Welcome to the 86th Carnival of Mathematics! is semiprime, nontotient, and noncototient. It is also happy since and . In fact, it is the smallest happy, nontotient semiprime (the only smaller happy nontotient is 68—which is, of course, 86 in reverse—but 68 is not semiprime). However, the most interesting mathematical fact about 86 (in my opinion) is that it is the largest known integer for which the decimal expansion of contains no zeros! In particular, . Although no one has proved it is the largest such , every up to (which is quite a lot, although still slightly less than the…
Math
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Most Topular Stories
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Carnival of Mathematics 86
The Math Less Traveled8 May 2012 | 12:05 pm -
The Math Ed War – Which Side Are You On?
Maths Tips From Maths Insider17 Apr 2012 | 1:59 pmThere’s a war going on.A war based on who’s right and who’s wrong when it comes to your child’s math education. Western countries such as the US and the UK fall far behind the Eastern powerhouses of China and Singapore when it comes to Math (did you see the US vs Them infographic I published recently?) and there’s a battle going on in Education circles around the world as to the best way to make sure your child will have the strong math skills needed to compete in the global economy.The following quotes are from an interview at EducationNext.org with W. -
Book review: In Pursuit of the Traveling Salesman
The Math Less Traveled7 Apr 2012 | 3:00 pmAs mathematical problems go, the “traveling salesman problem” (TSP) is a rare gem: it is simultaneously of great theoretical, historical, and practical interest. On the theoretical front, it is a well-known example of the class of “NP-complete” problems, which lie at the heart of the million-dollar “P vs NP” question (which I still intend to explain at some point). Historically, it has been studied for almost 200 years (given a sufficiently inclusive definition of “study”), and has occupied a place in the public consciousness for at least the… -
Math Rules
Scientific American - Math29 Apr 2012 | 8:00 amIn his new book, In Pursuit of the Unknown: 17 Equations That Changed the World , Ian Stewart recounts one of the worst jokes in the history of science. You can develop your own setup from first principles once you know the punch line: “The squaw on the hippopotamus is equal to the sum of the squaws on the other two hides.” Never mind how Native Americans were in possession of a hippopotamus--the important thing is that the Pythagorean theorem is so well known that comedy writers consider it fair game even if that game couldn’t possibly be found on the correct continent. -
New twist on ancient math problem could improve medicine, microelectronics
ScienceDaily: Mathematics News10 May 2012 | 12:27 pmA hidden facet of a math problem that goes back to Sanskrit scrolls has just been exposed by nanotechnology researchers.
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MATH - Google News
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Fun Math Game for Kids, Motion Math: Wings, Soars Onto The App Store - Number ... - Virtual-Strategy Magazine
16 May 2012 | 4:25 amFun Math Game for Kids, Motion Math: Wings, Soars Onto The App Store - Number Virtual-Strategy MagazineMotion Math, the pioneer of fun, interactive mobile math games, is releasing its newest learning game for iPad, iPhone and iPod touch – Motion Math: Wings (http://www.bitly.com/mmwings). The app, available now on the App Store as a Top Three App in the and more » -
Meet the 'worst' 8th grade math teacher in NYC - Washington Post (blog)
16 May 2012 | 4:06 amMeet the 'worst' 8th grade math teacher in NYCWashington Post (blog)Her score on the Teacher Data Report, the New York City Department of Education's effort to isolate a teacher's contribution to her students' (bigstock) performance on New York State's math and English Language Arts (ELA) tests in grades four through and more » -
Science plus math equals butterfly garden - Tbo.com
15 May 2012 | 11:03 pmScience plus math equals butterfly gardenTbo.comThe project incorporates classroom research on plants and butterflies, the math of setting up a budget and the environmental science of using drought-resistant plants and a rain barrel for water conservation. Nothing works better with most students -
Math Skills Required, Why? - IndustryWeek
15 May 2012 | 11:02 pmMath Skills Required, Why?IndustryWeekBy Jill Jusko More often than not, manufacturers emphasize the need for advanced math skills by skilled production employees today. Miles Free, director of industry research and technology for the Precision Machined Products Association, -
Summit looks for answers to boost math, science education - Mason City Globe Gazette
15 May 2012 | 10:48 pmSummit looks for answers to boost math, science educationMason City Globe GazetteDES MOINES — The answers were as simple as keeping students working on math problems during the summer and as daunting as transforming celebrity culture. But whether either, both or neither of those suggestions provides the solution to the problem State education department announces STEM training for teachersMPNnow.comall 4 news articles »
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Search for "math OR mathematics"
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The Mathematics of Obesity
16 May 2012 | 5:39 amHugh Pickens writes "The NY Times reports that Carson C. Chow, an MIT-trained mathematician and physicist, has taken a new look at America's obesity epidemic and found that a food glut is behind America's weight problem , with the national obesity rate jumping from 20 percent to over 30 percent since 1970. -
Gulf High Principal Brings Decades of Experience to Job
16 May 2012 | 5:31 amKimberly Davis started a new job this month. Davis officially assumed her role as Gulf High' s new principal May 7. An experienced educator and administrator, Davis has worked for the Pasco County School District since 1998. -
Interview with singer-songwriter Marq DeSouza: Part 1
16 May 2012 | 5:31 amVancouver-based Marq DeSouza is a former member of Solarbaby. He has shared the stage with artists like Sir Bob Geldof, Sarah Harmer, Drive By Truckers, Matthew Good, and Nickelback, and released five albums. -
Nkumba University Applications for August 2012/2013 Intake
16 May 2012 | 5:28 amNkumba University aims to promote education in business, arts, social sciences, technical, communication and cultural fields as well as stimulate the spirit of enterprise and entrepreneurship. -
Council Reduces Budget By $660,000
16 May 2012 | 5:28 amBy a majority vote, the Town Council has agreed to cut the proposed i»¿over $60 million budget for the 2012-2013 fiscal year by approximately $660,000 at its meeting Monday night.
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ScienceDaily: Mathematics News
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New twist on ancient math problem could improve medicine, microelectronics
10 May 2012 | 12:27 pmA hidden facet of a math problem that goes back to Sanskrit scrolls has just been exposed by nanotechnology researchers. -
It's official: Physics is hard
8 May 2012 | 9:38 amScientists have conducted scientific research on the difficulty –- from a computational complexity theory perspective -- of addressing some of the challenges of physics. -
First light: Researchers develop new way to generate superluminal pulses
3 May 2012 | 6:42 pmResearchers have developed a novel way of producing light pulses that are "superluminal" -- in some sense they travel faster than the speed of light. The new method could be used to improve the timing of communications signals and to investigate the propagation of quantum correlations. -
Study finds twist to the story of the number line: Number line is learned, not innate human intuition
25 Apr 2012 | 6:27 pmTape measures. Rulers. Graphs. The gas gauge in your car, and the icon on your favorite digital device showing battery power. The number line and its cousins -- notations that map numbers onto space and often represent magnitude -- are everywhere. Most adults in industrialized societies are so fluent at using the concept, we hardly think about it. We don't stop to wonder: Is it "natural"? Is it cultural? Now, challenging a mainstream scholarly position that the number-line concept is innate, a study suggests it is learned. -
Shedding light on southpaws: Sports data help confirm theory explaining left-handed minority in general population
25 Apr 2012 | 1:04 pmLefties (only ten percent of the general population) have always been a bit of a puzzle. Researchers have now developed a mathematical model that shows the low percentage of lefties is a result of the balance between cooperation and competition in human evolution. They are the first to use real-world data (from competitive sports, including baseball, boxing and hockey) to test and confirm the hypothesis that social behavior is related to population-level handedness.
