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  • Saturday's roundup: University Prep tops Math & Science - The Detroit News

    MATH - Google News
    1 Feb 2015 | 12:55 am
    Saturday's roundup: University Prep tops Math & ScienceThe Detroit NewsUniversity Prep defeated Detroit University Prep Math and Science, 85-48, Saturday afternoon at The Palace of Auburn Hills. Tremaine Brown had 18 points and six rebounds, and Colyn Waldron had 13 points and seven assists for University Prep (9-3).
  • Super Bowl XLIX: Meet the neuroscientist cheerleader battling stereotypes

    Search for "math OR mathematics"
    1 Feb 2015 | 7:48 am
    Note: We do not store your email address but your IP address will be logged to prevent abuse of this feature. Please read our Legal Terms & Policies More than a 100 million people are likely to tune into the Super Bowl tonight, and one cheerleader will use that platform to challenge stereotypes of the profession.
  • Mobile and interactive media use by young children: The good, the bad and the unknown

    Mathematics News -- ScienceDaily
    30 Jan 2015 | 7:26 am
    Mobile devices are everywhere and children are using them more frequently at young ages. The impact these mobile devices are having on the development and behavior of children is still relatively unknown. Researchers review the many types of interactive media available today and raise important questions regarding their use as educational tools, as well as their potential detrimental role in stunting the development of important tools for self-regulation.
  • Does Mathematical Ability Predict Career Success?

    Scientific American - Math
    29 Jan 2015 | 12:00 pm
    A study that has tracked students exceptional in math for 40 years checks their accomplishments -- Read more on
  • Closing the Math Gap for Boys

    NYT > Mathematics
    31 Jan 2015 | 9:00 pm
    An intensive tutoring and mentoring program in Chicago has produced big improvements for kids.
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    MATH - Google News

  • Saturday's roundup: University Prep tops Math & Science - The Detroit News

    1 Feb 2015 | 12:55 am
    Saturday's roundup: University Prep tops Math & ScienceThe Detroit NewsUniversity Prep defeated Detroit University Prep Math and Science, 85-48, Saturday afternoon at The Palace of Auburn Hills. Tremaine Brown had 18 points and six rebounds, and Colyn Waldron had 13 points and seven assists for University Prep (9-3).
  • North Hall's Science, Technology, Engineering and Math Academy drawing ... - Gainesville Times

    31 Jan 2015 | 7:52 pm
    Gainesville TimesNorth Hall's Science, Technology, Engineering and Math Academy drawing Gainesville TimesManzo was one of only three female students who enrolled in the inaugural class of North Hall's Science, Technology, Engineering and Math Academy. The 2-year-old magnet program is one of the many programs of choice offered by the Hall County School ...
  • Babson math professor talks statistics and Super Bowl - Boston Globe

    31 Jan 2015 | 6:19 pm
    Babson math professor talks statistics and Super BowlBoston GlobeCleary, who has a doctorate in statistics and is chairman of the mathematics and science division at Babson College in Wellesley, once taught a math and sports strategy class that packed them in at Bentley University in Waltham. In a particularly
  • Super Bowl Bets, Meet Math - Huffington Post

    31 Jan 2015 | 2:24 pm
    Super Bowl Bets, Meet MathHuffington PostWhile I'm not here to debate the ridiculousness of that figure - do you think any states could use that tax revenue? - I am here to say that if you're going to partake in any of that delicious, gray-area action, you may as well use math to give you an
  • Closing the Math Gap for Boys - New York Times

    31 Jan 2015 | 11:19 am
    New York TimesClosing the Math Gap for BoysNew York TimesThey're among 1,326 boys in 12 public schools in this city who are sweating over math for an hour every day. Kids like these fare worst on every measure of academic achievement, from test scores to graduation rates. On the 2013 National Assessment of ...Students participate in math competitionThe Daily CourierSmall class size is big benefit of private high schoolsOmaha World-Heraldall 5 news articles »
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    Mathematics News -- ScienceDaily

  • Mobile and interactive media use by young children: The good, the bad and the unknown

    30 Jan 2015 | 7:26 am
    Mobile devices are everywhere and children are using them more frequently at young ages. The impact these mobile devices are having on the development and behavior of children is still relatively unknown. Researchers review the many types of interactive media available today and raise important questions regarding their use as educational tools, as well as their potential detrimental role in stunting the development of important tools for self-regulation.
  • Maximizing access to mobile networks by seamlessly 'offloading' some traffic

    27 Jan 2015 | 6:58 am
    Mathematical analysis reveals how to maximize access to mobile networks by seamlessly ‘offloading’ traffic to smaller Wi-Fi and cellular systems.
  • Students master math through movement using Kinect for Windows

