Green party presidential candidate Jill Stein has been battling for recounts in swing states Wisconsin, Michigan and Pennsylvania for about a week now. Her argument? The American people deserve to know their voting system is secure and fair.


Most Popular Stories

Recount Roundup: Jill Stein's Embarrassing Stunt Puts Trump Further Ahead
Search for "math OR mathematics"7 Dec 2016  10:34 am 
Crunching the numbers: Researchers use math in search for diabetes cure
Mathematics News  ScienceDaily29 Nov 2016  11:34 amNew research by a mathematics professor has successfully reactivated oscillations in insulinproducing pancreatic beta cells — one of the first necessary steps to resurrecting the dormant cells and restoring the production of insulin. 
Commuting Patterns Help Forecast Flu Outbreaks
Scientific American  Math6 Dec 2016  8:15 amFlu forecasts within large metro areas like New York City might be improved by adding in data about the flow of commuters. Christopher Intagliata reports.  Read more on ScientificAmerican.com 
What America Can Learn About Smart Schools in Other Countries
Mathematics6 Dec 2016  2:00 amThe U.S. fared poorly, as usual, in a worldwide ranking of students’ test scores, but it showed significant gains among disadvantaged teenagers. 
Evaluation Research of DreamBox Learning Garners Recognition
Blog – DreamBox Learning11 Nov 2016  9:58 amWhen I was a classroom math teacher and a K12 district math coordinator, I spent many days and weeks reviewing, piloting, and evaluating print and digital math curricular resources with my colleagues. What struck me was how few programs have meaningful efficacy research showing how they improve student learning—especially digital math programs. Given how rapidly the edtech industry continues to grow, and how often new digital math programs and apps crop up, it’s critical that schools and districts understand whether the curricular solutions they’re investing in are working. This…




Search for "math OR mathematics"

Recount Roundup: Jill Stein's Embarrassing Stunt Puts Trump Further Ahead
7 Dec 2016  10:34 amGreen party presidential candidate Jill Stein has been battling for recounts in swing states Wisconsin, Michigan and Pennsylvania for about a week now. Her argument? The American people deserve to know their voting system is secure and fair. 
larch 3.3.21
7 Dec 2016  10:31 amThis is a tool for the estimation and application of logitbased discrete choice models. It is designed to integrate with NumPy and facilitate fast processing of linear models. 
Bryson DeChambeau's New Putting Stroke is Very Different
7 Dec 2016  10:30 amBryson DeChambeau is a very smart, very talented, and very unique golfer. He is the only player on Tour to play a single length set of clubs, meaning his 7iron is the same length as his 3iron making it possible for him to use the exact same swing for every club. 
Questioning homeschooling  Elgin Courier
7 Dec 2016  10:27 amQuestioning homeschooling Elgin Courier We spoke about what he had learned in his homeschooling educational experience. As it turned out, he's mostly illiterate and has no concept of basic math, in addition to many other subjects. 
Outside the Box: A female fund manager at Pimco explains how to get more women into finance
7 Dec 2016  10:27 amTo be more specific, I am among the 10% of all fund managers in the U.S. who are women, a startling data point that Morningstar highlighted in a recent report. I've worked in the financial services industry for nearly 30 years, and joined this exclusive club through hard work, a supportive family, a good sense for credit and a lot of helpful mentoring along the way.



Mathematics News  ScienceDaily

Crunching the numbers: Researchers use math in search for diabetes cure
29 Nov 2016  11:34 amNew research by a mathematics professor has successfully reactivated oscillations in insulinproducing pancreatic beta cells — one of the first necessary steps to resurrecting the dormant cells and restoring the production of insulin. 
Mothers' early support boosts children's later math achievement
22 Nov 2016  4:30 pmEarly math knowledge is as important as early literacy for children's subsequent achievement. In fact, research has shown that early math skills predict later school success better than early reading skills, and can even predict income in adulthood. Now a new longitudinal study has found that young children whose mothers supported them during play, specifically in their labeling of object quantities, had better math achievement at ages 4½ and 5 years. 
The mathematics of coffee extraction: Searching for the ideal brew
15 Nov 2016  7:13 amComposed of over 1,800 chemical components, coffee is one of the most widelyconsumed drinks in the world. Understanding the mathematics of coffee extraction can help identify the influence of various parameters on the final product. In a new paper, authors present and analyze a new multiscale model of coffee extraction from a coffee bed. 
Mathematical algorithms calculate social behavior
14 Nov 2016  11:30 amFor a long time, mathematical modelling of social systems and dynamics was considered in the realm of science fiction. But predicting, and at once influencing human behavior is well on its way to becoming reality. Scientists are currently developing the appropriate tools. This will allow them to simulate and improve security at major events or increase the efficiency of evacuation measures. 
Researchers found mathematical structure that was thought not to exist
14 Nov 2016  5:19 amResearchers found mathematical structure that was thought not to exist. The best possible qanalogs of codes may be useful in more efficient data transmission.



Scientific American  Math

Commuting Patterns Help Forecast Flu Outbreaks
6 Dec 2016  8:15 amFlu forecasts within large metro areas like New York City might be improved by adding in data about the flow of commuters. Christopher Intagliata reports.  Read more on ScientificAmerican.com 
What Is a LightYear?
3 Dec 2016  5:00 amDo you know what it is that a lightyear actually measures? Do you know why so many people find it confusing? And why they really shouldn’t?  Read more on ScientificAmerican.com 
The Math behind the Polls
29 Nov 2016  6:00 amWhen polls try to tease out what a group of people is thinking, what are they measuring and how can they go wrong?  Read more on ScientificAmerican.com 
Overthinking an Erdős Quote about Ramsey Numbers and Evil Aliens
12 Nov 2016  6:00 amPaulErdősversus. Moore's law  Read more on ScientificAmerican.com 
Ramsey Theory on Facebook
30 Oct 2016  7:00 amNot long ago, I noticed that I had six Facebook friends with the same birthday, and none of them knew each other. Here's why I was excited.  Read more on ScientificAmerican.com



Mathematics

What America Can Learn About Smart Schools in Other Countries
6 Dec 2016  2:00 amThe U.S. fared poorly, as usual, in a worldwide ranking of students’ test scores, but it showed significant gains among disadvantaged teenagers. 
$25 Million in Breakthrough Prizes Given in Science and Math
4 Dec 2016  5:16 pmThe awards went to more than a thousand physicists, life scientists and mathematicians in areas like genetics and string theory. 
James Simons’s Foundation Starts New Institute for Computing, Big Data
22 Nov 2016  2:47 pmThe new venture, the Flatiron Institute, will house programmers and scientists researching astrophysics, among other projects. 
A Numberplay Farewell
31 Oct 2016  10:00 amGary Antonick, outgoing writer of The Times’s Numberplay column, shares a lesson learned from seven years of puzzlesolving. 
Ian Stewart: Calculating the Cosmos
24 Oct 2016  10:00 amA calculation challenge by the mathematician Ian Stewart, author of the newly released “Calculating the Cosmos: How Mathematics Unveils the Universe.”