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Scientific American - Math
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In Their Prime: Mathematicians Come Closer to Solving Goldbach's Weak Conjecture
11 May 2012 | 8:00 amOne of the oldest unsolved problems in mathematics is also among the easiest to grasp. The weak Goldbach conjecture says that you can break up any odd number into the sum of, at most, three prime numbers (numbers that cannot be evenly divided by any other number except themselves or 1). For example: [More] -
Ancient Time: Earliest Mayan Astronomical Calendar Unearthed in Guatemala Ruins
10 May 2012 | 2:01 pmAn excavation of an archaeological site in Guatemala has uncovered Mayan astronomical records dating to the ninth century A.D. The tabulated numbers, which predate existing Mayan astronomical documents by several hundred years, chart the motion of the moon and also seem to relate to the orbits of Mars and Venus. (And good news: they do not predict the world will end this year --in fact, some of the numbers appear to refer to dates far in the future.) [More] -
Does Digital Piracy Really Hurt Movies?
8 May 2012 | 8:00 amThe shadowy nature of illegal media downloading makes it difficult for researchers to analyze the true relation between piracy and lost sales. Does every movie download represent a theater ticket left unpurchased, as the movie industry contends? Or are most downloaders people who never would have bought a ticket in the first place? [More] -
Spy-High: Amateur Astronomers Scour the Sky for Government Secrets
1 May 2012 | 7:00 amEarlier this year Iran's defense minister put the world on notice: His nation had developed the ability to "easily" watch spacewalking astronauts from the ground. The announcement was largely ignored, in part because it made the minister sound like a James Bond villain. The boast was also a bit anticlimactic, given that even amateur astronomers are already recording in detail what happens in low Earth orbit. Both the technology involved and the techniques used to observe satellites and even the occasional astronaut perched outside the International Space Station (ISS) are… -
Math Rules
29 Apr 2012 | 8:00 amIn his new book, In Pursuit of the Unknown: 17 Equations That Changed the World , Ian Stewart recounts one of the worst jokes in the history of science. You can develop your own setup from first principles once you know the punch line: “The squaw on the hippopotamus is equal to the sum of the squaws on the other two hides.” Never mind how Native Americans were in possession of a hippopotamus--the important thing is that the Pythagorean theorem is so well known that comedy writers consider it fair game even if that game couldn’t possibly be found on the correct continent.
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NYT > Mathematics
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A Mathematical Challenge to Obesity
13 May 2012 | 11:00 pmCarson Chow has used mathematical models to determine the causes of obesity, and ways to stem the epidemic. -
Catching Up With Jean-Baptiste Michel
5 May 2012 | 11:00 pmA French-Mauritian mathematician, engineer and researcher on what he’s reading and watching — and what he’s not. -
New York’s Top Technology Official, Carole Post, Resigns
13 Apr 2012 | 11:00 pmThe departure of the administrator, Carole Post, comes as the city is challenging the release of a report on a much-delayed modernization of the city’s 911 system. -
Bloomberg Defends Withholding Report on 911 System
3 Apr 2012 | 11:00 pmCritics said the administration was understating emergency response times to justify closing firehouses, but Mayor Michael R. Bloomberg said the report was not ready. -
World as Classroom and Crash Course for Exchange Students
27 Mar 2012 | 11:00 pmWhile Europe and North America still lead the list of destinations for foreign exchange students, the fastest growing regions include Latin America and Asia, a new report shows.
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Math-U-See
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We’re More Fun in Person, Math-U-See Newsletter, Vol. 35
2 May 2012 | 7:22 amIf you go to a fair, chances are good you’ll get to meet one of the Curriculum Counselors from Math-U-See. Susan Crothers is one of these talented and experienced individuals who has been with us for 16 years and used Math-U-See to teach her (now 25-year-old) child all the way through school. We sat down with her and asked if she would recommend visiting Math-U-See at a fair if you have a chance. Not surprisingly, her answer was a resounding “yes!” for several reasons. New Homeschoolers One of Susan’s true joys of staffing the Math-U-See booth at curriculum fairs is the chance to talk… -
5 Reasons to visit Math-U-See at Your Nearest Homeschool Fair, Math-U-See Newsletter Vol. 34
29 Mar 2012 | 9:52 amWe’re Multi-Sensory, so we’re better in person. Get a feel for our Manipulative Blocks and build your own multiplication problem. Listen to an explanation of how to teach place value or polynomials. See a lesson for yourself and learn how Steve has simplified the teaching of math. (As for taste and smell…well, we’ll work on that.) Get advice from our expert Curriculum Counselors. From assessment questions to help with specific math topics, we’re there to help. Remember, all of our Curriculum Counselors have had extensive training, and many of them have taught their own students. -
Homeschool Dad Works Himself out of a Job, Math-U-See Newsletter, Vol. 33
13 Feb 2012 | 12:32 pmHere are two missives I received from April, a homeschool mom. I was intrigued by her first email and asked for more information. She sent me the rest of the story in email number two. Email 1 We have been using Math-U-See for the past 8 years with our son and 2 daughters. Over the years, I have had several other homeschoolers say that they switched to a different curriculum because the higher level courses seemed too easy. However, after getting half way through the Algebra 2 curriculum, our son tested into PreCalculus/Trigonometry at the local community college as a high school junior. So… -
Building Lifelong Learners, Math-U-See Newsletter, Vol. 32
17 Jan 2012 | 1:35 pmFrom Ethan – A Lifelong Learner I was born at a young age and from the moment I entered the world my parents have been involved every step of the way. They raised and educated my three brothers and me at home with a philosophy of building lifelong learners. With four boys who each had a very different learning style, they were able to adapt and creatively develop an approach that produced a good outcome for all of us. More importantly than just having me memorize and repeat facts, my parents taught me how to learn and how to apply that learning. I believe this is what every home… -
Giving Thanks – Math-U-See Newsletter, Vol. 31
23 Nov 2011 | 2:38 pmGrowing up, our family had a tradition. Every year at Thanksgiving each of us would write a list of what we were thankful for in the past year. This year at Math-U-See we are thankful for many things and we wanted to share them with you. Peter, who teaches our online co-op classes, is thankful for the students that he has the privilege of teaching. Susan from customer service is thankful for many things: Customers with faithful hearts that are dedicated to their family core values and upbringing of their children. A country where we have the freedom to homeschool. Mentors and friends who…
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Wild About Math!
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Scott Laidlaw and Jen Harris – Inspired by Math #7 (Part 2 of 2)
22 Apr 2012 | 9:44 amHere's the second part of my interview with Scott and Jen from Imagine Education. Watch this video first, and listen to Part 1. -
Scott Laidlaw and Jen Harris – Inspired by Math #7 (Part 1 of 2)
8 Apr 2012 | 10:34 amA mutual friend introduced me some months ago to Jen Harris and Scott Laidlaw. Jen and Scott founded Imagine Education to produce and market an amazing Math Game, Ko's Journey. I rarely promote commercial ventures but I sincerely believe in the work that these two are doing. If you think that Sal Khan is changing the world of Math education, then hopefully you'll agree that what Jen and Scott are doing is 100 times more important. Their interactive learning environment engages students in an experience of mathematics through the magic of storytelling and through the primal identification with… -
Carnival of Math #85 packed with stuff!
