I suppose). Unfortunately, I'm guessing I'll get charged for my printing way before my students ever see a discount.<br /><br /><br />Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-36114970629990264852013-06-27T14:03:00.003-04:002013-06-27T14:03:38.543-04:00Getting Back on Track: A Blog Re-Launch!I've been reading quite a few different educational blogs (and Twitter accounts) lately which have all served to motivate me into re-launching my own educational blog. So, here goes:<br /><br />----<br /><br />Since I'm starting from scratch (though I won't be deleting any of the previous drivel that I published), I should first introduce myself.<br /><br />I'm a 30 something (ok, 30 exactly) math professor at a liberal arts college who doesn't have a Ph.D. (and after taking graduate math classes at two different schools, I no longer <i>want</i> a Ph.D.). The only downside to the extra letters that aren't on the end of my name is that college teaching positions are tenuous at best. <br /><br />Over the last seven years, I have taught a variety of courses at three different institutions including:<br /><br /><ul><li>Pre-Algebra</li><li>Algebra I</li><li>Algebra II</li><li>PreCalculus</li><li>Calculus I</li><li>Calculus II (scheduled to teach in spring 2014)</li><li>Combinatorics</li><li>Intro. to Statistics</li><li>Mathematics of Games & Gambling</li></ul><br />It's an eclectic group of courses, but most of them were a lot of fun to teach. I'd also like to think they were fun for the students, though I in some cases I have my doubts.<br /><br />It's those doubts that are impetus for this particular blog. My Fall 2013 schedule looks something like this:<br /><br /><ul><li>Calculus I (two sections plus two labs)</li><li>Mathematics of Games & Gambling</li></ul><br />It is my goal to make my three courses as fun for the students AND as rigorous as possible. Can those two ideas coexist? Well, sure, I believe they can or else I wouldn't be attempting it! <br /><br />As the summer progresses, I hope to start posting some of my course ideas. Eventually, I hope to have a vibrant blog following where ideas get bounced back and forth (and by all means, feel free to disagree with me). Until then, I'll blog like no one's reading.*<br /><br />*not hard to do when no one is actually readingNachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-18250819123943845932013-05-01T10:47:00.002-04:002013-05-01T10:47:26.138-04:00Redesigning Calculus I - Ideas Appreciated!The college where I work had finals last weekend and has graduation this coming weekend. After the festivities, I'll be officially done with work for a few months. <br /><br />Although I love getting some time off, it's not all fun and games this summer for me. In fact, I might end up doing as much (or more) work this summer as a I did last summer when I was prepping a brand new course offering. <br /><br />Why you ask? Well, I'm hoping to redo the entire Calculus I curriculum. For the past five years, I've been teaching Calculus I using a variety of textbooks. Unfortunately, none of them made me super happy - and based on polls I've given my students, the students didn't like them either. <br /><br /><b>Change #1: No required textbook</b><br /><br />I'm sure many of you have done this already, but for me (and my college), it's a big step. This means that I'll have to write all my own exercises for the students AND update my notes to make sure all necessary information is contained within the course materials. Luckily, my notes are fairly thorough so the second half of the problem shouldn't prove to be too difficult.<br /><br />I suppose I ought to back up and state <i>why</i> I got rid of the textbook. There were two main reasons. The first, as I mentioned above, was that I couldn't find a book that pleased both the students and myself. Some had only super easy problems, others had only hard problems. The books that fell in the middle seemed to have muddled descriptions within the pages. Semester after semester, no matter which book I used I would consistently get 60% or more of the students saying they never use the book (except to copy homework problems). I already provide about half the assignments in worksheet form (homework that I've written myself) so doing the second half hopefully won't be too difficult.<br /><br />The second reason I got rid of the textbook was because of the cost. $100+ for a used calculus book is terrible. It's even worse considering you can find most of the information online with a quick search on your smart phone (and not pay a penny - well, besides that smart phone data fee of course). <br /><br />Although I've gotten rid of the textbook, I would still like to offer the students a chance for a free open source Calculus book. Do any of you know of a good book (or multiple books) that are available for free? <br /><br />This is the first post in what will probably be quite a few posts detailing the changes I'm making to the Calculus I curriculum. As usual, I'd love to hear what you have to say!Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-86362203636663453322013-03-14T23:01:00.000-04:002013-03-14T23:01:13.442-04:00The Calculus Funk.I'm teaching Calculus I again this semester (two sections) and therein lies the problem.<br /><br />Again.<br /><br />And again. And again.<br /><br />I've been teaching Calculus I for way too long. If I'm being honest, it's gotten stale. My lessons are all on PowerPoints that have been scrubbed clean of errors and ambiguities. My stash of worksheets cover almost any area where a given class needs more practice. My review games are carefully tied to the material on the exams. Heck, even my labs are now a solid representation of how the course material is used "in the real world."<br /><br />And yet.<br /><br />I can't shake the funk.<br /><br />It's a case of "been there, done that."<br /><br />Even worse is the split of students this semester. One of my Calculus classes is scoring much, much higher than any previous class (in terms of class average). The other class? One of the lowest averages ever.<br /><br />Sometimes it's luck of the draw I guess. Sometimes it's the students within the class. And sometimes, just sometimes, it might be the instructor.<br /><br />I need to come up with new ideas and methods to engage my lower achieving class - clearly they aren't responding to the same things that my other class is. <br /><br />I have my theories on why, but there's little time for "why" right now. Right now, it's time for "how". <br /><br />How, that is, can I improve the class?<br /><br />Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-62897722998232286312013-01-24T18:00:00.000-05:002013-01-24T18:00:02.479-05:00Student Responses on First Day Survey in Games & GamblingI've been teaching in front of a college classroom every semester since I graduated from my undergrad institution back in 2005. In that time, I believe I've given a first day survey every semester (except maybe my first). The classes that I've taught have changed over the years (as has the institutions where I teach) - and the survey has changed as well, but the goal of the survey remains the same. I want to get to know my students as people AND I want to know what they know (and what they <i>think</i> they know) coming into the course.<br /><br />I asked the students a variety of questions on the survey - but I've only highlighted the "interesting" questions.<br /><br /><b>Why did you sign up for this course?</b><br /><br /><ul><li>Looked like a fun and informative course to fill a distribution requirement (9 people)</li><li>Heard it was a fun class (1 person)</li><li>Love games (1 person)</li><li>For distribution (without any mention of fun/interesting) (3 people)</li><li>Variety in math classes (3 people)</li></ul><div>Note: The first question was a short answer so I categorized the answers as best I could.</div><br /><b><br /></b><b>If you had to, which ONE of the following games would you play (with the goal to make money at a casino): </b><br /><br /><ul><li><b>Craps: 1</b></li><li><b>Roulette: 3</b></li><li><b>Blackjack: 11</b></li><li><b>Slot Machines: 2</b></li><li><b>Keno: 0</b></li></ul><br />The first question was designed to figure out my audience. The second was designed to figure out what preconceived notions the students had in regards to gambling. I also had a series of true/false and a few ranking questions on the survey (interesting to me but probably not great blogging fodder).<br /><br />What information can I glean from the two selected questions? Looking at question #1, it seems clear that the majority of the students signed up because the class sounded like a fun way to earn their mathematics distribution credit. While some mathematicians may cringe at that idea, I think it's awesome. It's not easy to have a non-majors mathematics class that the students are excited about <i>before they even step foot in the classroom</i>. <br /><br />The second question was interesting to me because the majority of the class decided that Blackjack was the way to go if the goal was making money. It's clear to me that movies like 21 (plus the glamorized depictions of casinos in movies like Ocean's 11 have an effect on people). It was also interesting that no one chose Keno (a wise move by the way) despite the fact that Keno is also available at a lot of non-casino locations (including the Maryland state lottery). <br /><br />I should mention (for those that are curious) that there isn't exactly a "correct" answer to the second question. Keno is clearly wrong in terms of things like expected value - but if you only have $1 to bet, you have a slim chance at winning say $10,000 in Keno - unlike any other game in the list! I didn't ask for any sort of written explanation from the students so I don't have any idea why each student chose the game they did. The real value (for me) will be the follow-up survey at the end of the semester where I'll put the same question <i>with a spot for a written explanation</i>. We'll see what they glean from the semester's worth of material!Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-61986443327734953662013-01-02T23:10:00.001-05:002013-01-02T23:10:20.472-05:00Another Semester is About to BeginAnother semester is about to begin, only this time my teaching load feels a lot lighter! Once again, I'm teaching two sections of Calculus I (with labs) and a section of the course I developed last semester (Mathematics of Games and Gambling). The Games and Gambling course went quite well last semester though I don't have the results of the anonymous survey that all our students take at the end of the semester. I expect there will be a few complaints but for the most part I'm expecting good things.<br /><br />So where does that leave me for Spring 2013*?<br />*It's weird writing 2013 isn't it?<br /><br />Well, I have two big goals for the semester.