tag:blogger.com,1999:blog-23320729734349088892024-03-14T09:02:58.862-07:00Algebra GameAlgebra sprinkled with Fun!
Play at:
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Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.comBlogger18125tag:blogger.com,1999:blog-2332072973434908889.post-45559631454134038022019-12-30T02:57:00.000-08:002020-04-16T05:19:41.603-07:00Julia Robinson Centennial and the Mathematical Tale of Hilbert's 10th Problem<span style="font-family: "verdana" , sans-serif;"><br />
The month of December in the San Francisco Bay Area was foggy, cold and wet. A warm remarkable Mathematical tale however was awaiting as I arrived at the former house of <a href="https://www.sciencenews.org/article/how-julia-robinson-helped-define-limits-mathematical-knowledge" target="_blank">Julia Robinson</a>, perched at the top of a hill at Kensington, California.</span><br />
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<span style="font-family: "verdana" , sans-serif;">The celebration of Julia Robinson Centennial kickstarted at Julia's former house with a reception organized by Nancy Blachman who founded the <a href="http://www.jrmf.org/" target="_blank">Julia Robinson Mathematics Festival (JRMF)</a>. It was a marvelous evening as I made new friends (math circle friends at the Bay Area, Howard Landman, Manuel Blum and his wife Lenore Blum who just retired from CMU) and catching up with old friends (Mark Saul and Nancy Blachman). I was especially delighted to get the autograph of Martin Davis and Yury Matiyasevich who were Julia's former collaborators. The celebration continued the next day with a <a href="http://www.msri.org/workshops/955" target="_blank">Symposium in Honor of Julia Robinson's 100th Birthday</a> organized by the Mathematical Sciences Research Institute, where prominent speakers e.g., Lenore Blum (who was Julia's former postdoc), Martin Davis, Yury Matiyasevich shared more on the highlights of Julia's mathematical quest. After her death, Julia's husband, <a href="https://en.wikipedia.org/wiki/Raphael_M._Robinson" target="_blank">Raphael M. Robinson</a>, also an eminent mathematician at UC Berkeley, created the Julia Bowman Robinson Fund for scholarships for graduate students at Berkeley, which received the bulk of the Robinsons' estate (the sale of Julia's former house) upon his death. The charitable Robinson mathematicians were truly highly remarkable persons.</span></span><br />
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<span style="font-family: "verdana" , sans-serif;">Julia Robinson was instrumental in resolving <a href="https://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem" target="_blank">Hilbert's 10th problem</a>, together with American mathematicians, Martin Davis, Hilary Putnam. </span></span><span style="font-family: "verdana" , sans-serif;">Hilbert posed his 10th problem along with twenty two others in 1900, now famously known as <a href="https://en.wikipedia.org/wiki/Hilbert%27s_problems" target="_blank">Hilbert's problems</a>. </span><span style="font-family: "verdana" , sans-serif;"><span style="font-family: "verdana" , sans-serif;">And this 10th problem was finally closed in 1970 by a young Russian mathematician Yuri Matiyasevich who built on the work of Robinson, </span></span><span style="font-family: "verdana" , sans-serif;">Davis and Putnam</span><span style="font-family: "verdana" , sans-serif;"><span style="font-family: "verdana" , sans-serif;">. </span></span><span style="font-family: "verdana" , sans-serif;">Out of Hilbert's 23 questions, this 10th problem was the only decision problem, asking for a computational procedure to determine the solvability of a Diophantine equation. Martin Davis' prediction that "Julia Robinson's conjecture is true and it will be proved by a clever young Russian" essentially came true. It was truly remarkable how leading mathematicians on both sides of the Iron Curtain could come together to complement each other's work in resolving Hilbert's problem seventy years after it was first posed. Lenore Blum's Public Lecture "</span><a href="http://www.msri.org/workshops/955/schedules/27749" style="font-family: verdana, sans-serif;" target="_blank">Julia Robinson: Personal Reflections, Her Work and Time</a><span style="font-family: "verdana" , sans-serif;">" gave a very comprehensive overview of the mathematical quest and Julia's personality. These mathematicians and logicians laid down very strong foundations for theoretical computer science as computer science becomes a mainstream academic discipline mushrooming in universities starting in the seventies.</span><br />
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<span style="font-family: "verdana" , sans-serif;">To show that Hilbert's 10th problem has no solution (i.e., no such algorithm exists) was a tour de force of mathematics and logic, requiring the invention of new mathematical tricks, connecting revolutionary concepts (Turing's halting problem with Diophantine equations in number theory) and the discoveries of new properties of the Fibonacci numbers (properties overlooked for centuries and discovered by </span></span><span style="font-family: "verdana" , sans-serif;">Yuri Matiyasevich</span><span style="font-family: "verdana" , sans-serif;">). What struck me the most was that to those </span><i style="font-family: verdana, sans-serif;">Diophantine equations that do have a solution</i><span style="font-family: "verdana" , sans-serif;"> (and therefore an algorithm to determine the solution), the quest for the algorithm by extraordinary mathematicians since ancient times is equally exciting!</span><br />