5 Apr 2012 | 10:05 pmCheck it out! -
Michael Schrenk on Webbots, Spiders, and Screen Scrapers
2 Apr 2012 | 9:43 am[Note: I created this podcast for one of my other blogs. It's not math-related but folks who are interested in the Web and in how intelligent agents can navigate the web might enjoy the audio. ] I produced this podcast because I was curious about intelligent web agents and noticed this new edition of Michael Schrenk's Webbots, Spiders, and Screen Scrapers. Why read Webbots, Spiders and Screen Scrapers? Gain a bottom-up understanding of what webbots are, how they're developed, and things to watch out for. Understand the mind set difference between traditional web development and webbot… -
1959 – Donald Duck – Donald in Mathmagic Land
23 Mar 2012 | 8:54 amIn case you've never seen this classic Math movie, I think you'll enjoy this.
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Ars Mathematica
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Classification of Finite Simple Semigroups and Moufang Loops
25 Apr 2012 | 4:09 pmI had a question that I was going to ask on Math Overflow, but after some research I managed to find the answer. Finite simple groups have a complete classification. I was wondering if there were any weakenings of the axioms of group that also allowed a complete classification of the simple objects. (Here, I mean no nontrivial quotients.) Surprisingly, there’s a classification for semigroups. In the theory of semigropus the term “Simple& is used for a weaker notion. Semigroups with no nontrivial quotients are known as “congruence-free”. The classification of… -
Stacks Project
20 Mar 2012 | 6:38 amI’ve been trying to learn about stacks, something that is much easier in the Internet age. The Stacks Project is a collaborative textbook that introduces the subject from the ground up, including all of the machinery necessary. The book is already up to 3000(!) pages. -
Geometric Logic at Sea
20 Feb 2012 | 6:48 amDoing a search for the definition of geometric logic, I have discovered that it’s mentioned in the movie The Caine Mutiny, by the notorious character of Captain Queeg: Ahh, but the strawberries that’s… that’s where I had them. They laughed at me and made jokes but I proved beyond the shadow of a doubt and with… geometric logic… that a duplicate key to the wardroom icebox DID exist, and I’d have produced that key if they hadn’t of pulled the Caine out of action. The upside of the technique is that it allows you to deduce the existence of… -
Commutativity Theorems for Rings
17 Feb 2012 | 10:19 amMathJax doesn’t work with RSS readers, so when I have some more time I will look into using a plug-in instead. Until then, sorry for filling up your RSS feed with dollar signs. Theo Raedschelders has written a nice sketch of Herstein’s commutativity theorem for rings. It is a generalization of Wedderburn’s theorem that a finite division ring must be a field. The theorem states that if for every pair of elements $a$ and $b$ there exists an $n > 1$ (which can depend on $a$ and $b$) such that $$ (ab – ba)^n = ab – ba, $$ then the ring is commutative. What’s… -
Quandles
14 Feb 2012 | 7:04 amAs of a few hours ago, all I know about quandles was that they had something to do with knots. Since in our modern connected age ignorance lasts only as long as you want it to, I decided to find out more. I found this slide deck by Bob McGrail explains both the definition of quandle and the motivation in knot theory in a measly six slides. (The rest of the talk is how to efficiently compute quandles.) Sam Nelson has a nice introduction to the general area of universal-algebraic invariants from the Notices, called Revolution in Knot Theory. Nelson also discusses the emergence of virtual knots.
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Loren on the Art of MATLAB
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Why is Answer to 3 < A < 7 Unexpected?
14 May 2012 | 3:32 amThere have been countless (not really!) times on the MATLAB newsgroup where a question of the sort written in the title has been asked (and answered). Let's go through the code to understand what's happening. DISCLAIMER: It's not my intention in this post to discuss non-scalar behavior. Contents Problem Statement WHAT??? First Part of Expression: low < A Second Part of Expression: previous output < high Look at the Types How to Get the Expected Answer Have Compound Expressions Caused You Problems? Problem Statement As part of program, suppose we need to see if some value lies between… -
Mathematics and Humanities: Understanding Sort Algorithms
27 Apr 2012 | 5:00 amSteve recently mentioned a video showing how the quiksort algorithm works, including an explanation from Bobby regarding the need for the final seconds to be sure that NaN values are sorted correctly. Contents Visualizing Quiksort Visualizing Other Sort Algorithms A Place Where Math Meets the Humanities Visualizing Quiksort With much amusement, many of us from MathWorks recently viewed this video depicting the quiksort algorithm in dance. I don't think you'll see a MATLAB animation quite like this! Visualizing Other Sort Algorithms If you are interested in similar visual depictions of other… -
Running Scripts on a Cluster Using the Batch Command in Parallel Computing Toolbox
20 Apr 2012 | 4:22 amI'd like to introduce this week's guest blogger Edric Ellis. Edric works for the Parallel Computing development team here at The MathWorks. In this post he will talk about using the batch command in Parallel Computing Toolbox. Sometimes, even when you've optimized your MATLAB® code, you find that you have so many simulations to run, or scenarios to explore, that running them on your desktop computer just takes too long. Parallel Computing Toolbox™ together with MATLAB Distributed Computing Server™ can help you to run your scripts and functions on a cluster of computers. As… -
Have You Visited MATLAB Central Recently?
10 Apr 2012 | 8:11 amI don't know if you visit MATLAB Central often, but there's a good reason to these days. Contents New at MATLAB Central Which Community Service Do You Use Most? New at MATLAB Central In addition to the usual services on MATLAB Central, File Exchange: download and share files Link Exchange: share resource Newsgroup: read and post to the Usenet newsgroup comp-soft-sys.matlab there are three new additions to MATLAB Central collection. I'll list them here and delve into more details in later posts. MATLAB Answers: ask and answer MATLAB questions Cody: solve and ask MATLAB problems (with code)… -
Considering Performance in Object-Oriented MATLAB Code
26 Mar 2012 | 8:35 amI’m pleased to have Dave Foti back for a look at objects and performance. Dave manages the group responsible for object-oriented programming features in MATLAB. I often get questions along the lines of what performance penalty is paid for using objects or how fast will an object-oriented implementation perform compared with some other implementation. As with many performance questions, the answer is that it very much depends on what the program is trying to do and what parts of its work are most performance-intensive. I see many cases where most of the real work is inside methods of an…
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Homeschool Math Blog
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Mother's day freebies & more
10 May 2012 | 6:38 amAurora from Supercharged Science is again giving away a great free gift! She has one of the top homeschool science curricula out there, and this is a free selection of activities and experimentsfrom her summer e-Camp program. You're going to get actual sections of e-Camp, complete with all the explanations, step-by-step videos, and lots more. And yet more... Currclick is giving away several Mother's Day freebies, one of which is my book Math Mammoth Place Value 2. So, here's your chance to get one of my books completely free. Enjoy! Maria -
See the first 4 million digits of Pi
25 Apr 2012 | 7:47 amThis online visualization represents the first 4,000,000 decimals of Pi within a single image. Each unique digit of Pi corresponds to a specific color, and is rendered as a 1x1 pixel dot. You can also search for the first occurrences of any specific decimal combination. -
Math Mammoth Grade 2 aligned to the Common Core Standards
20 Apr 2012 | 11:13 amMath Mammoth Grade 2 Complete Curriculum is now aligned to the Common Core Standards. I will record here the main changes in its content as compared to the earlier edition / version (through April 2012).You can tell the new edition and the earlier ones apart by their cover image: the edition aligned to the Common Core Standards has these new cover images.The topics of rounding and finding 1/4 of a number were taken off as they are not in Common Core Standards for grade 2.The topics of regrouping in addition and regrouping in subtraction are now split so that 2-A contains regrouping in… -
Math Mammoth Grade 1 aligned to the Common Core Standards
20 Apr 2012 | 10:22 amMath Mammoth Grade 1 Complete Curriculum is now aligned to the Common Core Standards. I will record here the main changes in its content as compared to the earlier edition / version (through April 2012).You can tell the new edition and the earlier ones apart by their cover image: the edition aligned to the Common Core Standards has these new cover images. What used to be chapter 4 (Place Value) switched places with Chapter 3 (Addition and Subtraction Facts within 0-18). The topics of rounding, even & odd numbers, and parenthesis were taken off as they are not in the Common… -
Geometry problems (challenges)
13 Apr 2012 | 3:43 pmSomeone sent me this linkhttp://fivetriangles.blogspot.com/It contains challenging geometry problems for middle and high school level. Unfortunately I didn't see solutions!This blog for teachers contains an unordered series of problems for middle and junior high school students. The problems are not intended to be ``clever'', but rather require only a knowledge of already-learned basic mathematics principles, applied in a more sophisticated manner than for the problems found in a typical textbook.