Blog – DreamBox Learning

Evaluation Research of DreamBox Learning Garners Recognition
11 Nov 2016  9:58 amWhen I was a classroom math teacher and a K12 district math coordinator, I spent many days and weeks reviewing, piloting, and evaluating print and digital math curricular resources with my colleagues. What struck me was how few programs have meaningful efficacy research showing how they improve student learning—especially digital math programs. Given how rapidly the edtech industry continues to grow, and how often new digital math programs and apps crop up, it’s critical that schools and districts understand whether the curricular solutions they’re investing in are working. This question should be at the top of every educator’s mind: What evidence exists that a math program is proven to improve... 
Digital Content Leads to More Effective Teacher Practice
3 Nov 2016  10:27 amThe findings from a new study by Project Tomorrow and DreamBox Learning provide education leaders with researchbased information and classroombased exemplars for how digital content enables personalized and differentiated learning environments. The stats don’t lie. New Research Results: Leveraging Digital Content to Differentiate Learning Read the full study to learn how teachers using digital content can more effectively personalize learning and differentiate instruction. Download the Full Study Now ... 
Game On: Fall Math Challenge Is Here!
24 Oct 2016  10:00 pmFall is here and that means it’s time for the 2016 Fall DreamBox Learning Math Challenge! Teachers and students in classrooms across the United States and Canada are hyped for a friendly competition to complete the most DreamBox lessons between October 24th and November 11th, and win rewards including tshirts, cool swag, and more! And students are not the only ones who can earn rewards—two teachers from classrooms winning the Grand Prizes will receive a scholarship to the 2017 National Council of Teachers of Mathematics Conference (NCTM)—just for using DreamBox! If you haven’t yet registered for the challenge, now’s the time to do it as registration closes October 28. The benefits of... 
Why Enhanced Reporting for More Effective Teacher Practice and Differentiated Digital Lessons Matters
20 Oct 2016  2:22 pmWhy Enhanced Reporting for More Effective Teacher Practice and Differentiated Digital Lessons Matters How do you measure and collect evidence of a student’s thinking and understanding in mathematics? And equally important, as you’re collecting evidence of a student’s learning and understanding, how do you meaningfully report that student’s progress and proficiency? Given that these are two of the key questions that drive our curriculum development and educator experience at DreamBox Learning, our team is honored to learn that our approach to those questions is worthy of another award. As recipients of Tech & Learning’s Best Upgraded Product Award for Excellence, DreamBox continues celebrating our... 
Celebrate National Hispanic Heritage Month: Five Hispanic and Latino Mathematicians
11 Oct 2016  9:00 pmNational Hispanic Heritage Month (September 15 to October 15) celebrates the contributions of the more than 17 percent of the U.S. population that is of Hispanic/ Latino heritage. Here are our five picks for Hispanic and Latino mathematicians throughout history who are worthy of a special nod:1. Alberto Pedro Calderón (19201998)(Image credit: Wikipedia)Calderón, widely considered one of the 20th century’s most important mathematicians, was born in Mendoza, Argentina and studied at the University of Chicago and the University of Buenos Aires. While in Chicago, he studied under Antoni Zygmund, a Polish mathematician who was an expert analyst. They went on to collaborate for more than 30 years!Calderón...



Loren on the Art of MATLAB

Videobased Motion Analysis with MATLAB
24 Nov 2016  7:00 amWe love MATLAB and we also have many other interests, too. Today's guest blogger, Toshi Takeuchi, found an interesting way to combine his passion for MATLAB with one of his interests, Argentine Tango! Contents<ul><li>Motivation</li><li>Loading Video</li><li>Playing Back Video in 1/2 Time</li><li>Creating the GUI</li><li>"Choose File" Button</li><li>"Play" Button</li><li>TangoPlayer in Action</li><li>Creating a Standalone App</li><li>Summary</li></ul>MotivationI started taking Argentine Tango classes at MIT when we had a record snow fall a few winters ago in Boston. I was originally planning to learn snowboarding (I even bought a used snowboard) but who would want to spend more time in the snow after having shoveled it day after day?I was drawn to Tango because I can do the figures once I... 
More thoughts about implicit expansion
10 Nov 2016  6:57 amMore thoughts about implicit expansionSteve Eddins returns with another thoughtful post on implicit expansion.Several people have expressed some trepidation about the increased possibility of making an undetected error because of the introduction of implicit expansion in MATLAB R2016b.Usually, people are worried about trying to perform elementwise addition of two samelength vectors, a and b, without realizing that one is a row vector and the other is a column vector. MATLAB R2016b will produce a matrix, whereas earlier versions of MATLAB produced an error. The concern is that a user might not realize that the computation wasn't what they intended, or that a user might run out of memory if a and b are... 
Notes on the Release Notes
7 Nov 2016  3:12 amToday’s guest blogger is Sowmini Sampath, from the Documentation group at MathWorks. Her team’s goal is to make it easier for you to learn how to use our products. Which means examples, examples, and more examples, right? But there’s other useful stuff too, if you need it. She is writing today about the Release Notes.Contents<ul><li>Motivation</li><li>Release Range</li><li>Compatibility Considerations</li><li>Text Filter</li><li>Sort or Filter by Category</li><li>We Welcome Your Feedback!</li></ul>MotivationMathWorks releases new versions of products twice a year, in March and September. You may upgrade with every release, or move to a new version less frequently. Either way, do you use the release notes to discover new capabilities and to look for changes to existing... 
MATLAB arithmetic expands in R2016b
24 Oct 2016  6:32 amWith pleasure, I introduce today's guest blogger, my colleague, Steve Eddins. He has been heavily involved in image processing capabilities in our tools and more recently has also contributed substantially to designing additions and improvements to the MATLAB language.Earlier this summer, I was writing some colorspace conversion code. At one point in the code, I had a Px3 matrix called RGB, which contained P colors, one per row. I also had a 1x3 vector, v. I needed to multiply each column of RGB by the corresponding element of v, like this:RGB_c = [RGB(:,1)*v(1) RGB(:,2)*v(2) RGB(:,3)*v(3)];But since I was using an internal developer build of MATLAB R2016 (released on September 14), I didn't type the... 
MultiArmed Bandit Problem and Exploration vs. Exploitation Tradeoff
10 Oct 2016  6:59 amCasino slot machines have a playful nickname  "onearmed bandit"  because of the single lever it has and our tendency to lose money when we play them. They also inspire the creativity of researchers. Today's guest blogger, Toshi Takeuchi, will introduce an interesting thought experiment known as multiarmed bandits. image sourceOrdinary slot machines have only one lever. What if you had multiple levers to pull, each with different payout. This is a multiarmed bandit. You don't know which lever has the highest payout  you just have to try different levers to see which one works best, but for how long? If you keep pulling the low payout lever, you forego more rewards, but you won't know which lever is...