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<span style="font-family: "verdana" , sans-serif;">Here, I'll point out some of these special cases. The l<a href="https://demonstrations.wolfram.com/SolvingALinearDiophantineEquationInTwoVariablesByTheEuclidea/" target="_blank">inear Diophantine equation in two variables</a> was solved completely many years ago by Diophantine (who else?) and relies on the Euclid's algorithm. This Diophantine equation is a mathematical statement that links the prime decomposition of natural numbers with the solvability of the equation (the notion of solvability means a computable program): Two natural numbers, say <i>a</i> and <i>b,</i> are relatively prime if and only if the linear Diophantine equations with integral variables <i>x</i> and <i>y</i>: <i>ax</i>+<i>by</i> =1 has a solution. The Euclid's algorithm is fundamental to its solution. Next, moving to the nonlinear world, another special case is the Pell's equation, which can be solved by the <a href="https://en.wikipedia.org/wiki/Chakravala_method" target="_blank">Chakravala method</a> invented by the great Indian mathematician Bhāskara II, and this algorithm was considered "the finest thing achieved in the theory of numbers before Lagrange" by Hankel. Another special case is the exponential Diophantine equation associated with the enumeration of dyadic distributions that connects to binary search tree algorithms that are fundamental in information theory and coding theory (e.g., construct</span> prefix-free code for compression). And, until only recently, the task of expressing the <a href="https://www.eurekalert.org/pub_releases/2019-09/uob-sot090619.php" target="_blank">sum of three cubes for 33 and 42</a> was completed in 2019 by supercomputers and massively parallel computational search algorithms. </span><span style="font-family: "verdana" , sans-serif;">It is undeniable that finding solutions to solvable Diophantine equations requires a skillful use of computers. </span><span style="font-family: "verdana" , sans-serif;">Further reading on how Julia's legacy impacts the future of computer science can be found in </span><a href="https://www.ams.org/notices/200803/tx080300344p.pdf" style="font-family: verdana, sans-serif;" target="_blank">Undecidability in Number Theory</a><span style="font-family: "verdana" , sans-serif;"> by Bjorn Poonen published in AMS 2008.</span><br />
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<span style="font-family: "verdana" , sans-serif;">This is an inspirational mathematical tale worth telling to many more students of mathematics and computer science.</span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8ldsOT_ivJiVXpI75U3kFtZwHzO1EhLt1i7vfn2aK2doZ21ynsmcH4vIehyX4BSZcB41wxohmOlm3KlE5kDw27h4r-1lg9lak7YkGpBAKshDtuIZsFIkgB9z7QqO0BBkAGMVSiuXG9bBg/s1600/IMG_7858.HEIC" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: "verdana" , sans-serif;"><img border="0" data-original-height="1200" data-original-width="1600" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8ldsOT_ivJiVXpI75U3kFtZwHzO1EhLt1i7vfn2aK2doZ21ynsmcH4vIehyX4BSZcB41wxohmOlm3KlE5kDw27h4r-1lg9lak7YkGpBAKshDtuIZsFIkgB9z7QqO0BBkAGMVSiuXG9bBg/s640/IMG_7858.HEIC" width="640" /></span></a></div>
<span style="font-family: "verdana" , sans-serif;">The Julia Robinson Centennial Reception held at Julia's former house</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSkh8JdQbIGCpu8pGBKgFT3JHVSWe2GU16Q2e2lmKcgfa8X4yWHAm5gTdLst7IFWOiJ2DifsWbAigHquajyIQCQxnqvOvcZq99hdexOj0FG_J_4JGSmAZ6kifl-M2cRude9GI-ncGI06rt/s1600/IMG_0714.HEIC" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: "verdana" , sans-serif;"><img border="0" data-original-height="1600" data-original-width="1200" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSkh8JdQbIGCpu8pGBKgFT3JHVSWe2GU16Q2e2lmKcgfa8X4yWHAm5gTdLst7IFWOiJ2DifsWbAigHquajyIQCQxnqvOvcZq99hdexOj0FG_J_4JGSmAZ6kifl-M2cRude9GI-ncGI06rt/s640/IMG_0714.HEIC" width="480" /></span></a></div>
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<span style="font-family: "verdana" , sans-serif;"> Nancy Blachman and myself beside the Christmas Tree at MSRI</span></span><br />
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<span style="font-family: "verdana" , sans-serif;">Martin Davis showing a picture of the collaborators who nailed down Hilbert's 10th Problem.</span></span><br />
<br />Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-54360360711358760442018-03-14T19:30:00.000-07:002020-01-18T06:17:11.304-08:00Promoting Equity in Mathematics Education<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFinE9n1BEfBSiPPuVd7KvYnRDibAMQ9m35vw6YE6I6Mo61WKgSPBDQclV9TlNgWqIfAQZ8z4gmAm8DeE_ylx1F4j61JG2b6eJtc9X39TJD5VQ6GQwwpbRU6gKFqflFcLtEfBNFak522lc/s1600/Screen+Shot+2018-03-21+at+6.17.08+pm.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Verdana, sans-serif;"><img border="0" data-original-height="291" data-original-width="779" height="236" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFinE9n1BEfBSiPPuVd7KvYnRDibAMQ9m35vw6YE6I6Mo61WKgSPBDQclV9TlNgWqIfAQZ8z4gmAm8DeE_ylx1F4j61JG2b6eJtc9X39TJD5VQ6GQwwpbRU6gKFqflFcLtEfBNFak522lc/s640/Screen+Shot+2018-03-21+at+6.17.08+pm.png" width="640" /></span></a></div>
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<span style="font-family: Verdana, sans-serif;"><span style="font-family: "verdana" , sans-serif;">In February 2018, I visited the Mathematical Sciences Research Institute at UC Berkeley to attend a </span><a href="https://www.msri.org/workshops/877" target="_blank">MSRI Workshop on Critical Issues in Mathematics Education 2018: Access to mathematics by opening doors for students currently excluded from mathematics</a><span style="font-family: "verdana" , sans-serif;">. Tertiary and K-12 educators across the nation and some including myself from overseas converged at this workshop packed with group discussions and lightning talks co-organized by Francis Su who was the President of the Mathematical Association of America. The MSRI has been a prominent driving force behind <a href="http://www.mathcircles.org/" target="_blank">math circle learning in the United States</a>, and so for me it was rightly a pilgrimage trip to MSRI which is perched right up at the top of the Berkeley hill, offering an unbeatable panoramic view of the Golden Gate Bridge and the Bay Area. </span></span><br />
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<span style="font-family: Verdana, sans-serif;">One striking takeaway from this workshop is <i>equity</i> in mathematics education. Roughly speaking, equity means giving students what they need to succeed in learning regardless of their personal or social circumstances. One of the plenary speakers, <a href="http://www.davekung.com/" target="_blank">Prof. Dave Kung</a>, gave a very powerful and fantastic talk that provoked the educators among the audience to ponder the question of "<i>I teach math?"</i> or "<i>I teach students?" </i> and where the audience would see themselves in the spectrum between these two extremes. The former is <i>speaking the content, </i>while the latter is <i>individualized instruction</i>. Dave held polls in between his plenary and it was interesting to watch the number of hands raised in the audience when Dave asked whoever had experienced a teacher at those two extremes and where the audience thought their current department might be standing in that spectrum. </span></div>