    26 Jan 2015 | 10:52 am
    Significant gains in the understanding of angles and angle measurements by elementary school students are seen in those who performed body-based tasks while interacting with a Kinect for Windows mathematics program.
  • Device for guided surgery of deviations in long bones patented

    26 Jan 2015 | 8:22 am
    A device that can be applied in surgeries to correct deviations in long bones has been patented by researchers. The research team found how to use the 3D reconstruction of an affected bone to determine the mathematical formula that in a given case is suitable to design such a device. This device is adjusted to a specific deviated bone and enables a surgeon to set the cutting angle that best suits the bone, and, also, to set the location and orientation of holes that accept the future addition of a corrective prosthesis. It enables realigning the body extremity that is operated on, and also…
  • Medical radiation may be reduced to one-sixth with new mathematical discovery

    26 Jan 2015 | 5:40 am
    One of this century's most significant mathematical discoveries may reduce the number of measuring points to one-sixth of the present level. This means reduced exposure to radiation and faster medical imaging diagnostics.
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    Scientific American - Math

  • Does Mathematical Ability Predict Career Success?

    29 Jan 2015 | 12:00 pm
    A study that has tracked students exceptional in math for 40 years checks their accomplishments -- Read more on
  • Apply for Science Communication Awards, Fellowships and Internship Programs

    29 Jan 2015 | 5:12 am
    Participation of broader audiences in science, technology, engineering, mathematics (STEM) requires engaging under-served audiences. The conduit of this engagement is communication. -- Read more on
  • 3 Super Bowl Fun Facts

    28 Jan 2015 | 5:00 am
    Want to amaze your friends at that Super Bowl party you're going to? All you have to do is hit 'em with some Super Bowl math fun facts. Keep on reading to learn what they are! -- Read more on
  • Genetic Memory: How We Know Things We Never Learned

    28 Jan 2015 | 4:00 am
    I met my first savant 52 years ago and have been intrigued with that remarkable condition ever since. One of the most striking and consistent things in the many savants I have seen is that that they... -- Read more on
  • Learn to Count like an Egyptian

    26 Jan 2015 | 5:30 am
    Last semester, I began my math history class with some Babylonian arithmetic. The mathematics we were doing was easy—multiplying and adding numbers, solving quadratic equations by completing... -- Read more on
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    Loren on the Art of MATLAB

  • Introduction to Market Basket Analysis

    Loren Shure
    29 Jan 2015 | 5:20 am
    You probably heard about the "beer and diapers" story as the often quoted example of what data mining can achieve. It goes like this: some supermarket placed beer next to diapers and got more business because they mined their sales data and found that men often bought those two items together.Today's guest blogger, Toshi Takeuchi, who works in the web marketing team here at MathWorks, gives you a quick introduction to how such analysis is actually done, and will follow up with how you can scale it for larger dataset with MapReduce (new feature in R2014b) in a future post.ContentsMotivation:…
  • What was Sheraton Trying to Tell Us?

    Loren Shure
    23 Jan 2015 | 12:31 pm
    What was Sheraton Trying to Tell Us?Today's post is by Sean de Wolski and me. We spent a few days this week at training for the start of the year, held in a Sheraton hotel.At the completion of our stay, we each got a note in our rooms. Here is a sample.Actually we read this in with the App from the Image Acquisition Toolbox and cropped the image (imcrop from Image Processing Toolbox) to just display the mysterious binary text.Using functionality from the Computer Vision System Toolbox, we then converted our binary text using the ocr (Optical Character Recognition) function.Icrop =…
  • Process “Big Data” in MATLAB with mapreduce

    Loren Shure
    15 Jan 2015 | 5:57 am
    Today I’d like to introduce guest blogger Ken Atwell who works for the MATLAB Development team here at MathWorks. Today, Ken will be discussing with you the MapReduce programming technique now available in the R2014b release of MATLAB. MapReduce provides a way to process large amounts of file-based data on a single computer in MATLAB. For very large data sets, the same MATLAB code written using MapReduce can also be run on the "big data" platform, Hadoop®.ContentsAbout the dataIntroduction to mapreduceUse mapreduce to perform a computationCreate a datastoreCreate a map…
  • Using RESTful Web Service Interface in R2014b MATLAB

    Loren Shure
    31 Dec 2014 | 7:08 am
    FT Guest blogger, Kelly Luetkemeyer, who is a software developer at MathWorks, returns with an article on accessing RESTful web services using MATLAB. Kelly's previous articles included Tracking a Hurricane using Web Map Service and Visualizing the Gulf of Mexico Oil Slick using Web Map Service. Kelly was the lead developer of the new RESTful web service interface feature in MATLAB.ContentsIntroductionObtain Job ListingsLearn more about MathWorks from FacebookUse RESTful Web Services to obtain Airport and Weather InformationDisplay Route from Boston Logan to MathWorksDisplay High Resolution…
  • Subclasses in MATLAB