Homeschool Math Blog

Meaning of factors in multiplication: four groups of 2, or 4 taken two times?
1 Dec 2016  4:19 pmSomeone asked me about the interpretation or meaning of the two numbers in multiplication, such as 4 × 2. Do you view it as four groups of 2, or as four, taken two times?Here's their question:"...I noticed that your explanation about how to interpret a math phrase, such as 4 × 2, is different from how I have understood it and taught it to my older daughter who was using RightStart Math at this level.Let me explain: I see that you are using the first factor to denote number of groups and the second factor tells how many are in each group (4 × 2 would be interpreted 4 groups of 2). On the other hand, I have taught and thought of it reversed, with the first factor telling how many are in each group and... 
Math Mammoth Thanksgiving sale
18 Nov 2016  2:16 pmGet 25% off of all Math Mammoth & Make It Real Learning products sold at MathMammoth.com site. :) Use the coupon code THANKSGIVING. The offer is valid till December 1, 2016. Start shopping > 
Thanksgiving Activity Pack
16 Nov 2016  5:50 amMy daughter Abby (11 years) recently created a Thanksgiving activity book filled with 101 different activities  dottodots, copythepictures, various types of matching activities, coloring pages, mazes, tracethedots, color by numbers, and much more! It is intended for children ages 48.You will find it at Currclick. 
More practice with bar models and problem solving
10 Nov 2016  9:51 amSomeone asked me about the BAR MODELS in the problem solving lessons in Math Mammoth grade 5.This person said that they had just completed every problem in the lesson Problem Solving with Bar Models 1, but her son is still having a hard time knowing how to make the bar model after reading the problem, and knowing what to do with the fractional part once it is figured out. She was wondering if there was something else for supplemental practice, and if she should look for mastery in this area at this point.MY ANSWER:I feel it would be good to achieve some degree of mastery at this point (in 5th grade). I suggest using the website Thinking Blocks for additional practice, in particular the "Multiplication and... 
Teaching the multiplication tables
3 Nov 2016  5:44 pmIt's probably that time when many are teaching the multiplication tables to their children or students. Check out my guide of how to teach them.And here's a link to videos that do the "structural" (not totally random) drill for you: Multiplication tables videos — presented in a specific order — easiest ones first — which makes learning them MUCH easier.



Denise Gaskins' Let's Play Math

Christmas with Alexandria Jones
6 Dec 2016  11:14 pmAlexandria Jones and her family are fictional characters from my old Mathematical Adventures newsletter. Their stories appear sporadically as I find time to transcribe them from the backissues. You can find them all on this blog page. Here are all the Alexandria Jones stories Christmas stories, with activity and craft ideas… Alexandria Jones and the Christmas Present Quandary Alex designs tessellation wrapping paper, hunts for the perfect Christmas tree, and comes up with a lively present for her brother. We meet the rest of Alex’s family — her father was introduced in an earlier issue — along with historical figures Maria Agnesi and Leonhard Euler, and we take a brief glance at mathematics from...</li></ul> 
What Do We Mean by ‘Understanding’?
4 Dec 2016  11:52 pm“You understand something if you have the ability to view it from different perspectives. “Changing your perspective makes your mind more flexible, it makes you open to new things, and it makes you able to understand things.” — Roger Antonsen Math is the hidden secret to understanding the world Check out the speaker’s footnotes for links and interesting tidbits about the images in the video. Want to help your kids learn math? Claim your free problemsolving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other promotions. 
Playful Family Math on Facebook
30 Nov 2016  11:53 pmWant to help your kids learn math and enjoy it? Check out my new Facebook discussion group called Playful Family Math. Join Playful Family Math on Facebook This is a positive, supportive discussion group for parents and teachers — and grandparents, aunts and uncles, caregivers, or anyone else — interested in talking about math concepts and creative ways to help children learn. A place where you can ask questions, share articles about learning math, tell us your favorite math games, books and resources. Let’s make math a playful family adventure! Want to help your kids learn math? Claim your free problemsolving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other... 
Math Teachers at Play #102 at Fraction Fanatic
29 Nov 2016  11:45 pmCheck out the new carnival of playful math for all ages at Fraction Fanatic blog. Each month’s carnival brings you a great new collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun. <ul> <li>Math Teachers At Play Blog Carnival 102</li> </ul> This month’s post features algebra games, calculus tips, paper folding, pattern blocks, arithmetic puzzles, triangle doodling, and much more. Click Here to Go Read the Carnival Blog! Hey, Blogger, Can You Spare a Time? Do you write an education or family blog? Classroom teacher, math coach, homeschooler, parent, college professor, unschooler — anyone interested in helping kids play around with math? Please consider volunteering to host the MTaP... 
Count Up to Christmas
28 Nov 2016  11:42 pmBack when we were still homeschooling, I always dropped the “regularly scheduled program” in December. School plus holiday prep added up to one stressedout mom. Instead, we read plenty of library books. And we played around with informal activities like the NrichMaths Advent Calendars: <ul> <li>Primary Activities</li> <li>Secondary Activities</li> </ul> For older students and adults, the online Plus Magazine offers a calendar of daily tidbits from their “Maths in a minute” series, explaining important mathematical concepts in just a few words” <ul> <li>Plus Magazine Advent Calendar</li> </ul> And for still more winter fun, check out the links in my old Christmas Math Puzzles and Activities post. And a Question for You How do you handle schoolwork...



Basic mathematics blog

Number Game
1 Dec 2016  3:27 am1. Think of any positive whole number. No fractions, no decimals,no percents. 2. Double that number. 3. Add 10 to that result in step 2. 4. Divide 
How to Do Synthetic Division
28 Nov 2016  7:24 amThis lesson will explain clearly how to do synthetic division 
20 4th Grade Math Problems Students should Know how to Solve
19 Nov 2016  3:06 pmA great variety of 4th grade math problems your students will love 
Geometry Postulates
15 Nov 2016  2:35 pmSome geometry postulates that are important to know in order to do well in geometry 
Area of a Kite
14 Nov 2016  7:32 amSo you want to know how to find the area of a kite? Here is how