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About.com Mathematics
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Prime Numbers
13 May 2012 | 3:17 amA prime number is a number that is bigger than one and cannot be divided evenly by any other number except one and itself. This article will help you find out if ...Read Full Post -
Derivative Calculator
9 May 2012 | 3:03 pmThis week I received an email with this online derivative calculator. It supports symbolic computation of the 1st, 2nd, ... derivative of a function. While typing, the input is displayed as a graphical formula, which facilitates entering the expression in a correct way. It doesn't show you the step by step, but that's your part! It gives you the answer to make sure your step by step is correct. Give it a try and let me know what you think....Read Full Post -
Paper Plate Math
7 May 2012 | 5:46 pmPaper plates are great for counting, multiplication, basic addition and subtraction facts and for identifying quantity. All you need is a handful of paper plates and some circle type stickers or a bingo dobber. The patterns are here and you'll also find some great strategies to help children learn many of the basics in math. Parents, homeschoolers and teachers will find these activities great! AND, the paper plates are more engaging than flash cards. Give them a try with children ages four to eight years of age. -
Division: Why It's So Confusing for Early Learners
3 May 2012 | 3:27 pmSomewhere along our academic timeline, we all learned how to divide. However, most of us don't remember how we learned to divide, nor did we give it a great deal of thought. Yet, many educators will tell you that young learners just don't get division. Let's just think about this for a minute. Take the question 73 divided by 3. So, we put this into a format on paper and the first thing we prompt our young learners with is " How many times does 3 go into 7?" Now, put yourself into the brain of our young learner. 3, into 7? Wait, isn't that 70? Or 7 tens? Why am I doing 3 into… -
How to Prepare Teachers to Be Effective Math Teachers
28 Apr 2012 | 4:47 amWhat does it take to be an effective math teacher? Some individuals will argue that those that grasph math concepts easily are necessarily the best teachers because they haven't experienced being out of the comfort zone and struggling to understand. Others feel that you really need to understand math to teach math. What does the research say? A IEA study, led by Michigan State University says teacher preparation is key. They have discovered that the countries that best prepare math teachers meet several key conditions. See the full article in Science Daily.
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Let's Play Math!
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Tell Me a (Math) Story
14 May 2012 | 5:35 am[Photo by Wellspring Community School. This article is an excerpt from my upcoming "Let's Play Math!" book series.] My favorite playful math lessons rely on adult/child conversation — a proven method for increasing a child’s reasoning skills. What better way could there be to do math than snuggled up on a couch with your little one, or side by side at the sink while your middle-school student helps you wash the dishes, or passing the time on a car ride into town? As soon as your little ones can count past five, start giving them simple, oral story problems to solve: “If you have… -
Quotable: The Art of Teaching
11 May 2012 | 6:02 amMost remarks made by children consist of correct ideas very badly expressed. A good teacher will be very wary of saying ‘No, that’s wrong.’ Rather, he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole of the art of teaching. — W. W. Sawyer Vision in Elementary Mathematics Get all our new math tips and games: Subscribe in a reader, or get updates by Email. -
Homeschool Mom’s Day at CurrClick
9 May 2012 | 5:46 amCurrClick has opened up their Mother’s Day festivities with several contests and free ebooks, including Math Mammoth Place Value 2. If you read last week’s PUFM lesson on place value, this would be a great book to practice “studying teaching materials” on. It contains several types of problems discussed in our textbook: manipulative pictures, expanded form, number line, skip-counting, and more — even some algebra puzzles. Enjoy! Get all our new math tips and games: Subscribe in a reader, or get updates by Email. -
Thinking (and Teaching) like a Mathematician
8 May 2012 | 5:40 amphotos by fdecomite via flickr Most people think that mathematics means working with numbers and that being “good at math” means being able to do (only slower) what any $10 calculator can do. But then, most people think all sorts of silly things, right? That’s what makes “man on the street” interviews so funny. Numbers are definitely part of math — but only part, and not even the biggest part. And being “good at math” means much more than being able to work with numbers. It means making connections, thinking creatively, seeing familiar things in… -
Are You Ready for the Math Carnival?
7 May 2012 | 1:01 pmphoto by UggBoy The Math Teachers at Play (MTaP) blog carnival is a monthly collection of tips, tidbits, games, and activities for students and teachers of preschool, primary, and secondary mathematics. Do you like to learn new things and play around with ideas? You’re sure to find something of interest in the carnival. If you are a homeschooler or classroom teacher, student or independent learner, or anyone else who writes about math — now is the time to send in your favorite blog post for next week’s MTaP carnival. The deadline is this Friday night, and the carnival will…
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Basic mathematics blog
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Story word Problem: linear equation
3 May 2012 | 2:20 pmA salesperson earns a $200 per week in base pay plus one-twentieth of his/her dollar sales volume. Find the salesperson’s dollar sales volume if he/she -
college student
2 May 2012 | 9:45 amAlvin's age is three times Elga's age. The sum of their ages is 40 . What is Elga's age? Let x be Alvin's age Let y be Elga's age x + y = 40 x -
Working together in Sales
28 Apr 2012 | 3:46 pmMichael Scott, by himself, can close 8 sales in 4 hours. If he works with Dwight, they can close 8 sales in 2 hours. How many hours does it take Dwight -
rectangle word problem
28 Apr 2012 | 2:13 pmthe length of a rectangle is 5 more than the width and the area is 24. Find the length and the width. The formula of the area of a rectangle is A = -
math and metric system
28 Apr 2012 | 1:51 pm660 centimeters is equal to how many meters? 1 meter = 100 centimeters If it was 600 centimeters instead of 660, you could easily get the answer. 100
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ChapterZero
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QOTD: total unimodularity
8 May 2012 | 5:54 pmI started reading Matousek’s discrete geometry book. Specifically, chapter 12 on applications of high-dimensional polytopes. Mostly because he apparently draws a connection between graphs and the Brunn-Minkowski theory, and I’m interested to see exactly what that connection is and if it has any interesting implications. I just finished the proof of the weak perfect graph conjecture (it’s been a while since I read a nontrivial pure math proof, so I haven’t actually *digested* it entirely). Now I’m on the exercises for that portion. So, here’s an interesting… -
Are there perturbations that preserve incoherence and give nicely conditioned “submatrices”?