<br />1. In Games & Gambling: Tailor the course to the individuals in the class. In other words, don't fall into the trap of doing exactly what I did last semester simply because the lessons are complete. Last semester I tried to hit the interests of the students, let's do it again.<br />2. In Calculus I: Come up with some way to make labs <i>enjoyable learning experiences</i> rather than current Mathematica syntax heavy monstrosities that they are now. I did manage to rewrite one lab last semester and had fairly good results - so I know it's possible.<br /><br /> What are your teaching goals for the upcoming semester?Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-47654744750354328162012-12-22T09:00:00.000-05:002012-12-22T09:00:10.146-05:00Instant InsanityAlthough one might take the title of this particular blog post to be an assessment of the craziness that is the end of another semester, I assure it's not meant to be that way. Quite the opposite in fact. My semester went quite well, especially the Mathematics of Games and Gambling class that I designed and taught for the first time. As I've down throughout the semester (though admittedly not nearly as often as I would have liked), it's time for another update for the course (here's a link to my last few course updates...published <a href="http://trialbyblogging.blogspot.com/2012/09/the-mathematics-of-games-and-gambling.html">back in September</a> and <a href="http://trialbyblogging.blogspot.com/2012/10/the-price-is-right-live-review.html">another in October</a>).<div><br /></div><div>Throughout the semester, I covered a variety of topics in the class (as a reminder, the class was designed for non-mathematics majors to take as an elective to fulfill distribution requirements). The topics that covered included (but are not limited to):</div><div><ul><li>Chuck-a-Luck</li><li>Roulette</li><li>Craps</li><li>Keno</li><li>Five Card Stud</li><li>Texas Holdem</li><li>Lotteries</li><li>Instant Insanity</li></ul></div><div>It is the final topic that shall be the focus of today's entry. </div><div><br /></div><div>For a few semesters now, I've lobbied my mathematics department to allow me to teach an experimental course. For the longest time, I wanted to do a 300-level Introduction to Graph Theory course. Alas, our mathematics major is quite small (and most of our majors aim to teach at secondary schools so their electives get filled by education required classes like geometry). As such, it has been deemed unlikely that I could ever get enough students to adequately fill up a Graph Theory course.</div><div><br /></div><div>Last spring, I changed gears and proposed the Mathematics of Games and Gambling course instead. As you can guess, that was approved (and has, for the record, been approved for the upcoming spring semester as well). Although I couldn't teach graph theory, I still managed to find a way to squeeze in a few days of graph theory (at a basic level) by using the 1980s puzzle "Instant Insanity."</div><div><br /></div><div>Before I describe how I taught the lesson, I will say that overall the lesson went extremely well. I even put a question on the final exam which almost every student got correct! If you have taught a lesson using Instant Insanity (or something similar), I'd love to hear about it. If you happen to be inspired in some way to use what I did in your own classroom, I'd love to hear about your experiences when they happen!</div><div><br /></div><div>Our class periods are just over an hour long, so for the first class of the unit I showed the students the original Instant Insanity advertisement after a short PowerPoint presentation that covered the various graph vocabulary that I wanted the students to know. </div><div class="separator" style="clear: both; text-align: center;"><object width="320" height="266" class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://0.gvt0.com/vi/CQ2gHSKZBEw/0.jpg"><param name="movie" value="http://www.youtube.com/v/CQ2gHSKZBEw&fs=1&source=uds" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="http://www.youtube.com/v/CQ2gHSKZBEw&fs=1&source=uds" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div><div><br /></div><div>The terms weren't difficult, but they weren't all simplistic either (bipartite graphs). </div><div><br /></div><div>The next class was much more of a riot (for me anyhow). I gave each student a colored sheet Instant Insanity puzzle blocks which they had to cut-out and tape together. Watching college students do something that many haven't done since a middle-school art class was definitely amusing (and somehow a bit worrisome too)!</div><div><br /></div><div>After constructing the blocks, the students spent the remaining time trying to solve the puzzle. While a few did succeed, the majority of the class did not successfully complete the confounding game. I didn't provide any hints as they left class that day, though I did encourage them to find a "mathematical way to solve the puzzle." </div><div><br /></div><div>The final day of the lesson was the big one - how to solve Instant Insanity puzzles using graph theory. To begin, we discussed how each block could be "unfolded" to a two dimensional image. </div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-_stVfq_x3Os/UNUvs8H5NhI/AAAAAAAAYvw/C5RDvC1sgfo/s1600/BlankRepresentation.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="http://2.bp.blogspot.com/-_stVfq_x3Os/UNUvs8H5NhI/AAAAAAAAYvw/C5RDvC1sgfo/s400/BlankRepresentation.png" width="297" /></a></div><div><br /></div><div>From there, we can easily pair the opposite sides.</div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-GGk-JFW-m9I/UNUrMZCGl1I/AAAAAAAAYvA/bOm2DNDo90Q/s1600/EmptyColorGraph.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://4.bp.blogspot.com/-GGk-JFW-m9I/UNUrMZCGl1I/AAAAAAAAYvA/bOm2DNDo90Q/s320/EmptyColorGraph.png" width="303" /></a></div><div><br /></div><div>Once the three pairs are made (front/back, top/bottom, left/right), all you need is a graph with four vertices (one for each of the four possible colors). Draw an edge that for each of the three pairings. For example, if the top color is blue and the bottom color is red, there should be an edge connecting the blue vertex to the red one. If the left and right colors both happen to be yellow, there would be a loop connecting yellow to itself. In total, there should be three edges for each graph (one graph per each of the four cubes). </div><div><br /></div><div>Using the four graphs (or if you prefer, a single graph that combines the four small graphs), you then look for a path that uses an edge from each cube once and that makes each of the four vertices have degree two. Once you find one such solution, find a second solution. The first solution corresponds to the front and back of the four cubes. The second solution corresponds to the left and right. Note: Once you've found the front/back and left/right, the top/bottom is forced (and therefore you do not need to worry yourself about those)!</div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-hbFj5Bi1-tM/UNUvbmqrjqI/AAAAAAAAYvo/OjczdfEHgl4/s1600/EmptyColorGraph2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="http://4.bp.blogspot.com/-hbFj5Bi1-tM/UNUvbmqrjqI/AAAAAAAAYvo/OjczdfEHgl4/s400/EmptyColorGraph2.png" width="378" /></a></div><div><br /></div><div>I've skipped over a few of the finer details, but in essence that's how you solve an Instant Insanity puzzle. For those who want to give it a go, here are three puzzles. It should be noted that some puzzles may not be solvable.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-iEQXaUn6_gA/UNUvDFEpmbI/AAAAAAAAYvQ/iV5XgHB4cfA/s1600/Problem01.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="233" src="http://3.bp.blogspot.com/-iEQXaUn6_gA/UNUvDFEpmbI/AAAAAAAAYvQ/iV5XgHB4cfA/s640/Problem01.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-L4p5htkj0V4/UNUvD4xVwSI/AAAAAAAAYvY/aMnrlg7DXIQ/s1600/Problem02.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="234" src="http://2.bp.blogspot.com/-L4p5htkj0V4/UNUvD4xVwSI/AAAAAAAAYvY/aMnrlg7DXIQ/s640/Problem02.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-qCCTP9NyZVQ/UNUvEQjCF5I/AAAAAAAAYvg/B5_6-jHwUso/s1600/Problem03.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="234" src="http://3.bp.blogspot.com/-qCCTP9NyZVQ/UNUvEQjCF5I/AAAAAAAAYvg/B5_6-jHwUso/s640/Problem03.png" width="640" /></a></div><div><br /></div><div>Good luck!</div>Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-41248116302997778432012-10-27T09:00:00.000-04:002012-10-27T09:00:07.304-04:00Letters of Recommendation...<div style="text-align: left;"><iframe align="left" bordercolor="#000000" frameborder="0" height="250" hspace="0" marginheight="0" marginwidth="0" scrolling="no" src="http://ad.doubleclick.net/adi/N7433.148119.BLOGGEREN/B6675098.3309;sz=300x250;ord=[timestamp]?;lid=41000000028007181;pid=UBM9780978170059;usg=AFHzDLvCx1K6z7-oxZahmnOEixVL_bvWEA;adurl=http%253A%252F%252Fwww.cdsbooksdvds.com%252Fproduct.jhtm%253Fsku%253DUBM9780978170059;pubid=590182;price=%2435.95;title=Instant+Recommendation+Letter+Kit+-+How+to+Write+Winning+Letters+of+Recom...;merc=CDS+Books+and+DVDS;imgsrc=http%3A%2F%2Fc373855.r55.cf1.rackcdn.com%2F9780978170059.jpg;width=101;height=135" vspace="0" width="300"></iframe>Although I love almost all aspects of my job, there are a few things that I don’t necessarily look forward to doing. One such thing is writing letters of recommendation. Around this time of year, many of our undergraduate seniors are preparing for graduate school – and part of that preparation requires them to secure <i>X</i> numbers of letters of recommendation. </div><div class="MsoNormal"><br /></div><div class="MsoNormal">Don’t get me wrong, I love (most) of our seniors – and I definitely want to write them great letters. I truly believe that they will do well in whatever program they choose, none of that is the issue at hand here. No, the issue is all on me. I’m a harsh critic of myself, and while you probably can’t tell based on the drivel that I put on this blog (among the <a href="http://fanofreds.blogspot.com/">two blogs</a> that I maintain), I do care.<br /><br />A lot. </div><div class="MsoNormal"><br /></div><div class="MsoNormal">Letters of recommendation are one of those things that can be super easy to write for a select student or two each year, but for the rest of the students… Oh boy. They can be exceedingly difficult, especially for students who I only had for a class or two or perhaps for a student who didn't get the best grades and/or perhaps didn't stand out in some other spectacular way.</div><div class="MsoNormal"><br /></div><div class="MsoNormal">For those of you who write letters for your students (or anyone for that matter), how do you do it? How do you make the letters unique (or don’t you worry about that)? Personally, I think a truly personalized letter is better – but then again, I've never served on an admissions committee. I can’t say that I know for sure what they look for – and if I did, well, I’d guess my own letter writing skills would be a bit better!