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<span style="font-family: Verdana, sans-serif;"><span style="font-family: "verdana" , sans-serif;">What Dave Kung brought out is an important pedagogical question but also one that is well formulated to ask whether and how, somewhere in the spectrum, technologies can help the disaffected students and even teachers. Going by the extent in which technologies have democratized information sharing in the last ten years, </span><span style="font-family: "verdana" , sans-serif;">it is thus necessary to consider what greater </span><span style="font-family: "verdana" , sans-serif;">role will technology play in order to address the </span><span style="font-family: "verdana" , sans-serif;">equity problem in mathematics education.</span><span style="font-family: "verdana" , sans-serif;"> Will it open up doors to many more students or will it shrink the equity gap between the haves and the have-nots? This one-week pilgrimage to MSRI has been extremely educational and has given me a sense on how to develop and deploy our educational software technologies going forward.</span></span></div>
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<span style="font-family: Verdana, sans-serif;"><span style="font-family: "verdana" , sans-serif;">For more than a year, we have been working on the <a href="http://algebragamification.com/jrmf/app" target="_blank">PolyMath App</a>, which first saw action at the Julia Robinson Mathematics Festival in Hong Kong in April 2017. Subsequently, we have partnered with a number of educators to promote the JRMF App at a few international and regional math outreach activities. Last October, the JRMF App was featured as <a href="https://www.theglobalmathproject.org/gmw/other-ways-to-play" target="_blank">a means to play <i>Exploding Dot</i> that James Tanton created for t</a></span><a href="https://www.theglobalmathproject.org/gmw/other-ways-to-play" target="_blank"><span style="font-family: "verdana" , sans-serif;">he 2017 </span><span style="font-family: "verdana" , sans-serif;">Global Math Project</span></a><span style="font-family: "verdana" , sans-serif;">. We also held a few interactive workshops with mathematics teachers at several well-established math education centers in Shanghai and the Shanghai World Foreign Language Middle School (上海市世界外国语中学). In February 2018, we worked with a group of forty secondary school mathematics teachers from the English Schools Foundation (ESF) international schools in Hong Kong. There was so much to learn from the teachers at the </span><span style="font-family: "verdana" , sans-serif;">front-line of the ever-evolving mathematics education landscape</span><span style="font-family: "verdana" , sans-serif;">. After the workshop was over, some ESF teachers even came forward to volunteer as math mentors at the <a href="http://www.algebragamification.com/jrmf" target="_blank">Julia Robinson Mathematics Festival in March 2018</a>!</span></span></div>
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<span style="font-family: Verdana, sans-serif;"><span style="font-family: "verdana" , sans-serif;">Using the </span><a href="http://algebragamification.com/jrmf/app" target="_blank">PolyMath App</a><span style="font-family: "verdana" , sans-serif;">, we shared with the teachers how they can quickly learn </span><a href="https://en.wikipedia.org/wiki/Binary_number" target="_blank">binary number system and arithmetic</a><span style="font-family: "verdana" , sans-serif;"> through game-play in our </span><a href="http://www.algebragamification.com/jrmf/app" target="_blank">PolyMath App</a><span style="font-family: "verdana" , sans-serif;">. Thereafter it was natural to introduce James Tanton's exploding dot as it revolves around place value number system once the teachers had become familiar with the</span><span style="font-family: "verdana" , sans-serif;"> binary number system. The binary system is the most basic and practical one, not just because we use it in computers, but also because binary number representation and its arithmetic manifest intriguingly in games and algorithms. In particular, we delved into the deep mathematical insights behind the <a href="https://en.wikipedia.org/wiki/Nim" target="_blank">NIM game</a> (also called the Fish-flavored Lollipop problem set in JRMF) and the algorithm behind the <a href="https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplication#Russian_peasant_multiplication" target="_blank">Russian peasant's method of multiplication</a> and a logical puzzle by Martin Gardner. </span><span style="font-family: "verdana" , sans-serif;">Working with these amazing teachers was an uplifting experience!</span></span></div>
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<br />Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-27861368975177885322017-06-26T04:34:00.001-07:002017-06-27T20:15:32.197-07:00The Julia Robinson Mathematics Festival in Hong Kong (Video, App and Abundant Math Opportunities)<span style="font-family: "verdana" , sans-serif;"><a href="http://www.algebragamification.com/JRMF" target="_blank">Hong Kong’s inaugural Julia Robinson Mathematics Festival</a> (JRMF) was held at the Singapore International School (Hong Kong) on April 1st 2017 from 10:00am to 1:00pm. In partnership with the American Institute of Mathematics, the JRMF makes mathematics accessible to every student of all abilities, and focuses on collaborative problem-solving, as opposed to the competitive nature of mathematics examinations and contests, so that students can enjoy the richness and beauty of mathematics without any anxiety.</span><br />
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<span style="font-family: "verdana" , sans-serif;">Guided by mathematics teachers and other mathematics lovers in the community, 248 students aged 10 to 14 worked on a variety of mathematical problems, puzzles and activities. Of these students, 230</span><br />
<span style="font-family: "verdana" , sans-serif;">(92%) came from local schools (Singapore International School, Chinese International School, Tung Wah Group Schools, ESF Island School among others). The mathematical activity at each table was specially designed to be initially easy and then progressively become challenging. These mathematically deep problem sets came with interesting names: "The Tower of Hanoi - and Beyond", "Broken Calculators", "The Game of Criss-cross", "Exploding Dot Puzzle", "Algebra Game", "Algebra Maze", "Leo The Rabbit", "Mobius Strip", "Number Game of Randomness", "Rubik Cube Machine!" among others.</span><span style="font-family: "verdana" , sans-serif;"> </span><br />