    Loren Shure
    17 Dec 2014 | 10:10 am
    I'm pleased to have Dave Foti back for a discussion of subclassing and class hierarchies in MATLAB. Dave manages the group responsible for object-oriented programming features in MATLAB.In computer science, a class represents a set of objects that share a common definition, usually including data and functions or behaviors. A subclass represents a subset of objects that share a more specific definition usually by adding or specializing data and/or functions defined in a superclass. In practice subclassing has been used to reuse functionality for a new and more specialized purpose. In recent…
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    Homeschool Math Blog

  • Math worksheets in PDF form

    29 Jan 2015 | 6:43 am
    Time to celebrate!I've been working hard on the various worksheet generators at, and now all of them make worksheets both in PDF and html formats!Below you can see examples of the variety of the worksheets: The advantage of the PDF format is that it's portable and you'll instantly see how it prints.The advantage of the html format is that you can edit it! Simply save the worksheet to your device and then open the file in a word processing software.The worksheets cover topics from grade 1 through pre-algebra, such as: all the basic operations, clock, money, measuring,…
  • Happy Face Math

    22 Jan 2015 | 3:10 pm
    Image credit Charlie SmithSome pointers/explanations in case you find these cryptic:A happy face to the power of -1 is the inverse of happy face.Happy face squared or cubed are pretty easy."sup" in mathematics is the supremum of a set.Then we have a partial derivative of Happy Face.Next, sine of Happy Face = Happy Face sign by the road.In the second column, Re( :) ) is the real part of Happy Face, which is Happy Face without the eyes (without i's).Im of Happy Face is the imaginary part of Happy Face = the eyes (the i's).[Note, i is the imaginary unit used with imaginary numbers.]Triangle…
  • Homeschool Buyers Co-op group buy for Math Mammoth

    19 Jan 2015 | 12:53 pm
    Homeschool Buyers Co-op is running a GROUP BUY for large Math Mammoth bundles at 40% discount – just for one week!The offer expires on January 26, 2015.
  • Math Mammoth January 2015 sale!

    15 Jan 2015 | 11:23 am
    From now till January 31, get 25% off of all Math Mammoth & Make It Real Learning downloads & CDs at Kagi store!Use the coupon code MAMMOTH at the order page at Kagi. At you can learn about the different books I sell and see samples. You will find links to Kagi's order pages on my site, on the various product pages. Or, if you are ready to order, you can use these direct links to the order pages: Order Light Blue seriesOrder the South African version of the Light Blue seriesOrder Blue seriesOrder Spanish versions of the Blue series booksOrder Golden and Green…
  • Math Mammoth printed books sale

    13 Jan 2015 | 10:43 am
    Math Mammoth printed books are on sale at Rainbow Resource Center starting today and running through January 19, 2015. The discount is 20%.
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    Let's Play Math!

  • Get in the Math Car

    Denise Gaskins
    28 Jan 2015 | 8:07 am
    Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Today’s quote is from @Mr_Harris_Math, via Twitter. Background photo courtesy of Forrest Cavale (CC0 1.0) via Unsplash. Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.
  • Math Teachers at Play #82 via Mrs. E Teaches Math

    Denise Gaskins
    26 Jan 2015 | 6:19 am
    The January math education blog carnival is now posted for your browsing pleasure, featuring 23 playful ways to explore mathematics from preschool to high school: Math Teachers at Play #82 Highlights include: Young children making bar graphs. A wide variety of math games. Fractions on a clothesline. Quadrilaterals on social media. Non-transitive dice. Writing in math class. Negative number calculations made physical. Inverse trig graphing. Function operations. And much more! Click here to go read Math Teachers at Play #82. Get monthly math tips and activity ideas, and be the first to hear…
  • Two Ways to Do Math

    Denise Gaskins
    21 Jan 2015 | 5:37 am
    Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Today’s quote is from Raoul Bott, via The MacTutor History of Mathematics archive. Background photo courtesy of Swedish National Heritage Board (CC BY 2.0) via Flickr. Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.
  • Calling All Math Teacher Bloggers and Homeschoolers: Carnival Time!

