Math-A-ThonThe Times of Trenton - NJ.comPRINCETON TOWNSHIP -- Sixth grade students from the Princeton Charter School participated in a Math-A-Thon that raised $6981.23 to benefit St. Jude and more »
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Google News: Math
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Math-A-Thon - The Times of Trenton - NJ.com
3 Jul 2009 | 9:12 pm -
Method to teach math may not add up - Orlando Sentinel
3 Jul 2009 | 7:51 pmMethod to teach math may not add upOrlando SentinelSANFORD - A skeptical reaction to a plan for extending the use of "inquiry math" in middle schools has led Seminole How can Georgia improve middle schools?Atlanta Journal ConstitutionTeachers learn innovative ways to help engage students in mathThe Republic.com (subscription)New Rock Island school nearly ready for its studentsQuad City TimesAlexandria Town Talkall 5 news articles » -
Years add up for longtime math teacher - Bolton Common
3 Jul 2009 | 2:45 pmYears add up for longtime math teacherBolton CommonThe school was very different in those times than it was now, and her first classes as a fourth and fifth grade math teacher were held in what is now the and more » -
Issaquah's math curriculum adoption is put on hold - Newcastle News
3 Jul 2009 | 2:07 pmIssaquah's math curriculum adoption is put on holdNewcastle NewsTeachers will continue to use the current math program, College Prep Mathematics, when students come back to class in the fall, said Patrick Murphy, and more » -
Math-based summer class prepares future engineers - Houston Chronicle
3 Jul 2009 | 12:55 pmMath-based summer class prepares future engineersHouston ChronicleThe program is one of several initiatives aimed at getting more women and minorities into math and science-related careers, said Irving McPhail, and more »
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Topix: Math
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Atif keeps enriching the English language ...
3 Jul 2009 | 9:44 pmAtif keeps enriching the English language ... Atif, You are doing for the English language what the bitter lemon has been doing to three languages in reverse. -
It's your business
3 Jul 2009 | 9:41 pmLeague of Women Voters Tuesday Topics, noon, YWCA, 225 S.W. 12th. Speaker: Norton Bonaparte, Topeka city manager, on city consolidation. -
Spin Zone
3 Jul 2009 | 9:38 pmYes, but progress has been made... My definition of the glass ceiling is "when the playing field is not level," meaning that qualified individuals do not have an equal chance to advance. -
Happy Fourth of (burp) July
3 Jul 2009 | 9:36 pmScott Paulsen takes time away from the farm to host an afternoon sports talk show each day on 1250 ESPN. -
Communities bug out over cuts to mosquito control
3 Jul 2009 | 9:32 pmThat's got the man whose job it is to fight the bugs worried - he's already running out of money.
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ScienceDaily: Mathematics News
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Report Calls For New Initiative To Improve Math Education For Preschoolers
1 Jul 2009 | 9:00 pmTo ensure that all children enter elementary school with the foundation they need for success, a major national initiative is needed to improve early childhood mathematics education, says a new report. -
Peeling Stickers May Lead To Stretchable Electronics; New Model Enables Precise Design Of Damage-resistant Materials
29 Jun 2009 | 5:00 pmA study of stickers peeling from windows could lead to a new way to precisely control the fabrication of stretchable electronics, according to researchers. -
Best Possible Cut From Gemstones With New Machine
26 Jun 2009 | 5:00 pmEmeralds, rubies and the likes are referred to as colored gemstones by experts. They sparkle and shine with varying intensity, depending on the cut. A new machine can achieve the best possible cut and extract up to 30 per cent more precious stone from the raw material. -
DNA Sudoku: Logic Of 'Sudoku' Math Puzzle Used To Vastly Enhance Genome-sequencing Capability
25 Jun 2009 | 11:00 amCombining a 2,000-year-old Chinese math theorem with concepts from cryptology, scientists have devised "DNA Sudoku" -- a pooling strategy that allows tens of thousands of DNA samples to be combined and sequenced all at once. The new strategy promises to reduce costs dramatically, with sequencing projects that cost $10 million in the past now estimated to cost less than $80,000. -
Using Math To Take The Lag Out Of Jet Lag
19 Jun 2009 | 11:00 amResearchers have developed a software program that prescribes a regimen for avoiding jet lag using timed light exposure.
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Scientific American - Math
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DNA Sudoku
1 Jul 2009 | 3:30 pmA 2,000-year-old math theorem, along with Sudoku, may soon help researchers untangle DNA at blazing speeds. [More] -
Grassoline: Biofuels beyond Corn
29 Jun 2009 | 6:00 amBy now it ought to be clear that the U.S. must get off oil. We can no longer afford the dangers that our dependence on petroleum poses for our national security, our economic security or our environmental security. Yet civilization is not about to stop moving, and so we must invent a new way to power the world’s transportation fleet. Cellulosic biofuels--liquid fuels made from inedible parts of plants--offer the most environmentally attractive and technologically feasible near-term alternative to oil.Biofuels can be made from anything that is, or ever was, a plant. First-generation… -
The Science of Economic Bubbles and Busts
22 Jun 2009 | 6:00 amIt has all the makings of a classic B movie scene. A gunman puts a pistol to the victim’s forehead, and the screen fades to black before a loud bang is heard. A forensic specialist who traces the bullet’s trajectory would see it traversing the brain’s prefrontal cortex--a central site for processing decisions. The few survivors of usually fatal injuries to this brain region should not be surprised to find their personalities dramatically altered. In one of the most cited case histories in all of neurology, Phineas Gage, a 19th-century railroad worker, had his prefrontal… -
Why Aren't More Women Tenured Science Professors?
19 Jun 2009 | 3:55 pmWomen who apply for tenure-track positions at top-tier research universities in math and sciences these days have a slightly better chance of landing the job than their male colleagues, says a new study funded by the National Science Foundation. [More] -
Stimulus Funds for Science Raise Concern about Misconduct
19 Jun 2009 | 6:00 amOne unintended side effect of Congress’s intense efforts to jump-start the U.S. economy is the threat of fraud. Earl Devaney, chair of a newly appointed federal watchdog agency, the Recovery Accountability and Transparency Board, has warned that without precautionary measures, as much as 7 percent of the stimulus package will end up in the hands of bad actors. Apply Devaney’s math to the $31 billion being spent on science--by the National Institutes of Health, NASA, the Departments of Commerce and Energy, and the National Science Foundation (NSF) combined--and stimulus funds…
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NYT: Mathematics
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Children: Self-Control Presages Math Gains in Young
22 Jun 2009 | 9:00 pmA simple behavioral test for children entering kindergarten can predict future mathematics skills, researchers say. -
Connecticut District Tosses Algebra Textbooks and Goes Online
7 Jun 2009 | 9:00 pmWestport teachers were frustrated at having to rush through the curriculum only to find students didn’t grasp important concepts, so they created their own online program. -
New York City Shows Gains in Math
1 Jun 2009 | 9:00 pmGains on the state maths tests were strongest in middle school, but officials cautioned results could be overstated. -
Complex Math, Simple Sum: 3 Awards in 5 Years
31 May 2009 | 9:00 pmWith a third member of its faculty recently awarded the Abel Prize, widely regarded as the Nobel of math, N.Y.U.’s Courant Institute of Mathematical Sciences has more than beat the odds. -
Out of Work in Finance, They Turn to Teaching
9 May 2009 | 9:00 pmA new program, Traders to Teachers, financed by a federal grant, will retrain dislocated workers and also ease the state’s shortage of math teachers.
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MathNotations
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Dorothy Revisited -- Another View...