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<span style="font-family: "verdana" , sans-serif;">See <a href="https://youtu.be/neDc_Deeg-g" target="_blank">Video Clip</a> below on how students had a blast at doing mathematics! </span><span style="font-family: "verdana" , sans-serif;">Dr. Mark Saul, Executive Director of The Julia Robinson Mathematics Festival, commented </span><i><span style="font-family: "verdana" , sans-serif;">"They're choosing to do the Mathematics. And that's what is important!". </span></i><br />
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<span style="font-family: "verdana" , sans-serif;">Students roamed freely around and chose to go to any table to work on the problem sets. The facilitator at each table rewarded students with a raffle for demonstrating persistence in working on the math problems on hand or showing collaborative learning spirit (e.g., helping fellow peers at the table). Thirty raffle prizes such as Festival T-shirts, math games and books were given out at the end of the festival. To let all the participants meet the man behind the mathematics (to see their human faces flashed across the screen), we have even named each of the Raffle prizes after brilliant mathematicians whose short biography are read out before drawing the lucky winner of the raffle prize (see image below). The facilitators and overseas guests (Dr. Mark Saul and VIP guests from Mainland China and Taiwan —see group dinner picture below) had the honor to give out the Raffle prizes to the lucky students!</span><br />
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<span style="font-family: "verdana" , sans-serif;">For the first time, mobile app software was leveraged at the JRMF for students to develop a stronger intuition to the mathematical problems through observation and experimentation. Even after the festival, the mobile app continues to encourage collaborative and creative problem-solving between the students and their parents and teachers. See our JRMF App screenshots below and install the <a href="https://itunes.apple.com/us/app/jrmf/id1218671354" target="_blank">Apple iOS version</a> or the <a href="https://play.google.com/store/apps/details?id=com.algebragamification.jrmfapp" target="_blank">Android version</a> to get a taste of some of the fun mathematics at the JRMF in Hong Kong!</span><br />
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<span style="font-family: "verdana" , sans-serif;">Amidst the fun in mathematics, participants took away fond memories of doing challenging mathematics. With the n</span><span style="font-family: "verdana" , sans-serif;">ew friendships forged, we look forward to the infinitely many</span><span style="font-family: "verdana" , sans-serif;"> opportunities and creative ideas to make Mathematics accessible to many more students. </span><span style="font-family: "verdana" , sans-serif;">A </span><a href="http://www.algebragamification.com/jrmf/JRMFHK_PressRelease.pdf" style="font-family: verdana, sans-serif;" target="_blank">Press Release</a><span style="font-family: "verdana" , sans-serif;"> and many more pictures and videos of the Festival can be found at the </span><a href="http://www.algebragamification.com/jrmf" style="font-family: verdana, sans-serif;" target="_blank">JRMF Hong Kong website</a><span style="font-family: "verdana" , sans-serif;">!</span><br />
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<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/neDc_Deeg-g/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/neDc_Deeg-g?feature=player_embedded" width="320"></iframe></div>
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<i><span style="font-family: "verdana" , sans-serif;">"They're choosing to do the Mathematics. And that's what is important!"</span></i><br />
<span style="font-family: "verdana" , sans-serif;"> — Dr. Mark Saul, Executive Director of The Julia Robinson Mathematics Festival</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxpTH_7IoJBxejRkhyvnBt_AW6ql2kQtsITGfJUffw6w-0L4LZlIKtLLMpslvKHXMM6hXX586KGMfE4uGv897HHacFVZaxRhWQAgCwPws5LCrT-4FV_yUb6ZmmUqy2xZtcEhtWdXejZk2J/s1600/RafflePrizeTiledMathematicians.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1237" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxpTH_7IoJBxejRkhyvnBt_AW6ql2kQtsITGfJUffw6w-0L4LZlIKtLLMpslvKHXMM6hXX586KGMfE4uGv897HHacFVZaxRhWQAgCwPws5LCrT-4FV_yUb6ZmmUqy2xZtcEhtWdXejZk2J/s640/RafflePrizeTiledMathematicians.jpg" width="494" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: "verdana" , sans-serif;"><span style="font-size: small;">Thirty Raffle Prizes named after Brilliant Mathematicians at the JRMF in Hong Kong</span></span></td></tr>
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<span style="font-family: "verdana" , sans-serif; text-align: center;">Screenshots of JRMF App used at JRMF in Hong Kong. The JRMF App </span><span style="font-family: "verdana" , sans-serif;">continues to encourage collaborative and creative problem-solving between the students and their parents and teachers even after the JRMF Festival ends.</span><span style="font-family: "verdana" , sans-serif;"> </span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyMIJnF2tcngkobThy3Dqrr7Ap9sdrMp3-q_S-K773mOcikuZ3ypW3dUAkSx5zNSEwU2J2GS4ExVmRcXQe03p2Y_mhYOLO5Kgbtp527AdiD1w3TXWSFDuguZHNtJGhH-BabEuJWYhduo-y/s1600/OverseasGuests.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="641" data-original-width="1265" height="323" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyMIJnF2tcngkobThy3Dqrr7Ap9sdrMp3-q_S-K773mOcikuZ3ypW3dUAkSx5zNSEwU2J2GS4ExVmRcXQe03p2Y_mhYOLO5Kgbtp527AdiD1w3TXWSFDuguZHNtJGhH-BabEuJWYhduo-y/s640/OverseasGuests.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: "verdana" , sans-serif; font-size: small;">JRMF Organizing Team and Overseas VIP Guests enjoying a "Festive Dinner" together: Dr Mark Saul, Executive Director of the JRMF, Ms. Cherry Pu and Team from Mainland China and Mr. Ho and Team from Taiwan.</span></td></tr>
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<br />Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-86447111026321376042017-02-14T18:48:00.000-08:002020-02-11T20:00:32.770-08:00Starting the Julia Robinson Mathematics Festival in Hong Kong<span style="font-family: "verdana" , sans-serif;"><br /></span>