    Denise Gaskins
    20 Jan 2015 | 10:25 am
    by Bob Jagendorf via flickr The monthly Math Teachers at Play (MTaP) math education blog carnival is almost here. If you’ve written a blog post about math, we’d love to have you join us! Each of us can help others learn, so in a sense we are all teachers. Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up to first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival. Click here to submit your blog post. Browse all the past editions of the Math Teachers at Play…
  • Ruth Beechick on Teaching

    Denise Gaskins
    14 Jan 2015 | 6:51 am
    [Feature photo above by Samuel Mann (CC BY 2.0) via Flickr.] Here’s one more quote from homeschooling guru Ruth Beechick. It applies to classroom teachers, too! Everyone thinks it goes smoothly in everyone else’s house, and theirs is the only place that has problems. I’ll let you in on a secret about teaching: there is no place in the world where it rolls along smoothly without problems. Only in articles and books can that happen. — Ruth Beechick You Can Teach Your Chile Successfully (Grades 4-8)
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    Computational Complexity

  • Reusing Data from Privacy

    29 Jan 2015 | 4:53 am
    Vitaly Feldman gave a talk at Georgia Tech earlier this week on his recent paper Preserving Statistical Validity in Adaptive Data Analysis with Cynthia Dwork, Moritz Hardt, Toniann Pitassi, Omer Reingold and Aaron Roth. This work looks at the problem of reuse of the cross-validation data in statistical inference/machine learning using tools from differential privacy. Many machine learning algorithms have a parameter that specifies the generality of the model, for example the number of clusters in a clustering algorithm. If the model is too simple it cannot capture the full…
  • A nice problem from a Romanian Math Problem Book

    26 Jan 2015 | 12:43 pm
    (All of the math for this problem is here)My Discrete Math Honors TA Ioana showed me a Romanian Math Problem book(She is Romanian) and told the following problem: (All ai in this post are assumed to be natural numbers) Show that for all n ≥ 6 there exists (a1,...,an) such that 1/a12 + ... + 1/an2 = 1. (sum of reciprocals squared) Normally my curiosity exceeds my ego and I would look up the answer.But it was in Romanian! Normally I would ask her to read the answer to me.But I was going out of town! Normally I would look it up the answer on theweb. But this is not the kind of thing the web is…
  • There Should be an Algorithm

    22 Jan 2015 | 5:03 am
    My high school daughter Molly was reading her Kindle and said "You know how you can choose a word and the Kindle will give you a definition. There should be an algorithm that chooses the right definition to display depending on the context". She was reading a book that took place in the 60's that referred to a meter man. This was not, as the first definition of "meter" would indicate, a 39 inch tall male. A meter man is the person who records the electric or gas meter at your house. Today we would use a gender neutral term like "meter reader" if technology hadn't made them obsolete. Molly hit…
  • The two defintions of Chomsky Normal Form

    19 Jan 2015 | 6:33 am
    I have eight  textbooks on Formal Lang Theory on my desk.  Six of them define a CFG to be in Chomsky Normal Form if every production is of the form either A-->BC or A--> σ (σ a single letter). With that definition one can show that every e-free grammar can be put in Chomsky Normal Form, and using that, show that CFL ⊆ P. There is a very minor issue of what to do if the CFL has e in it. Two of the books (Sipers and Floyd-Beigel) define a CFG to be in Chomsky Normal Form if every rule is A-->BC or A--> σ OR S-->e and also that S cannot appear as one of the two…
  • The Impact Factor Disease

    15 Jan 2015 | 10:34 am
    The Institute of Science Information (ISI) was founded in 1960 to help index the ever growing collection of scientific journals. The founder of ISI, Eugene Garfield, developed a simple impact factor to give a rough estimate of quality and help highlight the more important journals. Roughly the impact factor of a journal in year x is the average number of citations each article from years x-1 and x-2 receives in year x. Thomson Scientific bought out ISI in 1992 and turned the data collection into a business. Impact factors are not only being used to measure the quality of journals but of…
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    IMA Journal of Applied Mathematics - current issue

  • Erratum to: Poroelastic Materials Reinforced by Statistically Oriented Fibres - Numerical Implementation and Application to Articular Cartilage

    Federico, S., Grillo, A.
    16 Jan 2015 | 7:25 am
  • The tangential cone condition for the iterative calibration of local volatility surfaces

    De Cezaro, A., Zubelli, J. P.
    16 Jan 2015 | 7:25 am
    In this paper, we prove that the parameter-to-solution map associated to the inverse problem of determining the diffusion coefficient in a parabolic partial differential equation satisfies the local tangential cone condition. In particular, we show stability and convergence of the regularized solutions by means of Landweber iteration. Our result has an immediate application to the local volatility calibration problem of the Black–Scholes model for European call options. We present a numerical validation based on simulated data to this calibration problem and discuss the results. We also…
  • A homogenization analysis of the compressible flow between a slider and a moving patterned rough surface