Computational Complexity

A students unusual proof might be a better proof
6 Dec 2016  6:56 amI asked a student to show that between any two rationals is a rational. She did the following: if x < y are rational then take δ << yx and rational and use x+δ This is correct though more complicated then what I had in mind: (x+y)/2 I then asked her to prove that between two irrationals is an irrational. She did the following: if x < y are irrational then take δ << yx and rational and use x+δ SAME PROOF! I had a different proof in mind: the number of reals in (x,y) is uncountable while the number of rationals is countable, so there must be at least one (in fact uncountable many) irrationals in (x,y). (NOTE I originally had `the number of irrationals in (x,y) is ...' which, as comment by stu... 
Guest post by Samir Khuller about Visiting the Simons theory Inst for Computing
2 Dec 2016  1:22 pmGuest post by Samir Khuller on his visit to the Simons Inst. of Computing Visiting the Simons Institute for Theory of Computing A few days back I had the good fortune to spend four days at the Simons Theory inst. at UC Berkeley (for a workshop titled Learning, Algorihtm Design, and Beyond Worst Case Analysis,) Not only was the workshop extremely well run, the entire Institute is amazing  from wide open spaces for collaboration to an excellent staff and amenities for visitors (especially long term visitors who have shared office space). We were missing a Dagstuhllike venue in the US for a long time, and I think the Simons Theory Center partially makes up for this deficiency. Dagstuhl is of course a bit... 
A Few Interesting Computer Science Papers
30 Nov 2016  1:21 pmProbabilistic Rank and Matrix RigiditybyJosh Alman and Ryan Williams Leslie Valiant outlined an approach to proving circuit lower bounds from matrix rigidity. A matrix is rigid if you need to change many entries to significantly reduce the rank. Valiant showed that one could create a function with high algebraic circuit complexity from a rigid matrix. Of course one needs a rigid matrix and the Hadamard matrices (rows are Hadamard codes) seemed the perfect candidate. Alman and Williams say not so fast, in fact the Hadamard matrices are not that rigid and won't work for Valiant's program. Ryoan: A Distributed Sandbox for Untrusted Computation on Secret Databy Tyler Hunt, Zhiting Zhu, Yuanzhong Xu, Simon... 
Music Theory for Theorists
23 Nov 2016  3:36 amI fully completed and passed my first MOOC, Fundamentals of Music Theory, a Coursera course out of the University of Edinburgh. I played the tuba in college and grad school but really just practiced scales and (usually) hit the notes. I didn't really understand keys, intervals, chords and the such and I wanted to learn. Music theory has the same problem as C++, too much overloaded notation before you really understand what's going on. So here's a quick view of music theory without the mess. Think (theoretically) of an biinfinite sequence of notes. Every note is equivalent to notes a factor of twelve away from them (though in different octaves). Pick a note, label it 1, then the notes labelled 1, 3, 5, 6,... 
Should I tell HS students that if they do well I'll write them a letter OR do I want them to ...
21 Nov 2016  10:52 amI teach a 3week intense course for HS students on cryptography during the summer. Some of the students are very good, interested, and working hard. I also give out some extra credit assignments that some of them do. For such students I am glad to write letters of rec for college. I want to reward them for working hard and being interested not knowing that they will get a letter for it. These students don't quite know about colleges and letters and that stuff. I have two choices: 1) The first day tell them that if they do well I could write a letter for them. PRO this will encourage some of them to work harder CON I want them to work hard and BE interested (not just SHOW interest, though I doubt...



Natural Blogarithms

Is it a core requirement or just an elective?
11 Nov 2016  6:00 amThis week of Creation Care emphasis has coincided with a very busy time of the semester on the Plainview campus. We are in the first week of early registration for the Spring term which means faculty and students alike are pouring over course schedules and degree plans. As a result, my mind has unavoidably conflated the two. As I listened to Rachel Lamb’s message in chapel on Wednesday, I was challenged in a new way regarding the role of Creation Care in my daily walk with Christ. It was several years ago when we first began our Creation Care emphasis week at Wayland that I first made the connection between caring for the environment and my duty as a Christian to be a steward of God’s creation. ... 
Why I do what I do
24 Jun 2016  4:30 amAs I glance back over the previous post where I listed out those questions I intend to tackle here, openly on my blog, I noticed a somewhat glaring omission. There are no “Why?” questions, not even the most important one: Why do I do what I do? My life has taking only a small number of twists and turns. In fact, it almost seems as though I have been on track for this current career path ever since I decided to add a mathematics major my second year of college. For those that do not know, I first shopped for colleges based on my intent to enter fulltime vocational ministry. I found Wayland to be that place where there was the greatest personal attention and interest in my own personal success. Some... 
Summer Blog Project
23 May 2016  7:44 amI’m about to ramble so take this as fair warning. My blog has been around for a long time and has meandered through many identity crises. Sometimes, it’s a puzzle blog posting interesting mindbenders that need a keen intellect and occasionally, some mathematics. That’s all still here, by the way, which you can find with a notsodifficult search tool in the sidebar. It’s also been a devotional through my efforts to better understand our responsibilities as stewards of God’s creation. It’s been a log of classroom activities. At one time, I was posting periodically about what I had accomplished in each of my classes. For the last few years, it has been only a repository for sparse events and... 
Grand Canyon – A photographic tour
17 Mar 2016  11:13 pmThese are a collection of my favorite shots from our recent road trip to New Mexico and Arizona. Click to view slideshow. 
My 4x4x4 Assembly Fail
26 Jan 2016  8:25 pmSome time ago, my son shattered his 4x4x4 Rubik’s cube. The core was snapped but all the pieces were recovered. I tried gluing the core back together and reassembling. It went very well until near the end when it exploded and broke again. A replacement part is on the way. Click to view slideshow.



The Math Less Traveled

Dirichlet convolution
6 Dec 2016  9:51 amLet and be two functions defined on the positive integers. Then the Dirichlet convolution of and , written , is another function on the positive integers, defined as follows: The sum is taken over all possible factorizations of into a product of positive integers. For example, suppose and . Then At this point this may seem somewhat arbitrary, but over the next few posts we’ll see that it’s not arbitrary at all—this operation is deeply connected with the Möbius function and hence with primes and factorization. So what properties does have? <ul> <li> It’s commutative, that is, . This follows directly from the commutativity of multiplication: </li> <li> It’s also associative, that is, . This...</li></ul> 
The Möbius function proof, part 2 (the subset parity lemma)
3 Dec 2016  6:50 pmContinuing from my previous post, we are in the middle of proving that satisfies the same equation as , that is, and that therefore for all , that is, is the sum of all the th primitive roots of unity. We had gotten as far as the following lemma: Subset parity lemma: any nonempty finite set has an equal number of evensized and oddsized subsets. In fact, this lemma is the only remaining piece of the proof: if we can prove this then we will have a complete proof that . Just for fun, we’re actually going to consider two different proofs of this lemma today. The first proof The first proof will be by a combinatorial or counting argument, and was suggested in a comment by Andrey Mokhov. The idea is... 
The Möbius function proof, part 1
29 Nov 2016  7:43 pmIn my last post, I introduced the Möbius function , which is defined in terms of the prime factorization of : <ul> <li> if has any repeated prime factors, that is, if is divisible by a perfect square.</li> <li>Otherwise, if has distinct prime factors, . In other words, if has an even number of distinct prime factors, and if the number of prime factors is odd.</li> </ul> Previously, we also considered the sum of all the primitive th roots of unity. Today, we will begin proving they are the same: for all ! This is surprising since it is not immediately obvious what the two functions have to do with each other: one is about sums of complex numbers, and the other is about prime factorization. On the other hand, perhaps it is... 
The Möbius function
22 Nov 2016  11:08 amTime to pull back the curtain a bit! My recent series of posts on complex roots of unity may seem somewhat random and unmotivated so far, but the fact is that I definitely have a destination in mind—we are slowly and inexorably heading towards some really deep and beautiful mathematics. It has just taken a while to build up all the requisite concepts! Last time, we defined as the sum of all the primitive th roots of unity. We noted that and used this to deduce values of . In principle we could carry this as far as we want to compute for any , but this doesn’t necessarily give us any insight into the nature of . For example, is always either , , or ? Is there a nicer way to characterize , and/or... 
Computing sums of primitive roots
15 Nov 2016  4:24 amRemember this picture? It, and other pictures like it, express the fact that for a given , if we take the primitive roots for each of the divisors of , together they make up exactly the set of all th roots of unity. The above picture is for the specific case of : the th roots of unity (the dots on the bottom circle) are composed of the primitive roots for , , , , , and (the dots on each of the top circles). I proved this in another post. Of course, if two sets of complex numbers are the same, then their sums must also be the same. Let’s write for the sum of all the primitive th roots: in my previous post we worked out for certain but weren’t sure how to compute it in other cases. Well, today...