14 Apr 2012 | 12:56 pmLet \(\mat{P}_{\mathcal{U}}\) denote the projection unto a \(k\)-dimensional subspace of \(\C^{n}.\) We say \(\mathcal{U}\) is \(\mu\)-coherent if \((\mat{P}_{\mathcal{U}})_{ii} \leq \mu \frac{k}{n} \) for all \(i = 1, \ldots, n.\) Let \(\mat{A} \in \C^{n \times n} \) be a SPSD matrix whose top \(k\)-dimensional invariant subspace is \(\mu\)-coherent. Given \(\delta > 0\) and \(\mat{S} \in \C^{n \times \ell}\), where \(k < \ell \ll n,\) is there a matrix \(\mat{E}_{\delta,\mat{S}} \in \C^{n \times n} \) such that \(\hat{\mat{A}} := \mat{A} + \mat{E}_{\delta,\mat{S}}\) is SPSD, The… -
I discover vegetables taste good in Dijon sauce then proceed to spread the gospel
25 Mar 2012 | 4:43 pmI had a dozen eggs in the fridge that I need to use up by Wednesday; now I’m down to four. I made Jaffa cakes last week (not bad, but not memorable, and definitely not worth the effort: my main complaint is that the cake portion is bland and has a too-tough texture) and I left some chocolate blueberry cookie dough sitting in the fridge overnight which I’ll bake up tonight. That accounted for four of the eggs. This post is about the two meals that account for another four, and maybe the remaining four also Steak, eggs, and vegetables in sauce I’m in love with this dish… -
Puzzled by the definition of stationarity
15 Mar 2012 | 9:55 pmI’m reading Santosh Vempala’s survey “Geometric Random Walks: A Survey,” and already I’m puzzled at one of the very first definitions he gives. Define a Markov chain as a state space sigma algebra pair \((K, \mathcal{A})\) with transition probability measures given by \(P_u\) for each \(u \in K.\) A distribution \(Q\) on \((K, \mathcal{A})\) is called stationary if one step from it gives the same distribution, i.e., for any \(A \in \mathcal{A},\) \[ \int_A P_u(A) \, dQ(u) = Q(A). \] This definition makes sense in words, but mathematically it doesn’t seem… -
My Android ebook reading workflow (optimized for frequent turnover of ebooks)
29 Feb 2012 | 1:41 amSynopsis: Aldiko’s not appropriate if you plan on constantly rotating the collection of ebooks on your mobile device. Instead, a combination of Calibre, Moon+Reader, and DropBox seems to do the trick. Consider using Moon+Reader as your default reader unless you need Aldiko’s capabilities for dealing with large ebook collections, as Moon+Reader has a more polished reading experience than Aldiko. A major contributor to my decision to get an Android tablet was my desire to be able to read ebooks comfortably. Namely, with more portability and a form factor closer to the usual book…
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Computational Complexity
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Wall Street Complexity
14 May 2012 | 8:13 amThere is much blame to go around for JPMorgan Chase's two billion dollar loss last week but part of that blame came back to us. In a New York Times web piece, How Moore’s Law Affects Wall St. Trading, Quentin Hardy argues Faster, cheaper computing makes it possible to create more and better models for calculating cash movements, which can be turned into trading instruments. Areas like leasing, mortgages and project finance have exploded – as has the entire financial derivatives market — thanks to cheap computing... Soon, it becomes nearly impossible to say what is going on where,… -
So THATS why the 17x17 challenge was so hard. Or maybe not.
10 May 2012 | 1:30 pmOn November 30, 2009 I posted the famous 17x17 challenge: (Paraphrase) Find a 4-coloring of the 17x17 grid that has no monochromatic rectangles. For $289.00. It was solved in 2012 by Bernd Steinbach and Christian Posthoff (I posted about it here and will post their paper when they make it it is public, which should be soon.) Even though it was solved, it seemed to be a hard problem. On April 28, 2010 (before the problem was solved) I wondered WHY it was so hard and posted the following question: (Paraphrase) Consider the following problem: Given (N,M,c,f) where f is a partial c-coloring of… -
Paying to Publish
7 May 2012 | 3:09 pmYou proved a nice theorem, wrote up the paper and submitted it to a major computer science conference. Your paper was accepted! Congratulations. Now pay up. An author of every paper accepted at a CS conferences is expected to present that paper at the conference. To do so requires at the least paying the registration fees, travel and lodging to go the the meeting. That can easily run one to three thousand dollars (or more) depending mostly on how far you need to travel. You can use grant money for these expenses. Some conference offer support to those who need it, particularly students. CS… -
Is it well known that we need to redefine well known?