</div>Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-78162069460432228862012-10-15T09:30:00.000-04:002012-10-15T09:30:01.158-04:00The Price is Right LIVE: A ReviewAs <a href="http://trialbyblogging.blogspot.com/2012/10/the-price-really-is-right.html">I mentioned a few days ago</a>, I took my <i>Mathematics of Games and Gambling</i> class to see a showing of The Price is Right LIVE at our local community arts center. The show was last night and while I haven't seen my class yet to get their impressions of the show, here is my personal review of the Price is Right traveling show.<br /><br />In a word: <b>Semi-lame.</b><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-Q_h_1x0TMgo/UHYtRAbcGKI/AAAAAAAAWhI/ELOujf92lHY/s1600/PriceIsRight.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="231" src="http://1.bp.blogspot.com/-Q_h_1x0TMgo/UHYtRAbcGKI/AAAAAAAAWhI/ELOujf92lHY/s320/PriceIsRight.jpg" width="320" /></a></div><br />Ok, that's not even a real word, but it's how I feel.<br /><br /><b>The good:</b><br /><br />Many of people's favorite games are present. Punch-a-Bunch, Plinko, Cliffhangers, Any Number, and Hole in One were all played. The had one group of three people spin the big wheel. Two people got the chance to play for the Showcase (only one showcase - both players bid at the same time).<br /><br /><b>The bad:</b><br /><br />The show started late and ended early (or so it seemed). Extremely short amount of time spent actually playing any games. They showed a bunch of video clips from old shows - but nothing that you can't find on YouTube (for free). The prizes were borderline good for most of the show...certainly not great (even with lowered expectations). There was a refrigerator as a prize and a billiard table used as big prizes (neither were actually given away). The small (initial bid) prizes included a 4 handheld phone system for a house (seriously, who uses those any more?), a pair of diamond earrings, a popcorn machine, and a vacuum. <br /><br /><b>The terrible:</b><br /><br />The final showcase consisted of:<br />A new car (Nissan Versa I believe?)<br />A 3-day cruise to the Bahamas<br />An iPod touch<br />A 50 inch flat screen tv<br /><br />The first contestant bid $19,000 and change. The second contestant bid $20,000 and change.<br /><br />For the traveling show, the person who is closest to the actual price (without going over) wins ONE of the items in the showcase - in this case, the 3-day cruise. In order to win ALL of the items, you had to be within $100 of the actual price (i.e. not going to happen)!<br /><br />Actual retail price (according to the show)? $14,000 and change.<br /><br />The show ended on that note. A seemingly bogus final showcase, a pair of losing contestants, and a bunch of audience members feeling like the contestants were cheating. The best line I overheard while leaving the theater: "If a new car really cost $14,000, then everyone would have a new car."<br /><br />Never mind all the other stuff in the showcase...<br /><br />Since I was curious, here's a few numbers that I found via internet research*:<br /><span style="font-size: xx-small;">*note, all prices are guesses, I have no idea what the brands/companies were for some of the prizes</span><br />Price of 2012 Nissan Versa starting at: $10,999 (from <a href="http://www.nissanusa.com/all-new-versa-sedan/#">Nissan's website</a>)<br />3-day Cruise: $299<br />50 inch TV: LG ($699.00) one of the cheapest options<br />iPod touch: $179.00<br />Total: $12,176<br /><br />So is the game rigged? Well, I say yes but only because they make you <i>think</i> the showcase prizes are great when in reality they aren't nearly so good. I also found it weird that in Punch-a-Bunch, the host knew exactly where the one $2500 prize was hiding...and it appeared to be printed on a larger card. Makes me wonder if that particular hole had two cards residing in it, a $50 or similar prize if the contestant happened to select it and the big prize otherwise (the host showed the big prize to "prove" the fairness of the game). I say when you have to "prove" that you are on the up-and-up, you probably aren't really on the up-and-up.<br /><br />My suggestion to anyone who might see one of the live shows in their area - bid $1 and nothing more on the final showcase. Chances are, your opponent will over bid and you then you win the cruise. Don't bother trying to get too close, it won't work!<br /><br />What I don't understand is why the producers of the show don't <i>want</i> to have one person win the cruise. If the price is really only $300, that's paid for in a matter of 10 balcony tickets...a mere drop in the bucket. Why have people leave angry (even if the pricing seems fair now that I looked up all the costs)? If one of the two people had won the cruise, I think the entire audience mood at the end of the show would have been much better.<br /><br />I also question the length of the show. In a typical TV episode (granted, I'm sure footage is cut in order to fit it in 60 minutes - with commercials), there are six games played, the big wheel is spun by two groups of three people, and there are two final showcases.<br /><br />In the travel show, there were only five games played, the big wheel was spun by ONE trio of contestants, and there was only one final showcase. The entire show lasted just over an hour - and much of that time was "wasted" by showing the aforementioned video footage of old shows and for people making their way to the stage. <br /><br />In the end, I'm interested to hear my students' take on the show, but for me, I can't in good conscience recommend anyone go to the show. You'll have more fun watching old clips on your computer - save the price of the ticket. Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-86951848710603602372012-10-11T18:00:00.000-04:002012-10-11T18:00:06.541-04:00The Price Really Is Right!I've spent <a href="http://trialbyblogging.blogspot.com/search/label/Mathematics%20of%20Games%20and%20Gambling">a fair bit of time</a> discussing the happenings (and future plans) for my course that I am both developing and teaching this semester. Today, I figured I would discuss our recent activity mostly to serve as <a href="http://trialbyblogging.blogspot.com/2012/09/the-mathematics-of-games-and-gambling.html">another diary type entry</a> for myself next semester.<br /><br />My school's fall break is this week which means we get Friday off. Yeah, a one day break isn't overly impressive (but we do get the Wednesday before Thanksgiving off as well which I appreciate). Anyhow, it's often tough to cover much material in a short week for a distribution class since the students have all of Thursday, Friday, Saturday, <i>and</i> Sunday to forget. However, thanks to our local community arts center, I got lucky.<br /><br />You see, the traveling game show The Price is Right LIVE is coming to our town on Sunday. When I learned about the show, I instantly arranged for tickets (free for the entire class) and rearranged my course schedule to accommodate the game show. That meant both Monday and Wednesday were used to discuss Price is Right games and strategies.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-Q_h_1x0TMgo/UHYtRAbcGKI/AAAAAAAAWhI/ELOujf92lHY/s1600/PriceIsRight.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="288" src="http://1.bp.blogspot.com/-Q_h_1x0TMgo/UHYtRAbcGKI/AAAAAAAAWhI/ELOujf92lHY/s400/PriceIsRight.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Image source: <a href="http://content.clearchannel.com/cc-common/mlib/2036/01/2036_1264503009.jpg">http://content.clearchannel.com/cc-common/mlib/2036/01/2036_1264503009.jpg</a></td></tr></tbody></table><br />We spent one and a half days discussing the mathematics behind the game of Plinko! It ended up being a great way to review choice trees (using a small version of the Plinko! board). It also natural evolved into a way to discuss using a small problem to help us solve a larger version...and it perfectly illustrated the need for a formula or shortcut when trying to analyze the "real" board. In our case, the short cut is of course Pascal's triangle...which in itself is an excellent lead in to the next segment of the course where we will discuss the Binomial Theorem (and the MLB World Series).<br /><br />After spending the better part of two classes on Plinko!, I used the remaining class time to give a crash course on some other games that might be played during the live show (I emailed the producers of the program but they wouldn't divulge which games would be played). <br /><br />We looked at when to spin and when to "hold" during the Showcase Showdown.<br /><br />We talked about bidding strategies.<br /><br />We talked about basic strategies for a few of the games...and we ended yesterday's class with a video of what <i>not</i> to do which drew the expected laughs.<br /><div class="separator" style="clear: both; text-align: center;"><object width="320" height="266" class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="https://ytimg.googleusercontent.com/vi/xIK2z6fj38U/0.jpg"><param name="movie" value="https://www.youtube.com/v/xIK2z6fj38U&fs=1&source=uds" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="https://www.youtube.com/v/xIK2z6fj38U&fs=1&source=uds" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div><br />Overall, the students seemed quite excited for the opportunity to attend the show. The math wasn't easy for the Plinko! board but most students seemed to intently study the various problems and explanations. I had plenty of great questions about it during the lessons which convinced me that the students were truly engaging the material. I believe the allure of winning a car (supposedly they play a game where someone could win a car even in the traveling show) was a great motivator!<br /><br />Now that the lessons are over, I can only sit back and hope at least one of my students get the opportunity to go the stage. It'd be a lot of fun to say that students can take my class and possibly win a vacation to Bermuda or something!Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-21132086313484101162012-09-28T09:00:00.000-04:002012-09-28T09:00:03.556-04:00The Mathematics of Games and Gambling: A Course UpdateI haven't done well keeping the blog updated on a daily basis (or even a semi-daily basis) but that doesn't mean that I haven't been keeping track of what has (and hasn't) worked in my classroom. I've talked about my Mathematics of Games and Gambling course that I'm developing/teaching during the Fall 2012 semester a few times already (most notably <a href="http://trialbyblogging.blogspot.com/2012/08/the-mathematics-of-games-and-gambling.html">here</a> and <a href="http://trialbyblogging.blogspot.com/2012/08/the-mathematics-of-games-and-gambling_25.html">here</a>). Since I haven't mentioned much about the course since then, it's probably time to reflect on how things have gone through (almost) five weeks.