<span style="font-family: "verdana" , sans-serif;">We are very excited to announce that the inaugural Julia Robinson Mathematics Festival in Hong Kong is going to be held on April 1st (Saturday) at the Singapore International School (Hong Kong). This is open to students in Hong Kong, ages 10 to 14.</span><br />
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<span style="font-family: "verdana" , sans-serif;">The <a href="http://www.algebragamification.com/JRMF" target="_blank">Julia Robinson Mathematics Festival in Hong Kong 2017</a> </span><span style="font-family: "verdana" , sans-serif;">inspires students to explore the richness and beauty of mathematics through activities that encourage collaborative and creative problem-solving. This event is in joint partnership with the </span><a href="http://www.jrmf.org/" style="font-family: verdana, sans-serif;" target="_blank">Julia Robinson Mathematics Festivals</a><span style="font-family: "verdana" , sans-serif;"> and the Singapore International School (Hong Kong). Details at </span><span style="font-family: "verdana" , sans-serif;"><a href="http://www.algebragamification.com/JRMF">http://www.algebragamification.com/JRMF</a></span><span style="font-family: "verdana" , sans-serif;">.</span><br />
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<span style="font-family: "verdana" , sans-serif;">We started this as a grassroots activity with a few like-minded friends -- Jian Shen (former Princeton University Math Club President who then roped in other mathematicians working in finance), </span><span style="font-family: "verdana" , sans-serif;">Ken Shum. We all </span><span style="font-family: "verdana" , sans-serif;">wondered what differences we can make for Hong Kong students who are new to this type of mathematics initiative. And the Julia Robinson Math Festival in Hong Kong seems perfectly in sync with the United States' <a href="http://www.nationalmathfestival.org/" target="_blank">2017 National Math Festival</a>, the grandest carnival in mathematics. We are delighted to receive full support from Mark Saul (Executive Director of Julia Robinson Mathematics Festival) and also local academics like Professor Tony Chan (HKUST President), </span><span style="font-family: "verdana" , sans-serif;">sponsorship from the IEEE Information Theory Society and the Singapore International School (Hong Kong) whose vice-Principal Mr. Bernard Ng and I had a great time working together before.</span><br />
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<span style="font-family: "verdana" , sans-serif;">The </span><a href="http://www.jrmf.org/" style="font-family: verdana, sans-serif;" target="_blank">Julia Robinson Mathematics Festivals</a><span style="font-family: "verdana" , sans-serif;"> is a project founded by Nancy Blachman in partnership with the American Institute of Mathematics that started in 2007 at Google in the Bay Area (yes it's as old as the cool iPhone). Since then, the festivals have spread to many places worldwide. The idea of the Festivals is to allow young people to develop their talent for mathematics by providing problems, puzzles, and activities that are intriguing and accessible in a non-competitive atmosphere. A diverse audience of young people, school teachers, math lovers in the community come together to explore the joys and power of mathematics with the goal of broadening society's appreciation and support of mathematics. </span><br />
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<span style="font-family: "verdana" , sans-serif;"><span style="font-family: "verdana" , sans-serif;">We will have a number of <a href="http://www.algebragamification.com/jrmf/organization.html" target="_blank">math-lovers from the academia and industry</a> who will facilitate at each table of math and to give out raffle tickets! </span><span style="font-family: "verdana" , sans-serif;">The <a href="http://www.algebragamification.com/" target="_blank">Algebra Game Project</a> will of course have a table of its own for students </span>to explore the mathematics behind the game. There are also mathematical origami, puzzles and many more that we are creating and preparing right now! </span><br />
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<span style="font-family: "verdana" , sans-serif;">Stay tuned for April 1st! </span><span style="font-family: "verdana" , sans-serif;">Here is the Festival poster:</span><br />
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Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-7236747514421910032016-12-12T03:18:00.000-08:002017-09-25T19:37:17.505-07:00Camera Vibration in Canvas Based Unity Game<div style="background-color: white; color: #34495e; font-size: 15px;">
<span style="font-family: "verdana" , sans-serif;">Contributions by Alex Ling</span></div>
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<span style="font-family: "verdana" , sans-serif;">Currently I am maintaining a 2D Unity game (check it out <a href="http://www.algebragamification.com/" rel="external" style="background-color: transparent; color: #48b2f1; text-decoration: none; word-break: break-all;" target="_blank">here</a> if you are interested). I was trying to implement a feature that when the user gives illegal input, the whole screen would shake (or vibrate if you would) for a while.</span></div>
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<span style="font-family: "verdana" , sans-serif;">Here’s a GIF as a demo. When the user try to multiply of divide a variable with x, the whole screen will vibrate for 0.3 seconds.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX_8H8eQ8AfKpQrzF81hx0ifCdJsjKJ5GAsSNi65QAh4GNniNw0jJDz_pouVFVWWEJ4Df-yXucnx1ejBrk2llhpYXMF9uNPMAORXzgmbDg_BAswsRTxu5qRwW2fSRmI3cfjbgcCEN0tCM-/s1600/vibration.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX_8H8eQ8AfKpQrzF81hx0ifCdJsjKJ5GAsSNi65QAh4GNniNw0jJDz_pouVFVWWEJ4Df-yXucnx1ejBrk2llhpYXMF9uNPMAORXzgmbDg_BAswsRTxu5qRwW2fSRmI3cfjbgcCEN0tCM-/s400/vibration.gif" width="221" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">I know what you would say, what’s the big deal here? We can simply randomly move the main camera for 0.3 seconds to achieve the effect. I don’t blame you, because that’s what I thought at first glance.</span></div>
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<span style="font-family: "verdana" , sans-serif;">I attached a <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">CameraShaker.cs</code> script to the main camera. The script looks like this</span></div>