    Schwendeman, D. W., Please, C. P., Tilley, B. S., Hendriks, F.
    16 Jan 2015 | 7:25 am
    The compressible flow between a slider and a moving rough surface is examined asymptotically and numerically in the limit of very small gap height. The roughness is assumed to consist of a well-defined periodic pattern of grooves whose amplitude and wavelength are of the order of the gap height. A two-scale homogenization analysis is employed to determine a non-linear elliptic partial differential equation governing the leading order pressure in the gap on the scale of the slider. The equation involves coefficient functions that are determined numerically by averaging Stokes flows on the…
  • Complete solutions to a class of eighth-order polynomial optimization problems

    Gao, T. K.
    16 Jan 2015 | 7:25 am
    This paper presents a new class of eighth-order canonical polynomials in Rn. Based on the sequential canonical dual transformation, all extrema are obtained. The method can be used to solve the associated seventh-order non-linear algebraic equations. Optimality conditions are provided to find both global minimizers and local extrema. Applications are illustrated by examples.
  • An efficient numerical algorithm for the L2 optimal transport problem with periodic densities

    Saumier, L.-P., Agueh, M., Khouider, B.
    16 Jan 2015 | 7:25 am
    We present an extension of the numerical method of Loeper and Rapetti (2005, Numerical solution of the Monge–Ampère equation by a Newton's algorithm. C.R. Acad. Sci. Paris, I, 319–324) for the Monge–Ampère equation to non-uniform target densities and adopt it to solve the optimal transport problem with quadratic cost. The method employs a damped Newton algorithm to solve the Monge–Ampère equation. We show that the algorithm converges for sufficiently large damping coefficients, for the case where the source and target densities are sufficiently…
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  • Translate

    22 Jan 2015 | 8:59 pm
    It’s slightly old but I only recently saw this article about how Google Translate make use of linear transformation. The new book on my desk eta products and theta series identities has the following quote in the preface. In der Theorie der Thetafunctionen ist es leicht, eine beliebig grosse Menge von Relationen aufzustellen, aber die Schwierigkeit beginnt da, wo es sich darum handelt, aus diesem Labyrinth von Formeln einen Ausweg zu finden. Die Besch¨aftigung mit jenen Formelmassen scheint auf die mathematische Phantasie eine verdorrende Wirkung auszu¨uben – G. Frobenius, 1893…
  • Nested radicals

    7 Aug 2014 | 8:19 pm
    I was trying to solve an olympiad type problem involving a nested radical of the form [tex] \sqrt{a+b\sqrt{r}}.[/tex] I had managed to discover that [tex] \sqrt{a^2- b^2r} [/tex] is an integer but it turned out the trick is to rewrite [tex] \sqrt{a+b\sqrt{r}} = c + d\sqrt{r}.[/tex] Of course, one naturally asks if this is a specific incident or is there a general theory. This lead to digging up an article that I painstakingly photocopied from the library from back when photocopying was the norm. The article in question is by Susan Landau from 1994 in the Math. Intelligencer titled “How…
  • Millenium Bookball

    19 Jul 2014 | 9:54 pm
    is a pretty cool mathematical sculpture by George Hart. Gone with the Wind, Charlie and the Chocolate Factory, The Cat in the Hat, Green Eggs and Ham. What is not to like? Speaking of which, I still cannot believe that it was only because of my son who is now four that I read Dr Seuss for the first time in my life. Growing up with parents who do not speak English, I only started reading English books in Primary School. I still remember the joy when I did well in school examinations and the prize was to go to the school hall and select one free book for keeps.
  • On practice

    19 Jul 2014 | 9:56 am
    I’m sure I am interpreting this in a context different from Vygotsky who was quoting Lenin Man’s practice, repeated a billion times anchors the figure of logic in his consciousness.
  • Math videos

    9 Jul 2014 | 1:08 am
    “Speaker, I’d like to talk about twin prime numbers …” goes McNerney in the US Congress. This took place on 11 Feb 2014. More details may be found here. There is still hope in politics afterall. I would love to see the day when mathematics is discussed in our parliament. I’ve longed known about the discussion on the Monty Hall problem in the movie 21. But it was preceded by a short take on Newton’s or Newton-Raphson method. See the clip here at Mathematics in Movies site.
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    WordPress Tag: Mathematics

  • 371 What Pythagorean Triple Comes Next?