WordPress Tag: Mathematics

Semantics for Physicists
7 Dec 2016  10:17 amI once complained that my student Brendan Fong said ‘semantics’ too much. You see, he was actually in the computer science department at Oxford; I was his informal supervisor. Theoretical computer scientists love talking about syntax versus semantics—that is, written expressions versus what those expressions actually mean, or programs versus what those programs actually do. So Brendan was very comfortable with that distinction. But I felt my math grad students didn’t understand it. Bill Lawvere figured out a way to talk about syntax versus semantics that even mathematicians—well, even category theorists—could understand. It’s called ‘functorial semantics’. But physicists may not enjoy this idea unless... 
The End 2016 Mathematics A To Z: Principal
7 Dec 2016  10:00 amFunctions. They’re at the center of so much mathematics. They have three pieces: a domain, a r 
Why Use a MathRack?
7 Dec 2016  8:52 amWhat is a MathRack? The MathRack (an abacus or Rekenrek) is a mathematical calculating tool. Variations of the MathRack have been used by civilizations dating all the way back to approximately 2700 BC and were traditionally made up of beans, stones, beads, etc., assembled on a rack. Why Use a MathRack? The MathRack has a variety of uses and can help the development of all persons from the visually impaired to children just beginning to learn as well as everyone in between. Where to Buy a MathRack MathRack supplies teaching tools to support mathematical thinking strategies and aligns with common core state standards. Visit www.mathrack.com to shop now, utilize available resources, and get in touch today. 
More Category Theory: The Grothendieck Topos
7 Dec 2016  6:01 amIn Category Theory, we generalized the notion of a presheaf (see Presheaves) to denote a contravariant functor from a category to sets. In this post, we do the same to sheaves (see Sheaves). We note that the notion of an open covering was necessary in order to define the concept of a sheaf, since this was what allowed us to “patch together” the sections of the presheaf over the open subsets of a topological space. So before we can generalize sheaves we must first generalize open coverings and other concepts associated to it, such as intersections. A product, which is a diagram of objects , , , and morphisms and , and if there is another object and morphisms and , then there is a unique morphism ... 
an update.
7 Dec 2016  6:01 amIn my last post, I had hoped to post more consistently: 2. My intentions to post more regularly have been overshadowed by the fact that I am an inherently busy student. 3. My urges to write on this blog tend to come when I’m writing something else. Ah, the joys of procrastinating writing by, well, writing. from Irony. I guess that didn’t really work out. So here’s a summary of what’s happened since my last post. In the last 51 days, I: <ol> <li>Got offers from two universities in the U.K.</li> <li>Submitted my early application for a college in the U.S.</li> <li>Turned 17</li> <li>Had a college interview (the next day)</li> <li>Spent a week doing intense fitness including boxing (it was so much fun, despite the leg pain)</li> <li>Wrote a lab report</li> <li>Conducted...</li></ol>



Institute for Mathematics and Computer Science

Gifted Math: A Better Alternative to Acceleration
16 Nov 2016  10:00 pmFor mathematically talented children, acceleration is a commonly used approach to address their need to be challenged. Acceleration is often the most affordable option for schools, and it does help gifted children avoid unnecessary repetition. As such, acceleration works to a certain degree for all parties: Students are less bored; little or no extra work is required of teachers; districts incur little or no extra cost; and parents know that something is being done for their gifted child. Acceleration has become a "good enough" solution. While acceleration can save gifted math students from unnecessary repetition, by definition acceleration cannot go deeper than the standard curriculum, and deeper is... 
IMACS Success Spotlight: Fiona Brady
12 Oct 2016  10:00 pmCongratulations to IMACS graduate Fiona Brady who is beginning her studies at the University of Chicago. Fiona first attended IMACS HiTech Summer Camp when she was ten. Over the next eight years, she went on to complete IMACS’ universitylevel courses in University Computer Science, AP Computer Science: Java Programming, and Logic for Mathematics. Homeschooled since fifth grade, Fiona was awarded a National Merit Scholarship, named an AP Scholar with Distinction, and scored 2360 on the SAT. She is also a second degree black belt in Taekwondo and won a bronze medal at the 2013 AAU Junior Olympic Games. As a high school student, Fiona studied four years of undergraduate, advanced undergraduate, and... 
IMACS Success Spotlight: Zachary Farnsworth
19 Sep 2016  10:00 pmCongratulations to IMACS graduate Zachary Farnsworth who is beginning his sophomore year at Stanford. Zac began taking IMACS classes in first grade. Nine years later, he had completed all of IMACS Mathematics Enrichment and Computer Enrichment and IMACS UniversityLevel Computer Science. Zac graduated valedictorian of St. Thomas Aquinas High School, but not before being founder and captain of the Robotics Club and the Programming Team, earning the rank of Eagle Scout, and being named a National Merit Scholar Finalist and National AP Scholar. Having scored 2350 on the SAT, 800 on the SAT Math II Subject Test and 5′s on the AP Calculus AB, AP Computer Science, AP Calculus BC, and AP Statistics exams,... 
Gifted Math Program in Silicon Valley Has Roots in Owner’s Childhood
5 Sep 2016  10:00 pmThibault de Chatellus, President of IMACS California, and Assistant Director Debby Jensen are excited to bring IMACS' unique, logicbased enrichment program to families in Silicon Valley. The Institute for Mathematics and Computer Science (IMACS) has a new location in Silicon Valley! In today's IMACS Blog, we get to meet the President of IMACS California, Thibault de Chatellus (pronounced teebo), whose passion for making a positive impact led him to a new career in education. Thibault de Chatellus grew up in Boulogne, France, the second of four children whose parents made education a priority. Math education is very important in France and is used as a selection tool for admission to the most... 
Online Gifted Math Program to Grow to Several Hundred Students in Broward County Public Schools
3 Aug 2016  10:00 pmCorbin Diaz, a rising seventh grader in the BCPS/EMF program, is excited about learning advanced mathematics. Broward County Public Schools (BCPS) is increasing the number of middle school students enrolled in the Elements of Mathematics: Foundations (EMF) curriculum from 40 to several hundred students over the next several years. EMF was created for mathematically talented children by the Institute for Mathematics and Computer Science (IMACS), an independent teaching and educational research institute based in South Florida. EMF is an online curriculum that teaches prealgebra through precalculus plus several more advanced subjects in just three years. Graduates will be ready to study Advanced...