28 Jun 2009 | 4:59 amMathmom contributed some insightful thoughts about how most middle school students might feel about the probability investigation from the other day. I agree with her that some would be able to compute the results or even devise a general formula but "proving" it in the general case might be too ambitious. In my reply, I suggested there might be another way of deriving the formula 1/N for the probability of losing the game. Here's what I came up with. It still requires some careful development to show that the outcomes are equally likely but I will indicate how it could be done in the… -
Please Help Dorothy Go Home - A Probability Fantasy for Middle School and Beyond
24 Jun 2009 | 3:41 amSummer vacation is an appropriate time for fantasy. Enjoy the hiatus!The following investigation is not intended to be a math contest challenge. It reviews fundamental principles of probability and you might want to bookmark it for the fall. We can also simulate the first problem using the programming capabilities of a graphing calculator. I may post a simple program for this later on.The wizard will let Dorothy go home if she can pass three challenges.He shows Dorothy 3 playing cards, 2 of which are black and one is red. He shuffles them and turns them face down. "Dorothy, here's your first… -
"On The Road Again" With 'TC' -- A Real World Application of Geometry
15 Jun 2009 | 5:15 amAs my devoted readers know, Totally Clueless, affectionately known as TC, has contributed many insightful comments and profound ideas for us to think about. His sobriquet belies a brilliant creative mind of course. He recently sent me a geometry problem which was motivated by his own experiences driving to work. The problem itself is accessible to advanced middle and secondary students but the result is interesting in its own right and should generate rich discussion in class. I recommend giving this as a group activity, allowing about 15 minutes for students to work on, then another 15… -
An Equation Which May Be More 'Complex' Than It Appears!
13 Jun 2009 | 3:39 amMaybe I should rename this blog to Saturday 'Morning' Post. After all, no one reads that either anymore!As the school year comes to a close (and I'm assuming it's already over for some), here's an innocent-looking equation which might be worth discussing with your advanced algebra/precalculus students now or next year. I might have considered saving this for our next online math contest but it's complex nature makes it more suitable for discussion in the classroom than on a test. Have you seen exercises like this in your Algebra or Precalculus texts? Do students often delve beneath the… -
Two Geometry Problems To Sharpen The Mind - Never Too Late In the Year For That!
6 Jun 2009 | 4:48 amWell, the June SATs have arrived today so these problems come too late for that, but these kinds of questions can be used to review basic ideas while strengthening thinking skills. Both questions below are appropriate for both middle and secondary students, although the second requires knowledge of a fundamental geometry principle regarding the sides of triangles.There are other important principles embedded in these problems as well. In the end, I believe that students need to be exposed to many of these "contest-type" challenges to improve reading skill, learn how to pay attention to detail…
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Math-U-See Blog
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Math Man
2 Jul 2009 | 6:40 amBrenda over at “The Family Revised” wrote a fun post entitled “So, Is It Handwriting U See or Math Without Tears?” Here is a portion of the post… So last week after Sweetheart finished her math review, what did she make? Why Math Man of course! Oh come on. That’s funny. Read the full post to see “Math Man” compared with “Mat Man” -
Guest Post - Ice Cream and Math
12 Jun 2009 | 11:26 amGuest Post today from Nikowa at the Knowledge House Academy This week’s Math U See lesson is about memorizing the colors of the unit bars. Well I wanted to get creative so I did a Google search for “numbers, ice cream cone” & came up with this great site. I immediately printed it out & wrote (with a sharpie) each number (through 10) on them. Then we colored each ice cream scoop to match the corresponding unit bar. The boys LOVED putting it together & placing it on the wall! We named each level a different flavor! Hopefully this will “stick” with them. -
Another Great Video Testimony
19 May 2009 | 12:55 pmAnother great video testimony taken at Mass Hope, enjoy! j b lenoir download mp3 -
Mass Hope Videos
15 May 2009 | 7:34 amBrandon and Peter traveled up to the Mass Hope convention a few weeks ago to help out. Here are a few videos from the convention. Enjoy! -
Math-U-See at CHEF of Louisiana
27 Apr 2009 | 10:06 amHere some pictures from the CHEF of Louisiana homeschool convention. It was a good time, we met bunch of neat folks and ate Gumbo. A fun time was had by all.
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Wild About Math
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Now that the MMM #35 deadline has passed …
30 Jun 2009 | 5:38 pmMMM #35 turned out to be harder than I thought judging by the small number of submissions I received. I’ll be giving away four prizes on Friday - two to the early submitters, one to .mau. for consistently submitting entries to the contest for a really long time, and one to a randomly selected person with a correct submission. I’ll discuss some of the solutions on Friday but, for now, check out these pictures I made. I came up with this problem by playing with the Fibonacci series and arranging rectangles. Here is the problem description: Let F(0)=1, F(1)=1, and F(n)=F(n-2)+F(n-1). -
Can you sum this?
29 Jun 2009 | 3:39 pmHi, I’ve been playing with this series: Sn = 1×22 + 2×32 + 3×42 + … + nx(n+1)2 I’ve come up with a formula for determining Sn but I derived the formula in a fairly roundabout way. I’m interested to know if someone has an elegant way to derive the formula. ShareThis -
MMM #35: Is it too hard?
25 Jun 2009 | 7:03 amI’ve only gotten two solutions to the “Fibonacci Fun” problem I proposed. Is everyone on vacation and not thinking about Math, do people find the problem boring or is it too hard? I don’t think it’s one of my harder problems. I want to state that I approached the problem in a different way than each of the people who provided solutions. So, there are at least three ways to approach the problem. If you don’t know how to approach it I suggest looking for a pattern in the sum as you add more terms. Come on, give it a try! You could win $10. This time around,… -
MMM #35: Fibonacci Fun
22 Jun 2009 | 9:37 amBlinkdagger has announced the winner and the solution for MMM #34. Now, it’s time for MMM #35. I want to thank Blinkdagger for running 17 contests over the last year and a half. Quan and Daniel have done an excellent job of creating problems and engaging you with fun problem descriptions and great graphics. I’ll miss their participation. Here’s Monday Math Madness #35: Let F(0)=1, F(1)=1, and F(n)=F(n-2)+F(n-1). This is the familiar Fibonacci series. Simplify F(0)xF(1) + F(1)xF(2) + F(2)xF(3) + F(3)xF(4) + … + F(n-1)xF(n) + F(n)xF(n+1) Show your work. (more…)… -
MMM #33: We have a winner!
6 Jun 2009 | 8:52 amRandom.org picked Nikhil Chelliah as the winner for MMM #33. Congratulations, Nikhil! Here is the problem description: What’s the prime factorization of the smallest whole number that is divisible by all integers from 1 up to and including 50? Here is Nikhil’s solution: The least common multiple of a group of numbers, has, for each prime factor, as many occurrences as the greatest of the group of numbers. Which may make sense iff you already know what I’m talking about. One algorithm would involve finding the prime factorization of each number up to 50, then taking the most…
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Loren on the Art of MATLAB
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Find Largest Positive Value Next to Zero
1 Jul 2009 | 11:17 amRecently, Steve wrote a blog discussing code clarity/obscurity in the context of one-line code solutions. Simply stated, the problem he solved is this. Find the largest value in an array adjacent to a zero value. Must be zillions of ways, right? Contents An Example Steve's First Solution Good for Only Positive Values Steve's Second Answer Doug's answer Jos' Solution Next Start Over Repeated Zeros - Clarity of Problem Statement Your Thoughts? An Example Let me start with an example. If the array in question is A, A = [1, 5, 3, 0, 2, 7, 0, 8, 9, 1 0];the correct answer is 8. Steve's First… -
Rooting Around in MATLAB - Part 3
23 Jun 2009 | 11:08 amI recently wrote a pair of posts (1 and 2) about finding roots of equations, and how you might use MATLAB to explore this topic with emphasis on the method of fixed point iteration. Contents Set Up Example Reminder First Fixed Point Iteration Attempt Second Way to Rewrite Equation Let's Iterate Let's Try to "Zero" in on the Solution First Iteration Second Iteration Third Iteration A Few More Rounds Fixed Point Found! Wrapping Up the Series of Posts Set Upclear all close allExample Reminder Let me restate the example function. Let's start with a simple cubic polynomial f(x) which we define… -
Rooting Around in MATLAB - Part 2
16 Jun 2009 | 11:02 amIn a recent post, I started a series of posts about finding roots of equations, and how you might use MATLAB to teach some of this topic. In particular, I will introduce the idea of fixed point iteration. Contents Set Up Example Fixed Point Algorithm Let's Try to "Zero" in on the Solution First Iteration Second Iteration Third Iteration The Conundrum Confession The Series of Posts Set Upclear all close allExample Let me restate the example function. We'll start with a simple cubic polynomial f which I define as an anonymous function.f = @(x) x.^3 + x - 1; fplot(f,[-2 2]) title f grid on Fixed… -
Rooting Around in MATLAB - Part 1
11 Jun 2009 | 11:01 amI've been interested in teaching for a long time, including ways to use MATLAB. One concept that students might need to understand early in their college careers is that of finding roots or zeros of functions. To understand at least some of the algorithms, you might want to teach the students about fixed points for functions. It's the basis for some methods of solving equations or finding roots, algorithms such as Newton's method, finding square roots, and more. Contents Example Function Find the Roots or Zeros The Series of Posts Example Function Let's start with a simple cubic polynomial f. -
Hold Everything!