<br /><br />So far in class (through five weeks - aka fifteen 65 minute classes), we have:<br /><br /><ul><li>Learned the game of Chuck-a-Luck</li><li>Learned the game of Roulette (both American and European)</li><li>Learned the game of Craps (both street and casino)</li><li>Learned the game of Five Card Stud Poker</li><li>Learned about expected values</li><li>Learned about probabilities</li><li>Learned about choice trees</li><li>Learned about combinations and permutations</li><li>plus a variety of other (smaller) topics such as a few brain teasers and card puzzles, plus assorted vocabulary as it arises in various gaming contexts.</li></ul><br />We've also had a day where the class played craps, another where they played roulette, and today they happen to have a Five Card Stud Poker tournament. The class has had five take home assignments so far (all but one spanning multiple classes). Finally, the class took their first test on Monday of this week.<br /><br />With all that's been done so far - and, quite honestly, that is a LOT of material for a distribution math class, it's time to reflect on the good, the bad, and the things that I might (or might not) change next time I teach the course. <br />*Note: All observations are mine and mine alone. I have not polled my students yet nor issued any sort of survey thus far in the semester.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-AA_aBphfNok/UGUgoX7jPcI/AAAAAAAAWN0/k-oRliQL-j4/s1600/GoodChoiceBadChoice.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="265" src="http://3.bp.blogspot.com/-AA_aBphfNok/UGUgoX7jPcI/AAAAAAAAWN0/k-oRliQL-j4/s400/GoodChoiceBadChoice.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Image source: http://singlemindedwomen.com/women-relationships/duchess-digest-the-good-the-bad-and-the-solution/</td></tr></tbody></table><br /><b>The Good:</b><br />Students love games and they seem to be working to understand the mathematics as a way to get better at the games. I split the class into two separate tables when playing Craps - one table had every student (except one) turn their $300 into $1000+, while at the other table almost all the students went bankrupt. It was a great, though unplanned, lesson in the draw of the casino!<br /><br />The first round of testing had 6 of the 18 students earn an A on the exam. For a distribution math course, that's awesome. Even more impressive is the fact that the test was five pages long - and certainly not easy - and yet one-third of the class earned an A. <br /><br />The best part of the class though isn't the grades or even the "fun" stuff. Instead, the best part so far has been the students reaction to various problems, homework assignments, and in class activities. The overall attention and engagement levels are <i>through the roof</i> as compared to a typical distribution class. I can't say the class is at 100% in terms of engagement, but on any given day I would wager that at least 16 of the 18 students are fully engaged. Again, a remarkable number considering the fact that most of the students in the class are self-professed math-phobes.<br /><br /><b>The Bad:</b><br />I mentioned the results of the first exam in "The Good" section, but I would be remiss if I didn't mention it in "The Bad" section as well. Out of the 18 students, 4 of them ended up with Fs, including one student who left a pair of 21 point problems (out of 100 total exam points) blank. As I said above, the engagement is there for most, but not all, students.<br /><br />I think it's a bad thing that I have been unable to fit in time to play most of the games with the students and let them figure out their own strategies before we go over the mathematical analysis of each game. I was able to do that for Roulette but not for Craps.<br /><br /><b>Things to think about changing:</b><br />I don't think I have the exact right balance of rigor and exploration. I have a tendency to automatically analyze games logically as soon as I am introduced to them (my wife hates that, especially if we are playing against each other)! However, just because that's a natural thought process for me, it most definitely is not for the majority of the students in the class. I need to be better at guiding them through the analytical process. In the beginning of the semester, I used a few brainteasers/puzzles as warm-ups which worked quite well. Unfortunately, I haven't done much of that lately (mostly because the amount of material in the daily lessons hasn't allowed extra time).<br /><br />I think the first exam should have been in week 4 rather than week 5. I probably should have spent a full day on permutations and then a second day on combinations. I ended up doing both on the same day and while it worked for 80% of the students, that's not close enough to 100% for my tastes.<br /><br />Finally, I need to come up with a way to assess learning besides exams. Many of the students in the class that didn't score great on the exam actually seem to know the material but they "froze" during the exam. I think old math paranoia habits die hard... <br /><br />I guess there's not really much purpose to this blog entry other than as a self-diary of sorts. Of course, if you have any ideas for the course, by all means share them!Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-19498927510639609202012-09-18T12:30:00.001-04:002012-09-18T12:30:01.787-04:00The Job Application Process: I Didn't Miss This One Bit.I've been teaching at my current institution on a full-time basis for about five years now. Unfortunately for me, the college has a policy that people without a Ph.D. get canned after a set amount of time. That amount of time seems to depend on who you talk to, some say 5 years (obviously not true since I'm still there), most say 6 years, and a few say 7 years. Even in a "best case" scenario, I'd only be able to work there for about two more years. As such, I have officially jumped back into the proverbial hiring pool.<br /><br />My wife's job doesn't allow her to move from our current location so I'm bound geographically. Unfortunately, for a person in higher ed, that's dangerous since there simply aren't that many jobs out there. Of course, my options are further limited by my limited degree (and don't get me started on my mostly stellar teaching evaluations). <br /><br />Therefore, despite still having a job for the moment, I decided I better start applying for any (and all) jobs that might be a fit for me if they are at all geographically close. Last night, I finished an application for a vice president of student life position. Sure, it isn't a teaching gig but it is still in higher education <i>and</i> I would still be able to work with students, two things that I find important.<br /><br />Will I get the job? Eh, I don't have any idea. If I do, I'm sure the tone (and direction) of this blog will change. Of course, I have about two readers per day so I don't think anyone will mind.<br /><br />Until then, I'm still working and teaching...which means lots of lessons (and some grading). In my Calculus class, we looked at the product and quotient rules for derivatives on Monday. Tomorrow we will spend the class reviewing, though most of the review will be in the form of matching algebraic expressions (specifically with fractional exponents since incoming students to my calculus class seem to be universally weak with exponents/roots).Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com1tag:blogger.com,1999:blog-1869529593927152124.post-36423105428707607152012-09-12T09:30:00.001-04:002012-09-12T09:30:04.465-04:00So I Played Pong in Math Class TodayThat's right, I played pong in my Calculus I class today (assuming today is this past Monday). No, it wasn't this kind of pong...<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-0i-NFOm9i5s/UFADOCLyqcI/AAAAAAAAVl4/eHbvKvXTONo/s1600/beer-pong.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="262" src="http://4.bp.blogspot.com/-0i-NFOm9i5s/UFADOCLyqcI/AAAAAAAAVl4/eHbvKvXTONo/s400/beer-pong.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Image source: <a href="http://www.aboutdwi.com/blog/tag/teenagers/">http://www.aboutdwi.com/blog/tag/teenagers/</a> </td></tr></tbody></table><div><br /></div><div>...but it was based on that idea - with my own "twist" of course. </div><div><br /></div><div>My class had their first exam (limits - I'm still doing Calculus I in the "conventional" order). Anyhow, I often try to do some sort of review game with the class the day before the exam. During my couple of years of teaching, the review game was almost always Jeopardy. The students loved it then (they even added me to the "Men of Mathematics" poster in the hallway as the inventor of math jeopardy) Fun times for them, but honestly, Jeopardy is a total bore from my perspective...especially when done over and over.</div><div><br /></div><div>A couple of years ago, I managed to create a working "Who Wants to Be a Millionaire" game, complete with the lifeline allowing them to phone a friend using their cell phones. Great hilarity ensues when a team of four or five is all on the cell phone trying to explain (and then acquire) an answer to a question within the 60 second time limit.</div><div><br /></div><div>Flash forward to last year, I added in a game based on the bar trivia game (referred to as Quizzo in my neck of the woods). I guess the bar theme got extended a bit further this year with my Limit Pong game.</div><div><br /></div><div><b>Set-up:</b></div><div><br /></div><div>I found four identical boxes (I used baseball card boxes - <a href="http://fanofreds.blogspot.com/">something I have plenty of</a>) and labeled them as Team 1, Team 2, Team 3, and Team 4. I then took a bunch of styrofoam cups (approximately 30) and used a sharpie to put a point value <i>on the inside of the cup</i>. The point values varied, the majority of the cups were worth either +1 or +2, though I scattered in a few +5s and one +10. To keep things interesting (and to add some strategy to the game), I also added in a few -1s and -2s on the cups.</div><div><br /></div><div>From there, all I needed was a ping pong ball (I happen to advise the table tennis club on campus as well so that was easy enough to acquire). For the first time, I had to spend a bit of time going over the rules, but I imagine if I play the game again with the same class I could easily fit in a fifth round (and stay within the 65 minute class period).