mathrecreation

polynomial grid division examples
29 Nov 2016  9:35 amThere are not enough examples of polynomial division using the grid method out there. So, to remedy that, I have posted about 100 billion examples for your viewing pleasure. Please check ‘em out: https://dmackinnon1.github.io/polygrid/Jokes aside, I was looking for a small JavaScript project, and this one looked like it would be fun. It was, and I learned a few things by building it. The page will generate a small number of examples, but you can get a fresh batch by reloading. Each example is calculated on the fly, and rendered using MathJax. Currently, the displayed calculations look like this:About half the time the examples have remainders, and the calculations vary in length and complexity in no... 
Desmos polygonal number diagrams
18 Nov 2016  6:36 amPolygonal numbers are a favorite topic in recreational math and there are quite a few posts about them on this blog (such as this one,here). The image above hints at some of their interest: polygonal numbers, like the pentagonals shown above have numerical properties that translate nicely into visual properties in their associated diagrams.The very first post of this blog had some instructions for how to generate polygonal number diagrams using Fathom or Tinkerplots (two dynamic data environments; their successor CODAPseems to have the same capabilities), so attempting to do the same in Demos seemed like a good idea.The first few triangular number diagramsYou can play with the graph here. With it you can... 
doodling with Froebel
28 Oct 2016  7:48 amMaybe it is time to unplug, put that graphing calculator aside, lay out some graph paper, and pick up a pencil. But what to do? The tyranny of the blank page plagues not only writers, but doodlers as well.A great source of inspiration for how to fill that graph paper are nineteenth century Froebeliankindergarten text books. Froebel proposed a curriculum based on manipulating and creating using basic forms, realized in the form of "gifts" that were provided to students at various stages of their learning. The gifts were blocks, sticks, squares of paper, drawing tablets and other objects that were used to build, weave, cut, fold, and draw combinations of basic forms. Some old textbooks include nice... 
notes for a spirolateral bestiary
25 Oct 2016  7:12 pmThe simple rules for creating generalized spirolaterals produce a surprisingly diverse menagerie of paths which trace out some familiar and lessfamiliar shapes, including regular polygons, star polygons, tangles, wreaths and infinitely long springs.some spirolaterals (graph here)In the formula below, a represents the angle that you turn by at each step, and m represents the maximum length of the sides that you count up to before repeating. If m = 1, all sides are length 1, if m = 2, then the sides alternate between length 1 and length 2, for m = 3, the lengths of the sides form the repeating squence 1, 2, 3, 1, 2, 3... etc.If the angle that you turn by is a rational multiple of 2pi, then the first... 
more familiar spirals in Desmos: spirolaterals
20 Oct 2016  7:45 pmAfter thelast post about how to draw some types of spirals using Desmos, I was pointed to a treasure trove of spiral and Desmos goodness in the twitter microblogging of@Veganmathbeagleand @GHSMaths. I haven't yet had the chance to dig too deeply yet, but looking forward to it.Also,@Desmos kindly improved upon one set of spirals: the "polygonal numbers on quadratic spiral" family, showing how to connect the dots and link up the points of the spiral (the improved graph is here). The technique: use the functions for x and y to create a family of parametrically defined line segments. To create a line segment between two points A and B, you can introduce a parameter t which moves you from A to B as t varies...



Maths Tips From Maths InsiderMaths Tips From Maths Insider

11 Hot Math Education Research Studies to Boost Your Child’s Math Skills
15 Nov 2016  2:06 amHave you ever wondered what makes some people into natural mathematicians while others seem to struggle with grasping even basic concepts? Do you wonder whether there are things you should be doing to help your children reach their potential in math? Here’s my rundown of recent math education research into how we learn, and how best to develop your child’s math skills. 1 Babies’ spatial reasoning predicts later math skills. Stella Lourenco, a psychologist from Emory University conducted a study showing that babies with a stronger interest in a video stream of mirrored images went on to have greater mathematical skill at age four than those with less interest. This may be why some people seem to... 
Have You Seen These 15 Awesome Math Toys and Games?
31 Oct 2016  2:48 amAre you keen to help your children cement the math skills they’re learning, but finding them less than willing to spend their free time practising times tables or number bonds? Hopefully, you’ve had a chance to look around here at Maths Insider to see some of my suggestions for ways to make math practice more fun. Here’s a list of math toys and games with a definite emphasis on fun and a whole lot of math learning thrown in for good measure. Number skills builders for preschoolers 1 Smart Snacks Number Pops – a fun way to encourage number recognition and fine motor skills at the same time. Match the numbers to the dots and slide the coloured shell over the corresponding lolly. Contains 10... 
Sumaze Math App – Perfect for all Ages
1 Oct 2016  7:15 amSumaze! is a cool problemsolving app that helps kids and adults build an intuitive approach to math. I’ve been playing it for for past week and it really is kind of addictive! What I also love about it is that it’s low stakes – no timers and no negative audio sounds when you get the puzzle wrong, so it’s perfect for nervous young mathematicians! Sumaze’s puzzles involve arithmetic, inequalities, the modulus function, indices, logarithms and primes and players don’t need ANY previous knowledge of these topics in order to play. This app was created by the UK organization Mathematics in Education and Industry (MEI) and the Sigma network who provide support for excellence in mathematics and... 
8 Things to Love About Tabtor Math
1 Sep 2016  10:50 pmBy far the most popular post on Maths insider is my post, 8 Things to Hate About Kumon! As a former Kumon instructor who now works as an instructor with Tabtor (a play on the words Tablet and Tutor!) I’m writing this post to give a unique perspective as someone who has worked for both companies. At Tabtor I look after many, many exKumon students including a family with 4 kids who switched from Kumon so that their children could explore the wider curriculum that Tabtor offers. So whether your kids are currently doing Kumon, another math program or you’re just starting to look into math programs to support your child’s math, let me share with you the 8 things to love about Tabtor. 1. Tabtor is... 
12 Brain Building Math Board Games for Curious Kids
31 May 2016  6:02 amWith summer coming up, I’m on the lookout for a new game or two to liven up quiet afternoons. It’s an added bonus if I can sneak a little math practice in without anyone noticing what I’m up to. Here are my top twelve picks for fun games with math skills at the core. Take a look at this previous post on math board games for even more inspiration. 1. SmashUp Game Aliens, Ninjas, Pirates, Dinosaurs and more battle to smash more bases than the opposing team. Eight different factions and dozens of combinations to try. ‘It’s really fast setup, it’s really fast play … It’s easy to pick up the rules.’ 24 players, recommended for age 13+. 2. Melissa & Doug ShutTheBox A deceptively...