    29 Jan 2015 | 1:37 pm
    2^371 (mod 371) = 340, not 2. Therefore, 371 is definitely a composite number. Scroll down to see its factoring information. If you can figure out the simple pattern that these odd Pythagorean triples make, you can predict the next one in the sequence FOREVER by squaring only one number, and without ever taking a single square root! Every odd number is the short leg of at least one primitive Pythagorean triple! Here’s how I came to realize this amazing fact: Last week I was thinking about the difference of two squares applied to integers in general as I looked at this multiplication…

    Luther M. Siler
    29 Jan 2015 | 12:14 pm
    The new hotness for the boy lately has been Teen Titans Go!, which works for me because as it turns
  • Crunching Numbers

    Knit Personality
    29 Jan 2015 | 10:47 am
    There’s nothing that makes me more afraid Than a number, because it isn’t made; And though I resist The thought, I can’t shake it: Something can exist Without a maker to make it. xoxo
  • Debal Sommer - Mathematics [Tonkind]

    29 Jan 2015 | 10:25 am
    Debal Sommer – Mathematics Style: Tech House, Deep House Record Label: Tonkind Catalogue Number: TOK040 Release Date: 20-01-2015 Total Tracks: 4 Tracks Source: WEB Tracks: 1. Debal Sommer – Mathematics (Original Mix) (7:33) 2. Debal Sommer – Crazy People (Original Mix) (8:44) 3. Debal Sommer – Fugibeat (Original Mix) (8:12) 4. Debal Sommer – C’est La Vie (Original Mix) (11:16) Server Quality Size Format Link Report Dead 320kbps 82MB RAR Download Report Deep House, Tech-House…
  • Linear Algebra Lectures

    29 Jan 2015 | 8:19 am
    Hi guys. I’m currently studying linear algebra, and I find these lectures by MIT professor (Prof W. Gilbert Strang) quite useful. It’s been helping me a lot in my understanding. Hope you’ll be able to benefit from these lectures too! (: Here’s the first lecture :
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  • When is a rectangle an equilateral triangle?

    Dave Marain
    21 Jan 2015 | 1:52 pm
    As posted on ... Diagonal of a rectangle has length 6 and makes a 30° angle with a side. (a) Area of rectangle=? (b) If diagonal has length d, area=? Ans:9√3;(d^2)√3/4 COREFLECTIONS (1) A moderate difficulty problem for SATs? Appropriate or too hard for a PARCC assessment with both parts? (2) Should diagram be given or is drawing part of what's being assessed? (3) Will some students recognize that the expression in terms of 'd' is the formula for the area of an equilateral triangle of side length d? If no one does then is it our responsibility to model and…
  • How one 2nd grader knows his 7 Times Table!

    Dave Marain
    12 Jan 2015 | 2:12 pm
    As posted on twitter @dmarain today... Question to 2nd grader: 7×6 Child:42 How did you know that? Easy --- 6 touchdowns! I know all my 7's! Real/fake?? COREFLECTIONS 1) So do you think this is about a real 7-yr old? 2) Would this be useful to many or just for girls/boys who watch a lot of football? OR Is there a bigger issue here re the individual ways in which children learn? I think there are some HUGE implications here for teaching/learning in the Common Core and beyond... 3) All these "strategies" turning you off? Yearning for the good old days -- having children write…
  • Implement The Core: Quadratic Function SAT-Type Assessment

    Dave Marain
    9 Jan 2015 | 7:55 am
    As posted on Twitter @dmarain... The graph of f(x)=-(x-k)^2+h has one x-int and a y-int=-16. Coordinates of all possible vertices? Sketch graph(s). Ans:(+-4,0) COREFLECTIONS... (1) How do you feel about the "h,k switch" on an assessment? Would you revise it or leave it alone? (2) Level of difficulty here? How do you think your students would perform? Let me know if you use it! (3) Are you finding more of these types of questions in current texts? If not, what resources do you use to raise the bar? (4) What if the question had asked for the PRODUCT of all possible x-intercepts?
  • BREAK THE CODE: 12-91-1305

    Dave Marain
    8 Jan 2015 | 12:27 pm
    As tweeted  on Twitter @dmarain today: Break the code:12-91-1305 Then multiply these #'s by 4/3... And you'll get my OBJective here! Use contact form in sidebar to send me your answer/thoughts or leave a "hint" or question in Comments! VISIT ME DAILY ON TWITTER AT
  • Implementing The Core: B lives twice as far from A as from C. Draw that!

    Dave Marain
    8 Nov 2014 | 8:26 am
    From 11-8-14... A,B,C live on a straight road. B lives 5 times as far from A as from C. If AC=12 draw,determine all possible distances! COREFLECTIONS 1. 140 characters make the writing and interpretation of the problem challenging. But within each group of students there will usually be a few who will make more sense of it and they should be allowed to convince others in their group. When the inevitable hands go up and they ask "Do you mean...?" it's tempting to clarify but don't! Unless everyone is lost of course. The confusion will resolve itself in the…
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  • bus number factoring

    Dan MacKinnon
    27 Jan 2015 | 7:09 pm
    Each bus in Ottawa has a four digit number that identifies it (like 4476 above). One thing to do while riding, if you don't have a bus transfer to play with, is to pass the time factoring that bus identifier (it's also printed on the inside of the bus, in case you miss it getting in).We all know some basic divisibility rules to help with factoring: If it ends in a zero, it's divisible by 10, if it's even then its divisible by 2, if it ends in a 5 then it's divisible by 5. You may know that if the last two digits of a number are divisible by 4 then the whole number is also divisible by 4…
  • Some notes on the Kaprekar function