</div><div><br /></div><div><b>Rules:</b></div><div><b><br /></b></div><div>The rules were fairly simple. I split my class into four equal teams. Each team member got a worksheet packet for his or her self AND the team got an extra "team packet". I gave the teams a few minutes to work through the first page of the packet. The goal of the problem solving round is to fill out the team packet with the team's final answers. After time was up, the groups swapped packets and graded each other's pages. At this point, I posted the answers on a PowerPoint slide so that students could copy the solutions on their own, personal packets if they wished.</div><div><br /></div><div>Each round was worth a set amount of points (usually 1 point per question). At the end of the scoring phase, one member from each team (this role rotated each round) came up to the front of the class as the "thrower" for that round. Using the points earned during the round as a currency of sorts, the thrower could attempt to throw the ping pong ball (with a mandatory bounce) into their team's box OR they could select a cup (all cups were facedown so it was a mystery as to the point value) and then place the selected cup in a box. Positive point cups go in their team's box, negative point cups get to go in one of the other team's boxes. In my cases, each box could hold up to five cups, so once a box reached five cups you could stack (and therefore, replace less desirable cups).</div><div><br /></div><div>We repeated the process three more times, with a different student getting the opportunity to throw each round. At the end of the day, the highest point total (from the throws only) won! </div><div><br /></div><div>For the first attempt, I liked the game a lot (and it seemed popular with the students).</div><div><br /></div><div><b>The good:</b></div><div><b><br /></b></div><div>I did this activity in both of my Calculus I classes. In one class, the students recognized there was a strategy in terms of whether to throw the ball in the hopes of scoring points and grabbing cups (in hopes of making future throws worth more). By the way, a throw that lands in the box (but not a cup) was worth a single point. You might even say the teams attempted to <i>optimize</i> their score by carefully choosing throws and cups.</div><div><br /></div><div><b>The bad:</b></div><div><b><br /></b></div><div>The other class didn't grasp the strategy at all. The initial throwers all opted to fill their box with cups (as much as they could). The next group also grabbed cups (replacing as necessary). By the time the third and fourth throwers were up, they only had the option of throwing. On the other hand, the average team score was much higher with this group - though rumor has it some of them were well-versed in the art of beer pong.</div><div><br /></div><div><b>Things to try:</b></div><div><b><br /></b></div><div>I need to emphasize the solutions a bit better. Students got too excited about the throwing part and would sometimes not worry about problems they got incorrect. I suppose that's the danger of any game where the students are emotionally invested, but it's still a problem that I need to fix for next time. After all, what's the point of reviewing if the students don't make the best of the time and opportunity?</div><div><br /></div><div><b>Game modifications:</b></div><div><b><br /></b></div><div>The game itself worked fine, though I think it might be fun to have a bit more variety in terms of the number of cups. Scores would have been more impressive if the boxes held more cups - some teams scored zero points simply because they were lousy pong players. I don't mind skill having a role, but it didn't seem right that teams couldn't land a single ball in the box. The students really enjoyed it when they grabbed a negative cup and got to place it in one of the opponent's boxes. Both classes used some strategy in terms of the negative cups (using them to either wipe out big positive gain cups or to try and weaken the first place team).</div><div><br /></div><div>All told, it was a fun activity that my students really seemed to enjoy. I haven't finished grading the exams yet, so I can't even begin to make any guesses as to the effectiveness of the activity compared to previous year's games but I'm sure I'll try to make some conclusions at some point in the future. Until then, if you have any review games or other ideas to share with me, please do so!</div>Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-58356845676293646802012-09-04T10:00:00.015-04:002012-09-04T10:00:14.018-04:00Week 1 is in the Books!<br /><div class="MsoNormal">Happy (day after) Labor Day! While I’m guessing most of you had yesterday off, my school held classes. I’ve worked there for five or six years now so I’m used to working on Labor Day (and honestly, it’s hard to complain about working on the holiday when I just had roughly four months “off”). No one feels sorry for me.</div><div class="MsoNormal"><br /></div><div class="MsoNormal">One of my goals for the blog is to keep a running diary of thoughts and observations from my classes. After one full week, I have to admit that I’m looking forward to the semester! I have a pair of sections of Calculus I, the first class has 16 students and the second has 19 students. I appreciate having two sections with roughly the same number of students as it makes planning activities easier! <a href="http://trialbyblogging.blogspot.com/2012/08/first-day-of-classes.html">My first day of theCalculus</a> course went extremely well, but I do fear that I’ve lost a little steam and enthusiasm from the students now. I attribute that to a string of mostly lectures and problem solving in regards to limits. If there is one giant weakness to my teaching, it’s that I don’t have a steady stream of varied activities. Each semester I seem to plug in one or two new things to try (and I usually keep them for future semesters) but even so the course can get a bit monotonous. </div><div class="MsoNormal"><br /></div><div class="MsoNormal">Historically, about half of my students fail to fully grasp limits (and continuity) by the first exam. Most of the students are able to pass the exam, but limits at the Calculus I level are easy enough that I believe all the students should be able to muster at least a B on the exam. So far, my current crop of students is right on pace – most have grasped the concept but there are still four or five in each class that still don’t understand. I keep thinking that if I could come up with an activity that demonstrates the concept of the limit those students might also find themselves understanding all the course material. Unfortunately, I have yet to come across a suitable activity.</div><div class="MsoNormal"><br /></div><div class="MsoNormal">My third class is the Mathematics of Games and Gambling – a course that<a href="http://trialbyblogging.blogspot.com/2012/08/the-mathematics-of-games-and-gambling_25.html"> I am currently developing</a> from scratch. I had ambition plans for the course but it didn’t even take a full week for me to realize that I am going to have to go quite a bit slower than I had initially planned. After a week and a day, we have covered finite probabilities and played both Chuck-a-Luck and Roulette. In the next class, we do a mathematical analysis of Roulette (other than explaining the rules, I didn’t say much about Roulette in class yesterday). My goal was for the students to experiment as they played to see if they could come up with a strategy that was either good or bad. </div><div class="MsoNormal"><br /></div><div class="MsoNormal">In terms of bad strategies, the students offered some advice like “don’t bet a dollar on black and a second dollar on red at the same time” and “don’t bet on single numbers.” The first piece of advice is perfectly valid – and quite honestly, the second was as well in the sense that I only gave each student $10 to “bet” with. Of course, we all know that betting strategies in roulette are about as helpful as a beach volleyball in the arctic circle.</div><div class="MsoNormal"><br /></div><div class="MsoNormal">All things considered, I’m moderately pleased with the first week of classes. I wish I could figure out a way to teach Calculus without resorting to as many lectures but otherwise things have gone quite well. I should have a better handle on my Gambling students’ abilities once I grade their first homework assignment (which was collected yesterday). I think I've managed to display most of <a href="http://trialbyblogging.blogspot.com/2012/08/qualities-of-good-math-teacher.html">the traits that my students consider important in a good mathematics teacher</a>, though I don't think most of them find me funny*.</div><div class="MsoNormal"><br /></div><div class="MsoNormal">*When explaining the floor and ceiling functions, I like to ask my students what the floor of pi is. After getting the correct answer, I point out to them that they now know the floor of pi(e) is not actually crust but three. Each class produced three of four groans, a chuckle or two, and a lot of eyes (and heads) rolling. </div>Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com1tag:blogger.com,1999:blog-1869529593927152124.post-16803421894529364462012-08-28T08:30:00.001-04:002012-08-28T08:30:00.607-04:00Qualities of a Good Math TeacherI had a highly successful first day (more on that another day perhaps). For today's post, I thought it would be fun to see what qualities my students thought a successful math teacher must possess. They answered this question (<a href="http://trialbyblogging.blogspot.com/2012/08/first-day-plan-calculus-i.html">along with a host of others</a>) within the first 10 minutes of the opening class.<br /><br />I have three classes to teach this semester:<br /><b>The Mathematics of Games and Gambling</b> - a distribution level course. There is a mix of freshman through seniors in the course. Class size is 18. There is one math major in the course (a senior who needs credits).<br /><br />Calculus I - Section A - Mostly upperclassmen, about a third of which had me for a previous class. Class size is 21.<br /><br />Calculus II - Section B - All freshman (except two). Only one student had me for a previous class. Class size is currently 15 - it could potentially rise to 20 by the end of the week (though I doubt it).<br /><br />With that in mind, let's see what the students claimed as the qualities of a good math teacher (divided by class).