3 Jun 2009 | 11:37 amHave you ever tried to overlap more than one plot, only to find that you had to fiddle with a few times before it looked right? Perhaps this is because you aren't take full advantage of the function hold. Contents An Example Plot the Data and the Function Try Another Way Why Use Hold? A Better Way Will hold all Help You? An Example Suppose I want to plot two sets of data or functions on the same plot. How might I do that? There are several ways. Let's create some data and a function. t = 0:0.005:1; f = @(t) sin(2*pi*10*t); s = f(t); sn = s + 0.3*randn(size(t));Plot the Data and the Function…
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Homeschool Math Blog
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Office furniture giveaway
30 Jun 2009 | 10:06 amHere is your chance to win a piece of office furniture in this little giveaway contest:First go check www.csnOfficeFurniture.com website and find a piece you'd like to have if you are the lucky winner. It needs to be $135 or less in value.Then, to participate, purchase any of the Math Mammoth or Make It Real Learning products at Kagi store between now and July 9, 2009.In the comments field on the order page, put either the name of the piece of furniture you'd like to win or the URL to its web page. If you leave this comment field blank, I will not know that you wish to participate so it is… -
Math Teachers At Play #10
26 Jun 2009 | 3:00 amWelcome to the tenth edition of Math Teachers At Play blog carnival! Here with the heat of the summer, "less is more". We concentrate on teaching issues, but also get to "play" a bit with binary numbers, geometry, integers, and an optical illusion.TEACHINGWhat's a math teacher going to do with Wolfram | Alpha ?In case you haven't heard... Wolfram|Alpha is a new, computational search engine. And if you're a math teacher, you should be aware of it.Collection of Web Freebies discusses Wolfram|Alpha as your Personal Free Online Math Assistant.I wrote an introduction to Wolfram|Alpha as well. I… -
Wolfram|Alpha is here
22 Jun 2009 | 9:27 amWolfram|Alpha is a new, computational search engine. If you do a query where the answer has quantitative data, Wolfram|Alpha probably gives it.For example, try enter your last name. Wolfram|Alpha gives you information about the popularity of that name. For example, "miller" ranks 6th within the US and there are about 1,128,000 people with that surname.Enter a first name, and it will even give you a graph showing the name's popularity over the years. I just found out that Cindy's popularity peaked in about 1960. No wonder it is a common first name among the mothers who ask me questions about… -
Measuring worksheets
18 Jun 2009 | 2:45 pmI finally got around to creating another worksheet generator that had been "lacking" for a while from my "collection" - measuring units worksheets. Those where you ask kids to convert 6 cups to ounces, or 5 kg 40 g to grams.Measuring units worksheetsThese are free and printable. I've made lots of ready-made links for some common type worksheets, but of course with the generator you can customize it how you want. Both metric and customary units are included; however I did not include all possible metric units, because the focus here is for grades 3, 4, and 5. -
Integer subtraction
9 Jun 2009 | 10:02 amI recently finished another video of mine, this time on the topic of subtraction of integers. You can watch it here:Subtracting IntegersIn it, I explain three different models that we can use to justify the rules for subtracting integers to the students. The three models are:1) number line jumps;2) concept of difference;3) counters.Please read about these models in more detail in my updated article How to teach operations with integers.
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About.com: Math
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New Worksheets This Week
3 Jul 2009 | 7:46 amIf you're practicing a bit of algebra over the summer holidays, stay tuned! I too am focusing on adding a few more algebra worksheets to help you improve your algebra marks. This week, you'll find systems of equations using the elimination method, complete with answers on the 2nd page of the pdf. But, don't stop there, be sure to check out all of the algebra practice worksheets with answers. -
Divisibility
29 Jun 2009 | 12:48 pmDivisibility really just means 'can you divide a number by another. ' Throughout your math career, divisibilty makes its appearance over and over again. There's a great online tool that tells you the divisibility of a number and saves you the computational work. Check it out ,an online calculator that does all the work for you. Sure beats the old fashioned method. However, they too are worth knowing, and there are a number of strategies that help with divisibility, here are a few tried and true but if you have more, be sure to post them! -
Can You Really Teach Your Baby Math?
27 Jun 2009 | 12:32 amThe author of this book sure thinks you can! Although I'm a big advocate of early numeracy, teaching babies math may be a bit of a stretch, or let's just say that I'm a skeptic. Then again, if you're interested, be sure to check out the book.As for some great strategies for your pre-schooler, give these tips a try, or if your child is kindergarten age, help prep them with some of the concepts listed here. -
Algebra: Your Summer Goal?
22 Jun 2009 | 11:54 pmUpon beginning our summer holidays, we're just so full of goals and things we want to accomplish. If improving your understanding of Algebra happens to be one of your goals, these self-directed teaching books are for you, well maybe! Of course, individuals who learn on their own tend to be quick learners who can learn by seeing examples of questions with step by step answers. If this isn't your learning style, I would highly recommend going the tutor route instead. Wondering if you can make sense of examples? Try this one first on Quadratic Functions. -
The Use of Video Games in Schools
20 Jun 2009 | 10:46 amI've been somewhat of an advocate of video games in schools, however, I've encountered many nay-sayers along the way and they certainly have their valid points. But, when research provides evidence of positive impact, one really can't look the other way now can they? Here's a new report from Generation YesThe research report comes from a consortium of 31 ministries of education in Europe. The study was sponsored by the Interactive Software Federation of Europe. Worth the read!
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Let's Play Math
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Updates
24 Jun 2009 | 12:46 pmMath Teachers At Play #10 is now posted… Today is the last day to send in your submission to the next Math Teachers at Play blog carnival, which will be posted this Friday at Homeschool Math Blog. I am still trying to catch up on priorities at home, so I don’t know when I’ll be back to blogging. After Maria’s carnival this Friday, we don’t have another host scheduled until August. Would anyone like to volunteer, or shall we take a break for the summer? -
Who Broke the Internet?