Math ∞ Blog

Arbitrary Precision Integer Arithmetic in the Bourne Again Shell (BASH)
30 Nov 2016  12:11 pmThis is a brief post on quick ways to perform arbitrary precision integer arithmetic in the GNU Bourne Again Shell (BASH), either at the command prompt or in a shell script. It is partially a followup to the post Floating Point Arithmetic in the Bourne Again Shell (BASH) and overlaps some of the content in this previous post. The Bourne Again Shell, or bash, is the default command line processor (shell) for Mac OS X, the cygwin environment on MS Windows, and many other Unix and Unixlike systems. Especially if you work with numbers, you may want to perform quick arbitrary precision arithmetic at the command prompt (shell) or in shell scripts. This post covers three ways to perform arbitrary precision... 
Did Facebook’s News Feed Algorithm Elect Donald Trump?
10 Nov 2016  2:11 pmDozens of articles are trying to blame the election of Donald Trump as President of the United States on Facebook’s news feed algorithm, and especially its supposed propensity for factually untrue news stories. The liberal/leftwing The Intercept just posted an article Facebook, I’m Begging You, Please Make Yourself Better by Sam Biddle promoting this theory. Similar articles have shown up in the LA Times , New York Magazine, and many other sources. Donald Trump The premise of these articles is that Facebook created a filter or bubble around dumb, poorly educated, right wing proTrump voters bombarding them with factually incorrect news stories and conspiracy theories that convinced these idiots to vote... 
PreElection Polls That Were Wrong
10 Nov 2016  9:58 amFollowing up on my last post Big Data Flubs Donald Versus Hillary, here are some famous cases where preelection polls were wrong. The Literary Digest Predicts Landon Will Defeat Roosevelt in 1936 In 1936, the United States and the world were in the depths of the Great Depression. Unemployment and poverty were rampant. Hitler had risen to power in Germany. The communist government in Russia had skidded off the rails under Stalin, executing both supporters and opponents in an increasingly obvious reign of terror. A severe drought and unusually hot temperatures in 1934 had devastated agriculture in the midwest, the socalled “Dust Bowl”, leading to huge numbers of destitute migrants and economic refugees... 
Big Data Flubs Donald Versus Hillary
9 Nov 2016  1:44 pmDonald Trump’s unexpected upset victory over Hillary Clinton raises troubling questions about the use of mathematical models and “Big Data” in politics. With the possible exception of the USC Dornsife/LA Times Daybreak Election Poll, nearly all preelection polls and surveys appear to have significantly underestimated the level of popular support for Donald Trump in the United States. Underestimated and usually by about the same amount — a full six percentage points, not a small discrepancy. The New York Times published an article on October 12 “How One 19YearOld Man in Illinois Is Distorting National Polling Averages” debunking the USC/LA Times Poll. In retrospect, the “distortion” does not appear to... 
Algebra, Asimov, and Missing Steps
6 Nov 2016  6:00 amWhen I was young, I could not get algebra. In particular, I would encounter magical operations like this: followed by: followed by (AHA!): Obviously, x was three! Only it wasn’t obvious to me. Somehow on the left side of the equation would turn into on the other side of the equation. In general, pluses turned into minuses, minuses into pluses, multiplies into divides, and divides into multiplies. The algebra textbooks that I had access to never explained how this counterintuitive miracle worked nor, it seemed, could any teacher. And what by the way was the mysterious x anyway? Oh, it is a variable! Okay… And what is a variable? I was pretty lost. Fortunately, I was a fan of the science...



Motion Math

Promoting a Growth Mindset Through Personalized Mindset Coaching
30 Nov 2016  6:20 amMotion Math’s company mission is to help children find delight in intellectual challenge. When children learn to love the experience of struggling through frustration and confusion,... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
Factors of Learning – a new tool for personalization
20 Oct 2016  11:43 amWe’re excited to announce a new tool in the Motion Math teacher dashboard – Factors of Learning. This new report offers innovative data to help you build a student’s learning mindset – a... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
New game content…update your apps!
22 Sep 2016  10:38 amWe’re encouraging all Motion Math subscribers to update your apps, or politely ask your local IT guru to do so. (Even better, turn on “Automatic app updates” on your iPads.) Why?... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
The Loan Shark
22 Sep 2016  10:00 amWe’ve just added a new feature to the latest version of our economics simulation game Cupcake: the loan shark. Loans and debt are a significant economic and lifeskill issue worth discussing with... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
More ways to Match – new levels!
20 Sep 2016  5:26 pmHello Motion Math Educators! We hope your school year is off to a great start. We’ve been working hard to improve the Motion Math experience for administrators, teachers, and of course,... [[ This is a content summary only. Visit my website for full links, other content, and more! ]]



MIND Research Institute Blog

Infographic: Breaking Barriers to Math Success for English Language Learners
6 Dec 2016  9:00 amMath has been called the universal language. More than any other subject, math skills arethe top predictor for student success. But withlengthy word problems and other languageheavy instructional methods, how canEnglish language learners (ELLs) havethe same access to this essential and universal language? Taking Language Out of the Equation Author and Stanford Professor of Mathematics Education Jo Boaler providesresearchon howteaching math through visual representations improves student math performance significantly. Here at MIND Research Institute, mathematicians and neuroscience researchers have found thatteaching math using a gamebasedvisual learning approachthat activates the brain's... 
2016 Celebrating a Year of Growth
29 Nov 2016  9:00 amGrowth can mean a lot of things. At MIND, we measure growth first and foremost in the transformationwe see in student learning and particularly in theincreased level of engagement, perseverance and creativity in mathematical problem solving.All students deservethe opportunity to become empowered learners and future innovators. In 2016, we helpedmore than1,000,000students develop into rigorous problem solvers. Students like Ciera: We know that revolutionizing math educationdoesn't just happen in the classroom—it takes leaders in the corporate, nonprofit and education worldscoming together to engagewith the larger community. Thank you to ourvisionary partners, and we... 
Happy Holidays From JiJi and Friends! [Coloring Page Download]
22 Nov 2016  9:00 amHappy Holidays from JiJi and friends at MIND Research Institute! Looking for a fun activity for your classroom? Download this Holiday JiJi Coloring Page andyour students can share what they are thankful for with JiJi! Share your holiday message with JiJi via: <ul> <li>JiJi's Facebook wall</li> <li>Twitter, by tagging @JiJiMath</li> <li>Pinterest, with the #JiJiHoliday hashtag</li> <li>Or email your images and we'll post them for you!</li> </ul> 
What's Making a Difference in Math Education for ELLs?
18 Nov 2016  9:00 amBy 2025, nearly one out of every four public school students in the U.S. will be an English language learner (ELL). The call to provide equal access to effective math education for ELLs is one of the most important and challenging aspects in education today. We've gathered thoughts from some of our superstar ST Math educators on what’s making a difference for them. "ST Math removes the language barrier and provides access to standardsaligned content. The program replaces intimidating word problems with visual word problems that cover the same standards andstudents are more inclinedto persevere, building their stamina in problem solving." —Dr. Kalim Rayburn, Principal, Rea Elementary, Calif.... 
What If You Held Your Math Program Accountable for LongLasting Impact?
16 Nov 2016  9:00 amEducational programs are not being held accountable for longterm impact. This is a problem. The current ed tech market is not set up to expect accountability at scale, but rather to hop from fad to fad. This makes it especially challenging for education leaders to make wise choices, and it inhibits innovation and continuous improvement by program developers. Let’s take a look at three aspects of the problem, which feed into eachother: <ol> <li>Once an innovative new program is chosen, it is often not used broadly across an entire school, nor at scale across a whole district. This makes a statistical analysis based on published schoolwide scores impossible, leaving only rare, expensive, and slow...</li></ol>