4 May 2012 | 9:44 amA LONG time (so long ago I was a guest poster, not a co-blogger) I posted about how calling things that are on You-Tube rare is odd since ITS ON YOU-TUBE! ANYONE in the world can look at it! I now have a Contrasting thought: Can something be well known if its not easily found on the web? Last week I posted a proof that the intersection of a CFL and a REG lang is CFL that did not use PDA's. I thought it was NOT new and indeed, the comments politely gave me the proper reference. So far, so good. But wait--- some of them called the proof Well Known. Can a proof be well known if its not on the… -
Microsoft saves the Yahoo NY Researchers
3 May 2012 | 10:11 amI started working with David Pennock on prediction markets back when we both were at the NEC Research Institute in New Jersey a decade ago. After a major reorganization the dropped basic research from their mission, I went back to academics but David stayed in industry research first at Overture which soon was swallowed up by Yahoo. He ended up at Yahoo Research New York in a small but amazingly strong research lab including machine learning theorist John Langford and social scientist Duncan Watts. But with a new Yahoo CEO and Prabhakar Raghavan and Andrei Broder's departures for Google, it…
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The Math Less Traveled
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Fibonacci multiples
15 May 2012 | 10:26 amI haven’t written anything here in a while, but hope to write more regularly now that the semester is over—I have a series on combinatorial proofs to finish up, some books to review, and a few other things planned. But to ease back into things, here’s a little puzzle for you. Recall that the Fibonacci numbers are defined by Can you figure out a way to prove the following cute theorem? If evenly divides , then evenly divides . (Incidentally, the existence of this theorem constitutes good evidence that the “correct” definition of is , not .) For example, evenly… -
Carnival of Mathematics 86
8 May 2012 | 12:05 pmWelcome to the 86th Carnival of Mathematics! is semiprime, nontotient, and noncototient. It is also happy since and . In fact, it is the smallest happy, nontotient semiprime (the only smaller happy nontotient is 68—which is, of course, 86 in reverse—but 68 is not semiprime). However, the most interesting mathematical fact about 86 (in my opinion) is that it is the largest known integer for which the decimal expansion of contains no zeros! In particular, . Although no one has proved it is the largest such , every up to (which is quite a lot, although still slightly less than the… -
Carnival of Mathematics submissions due in a week
23 Apr 2012 | 8:49 pmI’ll be hosting the Carnival of Mathematics, and the submission deadline is coming up soon—Tuesday, May 1. Please submit something! It could be something you wrote, or something someone else wrote that you enjoyed. All mathematics ranging from elementary to advanced is welcome. -
Book review: In Pursuit of the Traveling Salesman
7 Apr 2012 | 3:00 pmAs mathematical problems go, the “traveling salesman problem” (TSP) is a rare gem: it is simultaneously of great theoretical, historical, and practical interest. On the theoretical front, it is a well-known example of the class of “NP-complete” problems, which lie at the heart of the million-dollar “P vs NP” question (which I still intend to explain at some point). Historically, it has been studied for almost 200 years (given a sufficiently inclusive definition of “study”), and has occupied a place in the public consciousness for at least the… -
New Carnival of Mathematics
5 Apr 2012 | 2:07 pmThe Carnival of Mathematics has been revived! A big thanks to Mike Croucher of Walking Randomly for organizing it for the past few years, and to Katie Steckles, Christian Perfect, and Peter Rowlett for taking over. The latest edition, carnival #85 (wow, has it really been going that long?) is now up at Peter Rowlett’s blog, Travels in a Mathematical World. Lots of cool stuff there, so be sure to check it out if you haven’t already. I’ll be hosting Carnival #86 here, so please submit something! The deadline is May 1st, and I’ll post the carnival sometime the week after…
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eon
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Coincidences
6 May 2012 | 10:40 pmI’ll be visiting China tomorrow and my mum kindly handed me a stack of RMB (China’s currency) that was left-over previously. I took a quick count and it totals exactly 1729 Yuan. What are the odds? -
The Rewards of Honesty
13 Mar 2012 | 8:15 pmThe New York Times published an article - which was re-published in the local papers - about a former mathematics professor Kim Myungho who self-published a book decrying the Korean judiciary. (Note the word “published” appeared thrice in the previous sentence.) In fact a movie already seen by several millions was made about Kim who [...] -
It’s Pi Day today
13 Mar 2012 | 7:51 pmA little creative tinkering yielded this mnemonic for Pi (apologies, latex died) to 15 places. “How I need a drink, alcoholic of course, after the heavy lectures involving Euclid’s algorithm” I’ve substituted “quantum mechanics” with “Euclid’s algorithm”, not exactly ideal since it is usually called Euclidean algorithm, plus do you count that apostrophe? But [...] -
Hardy on Number Theory
13 Mar 2012 | 7:42 pmThe elementary theory of numbers should be one of the very best subjects for early mathematical instruction. It demands very little previous knowledge; its subject matter is tangible and familiar; the processes of reasoning which it employs are simple, general and few; and it is unique among the mathematical sciences in its appeal to natural [...] -
Generalizations
26 Feb 2012 | 7:52 pmThere are two kinds of generalizations. One is cheap and the other is valuable. It is easy to generalize by diluting a little idea with a big terminology. It is much more difficult to prepare a refined and condensed extract from several good ingredients. — G. Polya From Induction and Analogy in Mathematics, 1954. But I actually [...]
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mathematics « WordPress.com Tag Feed
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Relation Composition as Matrix Multiplication
12 May 2012 | 9:47 pmSo today I initially wanted to jump straight into some category theory stuff. But I couldn’t decide exactly what I wanted to say, so I put that on the back burner. Not all is lost though. As I was reading through some old stuff I had written, I came across this interesting relationship between relation composition and matrix multiplication. I am assuming that if you are reading this, you already know what those things are. Just in case, I have both linked to wiki pages discussing them. This example will be a nice lead in to discussing categories since category theory can be used to… -
"non-linear" Economies
12 May 2012 | 6:54 pmEach quarter I join investment professionals from various backgrounds/firms for an economic forum; well, not much of a forum than meeting of minds. These deliberative hours serve no less building blocks of my investment outlook; we argue and amend our short and long-term views for the economy, and, as a corollary, for individual asset classes –such as government or corporate bonds, mortgages and stocks. In our first quarter 2012 forum the central topic — as it has been in past quarters and in many circles including the Fed Reserve and PIMCO — was on the optimization/counting… -
Why I Do
12 May 2012 | 6:19 pmI think a fitting start to answering the question of why we should study math is to pose why I study math. I am a math major, after all, so I should have some good reasons, right? Well, maybe. You see, when I started looking at colleges, I decided that I most definitely did not want to be a math major ever. Four years spent studying math intensively followed by a career doing some technical job that made me think way too hard and maybe even grad work in mathematics? That did not seem pleasant at all. So I decided that I would be an elementary school teacher. I liked math, just not enough to… -
Mary Fairfax Somerville - Mathematics by Candlelight
12 May 2012 | 12:32 pm“I was annoyed that my turn for reading was so much disapproved of, and thought it unjust that women -
Galway nuked, radiation fireball blasts Athlone :(
12 May 2012 | 10:55 amThe other day, a live World War II hand grenade was found in a garden just down the street from my h
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MathNotations
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SAT PLUS, DEF OF THE DAY, ETC...
15 May 2012 | 6:06 amDYSFUNCTIONAL DEF: ONE WHO STRUGGLES WITH FUNCTIONS The x- and y-intercepts of a line are 2t^3 and 3t respectively. If the slope of a perpendicular line is 3/2, the positive value of t is ? Ans: 3/2 RANDOM THOUGHTS 1. I've received several thoughts re my PolyAnagrams. I'm a word puzzle fanatic as you might have guessed by now and I enjoy writing these. Let me know if you'd like to see more or restrict a math blog to math! 2) I'm actually thinking of writing 50 of these and offering it on Amazon for a couple of bucks. My question for my readers is, would you buy it? 3) I'm still… -
SAT List and Count and a PentAnagram
12 May 2012 | 5:51 amFor how many pairs (x,y) of positive integers is 2x+3y<24? Ans:37 Ans to QuadAnagram: FILER,RIFLE,FLIER,LIFER Today's PentAnagram! Complete the sentence with FIVE 4-letter words which are anagrams of each other. Mr. Jones' students watched with ---- attention when he took a -----fall, onto the ----. But this was just ---- of a ---- he was setting Sent from my Verizon Wireless 4GLTE PhoneVISIT ME DAILY ON TWITTER AT twitter.com/dmarain -
An Explanation of the Probability Problem
11 May 2012 | 7:02 amFirst, here's a restatement of yesterday's probability question : Compare these 2 probabilities and explain method: (a) Prob of rolling exactly 3 sixes in 5 rolls of a fair die. (b) Prob of rolling exactly 3 sevens in 5 rolls of a pair of fair dice Discussion : Both are examples of binomial probability because they involve repeated independent trials each of which has 2 outcomes. The following explanation is intentionally detailed and 'repetitious'. The prob of a 6 on each roll is 1/6. Each roll produces only 2 outcomes, either a 6 (prob=1/6) or not a 6 (prob = 5/6). The prob of a 7 on… -
QuadAnagram Contest and maybe some math too
9 May 2012 | 8:35 amWell if you tried yesterday's TriAnagram you know the rules. This time we're looking for FOUR 5-letter words to fill in the blanks. The words are all anagrams of each other. John was so bored with being a ----- that he took his -----, went to the airport, saw his boss who was a regular ----- and now John is a bored -----. Ok, some math.. Compare these 2 probabilities and explain method: (a) Prob of rolling exactly 3 sixes in 5 rolls of a fair die. (b) Prob of rolling exactly 3 sevens in 5 rolls of a pair of fair dice We had 2 winners yesterday and each received my new New Math Challenge Book. -
135 and 144 are very special but why...