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<figure class="highlight cs" style="background-color: #f8f8f8; border-radius: 2px; box-shadow: rgba(0, 0, 0, 0.121569) 0px 1px 2px; color: #34495e; font-family: sourcesanspro, "Helvetica Neue", Arial, sans-serif; font-size: 15px; line-height: 1.1em; margin: 1em 0px; overflow-x: auto; position: relative;"><table style="border-collapse: collapse; border-spacing: 0px; margin: 0px; padding: 0px; width: 710.667px;"><tbody>
<tr style="border-collapse: collapse; margin: 0px; padding: 0px; width: 710.667px;"><td class="code" style="border-collapse: collapse; margin: 0px; padding: 0px; vertical-align: text-top; width: 710.667px;"><pre style="color: #525252; font-family: Menlo, Monaco, courier, monospace; font-size: 0.8em; line-height: 1.5em; overflow: auto; padding: 2em 1.4em 1.2em; tab-size: 4;"><div class="line">
<span class="keyword" style="color: #e96900;">using</span> UnityEngine;</div>
<div class="line">
<span class="keyword" style="color: #e96900;">public</span> <span class="keyword" style="color: #e96900;">class</span> <span class="title" style="color: #83b917;">CameraShaker</span> : <span class="title" style="color: #83b917;">MonoBehaviour</span> {</div>
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<span class="keyword" style="color: #e96900;">public</span> <span class="keyword" style="color: #e96900;">float</span> shakeAmount = <span class="number" style="color: #ae81ff;">0.7</span>f;</div>
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<span class="keyword" style="color: #e96900;">float</span> shakeTime = <span class="number" style="color: #ae81ff;">0.0</span>f;</div>
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Vector3 initialPosition;</div>
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<span class="function"><span class="keyword" style="color: #0092db;">public</span> <span class="keyword" style="color: #0092db;">void</span> <span class="title" style="color: #83b917;">VibrateForTime</span>(<span class="params"><span class="keyword" style="color: #0092db;">float</span> time</span>)</span>{</div>
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shakeTime = time;</div>
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}</div>
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<span class="function"><span class="keyword" style="color: #0092db;">void</span> <span class="title" style="color: #83b917;">Start</span>(<span class="params"></span>) </span>{</div>
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initialPosition = <span class="keyword" style="color: #e96900;">this</span>.transform.position;</div>
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}</div>
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<span class="function"><span class="keyword" style="color: #0092db;">void</span> <span class="title" style="color: #83b917;">Update</span> (<span class="params"></span>) </span>{</div>
<div class="line">
<span class="keyword" style="color: #e96900;">if</span> (shakeTime > <span class="number" style="color: #ae81ff;">0</span>){</div>
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<span class="keyword" style="color: #e96900;">this</span>.transform.position = Random.insideUnitSphere * shakeAmount + initialPosition;</div>
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shakeTime -= Time.deltaTime;</div>
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}</div>
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<span class="keyword" style="color: #e96900;">else</span>{</div>
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shakeTime = <span class="number" style="color: #ae81ff;">0.0</span>f;</div>
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<span class="keyword" style="color: #e96900;">this</span>.transform.position = initialPosition;</div>
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}</div>
<div class="line">
}</div>
<div class="line">
}</div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span>
<span style="font-family: "verdana" , sans-serif;">And in another script I call the <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">VibrateForTime</code> method:</span></div>
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<figure class="highlight cs" style="background-color: #f8f8f8; border-radius: 2px; box-shadow: rgba(0, 0, 0, 0.121569) 0px 1px 2px; color: #34495e; font-family: sourcesanspro, "Helvetica Neue", Arial, sans-serif; font-size: 15px; line-height: 1.1em; margin: 1em 0px; overflow-x: auto; position: relative;"><table style="border-collapse: collapse; border-spacing: 0px; margin: 0px; padding: 0px; width: 680px;"><tbody>
<tr style="border-collapse: collapse; margin: 0px; padding: 0px; width: 680px;"><td class="code" style="border-collapse: collapse; margin: 0px; padding: 0px; vertical-align: text-top; width: 680px;"><pre style="color: #525252; font-family: Menlo, Monaco, courier, monospace; font-size: 0.8em; line-height: 1.5em; overflow: auto; padding: 2em 1.4em 1.2em; tab-size: 4;"><div class="line">
<span class="comment" style="color: #b3b3b3;">// ...</span></div>
<div class="line">
<span class="keyword" style="color: #e96900;">if</span> (!OperationIsLegal(operation)) {</div>
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Camera.main.GetComponent<CameraShaker>().VibrateForTime(<span class="number" style="color: #ae81ff;">.3</span>f);</div>
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<span class="keyword" style="color: #e96900;">return</span>;</div>
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}</div>
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<span class="comment" style="color: #b3b3b3;">// ...</span></div>
</pre>
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</figure><br />
<div style="background-color: white; color: #34495e; font-size: 15px;">
<span style="font-family: "verdana" , sans-serif;">Then I ran the game and tried it… Oh wait! Why isn’t the screen shaking? I quickly found that it’s because the canvas’ <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">renderMode</code> property is at its default value <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">Screen Space - Overlay</code></span><br />
<span style="font-family: "verdana" , sans-serif;"><code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;"><br /></code></span></div>
<div style="background-color: white; color: #34495e; font-size: 15px;">
<img alt="" src="https://blog.yunolab.org/2016/12/12/Camera-Vibration-in-2D-Unity-Game/overlay.png" style="border: 0px; display: block; margin: 1em auto; max-width: 100%;" /></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span>