    Dan MacKinnon
    2 Dec 2014 | 5:50 pm
    Consider a 3 digit number, say 395. Take its digits and form the greatest and least possible 3 digit numbers and subtract them: 935 - 359 = 594. Now do the same with the result:  954 - 459 = 495. Try it again, and you see that the process has hit a fixed point: 954 - 459 = 495.The Kaprekar function involves taking a number, computing two shuffles of its digits (the shuffle with the greatest value, and the one with the least value), and then taking the difference of those two shuffles. So for an integer n, if g is the number you get from re-arranging the digits of n from greatest to…
  • GSP and LOGO (for MITx: 11.132x)

    Dan MacKinnon
    20 Oct 2014 | 7:51 pm
    Note: This post is an assignment for the Edx MOOC MITx: 11.132x Design and Development of Educational Technology. The assignment had to be posted online, and since it relates somewhat to the themes of this blog, I put it here.Educational Technology Then and Now: Geometer's Sketchpad and LOGOGeomter's Sketchpad (GSP) is an example of current educational technology that is based on design and educational principles that can generally be described as constructionist. Widely used in contemporary classrooms, GSP is based on ideas about computer-human interaction that date back to the 1960s, and…
  • circles, hexagons, flowers

    Dan MacKinnon
    2 Oct 2014 | 7:02 pm
    Was playing around with intersecting circles, as in this post.
  • A year of tinkering

    Dan MacKinnon
    29 Sep 2014 | 6:37 pm
    You really should take advantage of the free until August 2015 license that is currently being offered with a fresh download TinkerPlots. Would that it was freely available in perpetuity without condition, but a year of tinkering is nice.If you are a middle school teacher, then this is designed for you and yours. If, like me, you are not, you may find it fun to play with anyway.  Here is something I was playing with recently:An elementary school number sense activityIn the JUMP math curriculum for grades 3 and 4, there are lessons where students investigate the patterns formed when…
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  • Book Review: A Mind for Numbers

    John F. McGowan, Ph.D.
    26 Jan 2015 | 6:00 am
    A Mind for Numbers How to Excel at Math and Science (Even if you Flunked Algebra) by Barbara Oakley, Ph.D. JEREMY P. TARCHER/ PENGUIN Published by the Penguin Group Penguin Group (USA) LLC New York, New York 10014 2014 My Rating: 3/5 Introduction A Mind for Numbers is a good but not great book on techniques for learning math and science. The book covers a large range of methods including alternating between “diffuse” and “focused” thinking, “chunking,” practicing recall to firmly imprint knowledge in long term memory, the “memory palace” method…
  • Review of Falling Behind? Boom, Bust, and the Global Race for Scientific Talent

    John F. McGowan, Ph.D.
    12 Jan 2015 | 6:00 am
    Falling Behind? Boom, Bust, and the Global Race for Scientific Talent by Michael S. Teitelbaum Princeton University Press March 30, 2014 Introduction Falling Behind? is a recent (March 2014) book by Michael Teitelbaum of the Sloan Foundation, a demographer and long time critic of STEM (Science, Technology, Engineering and Mathematics) shortage claims. Falling Behind? is an excellent book with a wealth of data and information on the history of booms and busts in science and engineering employment since World War II, STEM shortage claims in general, and lobbying for “high-skilled”…
  • Mathematicians take this survey about your philosophical intuitions

    Antonio Cangiano
    20 Jul 2014 | 7:01 pm
    A group of researchers in philosophy, psychology and mathematics are requesting the assistance of the mathematical community by participating in a survey about mathematicians’ philosophical intuitions. The survey is available here: For the purposes of this survey, a mathematician is someone who holds an advanced academic degree in mathematics, teaches mathematics on a college or university level, uses advanced mathematics in the course of their work, or has published mathematical work in scholarly venues. Possibly related articles: Help us with your feedback by taking…
  • Martin Fowler’s Design Stamina Hypothesis and Video Compression

    John F. McGowan, Ph.D.
    14 Jul 2014 | 7:00 am
    Martin Fowler’s Design Stamina Hypothesis expresses a widely held belief among practicing software engineers and other technical professionals that is also taught in computer science curricula. Basically, the idea is that “good software design,” a vaguely defined concept, fairly quickly pays for itself through faster, better, cheaper software development in the long run. Martin Fowler, Chief Scientist for ThoughtWorks and a noted writer on agile software development, software design and refactoring, encapsulates this concept in this “pseudo-graph”: The remarkable…
  • Eugene Goostman, Teenaged AI, and the Definition of Number