8 May 2012 | 6:44 amUpdate... Mark James is our first winner today and he already has received his prize! Two to go... Charles Drake Poole is our 2nd winner! Joshua Zucker is our 3rd and final winner! Congratulations! First if you haven't seen my QuadAnagrams and Trianagrams on Twitter, I'll start you off with a fairly easy Triple- or TriAnagram.2 I opened my mouth ----- but my ----- braces still felt -----. Object: Replace the dashes with 3 different 5-letter words which are anagrams of each other. First 3 to email me at dmarain at gmail dot com with the solution to my TriAnagram and the unique property…
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Neoformix
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Movement in Manhattan Video
8 May 2012 | 2:20 amIn my last post about visualizing Movement in Manhattan I mentioned that it would be interesting to explore a more direct view of the data by using an animation. I have created such a video based on a fresh collection of tweets from Monday, April 30th. I gathered new data because I realized that my previous data set was collected over the weekend and I suspected that a weekday might provide more obvious patterns. It compresses 24 hours of data into 1 minute of video. Here it is: I was influenced by the 'Fireflies' video showing iPhone traces done by Michael Kreil. In particular, I like the… -
Movement in Manhattan
18 Apr 2012 | 6:35 amInspired by the beautiful and elegant Interactive Wind Map created by Fernanda Viegas and Martin Wattenberg I have begun to explore the flow of people within a city. An ideal dataset to do this would include the GPS traces from thousands of people wearing trackers for weeks as they go about their daily lives. Organizations such as crowdflow.net and OpenPaths collect voluntarily donated data of this type and might be fruitful to explore. I decided, instead, to use geolocated tweets to try and see how the movement of people is affected by the urban landscape. The image below shows an area of… -
Datavis Subgroup Word Analysis
5 Mar 2012 | 1:30 amThis is Part 4 of a set of posts related to the analysis of the Data Visualization Field on Twitter. For context or more information you may want to read those other posts first. They are: The Data Visualization Field on Twitter Data Visualization Field Subgroups Datavis Blue-Red Connections In the previous posts we have seen that there are two fairly cohesive subgroups of twitter accounts that emerged from our analysis of the original 1000 accounts. I've been calling them the 'blue' and the 'red'. They were determined by looking exclusively at the references to twitter IDs within the tweets… -
Datavis Blue-Red Connections
2 Mar 2012 | 9:30 amThe recent post on Data Visualization Field Subgroups had an interesting reaction on Twitter that I didn't expect. Many people that were placed in the 'red group' by the community detection algorithm in Gephi joked about being part of the 'team' and being happy to represent it and be grouped together with the others. Jen Lowe lightheartedly suggested a scrimmage at #eyeo between the red and blue. There was much less reaction from the 'blue group', likely because I'm embedded within the reds myself and so they likely paid more attention to my posts and the subsequent reaction on twitter. There… -
Data Visualization Field Subgroups
28 Feb 2012 | 9:30 amThere was some interesting discussion yesterday on Twitter about my post on the Data Visualization Field on Twitter. Moritz Stefaner pointed out that he didn't see a big improvement over his VIZoSPHERE and a quite similar topology. Furthermore, he noted that if you rotate my version 90 degrees counter-clockwise many of the primary nodes line up fairly closely with his. He's right, and it's something I missed noticing completely. It's not really surprising that an analysis of most of the same twitter accounts using a different connectedness metric would yield similar results. I do still feel…
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Institute for Mathematics and Computer Science
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The Building Momentum Toward Individualized Education
10 May 2012 | 6:00 am“In an online world, colleges have to think hard about how they are going to take communication, which comes over the Web, and turn it into learning, which is a complex social and emotional process.” -David Brooks, New York Times, May 3, 2012 Over the last 15 years, the advances in our ability to share information broadly and quickly have been nothing short of astounding. More recently, we have started to witness technology’s influence on education. As Peter Haskell, math department chairman at Virginia Tech, said in a recent article, “How could [computers] not change… -
Sophie Germain: Mathematical Muse
26 Apr 2012 | 6:00 amThis week’s post by guest author, Dr. Dora Musielak, includes selected excerpts from her book, Sophie’s Diary: A Mathematical Novel. The story is inspired by French mathematician, Marie-Sophie Germain, the first and only woman in history to make a substantial contribution to the proof of Fermat’s Last Theorem. Little is known of Germain’s adolescence prior to the time she began corresponding with great mathematicians such as Lagrange, Legendre, and Gauss. As Dr. Musielak explains in the MAA Books blog post, this book imagines how Sophie might have learned mathematics on… -
Computational Thinking for Kids
12 Apr 2012 | 6:00 amUnless you’ve been hiding under a rock for the past year, you’ll have noticed that the campaign to teach kids (and adults) how to code is everywhere you turn. As parents, politicians, and educators debate how to produce more graduates in technology fields, the push to introduce computing at an earlier age gets stronger. For example, MIT’s Lifelong Kindergarten group is collaborating on programming software aimed at kids in preschool to second grade. There are even board books for babies on HTML and CSS! We suspect that such novelties are more for tech parents’ enjoyment. -
The Price of Free for Gifted Students, Part 2: Curriculum
29 Mar 2012 | 6:00 amIn our prior blog post where we discussed the importance of effective teachers for gifted students, we also made the point that such teachers should be armed with higher quality curricula better geared toward bright kids. This week, we delve more deeply into what raises the quality of curricula and renders them more suitable for bringing out the best in talented students. Fast Forward vs. Delve Deeper Let’s start with the obvious. Gifted students often understand new information after having it explained to them once. This is in contrast to a typical student who benefits meaningfully… -
The Price of Free for Gifted Children
15 Mar 2012 | 6:00 amMathalicious blog recently posted a well-written and compelling article about the consequences of our nation’s sudden elevation of the popular video tutoring Web site, Khan Academy. If you haven’t read the piece, you absolutely should because it explains beautifully the key reasons why parents and school administrators should be cautious about jumping on the bandwagon of free, technology-based resources as a means of effective teaching. We won’t rehash here what’s already been said well by Mathalicious, nor do readers of this blog who like KA need to rally to its…
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mathrecreation
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return to the island of liars and truthers
9 May 2012 | 6:14 pmThis post has the answers to the puzzles in the last post, so you might want to read that one first. Jeff left a comment suggesting another question that I wish that I had worked into my little story of the islanders, so this late addition was put in as part 5 which you may have missed if you read the post early. Also there was an error in part 3 which meant that although you could solve the puzzle it didn't really work well, so this was fixed also. Sorry for any remaining errors. Throughout we are assuming usual two valued logic and the law of the excluded middle, which you either believe or… -
on the island of liars and truthers
7 May 2012 | 9:42 pmI've been looking at logic puzzles over the last couple of days - my favorites are the ones that involve the Island of Liars and Truthers. These logic puzzles are particularly appealing because they can be thought of as variations and elaborations of the famous liar paradox, known and loved by all. I've come across these in various places - there are quite a few examples of these on the Internet, but if you just google "liars and truthers" you get lots of hits pertaining to conspiracies, so you have to go one further and google "liars and truthers logic puzzle" or "island of… -