9 Jun 2009 | 11:27 amMy Internet connection has been like a yo-yo: up and down, but mostly down. DH — who has little patience for blogging — says that’s just as well, because my main job this summer needs to be a major decluttering and housecleaning project. So I’ll be back when I can, but I don’t know how soon… In the meantime, check out the Carnival of Mathematics #53. And be sure to send in your entry for this week’s Math Teachers at Play blog carnival, to be published this Friday at Homeschool Bytes. [Edited to add: Math Teachers at Play #9 - Game Time! now posted. -
Math Teachers at Play #8
29 May 2009 | 4:20 am[Photo by jaaron.] Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! We accept entries from anyone who enjoys playing around with math, as long as the topic is relevant to students or teachers of preK-12th grade mathematics. Some articles were submitted by their authors, other were drawn from the back-log in my blog reader, and I’ve spiced it all up with a few math jokes courtesy of the Mathematical humor collection of Andrej and Elena Cherkaev. Let the mathematical fun begin… ELEMENTARY CONCEPTS [Photo by David Mezzo Van Couvering.] Q: How do… -
Reminder
26 May 2009 | 4:37 amIf you blog about learning or teaching math, be sure to send in your submission to the Math Teachers at Play blog carnival. Tomorrow is the deadline for this week’s edition. [And if you've been wondering: Yes, I will get back to blogging, someday. Hubby laid down the law, so Spring Cleaning is the priority these days. I hate housework! But I am making progress, a little at a time....] -
Math Teachers at Play #7
15 May 2009 | 7:08 am[Photo by rick.] The math is sizzling at Homeschool Bytes with the Math At Play Blog Carnival — Onomatopoeia Edition. There is something for everyone, from elementary multiplication and division to exponential functions and geometric series. Check it out! And while you’re playing around with math, don’t forget the Carnival of Mathematics #52, which went up last week at The Number Warrior. Plenty of fun there, too. Does anyone know where the next one will be? There is also the Carnevale Della Matematica # 13. (Google’s attempt at translation.) [Hat tip: The Number…
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Logic Matters
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Rum and reason
30 Jun 2009 | 12:23 pmLong time readers will remember I used to link to The Daughter's cooking blog, BakeMeHappy (that's still on line, full of good things, and beautifully written -- but apart from a little late flurry, it really came to a halt a year ago). She's now left Italy, and is cooking up a storm in the Bahamas: and to go with that move, there's a new blog, Rum & Reason, promising more great food and another good read. Enjoy! -
Rosser's Theorem
26 Jun 2009 | 9:01 amWolfgang Rautenberg's very nice A Concise Introduction to Mathematical Logic states Gödel's first theorem in the usual sort of way. Roughly: given a suitably axiomatized omega-consistent theory T containing enough arithmetic, there's a Pi_1 undecidable sentence. He proves this by appeal to the diagonalization lemma applied to the predicate not-Prov (where Prov suitably expresses provability in T)A fixed point G for this is neither provable nor disprovable. And being equivalent to not-Prov('G') that's undecidable too. But not-Prov by construction is Pi_1, so that gives us a Pi_1 undecidable… -
Functions and gunctions
22 Jun 2009 | 2:54 amTim Gowers has a very nice piece on his blog about functions, multivalued functions, relations and the like, called "Why aren't all functions well-defined?". -
The book problem
21 Jun 2009 | 12:51 amSo you start buying books -- I mean academic, work-related, books of one kind or another -- in your late teens. As retirement age looms you've been doing it for more than forty-five years. Suppose you average a couple of books a month. Not that very difficult to do! You buy a few current books on topics that you are working on; books for reference; books you feel you should read anyway, given the ripples they are producing; books for seminars or reading groups you belong to; books it is useful to have to hand for teaching (the textbooks the kids are reading, or just useful collections of… -
Gowers on Razborov's theorem about monotone circuit complexity
20 Jun 2009 | 2:40 pmI mentioned before that I'd been to Tim Gowers's lectures on computational complexity. As I noted before, videos of his lectures are available here. But, as promised, he has also written up the proof which was the topic of the first part of the course, namely Razborov's demonstration that the monotone circuit complexity of the clique function is superpolynomial. You can read it here. Tim Gowers puts a lot of effort into making the ideas seem reasonably "natural". Enjoy! -- if you have a taste for this sort of thing.
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The Unapologetic Mathematician
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Dirac Notation II
1 Jul 2009 | 11:06 amWe continue discussing Dirac notation by bringing up the inner product. To this point, our notation applies to any vector space and its dual, with the ket denoting a vector and the bra denoting a linear functional . The evaluation is then denoted by the bra-ket pairing . But the neat thing about this notation is that it makes bras look like some sort of reflection of kets. And they are, in a sense. The dual space is some sort of reflection of the vector space , but there’s no clear mapping from vectors in one space to vectors in the other; unless, that is, we pick a specific… -
Dirac notation I
30 Jun 2009 | 8:17 amThere’s a really neat notation for inner product spaces invented by Paul Dirac that physicists use all the time. It really brings to the fore the way a both slots of the inner product enter on an equal footing. First, we have a bracket, which brings together two vectors the two sides of the product are almost the same, except that the first slot is antilinear — it takes the complex conjugate of scalar multiples — while the second one is linear. Still, we’ve got one antilinear vector variable, and one linear vector variable, and when we bring them together we get a… -
Sunday Samples 127 (one day late)
29 Jun 2009 | 10:55 amOkay, everybody in the world now knows that Michael Jackson died. And yes, it’s a big deal. But there’s a lot of reputation-burnishing going on out there, one piece of which I’d like to talk about today. Everyone talks about the music video for “Thriller”, which was really great. It was practically a movie in its own right. But just as Rob Reiner can make North and Steven Spielberg can make The Lost World, so could Michael Jackson release a great, big stinker. And the one that comes most readily to mind is 1991’s “Black or White”. Yes, it hit… -
Updates
26 Jun 2009 | 1:59 pmAs a much-anticipated visit approaches, my apartment is asymptotically approaching neatness. My former students’ comprehension of the word “asymptotically”, however, remains constant. And this morning I received the proofs to a paper that was accepted for publication two years ago: “Functors Extending the Kauffman Bracket”. So yeah, I get out with it finally appearing in print, but in the meantime my career is shot. -
Matrices and Forms II
25 Jun 2009 | 11:54 amLet’s pick up our discussion of matrices and forms and try to tie both views of our matrix together. We’re considering a bilinear form $ on a vector space over the real or complex numbers, which we can also think of as a linear map from to its dual space . We can also consider a sesquilinear form on a complex vector space, which is equivalent to an antilinear (conjugates scalars) map from the space to its dual. We got a matrix by picking a basis for and plugging basis vectors into our form And we also found that this is the matrix of the map from to , written in terms of the basis…
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Basic-Mathematics
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Mayan numeration system
2 Jul 2009 | 10:18 amThis lesson will give you a deep and solid introduction to the mayan numeration system -
Cheap online tutoring
30 Jun 2009 | 1:55 pmVery cheap online tutoring is now possible.Introducing on demand tutoring with TutorVista, worlds Largest Online Tutoring Company. -
Roman numeration system
29 Jun 2009 | 1:57 pmThis lesson will give you a deep and solid introduction to the roman numeration system -
Egyptian numeration system
29 Jun 2009 | 9:52 amThis lesson will give you a deep and solid introduction to the Egyptian numeration system -
Tally numeration system
29 Jun 2009 | 8:32 amThis lesson will give you a deep and solid introduction to the tally numeration system
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The Math Mojo Chronicles
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Monsoon Season
10 Jun 2009 | 5:47 pmGalileo and Maia on a date at the Unadilla Drive-In movie It’s a monsoon season here in upstate New York. Today we had one of those storms that used to make bronze-age people believe in things like the apocalypse (or for some Timothy LaHaye readers, still does). But up here in the Catskill Mountains of New York we know better – it’s really Rip van Winkle’s bowling party. We have two beautiful golden retrievers ,Galileo and Maia. Galileo is almost 110 pounds of majestic muscle and fur. A more noble looking creature you will never find. As he sits here at my feet,… -
What if I Fail 9th Grade Math? (Part 6)