    John F. McGowan, Ph.D.
    16 Jun 2014 | 7:00 am
    Eugene Goostman, an artificial intelligence program purporting to be a thirteen year old boy from the Ukraine, recently prompted a spate of breathless news articles reporting that an AI had finally and for the first time passed the famous Turing Test, fooling humans into thinking they were conversing with another human being and not with an AI program. This in turn prompted a number of critical responses, notably one by AI pioneer Ray Kurzweil who reported the following rather unconvincing exchange with Eugene: Question: How much is two plus two? Eugene: Now I’m sure that you are one of…
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    CSE Blog - quant, math, computer science puzzles

  • Box in Box problem

    Pratik Poddar
    23 Jan 2015 | 2:31 am
    Source: Sent to me by Sudeep Kamath Problem: Airline check-in baggage has size restriction by ​so-called ​linear dimension: length + breadth + height should not exceed 62 inches. Prove that you can't "cheat" by packing a box with higher linear dimension into a box with ​lower​ linear dimension.
  • Fibonacci Multiple Puzzle

    Pratik Poddar
    21 Jan 2015 | 2:30 am
    Source: Mailed to me by Kushagra Singhal, IIT Kanpur, PhD Student at University of Illinois at Urbana-ChampaignProblem: Prove that for any positive K, every Kth number in the Fibonacci sequence is a multiple of the Kth number in the Fibonacci sequence.More formally, for any natural number n, let F(n) denote Fibonacci number n. That is, F(0) = 0, F(1) = 1, and F(n+2) = F(n+1) + F(n). Prove that for any positive K and natural n, F(n*K) is a multiple of F(K).
  • Gold Silver Numbers Puzzle

    Pratik Poddar
    19 Jan 2015 | 3:00 am
    Source: Mailed to me by JDGM ("regular commenter JDGM")Problem:The integers greater than zero are painted such that:• every number is either gold or silver.• both paints are used.• silver number + gold number = silver number• silver number * gold number = gold numberGiven only this information, for each of the following decide whether it is a gold number, a silver number, or could be either:1.) gold number * gold number2.) gold number + gold number3.) silver number * silver number4.) silver number + silver number
  • Maximum Number of Collinear Points

    Pratik Poddar
    28 Dec 2014 | 3:39 am
    Source: Asked to me by a friend - who was asked this question in an interview at Facebook Problem: Given n points on a 2D plane, find the equation of the line with maximum number of collinear points. What is the time complexity of your algorithm?
  • Mathematics of SET game

    Pratik Poddar
    21 Dec 2014 | 3:00 am
    Source: Sent to me by Pritish Kamath ( Problem: Have you ever played "SET"? You have to play it. Even if you have not played the game, the game can be stated in a more abstract way as follows: There are 12 points presented in F34 and the first person to observe a "line" amongst the 12 given points gets a score. Then the 3 points forming the line are removed, and 3 random fresh points are added. Problem 1: How many points in F34 are…
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    Marauders of the Lost Sciences

  • Hilbert on the foundations of geometry

    1 Feb 2015 | 2:10 am
    Here Hilbert proves that the Axiom of Continuity isn’t derivable from the other axioms. This is done by finding mathematical structure which satisfies the other axioms but not the Axiom of Continuity (Archimedes’s Axiom). …the axiom of Archimedes may be … Continue reading →
  • Lord Rayleigh’s advice to stifled genius

    30 Jan 2015 | 11:25 pm
    This is a special post for anyone stifled by highly respected, but wrong, giants in their fields. In 1845 a Englishman named John James Waterston wrote an early groundbreaking paper on kinetic theory and submitted it to the (British) Royal … Continue reading →
  • Brouwer on Intuitionism versus Formalism in the foundations of mathematics

    30 Jan 2015 | 2:10 am
    Brouwer, of the “fixed point theorem” fame, wrote a long article about Intuitionists vs Formalists. Many mathematicians aren’t aware of the force this debate once had and perhaps still does in mathematical logic and set theory. Brouwer’s essay is impossible … Continue reading →
  • Fisher’s Information

    29 Jan 2015 | 2:10 am
    Information theory in statistics has come to be somewhat associated with Bayesians, but Fisher was introducing information type considerations in statistics before that. Here Fisher talks about what became known as Fisher’s Information, which can be viewed as an approximation … Continue reading →
  • Ehrenfest on Adiabatic Invariants in the early Quantum Theory

    28 Jan 2015 | 2:10 am
    Who knows, maybe after nearly 100 years some of these early Quantum Theory considerations will prove useful when looked upon by fresh minds. Stranger things have happened in the history of science. In these researches I especially made use of … Continue reading →
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