<br /><br /><b>Mathematics of Games and Gambling student responses:</b><br /><br /><ul><li>Fun & Interesting</li><li>Thorough, patient</li><li>Interactive, knows the material, is excited about the material</li><li>Explains well, takes time, offers homework to help prepare for tests</li><li>Helpful & receptive to questions I may have; Makes subject matter interesting</li><li>Multiple ways to find a solution</li><li>Patient, eloquent, sense of fun</li><li>Explains lessons and hands on</li><li>Patient</li><li>Understanding, approachable</li><li>Knows what he is talking about; Is clear when explaining steps</li><li>Explains well and is hands on</li><li>Answers students' questions</li><li>Knows math; Gets the students interested in math (Texas Hold 'em? Yes please)</li><li>Strict, but fun, explains things, not everyone's BFF</li><li>Explanation skills, patience</li></ul><br /><br />As you can see, there is quite a diversity in what makes for a good math teacher. However, the one word that appeared a lot is <b>patience</b>. By my count 7 of the 16 respondents either named patience outright or alluded to patience in their qualities. The other attribute that was named a lot was <b>fun</b> or <b>excitement </b>(four out of the 16 alluded to fun in their comments). For a distribution class, I thought the comments were quite telling! The students want to see why the subject of math is interesting or fun, but they want to be shown in a clear, precise, (and perhaps slow) manner. If I had to try to summarize this class' thoughts into a single sentence, it would be: A successful (distribution) math teacher has a love for the subject which they can translate into thoughtful, fun, and well-structured lessons.<br /><br />Moving out of the distribution course, I have a pair of Calculus I sections. First up, <b>the (mostly) freshman section of Calculus and their thoughts on makes for a good math teacher</b>.<br /><br /><ul><li>Understanding of info, communication</li><li>Interactive, Hands on</li><li>Engaging, able to make course interesting and fun</li><li>Experience</li><li>They can somehow make class fun and not all lecture</li><li>Gives a lot of problems to practice with</li><li>Helpful, insightful, explains things well and goes over things extra times</li><li>Funny, helpful, smart</li><li>Can teach a topic in different ways to help better understand something</li><li>Organized, smart</li><li>Explains/teaches well, interactive, approachable</li><li>Enthusiasm</li></ul><br /><br />For my (mostly) freshman section of Calculus I, the differences in what makes for a good teacher (as compared to the distribution course) were quite stark. The idea of being fun wasn't nearly as prevalent. The idea of patience was essentially non-existent. Instead, words like "smart", "insightful", and "organized" make an appearance. Since the majority of the students in the class hadn't had more than one college class (as in, a single meeting of one class since this class meets in the morning), it seems that many of the qualities are a direct response to the stereotypical college professor.<br /><br />Finally, <b>my second section of Calculus I (a class in which there were only a couple of freshman and plenty of students who have had me for previous courses) had this to say about successful math teachers</b>.<br /><br /><ul><li>Able to fully answer questions & visibly demonstrate answer; able to make learning fun</li><li>Approachable</li><li>Explains everything</li><li>Patience, intelligence</li><li>Funny, respectful, patient</li><li>Someone who explains well and works problems on the board</li><li>Explains new material in detail</li><li>Goes at a good pace and is clear</li><li>Funny, helpful, interesting, knowledgeable</li><li>Patience, clarity, authority</li><li>Good at math</li><li>If they can teach me, they can teach anyone</li><li>Answers every question</li><li>Approachable</li><li>Interactive, entertaining, available</li><li>Doesn't assume we remember how to do everything from precalc*</li></ul><br />*not one of my former students for the record!<br /><br />I wasn't surprised by the across the board responses from this class based on the heterogeneous mix of students in the course. The freshman all said things to the freshman in the previous class while the upperclassmen usually went with something along the lines approachable or explains things well.<br /><br />Can you make any broad assumptions or observations from my data? I don't know (well, you can make assumptions but how accurate are they)? If you put all the responses into a single list, it's interesting how much higher "fun" and "patient" rank as compared to "knowledgeable". Even more telling, I teach at a liberal arts college so the answer of "prepares me for a future job" was essentially non-existent! <br /><br />Do you ask your students anything along the lines of what I did? Or, if you are a non-student reading this, what qualities do <i>you</i> think a good math teacher should exhibit?Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-82262014704320780042012-08-27T08:00:00.000-04:002012-08-27T08:00:16.712-04:00First Day of ClassesIt's finally here - the start of another school year! Today, I'll teach <a href="http://trialbyblogging.blogspot.com/2012/08/first-day-plan-calculus-i.html">my first lesson in Calculus I</a> (twice actually - I have two sections this semester). I will also teach the first class <i>ever</i> of The Mathematics of Games and Gambling at my college. Although I will have a busy semester, I am hoping to use this blog to chronicle my journey through the semester. Good luck to all of those who begin teaching today - and good luck to all the students as well!Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com1tag:blogger.com,1999:blog-1869529593927152124.post-66006516226537060682012-08-25T10:00:00.000-04:002012-08-25T10:00:00.196-04:00The Mathematics of Games and Gambling: Planning Part 2<i>Note: This post originally appeared on my other (non-education related) blog <a href="http://fanofreds.blogspot.com/2012/06/mathematics-of-games-and-gambling-part.html">Nachos Grande</a>. I'm slowly moving all the education related posts over to this blog. Don't worry, there aren't many that need to be moved. This particular entry was the second in what was supposed to be a fairly lengthy series. Unfortunately, I never got around to writing a third planning post. Thus, any future planning posts you see in relation to my Mathematics of Games and Gambling class will be new!</i><div><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-JUCYEEykkKA/T-FFqJQSBUI/AAAAAAAAR8A/02VuFBW-YtQ/s1600/Roulette.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="275" src="http://2.bp.blogspot.com/-JUCYEEykkKA/T-FFqJQSBUI/AAAAAAAAR8A/02VuFBW-YtQ/s400/Roulette.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Image source: <a href="http://entertainment.howstuffworks.com/how-to-play-roulette.htm">http://entertainment.howstuffworks.com/how-to-play-roulette.htm </a> </td></tr></tbody></table>This is the second in what will (hopefully) be an ongoing series throughout the summer as I plan my new course that I'm teaching this fall. You might want to <a href="http://fanofreds.blogspot.com/2012/04/mathematics-of-games-and-gambling.html">read the first post</a> in order to see why I'm doing this and to catch up with me.<br /><br />It's taken me over a month, but I finally have the first week of the course figured out and the lessons are (mostly) finished. When I teach, I usually use PowerPoint so part of my course planning involves making the PowerPoint presentation to go along with the day's topic. I also usually allow my students to print out the slides beforehand (if they so desire) so I have to add lots of animations to keep the work to problems (and the solutions) hidden from those who don't want to see the answers while they are working the problems out in class. Obviously, it is a lot of work - but based on student feedback, it's appreciated by the majority of them. Of course, there's always one or two students who tell me I should write on the board all the time instead of using the PowerPoint (they obviously haven't paid attention to my handwriting)!<br /><br />Before I put together the first week of lessons, I sketched out the full schedule of the semester - and if time allows (and there's enough interest out there), I'll probably do a post covering each of the major topics as I complete them. In this way, I can motivate myself to work harder all summer - and be accountable for my actions if I don't!<br /><br />I've decided to start the course with a week long study of finite probabilities. At the college where I work, the entire first week is known as Drop/Add week which means theoretically a student can add my class on Friday at 3:59 PM and expect to do well in the course (despite missing three classes already - it's a Monday, Wednesday, Friday morning class). As a professor, I hate the drop/add week because you can't cover too much or new students have little hope of catching up, but you can't cover too little because then the students who attend the first week get bored and think the class is lame. It's a tough life.<br /><br />So, I usually do some form of compromise. In this case, it's going to be a week of finite probabilities. We'll look at dice and cards on Monday and Wednesday and then switch over to Roulette on Friday. I think I can arrange to get a roulette wheel for the day so we'll probably "play" a little Roulette as a class as well. I'm debating about giving each student a "gambling bank account" of fake cash to use over the course of the semester. Will they listen to the odds and keep the money safely in the bank or will one student's success convince ten others to try their luck (with undoubtedly poor results)? It should be fascinating (at least for me).<br /><br />Once the second week begins, it's the proverbial pedal to the metal as we plow through a bunch of topics. I think the second week will pick up with Roulette and mathematical expectation. Speaking of that, did you know that the expected value of a $1 bet on ANY* type of Roulette bet on an American Roulette wheel is -0.0526? That is, you should expect to lose on average 5 cents for every dollar you bet in Roulette. No wonder the casinos love the game!<br /><br />*<span style="font-size: xx-small;">There is one bet (the five-number bet) on the American wheel that gives the house an even greater edge of 7.89% or almost 8 cents per dollar. See the image below for more details on the possible Roulette bets on an American wheel.</span><br /><br />And for those that are wondering, there are two types of Roulette wheels in use around the world. The "original" wheel (which is used basically everywhere except in the US) has the numbers 1 - 36 plus a green 0 spot. The American wheel is identical except it adds a green 00 spot to go along with the single 0 spot. In other words, the house advantage doubles on an American wheel! It's not hard to see why Roulette isn't terribly popular in America and yet it is quite popular everywhere else around the world.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-iQiXnXmRnXA/T-HjJzBInbI/AAAAAAAAR9Q/K5I5GFvs51I/s1600/RouletteBetAmerican.