9 Jun 2009 | 4:51 amThis is a continuation from the previous posts: What if I Fail 9th Grade Math? (Part 1) What if I Fail 9th Grade Math? (Part 2) What if I Fail 9th Grade Math? (Part 3) What if I Fail 9th Grade Math? (Part 4) What if I Fail 9th Grade Math? (Part 5) At the end of the previous post, a reader wrote in: “i have the same problem. i am in grade 12. i used to grasp those integers, algebra and simple geometric problems with lot of ease and faster than others. then i started falling down not only in grades but also in work ethic. now i got 70 in grade 12 and thats the highest ive gotten in high… -
What if I Fail 9th Grade Math? (Part 5)
8 Jun 2009 | 7:35 amThis is a continuation from the previous posts: What if I Fail 9th Grade Math? (Part 1) What if I Fail 9th Grade Math? (Part 2) What if I Fail 9th Grade Math? (Part 3) What if I Fail 9th Grade Math? (Part 4) A reader (Trevor) wrote in: i am going to fail math 9 . what ill happen if i fail. i cant go to summer school my family refuses to take me. if anyone knows if i will go to the 10th grade or will be in 9th again please tell me thank u. Professor Homunculus sez: Trevor, There’s no way for me to tell you what your school will decide. Each school is different. Your family refuses to… -
Long Division Shortcut Hint
5 Jun 2009 | 6:46 pmYou may have read other posts about this long division shortcut at Math Mojo. Long division shortcut Part 1 Long division shortcut Part 2 The main page to go to to learn the basics of the shortcut is: Long Division Shortcut at Mathmojo.com At that page, someone asked: I have attempted this question using your method: 44872 / 79 Using your method I get the answer 569, when the answer is 568. Please elaborate for me. When I tried the example myself, I almost got 569 as well, but then I realized what the problem was. I think fellow who wrote, as well as I, fell prey to a very easy trap to… -
More about Constructivism
21 May 2009 | 12:37 pmAh, math ed. I hate it. Yes, I hate it. It has become a corporate tug-of-war for the hearts and minds of petty pedagogues, and your kids are in the crossfire. Should it be Math-U-See? TERC, Singapore, Saxon, or one of the other over-marketed mind-usurpers? I like math. I love math. I hate to see it co-opted by these impostors. OK, some are worse than the others. Before you say, “Hey, but Math Mojo is also trying to sell me something…” let me tell you now – you are correct. But I’m not trying too hard, and I don’t want you to buy in to my…
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The Everything Seminar
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What killed Madame Curie? (Part 3)
27 Jun 2009 | 4:48 pmIthaca, NY, 1948 After a wrong turn in Albuquerque, I caught up with Bugs Bunny, alias Richard Feynman, somewhere near the ends of the earth. Up to my elbows in snow-drifts, I spied on the little window to his office, in which he seemed to be doing normal professor-things, plus wild gesticulations. I decided on a particularly frozen morning that I would have to risk visibility if I was to get answers, so I enrolled at Cornell, posing as a G.I. bill student. In Professor Feynman’s introductory physics lectures, I could see that there was something remarkable happening here. … -
What killed Madame Curie? (Part 2)
7 Jun 2009 | 11:55 pmLos Alamos, 1946 I should have sought Dr. Fermi right away, back when it was easy. When Mademoiselle Curie gave me the lead, Enrico was a quiet university professor in Rome. Since then, he’s got a lot harder to find, and it seems that the professor has government ties— secrets as big as the men who hide them. I chanced upon a tip leading me to a project in Manhattan, and though I found Fermi on the books as a Columbia professor, I had just missed the man himself. Asking an associate about where in the New World this Italian Navigator might be, he turned bright red and… -
What killed Madame Curie? (Part 1)
21 May 2009 | 1:32 pmJuly, 1934 I was called to investigate the recent death of a famous physicist: Marie Curie, born Manya Skłodowska. When I arrived on the scene, she was in her death-bed, her face long and grey, a ghostly shadow in the warm light of the mountain sanatorium. Her daughter Eve was there. “It’s so quiet,” she said, “so fearfully motionless—” We made our introductions, but she was obviously distracted. “So motionless, those hands. No longer nervously shaking, constantly moving, always working…” I took a look at the hands, still and… -
Card Shuffling II – The Riffle Shuffle
20 Apr 2009 | 9:08 pmIn my previous post on card shuffling, I established a basic framework in which we will work. We are given a probability distribution on and we wish to determine when first begins to decay exponentially, where is the -fold convolution of One key feature of card shuffling theory, as well as much of finite Markov chains in general, is that the tools available are often very particular to a small class of problems. There just aren’t very many big hammers around. Even though the theorem described in the previous post was quite general, it was non-quantitative, and so not especially useful… -
Card Shuffling I
19 Apr 2009 | 7:52 amJust about anyone interested in mathematics has studied a little probability and probably done some easy analysis of basic card games and dice games. Completely off topic for a second, am I the only one who has noticed that basic probability homework exercises are the only situation, aside from funerals, that anyone will ever use the word “urn?” For whatever reason, probabilists love that word. Anyway, in any real card game, the computations tend to get complicated rather quickly, and most people get turned off from the discussion. With some ingenuity, however, one can answer some…
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bodmas blog
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Interface for web site
3 Jul 2009 | 1:34 pm“Despite my passion for software I’ve been very interested in being outdoors and blending better my physical presence with the real world. If I could I’d prefer to just spend all my time outdoors; doing work such as annotating the real world with appropriate meta-data.”Anselm Hook’s use this interview Anselm Hook’s personal site has colour coded rectangles showing recent additions (scroll down a bit). This is taking me back to an old idea (before I started using WordPress),a fridge magnet interface. I need to improve my JavaScript, so watch this space over… -
A Red Herring
2 Jul 2009 | 12:40 pmI’m doing a presentation about Moodle and how we need to broaden use of the communications tools next Wednesday. I’m working to a 20 minute time allowance. I’ll be ‘signposting’ people here at various points as we cross large and complex issues. The Red Herring category will mark those extra bits, cut material, and digressions that could not be pursued. The category will also provide referencing for sources that I use. The image is actually of the Blueback Herring, and thanks to the authors of the Fishes of New York Web site for providing a high quality image for… -
Summer: Mobile technology
28 Jun 2009 | 7:05 amThe English Summer is upon us and I’ve been caught in thunderstorms twice. All the classes finish soon and I’m ramping up the staff development. I’ve been thinking about how people will interact with the Internet over the next few years. I hate to admit it, but the future is probably with small portable devices rather than Web Books. I think there may be a ‘student’ use-case (see comments on the article linked in this paragraph) where a decent screen and day long battery life make a Web book attractive, but people who are not in full time education will be… -
48 Numeracy Questions
23 Jun 2009 | 7:11 amDownload a PDF with 48 Numeracy Level 1 questions broken down into 4 ‘days’ worth of homework. Each homework lasts about 20 minutes. Whole numbersFractions, decimals and percentagesUnits, areas, volumesMoney! You will need to do your own answers until I get near my scanner. I wanted to show standard methods in these questions. I’m thinking of giving homework broken down into 10 or 20 minutes a day next year. -
Classifying Moodle courses
12 Jun 2009 | 2:37 pmMoodle Venn DiagramView more Keynote presentations from keithpeter. Just a way of looking at Moodle courses that Alan Staley described during a Moodle User Group meeting some time ago. I’ll be working this one up for next year’s technology supported learning course.
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ChapterZero
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God is Not Great
22 Jun 2009 | 6:32 pmThis weekend I was starved for a good book to read, and there wasn’t any palatable science fiction or fantasy available (I even broke my self-enforced restriction and visited Borders), so I picked up “God is Not Great: How Religion Poisons Everything” by Christopher Hitchens. Wonderful! At least so far, I find myself nodding in agreement at a lot of the points he makes. Points that I’ve thought over and agreed with for so long that I don’t think about them incessantly anymore, the way I did when I first deprogrammed myself from SDA. Maybe when I finish it… -
Grassmanian problem?
22 Jun 2009 | 5:08 pmI’ve reduced a problem to the estimation of where is a random (uniform) dimensional subspace of (abusing notation, where is an orthonormal matrix ) and is a fixed orthonormal matrix. But, how the hell do I find a bound form this norm? I know that it’s strictly less than 1, and as , the norm goes down as you’d intuitively expect. But I’ve no idea how to prove this rigorously; i.e. how to get a meaningful bound on the norm that holds with high probability. Think of as a polytope, then one way of thinking of this is: how does the maximum radius of a polytope change when… -
Buggy installation?