Ash Tutors

Benefits of a private maths tutor over classroom learning
29 Nov 2016  6:52 amBenefits of a private maths tutor over classroom learning Reading Time: 6 minutes So you've pondered long and hard about hiring a private maths tutor for your child. They've been having a few issues at school, and even though you know you could probably help them, there's that 'emotional' thing going on, and you'd prefer a calm household. "But hang on!" says your husband. "What about the cost? It can get pretty pricey over time, and there's no guarantee it'll make any difference. Why aren't the teachers doing their job? That's precisely why our child goes to school, yet here we are, considering spending a large sum on the services of a private maths tutor! " And so the argument... 
3 fun and easy science experiments to do at home
3 Nov 2016  9:16 amHere are 3 very easy, safe and fun science experiments that you can do with children at home. No special equipment is needed and most of the things needed you will already have at home. 1. Make your own crystals Probably everyone's favourite experiment and there are many variations on growing crystals at home but this one uses plain table salt and is probably the quickest and easiest. What you'll need Table salt  sodium chloride300 ml tap waterClean glass jam jar Piece of string 
Help your child tell the time
3 Nov 2016  5:30 amTeaching children to tell the time has always been considered to be a bit tricky. True, it is not the easiest skill to teach, but it is by far one of the most rewarding. Why is it so hard? We spend years teaching kids about our number system based on '10'. Everything from Place Value to measurements follows the reassuringly logical premise that things come in 10s, 100s and 1000s, and so on. Then we suddenly throw in a system based on 5s, 12s, 24s and 60s! Where's the logic in that? No wonder they get confused! In addition, we use various methods for saying the same time, we use Roman numerals, digital clocks, and sometimes don't even have digits at all. The whole thing is a mess! So, with that in... 
Short story ideas and writing prompts
1 Nov 2016  5:59 amIs your child often stuck for words and in need of some ideas? Sometimes it’s really difficult to start writing when you are faced with just a blank page. Writing prompts are a great way to get the creative juices flowing again and even if they spend only 5 or 10 minutes on a prompt, it's often enough to divert their attention and get them back to working on their original piece again. If they are using writing prompts, don't be too bothered about the direction in which they are heading or if what they have written is good or not. The whole idea is to get into the flow of creative writing. Here are 5 writing prompts to stretch their imagination and help them put pencil to paper and write every... 
5 top ideas for outdoor learning
1 Nov 2016  3:53 amWhatever the season, outdoor learning is a brilliant way to get everyone outside in the fresh air as well as engage children who are not so much into pen and paper learning. So, here are 5 top ideas for outdoor learning that all the family can take part in. Let it snow! Snow offers a real handson learning experience for younger children and building a snowman teaches a number of skills including balance, coordination, thinking, maths, science and motor control. Before you set off outside, involve the children in the preparation and ask them to gather together items of clothing they think will keep them warm in the snow. Give younger children the opportunity to create sentences with new winter words...



StudyPug

Auditory Learner in the Modern Age
2 Dec 2016  2:14 pmLearning is a complex, but important, process that everyone must master to be successful. Interestingly, not everyone learns the same way or at the same pace. It is important to identify a learning method that works for you as early as possible in your school career because you’ll need it throughout your life as new tasks and information come your way. Education experts have identified four separate learning styles: auditory, visual, kinesthetic (or physical) and read and write. Your own learning style may match one of these categories perfectly or it may be a combination of two styles of more. When it comes to learning, there is no right or wrong, good or bad. It is simply a matter of determining which... 
How to Form, Organize & Run a Great Study Group
16 Nov 2016  12:19 pmLike it or loathe it, studying is a fact of student life, whether you’re in high school or university. In fact, it’s essential to success in education, so the sooner you make it into a habit, the more rewarding your educational journey will be. When most people picture studying, the image that comes to the mind’s eye is of a person sitting alone at a desk, striving to focus and absorb as much information as possible. However, more and more students are finding that there is an alternative means of learning the necessary information, especially when taking on the most challenging topics: the study group. What is a study group, you ask? Good question. It can be defined as a group of students with the... 
How to Get Good Grades in College and How to Deal With a Drop in Grades
28 Oct 2016  9:07 amYou’re graduating from high school and the future looks rosy. You’ve been accepted at the university of your choice, a prestigious one, and you’re planning on attending medical school after you earn your bachelor’s degree. As a straightA student, you’re confident about your career path – what could possibly go wrong? Is a D a Passing Grade in College? Actually, one likely scenario features a drop in your grades. As surprising as that may sound, especially if you’re prepared to put in your usual effort, most students see their grades fall once they enter university. A research study by Felice Martinello, a professor at Brock University in St. Catharines, Ontario, and colleague Ross Finnie,... 
How to Deal With a Drop in Grades
14 Oct 2016  3:18 pmAs parents, you love your children and want them to succeed in everything they undertake. When it comes to school that generally translates to expecting them to bring home good grades — or grades in line with their natural abilities. When your child has been working up to the level of his or her ability and, all of a sudden, grades drop, it’s not surprising that you will worry. However, before you react strongly and try to try to rectify the situation, it’s important to take a deep breath and evaluate what is going wrong. Try not to be accusatory. By using “what” questions, rather than “why” questions, you’ll get more facts, and your child won’t be tempted to avoid blame by making... 
Study Skills for High School 101
23 Sep 2016  4:51 pmAs you begin your high school career, all of a sudden, grades become very important. Not only do they show your mastery of a subject and bring you pride; they have direct bearing on your opportunities to attend prestigious colleges and universities. College may still seem like it’s a long way off, but students who learn how to study and earn good grades early in their high school careers will have an easier time achieving the successes they want later. Not only will they gain entrance to the best postsecondary institutions; they will also have learned the discipline and focus necessary to success in many walks of life. You, too, can be one of the successful students whose report card features lots of...