envelope doodle design family
24 Apr 2012 | 8:59 pmI'm still playing with some simple designs and also with the "envelope doodle" of a few posts back. I called it "envelope doodle" because, it's a doodle that I used to do (I think in middle school every time we were given graph paper) and it's made up of a bunch of lines that form the envelope of a curve. Both the first (the one made of squares at the top of the post) and last (the one below on the right) design look like standard tiles that you might find on any floor. Some family resemblance might be clear, but it is a little surprising that both are stages in the same… -
some simple designs
17 Apr 2012 | 10:37 pmThe images at the top and bottom of this post were made in Processing and were inspired by some of the exercises from the 1972 book Principles of Two-Dimensional Design by Wucius Wong. Forty years ago this book introduced a language for thinking and talking about the then emerging world of modern design. Today it could also be a source of exercises in basic programming, particularly well-suited for Processing. Wong's later book, Principles of Three-Dimensional Design includes really nice examples of geometric sculpture, many based on polyhedral forms. -
phyllotaxis multiplication colouring pages
5 Apr 2012 | 9:19 pmI thought I would try to make some printable colouring pages of phyllotaxis spirals - thinking that they could be coloured-in using multiplication-table / skip-counting rules to make patterns like the ones shown in the previous post. I've put a two-page pdf here - page one has a spiral with the numbers filled in (as above), and page two has one without numbers (for unfettered colouring). When colouring these in, you might just shade the multiples of five - and get the picture below. As you colour, you'll see the spiral pattern formed by the sequence 5, 10, 15, ... You also can't avoid…
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Maths Tips From Maths Insider
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9 Ted Talks to Get Your Teen Excited about Math
1 May 2012 | 5:44 amDo have a tough time getting your teen or pre-teen interested in talking about math? Well there’s a cool new website Ted Ed which takes ideas worth talking about in areas such as the arts, health, psychology as well as mathematics and creates lessons, quizzes and talking points to help kids engage more deeply with the topics. Here are 9 engaging videos from Ted Ed featuring math ideas worth talking about. Grab your teen, pick a video and give the quizzes a go!1. How Folding Paper Can Get You to the MoonThe incredible potential associated with exponential growth can be seen through… -
Got a Pre-Teen? Try This Mental Math Bootcamp!
1 May 2012 | 3:06 amIn the UK it’s coming up to SATS time for Year 6 (Grade 5) kids. Mental math word questions are an important part of these tests and being able to work with numbers in real-life situations is an essential life skill .The cool people at compare4kids.co.uk have created a tough 15 day Mental Math Bootcamp app to get your kids (and your!) mental math skills in tip top shape. Check it out below!Some useful tips:Your child can change their answer as many times as they want within the time limit for each questionThey’ll need to press enter/return once they’ve written their… -
10 Cool and Funky Kindergarten Math Videos
24 Apr 2012 | 7:57 amIf you’ve got a little one who loves learning through songs, check out the You Tube Videos below which cover essential math topics like money, measurements shapes and subtraction:1. They Might Be Giants Nonagon2. If You Subtract With a Pirate3. Hip Hop Around the Clock4. Counting Down From Twenty 5. Even Numbers 6. Shapes song 7. Measure Yeah Measure 8. Counting by Five 9. What Makes 10 10. Show Me The Money -
The Math Ed War – Which Side Are You On?
17 Apr 2012 | 1:59 pmThere’s a war going on.A war based on who’s right and who’s wrong when it comes to your child’s math education. Western countries such as the US and the UK fall far behind the Eastern powerhouses of China and Singapore when it comes to Math (did you see the US vs Them infographic I published recently?) and there’s a battle going on in Education circles around the world as to the best way to make sure your child will have the strong math skills needed to compete in the global economy.The following quotes are from an interview at EducationNext.org with W. -
10 Hot Pieces of Research to Help Boost Your Child’s Math
10 Apr 2012 | 6:04 amThis is a guest post by Neltje M from MyCriminalJusticeCareers.com.Often, kids say that the subject that they “hate” the most is math. Math can be difficult for some students because they just don’t understand the way that math works. I know for myself, math was never something that came easy. I had to spend agonizing hours over a couple of problems when I was in high school. Now that I have my own children, I realize their pain. However, instead of thinking negatively about math, there has been research that has shown that children are much more adapt to learning math than you…
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MathFour
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Curiosity Based Learning with 100 Floors iPhone App
8 May 2012 | 10:06 amFrom Floor 1, you can tell what you have to do.I’ve become slightly addicted to this free iPhone game called 100 Floors. It has strange and interesting parallels to leraning math.It has no instructions and no hints. And upon first entry to the app, you feel lost, confused and annoyed. (Already starting to sound like a math problem, right?)Based on the name of the game and the view of “Floor 1,” it’s clear that the idea is to open each set of elevator doors.But with just a bit of patience and curiosity, you find yourself challenged just enough on each subsequent floor… -
Everyday Math Exposure: Just Saying It Helps
7 May 2012 | 9:12 amPreviously in an article about math anxiety parents may feel, I mentioned how grown-ups inadvertently teach kids to be scared of certain things.It’s not our fault. We learned it from adults when we were younger.But we still do it.“I hate rats.”“Math? I’ve always had math anxiety.”“Ew, roaches, yikes!”“Math is hard. I don’t do math.”What’s psychology got to do with it?From the principles of psychology, we know that hearing other people talk about things, we adopt some of those same attitudes – especially being young… -
Math Picture Book & Activity: What’s Your Angle Pythagoras?
5 May 2012 | 6:34 pmThis is part of the Teaching Math with Picture Books series.Check out this activity you can do with What’s Your Angle Pythagoras?Will you do it? What else can you do? Tell us in the comments.And share this on twitter!Related Articles:Math Picture Book: One, Two, Three!Math Picture Book: Sir Cumference and the Great Knight of AnglelandMath Picture Book: 1+1=5 And Other Unlikely AdditionsPrime Numbers Are Fun to Learn!This post - Math Picture Book & Activity: What’s Your Angle Pythagoras? - first appeared on MathFour, a blog dedicated to helping teachers, tutors, parents and… -
Differentiated Instruction
4 May 2012 | 6:50 amI just learned what the phrase “differentiated instruction” means. Jeanette Stein told me on #MathChat that for her, differentiated instruction isMeeting kids where they are at to take them where they can go.I love it!So I read the article Jeanette shared from Teach-ology. Seems differentiated instruction is a fancy term for focusing on the individual students rather than the teacher.I’ve been doing it for years!The first few semesters I taught math (back in 1996), I would lecture. I mean straight up, lecture. But soon I learned that it wasn’t about me.Over the next… -
#AnyQs at OTC Houston
3 May 2012 | 9:36 amWil and I attended OTC Houston yesterday with our eyes open for math. We looked at everything in the style of #AnyQs, the Any Questions? Game popularized by Dan Meyer and Colin T. Graham.The idea is to see, hear or otherwise observe something and ask the first questions that come to mind. Ideally, one of the questions you might ask could lead to using and discovering mathematics to answer it.For this set of images from OTC Houston, you can play two ways:Open this text file to write your questions and then copy and paste it into the comments.Tweet out individual questions using the handy…