16 Jun 2009 | 4:58 pmI apologize if you’ve been trying unsuccessfully to access the site. I don’t know why, but lately this server has been intermittently inaccessible: not only does it not serve pages, I can’t log in via SSH. The support people said something is hogging memory, but I’ve no idea what that something is. I tried turning off the WP cache plugins, because I read that those can fubar the server when they’re buggy .. I recently updated the WP install, so hopefully that’s the culprit and removing caching solved it. We’ll have to wait and see.Possibly relevant… -
my sentiments exactly, but worded more precisely
8 Jun 2009 | 1:09 amThe least action principle is a concept that doesn’t sit well with me. Everytime I’ve seen it (usually in some abortive attempt to teach myself Lagrangian and Hamiltonian mechanics) it has seemed awfully unmotivated. I came across an introduction to the subject that admits that it is natural to have that reaction, and explains why more eloquently than I have hithertofore: This makes learning physics a curious experience. Each person has to learn it the same way we have learned it as a population, beginning to see the patterns by recognizing them in our experience, and then… -
Name that book
6 Jun 2009 | 4:09 pmThere were things he knew which he was unique in knowing. He knew, for instance, that the dead inhabit another sphere; also that in their lonely nether existence they go on doing all the things they’ve done in life. The writers write masterpieces they can never publish, each line perfectly composed, each paragraph polished, each story a gem. Where time isn’t a problem and deadlines don’t exist, things get done right. The architects plot their cities of the mind, beautiful aerial constructs flung across fantastic worlds and spanning sculpted oceans and continents, each brick…
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Computational Complexity
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FOCS Papers
3 Jul 2009 | 4:35 amFor this pre-Independence Day post Bill suggested I write about the math knowledge of our founding fathers or how "P=NP" will declare itself independent of ZFC. Luckily FOCS announced the accepted papers so I can talk about that instead. First the lists.Accepted PapersAccepted Papers with AbstractsAccepted Papers with available PDF links (Shiva Kintali)Algorithmic Game Theory (Noam Nisan)Geometry and Topology (Jeff Erickson)Streaming (Muthu Muthukrishnan)PC Chair Dan Spielman discusses the review process though he doesn't talk about the usefulness of the 2-page addendum or the… -
Learn PCPs at DIMACS
2 Jul 2009 | 8:58 amPrahladh Harsha asked me to post the following announcement on the blog. I don't usually post announcements but this seems like an excellent opportunity to learn about approximation and PCPs from the masters. You can find many more links and short announcements on my Twitter Feed where you would also learn the FOCS accepted papers list is out. My thoughts on the FOCS papers tomorrow. DIMACS Tutorial on Limits of Approximation Algorithms: PCPs and Unique Games When: July 20 - 21, 2009 Where: DIMACS Center, CoRE Building, Rutgers University I would like to advertise an… -
2pi-day? Other holiday possibilities!
1 Jul 2009 | 9:03 amMay 28 should be Pi-day instead of March 14 since pi should be what we now call 2*pi (6.28...) since 2*pi comes up in more formulas than pi. (When I blogged about this here one of the commenter's suggested 2*pi*i.) So what-should-be-pi-day was last Sunday. To honor this day I asked people what day or concept they would want to make a holiday. Here is what I got. Multicultural day. OR give every ethnic group a holiday. This may lead to the 4-day work week. Mid-autumn day to give us a break. Pi-Day (March 14) Mole Day (Oct 23) Talk like a pirate day (Sept 19.) Did pirates really talk that way… -
The NSF Annual Report
30 Jun 2009 | 6:39 amThe NSF has been getting very strict about having PIs (primary investigators) fill out an annual report listing publications and activities related to their grants. The report is due 90 days before the anniversary of the start of the grant, so if you have a grant that started in the fall you are probably getting notices reminding you that your report is now overdue. There are few academic tasks more painful than filling out annual grant reports but best to just grit your teeth and do it or the NSF could cut off your money. Would you rather the alternative, not having to do a report… -
Re-request/when to include a known proof in a paper?
29 Jun 2009 | 9:25 amIn my post of June 24 I requested some help on a sum (among other things). In particular, we had a summation result that we were using in a paper and we wanted to know if it was new or not. We got three comments relevant to it Method of differences due to Pascal discrete calculus analog of the fact that the nth degree Taylor expansion of a polynomial is the polynomials. The first lemma is a direct consequence of the method of finite differences; it says that the nth forward difference of a polynomial of degree n-1 is identically zero. The inner summation in the second identity is basically…
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Natural Blogarithms
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List Your Self: Turning Points
15 Jun 2009 | 12:14 pmI have a book on my shelf that I’ve probably had for close 15 years. Every once in a while I pull it off the shelf and tell myself that I should read it and try it out. The book is called “List Your Self: Listmaking as the way to Self-Discovery”. The subtitle says that it is “A provocative, Probing and Personal Expedition Into Your Mind, Heart, and Soul” Seems to me that this is not only great fodder for a blog but also for a social network like facebook. While many meme’s that go around annoy me to no end, there have been a few that have allowed me… -
The Real Story
4 Jun 2009 | 7:23 pmLast week, a friend on Facebook pointed me to a story that seemed like it would be of interest to mathematician like myself but upon reading the story, there were a number of quirky details in the story and some important details missing. It made me suspicious. STOCKHOLM (AFP) - A 16-year-old Iraqi immigrant living in Sweden has cracked a maths puzzle that has stumped experts for more than 300 years, Swedish media reported on Thursday. In just four months, Mohamed Altoumaimi has found a formula to explain and simplify the so-called Bernoulli numbers, a sequence of calculations named… -
Number Puzzle #8
24 Feb 2009 | 8:32 amThe four numbers A, B, A+B and A-B are all prime. The sum of these four numbers is A) EvenB) Divisible by 3C) Divisible by 5D) Divisible by 7E) Prime Source: 2002 AMC 10/12B #15 -
Camtasia Screen Capture Problem Solved
23 Feb 2009 | 8:18 amI was having a problem when using Camtasia Studio to do a screen capture of an algebra lecture. On my laptop, the capture works just fine but on my desktop it was very jumpy. For those who don’t know, I use a Wacom Tablet, Microsoft OneNote and Camtasia to produce a series of videos for our online Algebra sequence. Whenever I would begin recording, the system would slow down enough that the writing on the screen was broken and hard to read. The sound capture was fine, it just seemed that the CPU was not able to keep up with capturing the video on the screen and allow… -
Number Puzzle #7 – A solution
22 Feb 2009 | 1:34 pmI love these kinds of puzzles because there is only one solution but there are several ways to get there. It’s at least as interesting to hear the different approaches as it is to solve it. Here was the puzzle posted last week: Mr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with 4-digit number in which each of two digits appears two times. “Look, daddy!” she exclaims. “That number is evenly divisible by the age of each of us kids!” “That’s right,” replies Mr. Jones, “and the last…
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Precal Blog
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Rational Functions
9 Jun 2009 | 6:39 pmFirst of all, i’m very sorry that this blog is being posted so late. It may be a little irrelevant, seeing as fifth hour is in the middle of there exam right now, but hopefully this will help anyone who still needs to finish their portfolio =] Rational functions were named because they consist of a ratio between two polynomials. At the beginning of the year, the only thing that we learned was that these graphs were big and messy. But today [well, actually a couple weeks ago] we learned how you really graph them. When looking at rational functions, we have to look at both global… -
Inverse Cotangent Issue
5 Jun 2009 | 8:56 pm -
Questions?
2 Jun 2009 | 7:55 pmWell i was supposed to type up the questions of the class…but no one gave me any questions…so i guess i’m just going to write about what i’d like to review in class tomorrow! The one thing I’d really like to go over is learning target 35…I know we went over this in class and I have the ntoes for it..but i would just like to refresh my memory and make sure I’m not missing anything about how to derive it! I don’t really know what else people have questions on, so I hope tomorrow we just brush up on all the learning targets and people can bring… -
Limits with Trig!