<span style="font-family: "verdana" , sans-serif;">When this property is set as <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">Screen Space - Overlay</code> or <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">Screen Space - Camera</code>, the canvas is always attached to the screen (and of course the camera), and so it’s vibrating with the camera. That’s why we can’t see any vibration happen.</span></div>
<div style="background-color: white; color: #34495e; font-size: 15px;">
<span style="font-family: "verdana" , sans-serif;"><br /></span>
<span style="font-family: "verdana" , sans-serif;">So the solution is simply set the <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">renderMode</code> property to <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">World Space</code> in the inspector. In this way the canvas and the camera are decoupled and so the vibration can be seen. </span><span style="font-family: "verdana" , sans-serif;">This should work in most cases, but for me, I found that when set to </span><code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">World Space</code><span style="font-family: "verdana" , sans-serif;">, the light blue operator when dragged (see the above GIF) will not be displayed. That’s because to position the blue operator at mouse position the coupling between canvas and camera(screen) is needed.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
<div style="background-color: white; color: #34495e; font-size: 15px;">
<span style="font-family: "verdana" , sans-serif;">So my final solution is, set the <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">renderMode</code> of the canvas to <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">World Space</code> when the vibration start, and set it back to <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">Screen Space - Overlay</code> once the vibration finish. Since the vibration time is short, this should not affect the display of the light blue operator. </span><span style="font-family: "verdana" , sans-serif;">The final version of </span><code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">CameraShaker.cs</code><span style="font-family: "verdana" , sans-serif;"> is shown below:</span></div>
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<figure class="highlight cs" style="background-color: #f8f8f8; border-radius: 2px; box-shadow: rgba(0, 0, 0, 0.121569) 0px 1px 2px; color: #34495e; font-family: sourcesanspro, "Helvetica Neue", Arial, sans-serif; font-size: 15px; line-height: 1.1em; margin: 1em 0px; overflow-x: auto; position: relative;"><table style="border-collapse: collapse; border-spacing: 0px; margin: 0px; padding: 0px; width: 710.667px;"><tbody>
<tr style="border-collapse: collapse; margin: 0px; padding: 0px; width: 710.667px;"><td class="code" style="border-collapse: collapse; margin: 0px; padding: 0px; vertical-align: text-top; width: 710.667px;"><pre style="color: #525252; font-family: Menlo, Monaco, courier, monospace; font-size: 0.8em; line-height: 1.5em; overflow: auto; padding: 2em 1.4em 1.2em; tab-size: 4;"><div class="line">
<span class="keyword" style="color: #e96900;">using</span> UnityEngine;</div>
<div class="line">
<span class="keyword" style="color: #e96900;">using</span> UnityEngine.UI;</div>
<div class="line">
<span class="keyword" style="color: #e96900;">public</span> <span class="keyword" style="color: #e96900;">class</span> <span class="title" style="color: #83b917;">CameraShaker</span> : <span class="title" style="color: #83b917;">MonoBehaviour</span> {</div>
<div class="line">
<span class="keyword" style="color: #e96900;">public</span> <span class="keyword" style="color: #e96900;">float</span> shakeAmount = <span class="number" style="color: #ae81ff;">0.7</span>f;</div>
<div class="line">
<span class="keyword" style="color: #e96900;">public</span> Canvas canvas;</div>
<div class="line">
<span class="keyword" style="color: #e96900;">float</span> shakeTime = <span class="number" style="color: #ae81ff;">0.0</span>f;</div>
<div class="line">
Vector3 initialPosition;</div>
<div class="line">
</div>
<div class="line">
<span class="function"><span class="keyword" style="color: #0092db;">public</span> <span class="keyword" style="color: #0092db;">void</span> <span class="title" style="color: #83b917;">VibrateForTime</span>(<span class="params"><span class="keyword" style="color: #0092db;">float</span> time</span>)</span>{</div>
<div class="line">
shakeTime = time;</div>
<div class="line">
canvas.renderMode = RenderMode.ScreenSpaceCamera;</div>
<div class="line">
canvas.renderMode = RenderMode.WorldSpace;</div>
<div class="line">
}</div>
<div class="line">
<span class="function"><span class="keyword" style="color: #0092db;">void</span> <span class="title" style="color: #83b917;">Start</span>(<span class="params"></span>) </span>{</div>
<div class="line">
initialPosition = <span class="keyword" style="color: #e96900;">this</span>.transform.position;</div>
<div class="line">
}</div>
<div class="line">
</div>
<div class="line">
<span class="function"><span class="keyword" style="color: #0092db;">void</span> <span class="title" style="color: #83b917;">Update</span> (<span class="params"></span>) </span>{</div>
<div class="line">
<span class="keyword" style="color: #e96900;">if</span> (shakeTime > <span class="number" style="color: #ae81ff;">0</span>){</div>
<div class="line">
<span class="keyword" style="color: #e96900;">this</span>.transform.position = Random.insideUnitSphere * shakeAmount + initialPosition;</div>
<div class="line">
shakeTime -= Time.deltaTime;</div>
<div class="line">
}</div>
<div class="line">
<span class="keyword" style="color: #e96900;">else</span>{</div>
<div class="line">
shakeTime = <span class="number" style="color: #ae81ff;">0.0</span>f;</div>
<div class="line">
<span class="keyword" style="color: #e96900;">this</span>.transform.position = initialPosition;</div>
<div class="line">
canvas.renderMode = RenderMode.ScreenSpaceOverlay;</div>
<div class="line">
}</div>
<div class="line">
}</div>
<div class="line">
}</div>
</pre>
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</figure><br />
<div style="background-color: white; color: #34495e; font-size: 15px;">
<span style="font-family: "verdana" , sans-serif;">Let’s take a closer look at what I did in <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">VibrateForTime</code>:</span></div>
<br />