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="259" src="http://4.bp.blogspot.com/-iQiXnXmRnXA/T-HjJzBInbI/AAAAAAAAR9Q/K5I5GFvs51I/s320/RouletteBetAmerican.gif" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Image source: <a href="http://www.bestamericanroulette.com/roulette-guide/american-roulette-odds/">http://www.bestamericanroulette.com/roulette-guide/american-roulette-odds/ </a> </td></tr></tbody></table><br />For the first week of my lecture, the main goal is for students to learn how to compute expected values (such as the one quoted above for Roulette). Expected values aren't terribly difficult (but they prove to be an extremely valuable tool when analyzing some games)! Essentially, you can compute expected values by summing up each individual event's probability multiplied by that event's respective payoff. The one catch is that each of the events with probabilities have to be <a href="http://www.proofwiki.org/wiki/Definition:Pairwise_Disjoint">pairwise disjoint</a>. <br /><br />As with any course that discusses mathematical expectation, the section will conclude with a problem known as St. Petersburg paradox. Essentially, the idea of the paradox is to flip a coin as many times as you can until you flip a tail (which forces you to stop). The payoff is based on the number of heads you flipped before landing the tail. If <i>n</i> represents the number of heads you landed, your payoff is 2^<i>n</i>. The questions (that I won't answer here for those who want to think about it) are:<br /><br /><ul><li>What is the expected payoff for this game? </li><li>Is it realistic?</li></ul><br />If all goes well, I should be able to write about games like Craps and Chuck-a-Luck and maybe even some computational rules (along with counting rules) next time as that's where the course is now headed. I've got about two more months of summer to make this happen!</div>Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com6tag:blogger.com,1999:blog-1869529593927152124.post-49789741744600006252012-08-24T12:01:00.000-04:002012-08-24T12:01:00.190-04:00First Day Plan: Calculus II hope to document some of my classes throughout the upcoming semester on the blog. I figure it might be a good way to spark some dialogue with other readers on ideas and (especially) improvements. It will also serve as a nice diary of sorts for myself when it comes time to assess what did and did not work. <br /><div><br /></div><div>For today's post, I present my plans for Day 1 of my Calculus I course. In the past (I've taught Calculus I for three or four years now), I jumped right into the first lecture on limits after spending about 10 minutes going over the highlights of the syllabus (and explaining our course management software - Moodle). After the introductory lesson I limits, I usually handed the students a PreCalculus (and algebra) review worksheet. Here's one page of my review worksheet...</div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-cnECMggzVdI/UDbzE9oyUHI/AAAAAAAAUxo/2FlYCau9Keo/s1600/scan0001.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="http://2.bp.blogspot.com/-cnECMggzVdI/UDbzE9oyUHI/AAAAAAAAUxo/2FlYCau9Keo/s640/scan0001.jpg" width="466" /></a></div><div><br /></div><div>As you can see, the worksheet isn't trivial for the students - but it's terribly boring. Even worse, there are three more pages of similar work, including a page of graphing. I have found that my students need the review (hence the worksheet) but based on many of the edu-bloggers posts that I've read over the summer, I decided to try something different this year.</div><div><br /></div><div>This time around, I have different ideas (most of which I've stolen from a variety of great bloggers). I plan to greet my students as they arrive in the door with a PowerPoint displaying the course name (and my name). That way, in case a poor freshman wanders into the wrong classroom he or she will (hopefully) figure it out right away and leave before they get too embarrassed by the gaffe. As the students file in and admire my beautiful slide (just kidding), I will hand them a survey called "Who Am I?" I stole the idea (even the name) from Dan over at <a href="http://blog.mrmeyer.com/?p=324">dy/dan</a>.</div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-hHPI-w6zLpw/UDb08HMkzYI/AAAAAAAAUxw/GZ5l9j5ORaA/s1600/scan0002.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="http://2.bp.blogspot.com/-hHPI-w6zLpw/UDb08HMkzYI/AAAAAAAAUxw/GZ5l9j5ORaA/s640/scan0002.jpg" width="488" /></a></div><div><br /></div><div>This will give the "early birds" something to do and I hope it will also set the tone that my class isn't going to be a "typical" math class (whatever typical means...mostly bad things I'm afraid). After I introduce myself, we are going to split up and jump right into an ice breaker activity (cup stacking, also stolen from <a href="http://blog.mrmeyer.com/?p=692">dy/dan</a>).</div><div><br /></div><div>At this point, I should be able to say that I've spoken to every student in the class and hopefully interacted (either formally with math questions or informally based on something I saw on their Who Am I? page). Following the cup stacking activity (which I'm estimating about 10 minutes - I have a PowerPoint presentation that will serve as a prompt for each question). The students will first guess how many cups are necessary by themselves and then answer all remaining questions as a group (including comparing each of the guesses). I just went through my school's Writing Across the Curriculum training so the idea of writing responses to questions is fresh in my mind!</div><div><br /></div><div>At this point, there should be about 30 minutes remaining (give or take a few) in a 65 minute class. With most of the remaining time, I'm going to do a variation of a drawing activity (that I also saw on a blog but I don't remember where - probably dy/dan since that's where everything else came from but I can't be sure). Basically, the idea is to have one student in each group act as the "eyes" and a second to act as the "hands". The eyes are looking at a picture on the PowerPoint slide while the hands have their back to the screen. The eyes have to describe what they see and the hands have to listen to the description and make the best drawing they can. </div><div><br /></div><div>My pictures begin with a happy face (very simple) and then progress through an increasingly challenging series of graphs (linear all the way to horrible discontinuous graphs). In fact, one of the graphs was pulled directly from my Day 3 lesson (foreshadowing - ooooh!). The final drawing should be a riot - after a bunch of mathematical functions, the final drawing is of a train (and fairly detailed at that). It should be fun!</div><div><br /></div><div>Finally, in the last couple of remaining minutes in the class, my students will be given their assignment - essentially a longer survey (with a little bit of mathematical review thrown in). </div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-vWL7VGVpJpU/UDb3dXG1_-I/AAAAAAAAUyA/6YO2DjlBz88/s1600/scan0003.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="http://3.bp.blogspot.com/-vWL7VGVpJpU/UDb3dXG1_-I/AAAAAAAAUyA/6YO2DjlBz88/s640/scan0003.jpg" width="518" /></a></div><div><br /></div><div>I've scanned the final page of the survey, mostly because it's the one original bit (the beginning questions in the survey are inspired by a post on <a href="http://longtailsofinterest.blogspot.com/2010/08/calculus-questionnaire.html">Long tails of \int e^r est</a>) of my day one lesson.</div><div><br /></div><div>As I write out my lesson (something I rarely do besides the PowerPoint), I think I've got a day that should be more interesting than the usual "syllabus day" for day one. In fact, you might have noticed that I didn't mention going over the syllabus at all - I actually have three slides dedicated to it (one on my contact information and office hours, one on the grading scheme since that's all students care about anyway, and the final on the Moodle course page password). The syllabus is wedged in between the two main activities - and will be handed out while students are reorganizing themselves. </div><div><br /></div><div>I have no idea if the new plan will make the class any better at algebra and/or PreCalculus as compared to previous semesters where the main assignment was the lengthy worksheet, but if I had to guess I'd say the students won't be any worse on average. I know for a fact that the day will be more fun - I hate syllabus days as much as anyone, and the students seem to hate it if I jump right into a lecture on day 1. Hopefully they will be too busy having a good time to realize that they are learning (or at least reviewing) mathematical concepts. </div><div><br /></div><div>"Did you just describe that graph with the word multiplicity? What does that mean again?"</div><div><br /></div><div>At least, that's what I hope to hear on Monday. We shall see.</div>Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com3tag:blogger.com,1999:blog-1869529593927152124.post-90303004718400544392012-08-23T18:30:00.001-04:002012-08-23T18:30:02.845-04:00The Art of Paper Folding: Kawasaki's Rose Bud<iframe align="left" frameborder="0" marginheight="0" marginwidth="0" scrolling="no" src="http://rcm.amazon.com/e/cm?lt1=_blank&bc1=000000&IS2=1&bg1=FFFFFF&fc1=000000&lc1=0000FF&t=nachgran-20&o=1&p=8&l=as4&m=amazon&f=ifr&ref=ss_til&asins=4889961844" style="height: 240px; width: 120px;"></iframe>As I'm sure you'll see by reading more of my blog (or check my <a href="http://fanofreds.blogspot.com/"><i>other</i> blog</a> to find bits and pieces of information scattered about), one of my non-sport interests (besides teaching math) is origami. I happen to use origami in the classroom occasionally (especially during our math colloquiums) but that's not the point of this post. <br /><br />Instead, I'd like to highlight one of the more famous "modern" models in orgami, Kawasaki's Rose. According to Kawasaki's book <i>Roses, Origami, & Math,</i> the rose is an extremely challenging model to fold. Since my wife asked me to fold three flowers to send to a friend in the Navy who lost a family member recently (real flowers wouldn't ship overseas nicely), I decided to do the next best thing as compared to the rose, I folded three of Kawasaki's Rose Buds.<br /><br />The rose bud model is almost the same as the rose model - and as you can hopefully see via the instructions and photos below, the end result is still quite beautiful.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-25Jy0pOMmqQ/UDWQdXD6X5I/AAAAAAAAUu0/G_VXUs6eAts/s1600/IMAG0184.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="238" src="http://1.bp.blogspot.com/-25Jy0pOMmqQ/UDWQdXD6X5I/AAAAAAAAUu0/G_VXUs6eAts/s400/IMAG0184.jpg" width="400" /></a></div> The first step is to crease the paper into 64 squares...<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-jM_C59r1t-4/UDWQjQtjKbI/AAAAAAAAUu8/2Ajq5wd2rv0/s1600/IMAG0185.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="191" src="http://3.bp.blogspot.com/-jM_C59r1t-4/UDWQjQtjKbI/AAAAAAAAUu8/2Ajq5wd2rv0/s320/IMAG0185.jpg" width="320" /></a></div> Then, do what Kawasaki coined as a twist fold. Basically, the paper shrinks to a 7 by 7 grid with the overlap happening in the middle of each side. The twist results in a small square being formed in the center of the paper. With a little practice, this fold is actually fairly simple.