29 May 2009 | 9:08 amLast week in class we were given the the nine “laws” of limits. Here are the last two: 8. limit x->0 (sin x)/(x) = 1 9. limit x->0 (1-cos x)/(x) = 0 We were told to accept #8 as true without any proof (we will learn how to prove it next year in Calculus). We were, however, shown how to prove #9, provided that #8 is true. ((1-cos x)/x) * ((1+cos x)(1+cos x)) = ((1-cos2 x)/(x(1+cos x))) = ((sin2 x)/(x(1+cos x))) = ((sin x * sin x)/((x(1+cos x))) = ((sin x)/x) * ((sin x)/(1+cos x) = (as limit x->0) 1 * 0 = 0 Then, we were given a worksheet with trigonometric functions,… -
Limits: Definitions
28 May 2009 | 3:27 pmThese three things identify a function as having a limit. x is the x-value you plug in, f(x) is the y-value you get out, a is the x-value that gives you the limit, L is the y-value of the limit itself. 1. If x is close to a but not equal to a, f(x) is close to L. 2. As x gets closer and closer to a but not equal to a, then f(x) gets closer to L. 3. We can make f(x) as close to L by making x close to a but not equal to a. Number one means that if the x-value you plug into the equation is close in value to a but not equal, then the y-value you get will be close in value to the limit. Number…
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Rational Mathematics Education
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You Want Proof? I'll GIVE You Proof!
13 Jun 2009 | 10:17 amOnce again, the fires of discord are raging on math-teach@mathforum.org. One of the threads I've been embroiled in revolves on several axes: one is about teaching pure mathematics in K-12. Another is about visual proofs. The one I wish to specifically deal with here is the one that links the two: what comprises the nature of proof in elementary school mathematics classrooms and how do we get students in those grades to develop their notions of what a mathematical proof actually is?The problems in having this sort of conversation in a hostile forum like math-teach are legion. One problem is… -
Math Test - a poem.
3 Jun 2009 | 2:07 pmI occasionally get requests to post guest pieces at RME, but invariably they prove to be from people looking to promote some sort of commercial web site or service. As those so requesting fail to offer to adequately grease my palm, I always refuse, sometimes in less than friendly fashion.However, I received a work today of such outstanding literary merit, so fraught with relevance to many of the concerns of this blog, that I could not refuse despite the lack of financial incentives from the author. For now, I am going to publish this without attribution to the author, though in due course his… -
Professor Frank Quinn Says: "Calculators? Whoa!"
25 May 2009 | 10:15 amFrank Quinn doesn't like calculators:(what about his dog?)The current (May 2008) NOTICES OF THE AMS contains the following opinion piece from Virginia Tech mathematician, Frank Quinn. It bears noting that the mathematics education folks at his university are members of the math department, which must make for some fun faculty meetings.K–12 Calculator WoesIn the third grade my daughter complained that she wasn’tlearning to read. She switched schools, was classified asLearning Disabled, and with special instruction quicklycaught up. The problem was that her first teacher useda visual word… -
Do I Repeat Myself? - Getting Rote Right
22 May 2009 | 8:15 pmJoseph Mazur, dangerous guyIf you want to get educational traditionalists all aflutter, say something the implies that rote learning may not be all it's cracked up to be. It's about as effective in stirring up ire as burning a US flag in front of the local branch of the American Legion (though I think impugning rote learning isn't likely to get one arrested, jailed, or fined. Yet.)Because I'm basically a bad person, I like to post without comment quotations I consider interesting and potentially provocative on lists inhabited by knee-jerk anti-progressives and educational conservatives. The… -
See How They Run, Like Pigs From A Gun. . .: Vern Williams and the NMP Report
13 May 2009 | 6:18 amLast week, there was a public conversation/Q & A session on the National Math Panel Report between two members of the body that produced it: Vern Williams and Francis "Skip" Fennell. Unfortunately, work commitments prevented me from hearing it live and attempting to participate by submitting questions. I had to satisfy my curiosity as to how anti-progressives through the voice of Mr. Williams, would try to spin matters by reading the transcript this morning.Or, I should say, as much of it as I could tolerate given that I had made the error of eating my breakfast before assaying the task.
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The Math Factor Podcast
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FY. Weights in a Row
2 Jul 2009 | 1:44 pmWhat can you say about a sequence if you know that each term is a weighted average of the terms to either side? For example, in the sequence 1, 2, 4, 8, 16, … each term is exactly 2/3rds of the previous term, plus 1/3rd of the following term. What other sequences have exactly that property? For a given value p, what sequences s1, s2, s3, … sn have the property that each sk = p s(k-1) + (1-p) s(k+1) ? Does knowing s1 also fix the remaining terms? Amusingly, this actually will help with last weeks puzzle! -
FW. Walk Around the Clock
2 Jul 2009 | 1:16 pmA quick puzzle from one of our listeners, which has a surprising and interesting solution: Standing at 4:00, repeatedly flip an unfair coin, moving clockwise if it comes up heads, and counterclockwise if it comes up tails. What is the probability that you visit every hour 1-11, before you reach 12:00? In our next post we’ll ask a seemingly unrelated question that turns out to help quite a bit… -
FV. Singmastery!
12 Jun 2009 | 11:02 pmDavid Singmaster, Puzzler Extraordinaire, early master of the Rubik’s Cube, poser of the Singmaster Conjecture, etc, etc, engages in some wordplay. -
Morris: Infinite Products
8 Jun 2009 | 1:16 pmThis made me smile. I hope it makes you smile too. What is If you think they are the same then why? If you think they are different then why? -
Yoak: Face Up
28 May 2009 | 5:10 pmThis is a classic puzzle from Martin Gardner that also appears in Peter Winkler’s Mathematical Puzzles: A Connoisseur’s Collection. (At least I think so. My copy is buried in a box somewhere.) First, a warm-up puzzle: You’re blindfolded and I will place two cards on the table in front of you, each either face up or face down at my option. We’ll then play a game taking turns. On your turn, you may turn over either one or both cards. On my turn, I may either swap the positions of the cards without changing which might be face up or not at my…
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WordPress Tag: Mathematics
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Semiotics and Prerogative
3 Jul 2009 | 6:25 pmGiven signs and their denotations, a language represents relations between signs and also perhaps between signs and niches of the real world. Gödel has proven that any fixed formal system is incomplete. A successful formal system requires an organic nexus to assess and introduce new signs. Victoria University of Wellington has successfully proven the failure of the Victorian headless system. -
Responses to multiple POV Logic Puzzles
3 Jul 2009 | 5:11 pmThere are a group of 5 good logic puzzles (I think they are good), and their responses need a place. Here it is. -
TED: Mathematics and History revisited
3 Jul 2009 | 1:17 pmAs a gamer and game designer and game player, I approve this message. (I first saw this video at Assorted Stuff, rather than the main TED.com website) We need better instruction in mathematics. There was the recent story of a school in the tampa bay area. They locked up their math books, and changed their entire style of teaching. *I* need to change my entire style of teaching, too, when it comes to History. I’ve got to stop thinking of my assigned textbooks as the key tools for the study of history, and start thinking about how to turn my students’ brains into the key tools… -
Lorenz Stoer - Geometria Et Perspectiva (Augsburg, 1567)
3 Jul 2009 | 12:17 pm -
Logic Puzzles from multiples points of view 4/5
3 Jul 2009 | 10:15 amOver the next few days I’ll be posting a group of five puzzles, related by a “multiple points of view” theme. None of these puzzles belong to me. And I don’t know where to extend credit. I think they’ve just sort of existed, forever. Prisoners with Hats Three perfectly logical prisoners are seated facing each other, with hats on their heads. Each hat has a counting number {1, 2, 3, 4, …} on it, and each prisoner can see the hat of the other two prisoners, but not his own. The warden says, I will set free the man who can tell me his own number, but execute any…
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Mr. L's Math
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Strategy Games and Other Fun Resources from N.C.T.M.