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-z9Pvg2ubNuI/UDWQtWQ9c-I/AAAAAAAAUvE/A7IZDpq8BN0/s1600/IMAG0186.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="191" src="http://3.bp.blogspot.com/-z9Pvg2ubNuI/UDWQtWQ9c-I/AAAAAAAAUvE/A7IZDpq8BN0/s320/IMAG0186.jpg" width="320" /></a></div> After doing the twist, you slowly gather up each of the four corners to form what sort of looks like a long rectangular box.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-U1oYqI3i09Y/UDWQ0Mt2XgI/AAAAAAAAUvM/nprJenCvF5Q/s1600/IMAG0187.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="191" src="http://4.bp.blogspot.com/-U1oYqI3i09Y/UDWQ0Mt2XgI/AAAAAAAAUvM/nprJenCvF5Q/s320/IMAG0187.jpg" width="320" /></a></div> You can see the box shape here. The right edge (in terms of the photo) is opened up slightly in order to form the first of the four petals.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-vOXO6wDkQY0/UDWQ57dBB5I/AAAAAAAAUvU/56KKXYgOkEI/s1600/IMAG0188.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="191" src="http://3.bp.blogspot.com/-vOXO6wDkQY0/UDWQ57dBB5I/AAAAAAAAUvU/56KKXYgOkEI/s320/IMAG0188.jpg" width="320" /></a></div> For your first attempt, I highly recommend using small paperclips to hold the various folds together. However, when all is said and done, the flower will stay together without any outside assistance. I hadn't tried to fold the Rose Bud before so I used the paperclips for the first flower. I did not use them for the second two attempts - each of which were quite a bit easier than the first try!<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-fXxEX660Zvo/UDWRCMXhd8I/AAAAAAAAUvc/LqSKR8JEPpI/s1600/IMAG0189.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="191" src="http://1.bp.blogspot.com/-fXxEX660Zvo/UDWRCMXhd8I/AAAAAAAAUvc/LqSKR8JEPpI/s320/IMAG0189.jpg" width="320" /></a></div>There's one finished Rose Bud...and now, three more...<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-hyji8F251z0/UDWXXeibBdI/AAAAAAAAUvs/5oMWfA_6D-c/s1600/IMAG0190.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="238" src="http://3.bp.blogspot.com/-hyji8F251z0/UDWXXeibBdI/AAAAAAAAUvs/5oMWfA_6D-c/s400/IMAG0190.jpg" width="400" /></a></div><br />Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-28013604361773317292012-08-21T18:00:00.006-04:002012-08-21T18:00:06.048-04:00The Mathematics of Games and Gambling - Planning Part 1 <table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-Qbg4223jJcE/T56oPDbRiiI/AAAAAAAAP-M/nKMiD75VUUU/s1600/Roulette.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="263" src="http://2.bp.blogspot.com/-Qbg4223jJcE/T56oPDbRiiI/AAAAAAAAP-M/nKMiD75VUUU/s400/Roulette.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Image source: www.casinogames.org</td></tr></tbody></table>*Note* This post was <a href="http://fanofreds.blogspot.com/2012/04/mathematics-of-games-and-gambling.html">originally published on my other blog</a>. I'm planning on moving my education related posts over to the new blog - what better way than to begin with the course that has inspired me to write this new blog?<br /><br />By now, most of my loyal readers probably know that I teach college mathematics. In fact, I’ve been teaching at the college level since the year I got out of undergrad (starting with a teaching assistantship in grad school). I’ve been fortunate that I haven’t had to scramble (too much) since then in order to have a teaching job for each upcoming academic year. For the past five years, I’ve been teaching at a four year undergraduate institution (which I love) teaching mainly Calculus and PreCalculus (though I’ve also dabbled in Combinatorics and Statistics a couple of times). Well, I’m pleased to announce that next fall I’ll be teaching a brand new course titled “The Mathematics of Games and Gambling.”<br /><div class="MsoNormal"><br /></div><div class="MsoNormal">Throughout the summer (as I plan the course), and perhaps throughout the school year as well, I plan to occasionally post a blog entry or two on my teaching progress along with any ideas/problems that I have with the course. It is my hope that I’ll have a bit of “diary” of sorts in regards to the course. For now, I’m thinking I’ll post the entries here at Nachos Grande but I may end up starting an “education only” blog just to keep things somewhat on theme at both blog destinations.</div><div class="MsoNormal"><br /></div><div class="MsoNormal">Luckily, for today’s post, there is a tie between one of the first topics I want to discuss in my course and the main ideas of the blog – namely, gambling! In my course, we are going to mostly look at gambling in terms of casinos but we may also dabble in sports gambling a bit, specifically with odds and various ways to make (or lose) money.</div><div class="MsoNormal"><br /></div><div class="MsoNormal">The college that I work at is located in Pennsylvania, but we draw a lot of students from surrounding states (including a whole bunch students from New Jersey). As such, current articles such as that discuss <a href="http://www.casinotop10.net/New-Jersey-Voters-Say-Yes-to-Sports-Betting">the legalization of sports betting</a> in places like New Jersey will probably get a lot of play in the course. As someone who tries to teach without always resorting to the “lecture and exam” pattern that so many math professors find themselves trapped in, I am always looking for new and exciting ways to draw my students in to the material and concepts. Anytime you can draw in a student’s hometown (or at least home state), there is an instantaneous connection!</div><div class="MsoNormal"><br /></div><div class="MsoNormal">In fact, this particular course is designed entirely around the idea that interested and motivated students will learn mathematics! The course isn’t for our majors (though I think there is a math major or two signed up “just for fun”), but rather, it is designed to give our distribution students a different outlet for their mathematics requirement (other than the usual statistics course). Obviously I have no idea at this point whether or not the plan will work, but I can say that the course had strong numbers during spring registration which leads me to believe that I am on to something!</div><div class="MsoNormal"><br /></div><div class="MsoNormal">Anyhow, back to the structure of the course – one of the things that I’m debating about in my head (and now on the blog) is how much weight and importance to give various topics. The course description is intentionally vague, and I do want to be sure to feature some games/activities that the individuals in the class find interesting, but there are other topics that I always want to make sure I include within the course. </div><div class="MsoNormal"><br /></div><div class="MsoNormal">There will be a few topics that are no brainers – poker for one since we get a fun way to experiment with ideas of permutations and combinations. Other no brainer topics will include roulette, black jack, and Monopoly. I’d like to include backgammon because there’s a lot of approachable mathematics in that game, but quite honestly, I’ve never played the game myself so I don’t know that I’d be the best instructor for that one! I plan to look at games like Chuck-a-Luck, Bingo/Keeno, and Connect Four as well. I’d also like to discuss and investigate some online casinos, like <a href="http://www.casinotop10.net/bwin-casino.shtml">bwin casino</a> (which also happens to be a huge sponsor for the Portuguese soccer league cup)! </div><div class="MsoNormal"><br /></div><div class="MsoNormal">Besides the common (and not-so-common) games in the course, I also want to spend a bit of time discussing gambling. We will take a look at state (and multi-state) lotteries – and I have a fun little “Tips to win the Lottery” article that I printed off back when the gigantic MegaMillions lottery was all the rage. That should draw some laughs (or at least I hope it will draw laughs by that point in the semester once students realize the follies in “hot numbers” or “numbers due”)! </div><div class="MsoNormal"><br /></div><div class="MsoNormal">I also plan to spend a little bit of time discussing sports (and prop) betting – specifically talking about betting lines and how they affect payouts (and betting practices)! I have already spoken to one of the psychology professors about a guest lecture on the psychology of gambling as well – it should be a great, well-rounded course! Who knows, it may even help to shape the future direction of other distribution mathematics courses, both at my current institution and at other colleges!</div>Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0tag:blogger.com,1999:blog-1869529593927152124.post-30886146489714574842012-08-20T21:29:00.000-04:002012-08-20T21:29:09.208-04:00Welcome!Welcome to my newest blog: Trial by Blogging. It is my goal to use this blog to highlight my various attempts at improving education. Some of you may know me from the baseball (and baseball card) centric blog: <a href="http://fanofreds.blogspot.com/">Nachos Grande</a>. I won't be giving up that blog anytime soon but I have decided to try and split the education related posts away from the sports stuff. Of course, I would encourage you to check out my other blog as well if sports are something you are interested in!<br /><br />In order for you to have a little bit of information of where I am coming from, allow me to introduce myself. I am an (almost) 30 year old mathematics instructor. I've been teaching at various colleges almost non-stop since I graduated from my undergraduate college. I attended a 4 year liberal arts college majoring in both mathematics and computer science. Math ended up being my true love though so I did a bit of advanced schooling, eventually culminating in a Masters degree in education (with a math concentration). It's a long story as to how I ended up with that particular degree, perhaps for another day. Since obtaining my Masters, I've been teaching at the same four year college in the Mathematics department. To date, I have taught PreCalculus (with labs), Calculus I (with labs), Introduction to Statistics, Combinatorics, and our majors colloquium. I am also currently designing (and teaching) a brand new course offering: The Mathematics of Games and Gambling. <br /><br />You will probably find plenty of more background on myself in future blog posts. For now, it's a matter of trying to find a template that I don't despise and getting ready for the new semester (which begins in six days)! <br /><br />Finally, if you have your own education related blog, let me know in the comments below. I'd be happy to add your blog to my blog roll!Nachos Grandehttp://www.blogger.com/profile/02911007368272468591noreply@blogger.com0