3 Jul 2009 | 4:07 pmHere’s some fun to brighten your summer days! NCTM has a nice resource page for teachers and students full of website links and paper/pencil activities. You can find the site titled “Let the Summer Games Begin!!!” And these resources are not just for the summer. I’ve already planned to use some of them during the upcoming school year to teach thinking skills - you just can’t get enough motivating, engaging activities! To receive all new posts - subscribe via email or RSS Web Feed. Related posts:Meet Mr. L -
Summer Splash - the Association of Illinois Middle Schools Annual Conference
23 Jun 2009 | 6:30 pmI just finished presenting a workshop for the Association of Illinois Middle Schools Annual Conference in Normal, Illinois (home of Illinois State Univ.) and enjoyed it tremendously. I had the pleasure of interacting with 150 middle school teachers and once again working with the AIMS staff - a real class act! Here’s what the AIMS Executive Director had to say in her March Newsletter: Deb Discusses… The Aha! Moment A brief chat with Deb Schrock, AIMS Executive Director Back in December of 2006, I was facilitating the Bill Lombard workshop in Lisle.His topic was Activities to… -
Free Online Math Courses for Teachers
19 Jun 2009 | 6:20 pmGuest post by Karen Schweitzer Need to brush up on your math skills or prepare materials for a new math class. There are many different colleges and universities that offer free online math courses at the undergraduate and graduate level. Here are ten courses that would be useful to teachers. Numbers, Units, and Arithmetic - This introductory math course from the UK’s Open University offers a basic review of whole numbers, decimals and fractions. The course is split into three self-study modules and takes approximately five hours to complete. Algebra I - This undergraduate level Algebra… -
Meet Mr. L
17 Jun 2009 | 3:58 pmBill is the 2006 California League of High Schools northeastern California Educator of the Year Bill Lombard currently teaches at Foothill High School, ten miles east of Redding. He has taught at the high school level for twenty years, at the middle school level for six years, two years at Shasta Community College, and three years at the adult/teacher level as the Manager of the Teacher Education and Computer Center based in Redding. For the last fifteen years Bill has presented mathematics curriculum to teachers at conferences and workshops. He and his co-author, Brad Fulton, have written… -
What Are the Odds of Losing Your Lunch? - A Probability Adventure
17 May 2009 | 11:57 amHere’s a neat problem recently under discussion in our school district: “Four kids, each with their own lunch, go on a trip. When it’s time to eat, the four identical-looking lunches are mixed up and the kids randomly choose one. what is the probability that exactly one kid gets his own lunch?” This problem is nice because it can be solved several ways, allowing students to see how others solve the problem. By relating the different methods of solution, students build and strengthen their own problem-solving abilities. It’s also a nice problem because it reminds…
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MathNotations
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Dorothy Revisited -- Another View...
28 Jun 2009 | 4:59 amMathmom contributed some insightful thoughts about how most middle school students might feel about the probability investigation from the other day. I agree with her that some would be able to compute the results or even devise a general formula but "proving" it in the general case might be too ambitious. In my reply, I suggested there might be another way of deriving the formula 1/N for the probability of losing the game. Here's what I came up with. It still requires some careful development to show that the outcomes are equally likely but I will indicate how it could be done in the… -
Please Help Dorothy Go Home - A Probability Fantasy for Middle School and Beyond
24 Jun 2009 | 3:41 amSummer vacation is an appropriate time for fantasy. Enjoy the hiatus!The following investigation is not intended to be a math contest challenge. It reviews fundamental principles of probability and you might want to bookmark it for the fall. We can also simulate the first problem using the programming capabilities of a graphing calculator. I may post a simple program for this later on.The wizard will let Dorothy go home if she can pass three challenges.He shows Dorothy 3 playing cards, 2 of which are black and one is red. He shuffles them and turns them face down. "Dorothy, here's your first… -
"On The Road Again" With 'TC' -- A Real World Application of Geometry
15 Jun 2009 | 5:15 amAs my devoted readers know, Totally Clueless, affectionately known as TC, has contributed many insightful comments and profound ideas for us to think about. His sobriquet belies a brilliant creative mind of course. He recently sent me a geometry problem which was motivated by his own experiences driving to work. The problem itself is accessible to advanced middle and secondary students but the result is interesting in its own right and should generate rich discussion in class. I recommend giving this as a group activity, allowing about 15 minutes for students to work on, then another 15… -
An Equation Which May Be More 'Complex' Than It Appears!
13 Jun 2009 | 3:39 amMaybe I should rename this blog to Saturday 'Morning' Post. After all, no one reads that either anymore!As the school year comes to a close (and I'm assuming it's already over for some), here's an innocent-looking equation which might be worth discussing with your advanced algebra/precalculus students now or next year. I might have considered saving this for our next online math contest but it's complex nature makes it more suitable for discussion in the classroom than on a test. Have you seen exercises like this in your Algebra or Precalculus texts? Do students often delve beneath the… -
Two Geometry Problems To Sharpen The Mind - Never Too Late In the Year For That!
6 Jun 2009 | 4:48 amWell, the June SATs have arrived today so these problems come too late for that, but these kinds of questions can be used to review basic ideas while strengthening thinking skills. Both questions below are appropriate for both middle and secondary students, although the second requires knowledge of a fundamental geometry principle regarding the sides of triangles.There are other important principles embedded in these problems as well. In the end, I believe that students need to be exposed to many of these "contest-type" challenges to improve reading skill, learn how to pay attention to detail…
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Neoformix
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Shaped Word Cloud: Canada
1 Jul 2009 | 3:05 amHappy Canada Day ! This is a Shaped Word Cloud created from the text of approximately 168,000 tweets containing the word 'canada'. The tweets were gathered over an 11 month period from July 31, 2008 to June 30, 2009. Basically, the larger the word the more frequently it appears in the text. Stop words were discarded. I also adjusted the size based on the relative frequency of the word in the canada dataset versus a baseline dataset containing tweets about india and china. A word like 'country' or 'travel' is used approximately the same for canada as for india and china and so will be… -
Word Search: Canada Map
30 Jun 2009 | 5:05 amHere is another Shaped Word Search in honour of Canada Day tomorrow, July 1st. This one is in the shape of a map of Canada and uses Provinces, Territories, and cities in the word list. Click on the image or here for the PDF version. Feel free to print this in any newspaper or magazine. I only ask that you keep the reference to http://neoformix.com and that you send me an email letting me know. Click on the image to download a hi-res PDF version suitable for printing -
Word Search: Maple Leaf
30 Jun 2009 | 5:00 amIn honour of Canada Day tomorrow, July 1st, I have created a Shaped Word Search with a maple leaf design and words I associate with Canada. I improved my tool slightly to sort the words in alphabetical order so it is more convenient to look them up. Thanks to Joe S. for the suggestion. Click on the image or here for the PDF version. Feel free to print this in any newspaper or magazine. I only ask that you keep the reference to http://neoformix.com and that you send me an email letting me know. Click on the image to download a hi-res PDF version suitable for printing -
Word Portrait: Michael Jackson
27 Jun 2009 | 5:00 amHere is a Word Portrait of Michael Jackson created from the titles of many of his top songs. Click on the image to see a larger version -
Twitter Venn: Celebrity Deaths
26 Jun 2009 | 1:10 amHere is a Venn Diagram made with Twitter Venn that shows the relative frequency of tweets made about the recent deaths of three celebrities - Michael Jackson, Farrah Fawcett, and Ed McMahon. This analysis was done around 7am EST today and the absolute numbers for tweets/day will certainly increase as more people in the US come online. I expect the proportions among the various combination regions to stay roughly the same. A couple of points of interest: Celebrity interest ranked by number of tweets is Michael > Farrah > Ed with ratios 62:6:1 Ed was mentioned together with both Michael…