<figure class="highlight cs" style="background-color: #f8f8f8; border-radius: 2px; box-shadow: rgba(0, 0, 0, 0.121569) 0px 1px 2px; color: #34495e; font-family: sourcesanspro, "Helvetica Neue", Arial, sans-serif; font-size: 15px; line-height: 1.1em; margin: 1em 0px; overflow-x: auto; position: relative;"><table style="border-collapse: collapse; border-spacing: 0px; margin: 0px; padding: 0px; width: 680px;"><tbody>
<tr style="border-collapse: collapse; margin: 0px; padding: 0px; width: 680px;"><td class="code" style="border-collapse: collapse; margin: 0px; padding: 0px; vertical-align: text-top; width: 680px;"><pre style="color: #525252; font-family: Menlo, Monaco, courier, monospace; font-size: 0.8em; line-height: 1.5em; overflow: auto; padding: 2em 1.4em 1.2em; tab-size: 4;"><div class="line">
<span class="comment" style="color: #b3b3b3;">// ...</span></div>
<div class="line">
canvas.renderMode = RenderMode.ScreenSpaceCamera;</div>
<div class="line">
canvas.renderMode = RenderMode.WorldSpace;</div>
<div class="line">
<span class="comment" style="color: #b3b3b3;">// ...</span></div>
</pre>
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<span style="font-family: "verdana" , sans-serif;">Before setting the <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">renderMode</code> to <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">WorldSpace</code>, I set it to <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">ScreenSpaceCamera</code> first. That’s because by setting it to <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">ScreenSpaceCamera</code>, the canvas will be automatically positioned and scaled to fit in the camera. If I jump from <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">ScreenSpaceOverlay</code> directly to <code style="background-color: #f8f8f8; border-radius: 2px; color: #e96900; font-size: 0.8em; margin: 0px 2px; padding: 3px 5px; white-space: inherit;">WorldSpace</code>, the canvas will be out of the sight of the camera, and we will need to manually reposition the canvas in that case.</span></div>
Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-68372537606804817432016-09-21T02:48:00.001-07:002020-02-14T19:41:17.043-08:00Algebra Game and Algebra Maze on Google Play Store!<div>
<span style="font-family: "verdana" , sans-serif;">We recently launched our first mobile apps Algebra Game and Algebra Maze</span><span style="font-family: "verdana" , sans-serif;"> on the Google Play Store. </span><span style="font-family: "verdana" , sans-serif;">From day one, the <a href="http://www.algebragamification.com/team" target="_blank">Algebra Game team</a> members basically hit the ground running to</span><span style="font-family: "verdana" , sans-serif;"> p</span><span style="font-family: "verdana" , sans-serif;">ut ideas into code. </span><span style="font-family: "verdana" , sans-serif;">Designing mathematical games in mobile apps is a challenging experiment - binding mathematical elements with the human-computer interface is an art, </span><span style="font-family: "verdana" , sans-serif;">making the same piece of software work on different hardware is trial and error, </span><span style="font-family: "verdana" , sans-serif;">walking through the</span><span style="font-family: "verdana" , sans-serif;"> entire online app submission process is new to us! And this whole process doesn't stop there. It continues in a loop whenever new bugs/ideas surface. D</span><span style="font-family: "verdana" , sans-serif;">eveloping software is truly a humble learning experience. </span><span style="font-family: "verdana" , sans-serif;">We are working hard on the iOS mobile apps - so expect to see them in App Store soon.</span></div>
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<span style="font-family: "verdana" , sans-serif;">We are also excited to have made inroads into understanding the mathematics behind Tao's Algebra Game</span><span style="font-family: "verdana" , sans-serif;">. Figuring out the math to compute the fewest moves for puzzle generation </span><span style="font-family: "verdana" , sans-serif;">thereby answering some of <a href="http://algebragame.blogspot.com/2015/07/terence-taos-algebra-game.html" target="_blank">Terence Tao's questions</a> is actually the ultimate endgame for </span><span style="font-family: "verdana" , sans-serif;">us :) This can help in cleverer puzzle generation and we will flesh out that once the math is neatly ironed out. </span><span style="font-family: "verdana" , sans-serif;">The Algebra Maze</span><span style="font-family: "verdana" , sans-serif;"> on the Google Play Store currently has forty-five levels altogether, </span><span style="font-family: "verdana" , sans-serif;"> but</span><span style="font-family: "verdana" , sans-serif;"> we have embarked on newer game design for the Algebra Maze and even contemplating new functionality in these mobile app games to bring out the social element: <i>Math is social!</i></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYVYCPWyDM4eq_Nb_DpgqNuo7j6rfp7bTMItCA8u9kjfgctH1Vwqh1EuhW7JRfymSi6p0ohhfSurdQz4IVexu3-hm-vYcNYLqNi8zm2bVmQuH9338WLLA0LgVa5i02J3_yjvETxfWsC2xA/s1600/Screen+Shot+2016-09-20+at+10.32.43+pm.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="282" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYVYCPWyDM4eq_Nb_DpgqNuo7j6rfp7bTMItCA8u9kjfgctH1Vwqh1EuhW7JRfymSi6p0ohhfSurdQz4IVexu3-hm-vYcNYLqNi8zm2bVmQuH9338WLLA0LgVa5i02J3_yjvETxfWsC2xA/s640/Screen+Shot+2016-09-20+at+10.32.43+pm.png" width="640" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">Ultimately, </span><i style="font-family: verdana, sans-serif;">user experience matters the most.</i><span style="font-family: "verdana" , sans-serif;"> And we expect to get as much feedback as possible to further improve our mobile app games. </span><span style="font-family: "verdana" , sans-serif;">Check them out and let us know! We will be glad to hear from you. </span><span style="font-family: "verdana" , sans-serif;">Algebra Game Team members meanwhile take a break from crunching maths and writing software to savor yummy mooncakes.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnwmcZahOdyxwmDksEb51GuIu3XX6mPCqhyphenhyphenPyVME3ppF3kY8enc9uVNQ3_PIYZVEtJoGpOGRqWBxc4JGlRvv0icgaj_MvEae5wfaJSjFt5kf4BO9IEkutYzG6FCyFlPQrX4L-YDdBzBsTh/s1600/20160923_104006.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnwmcZahOdyxwmDksEb51GuIu3XX6mPCqhyphenhyphenPyVME3ppF3kY8enc9uVNQ3_PIYZVEtJoGpOGRqWBxc4JGlRvv0icgaj_MvEae5wfaJSjFt5kf4BO9IEkutYzG6FCyFlPQrX4L-YDdBzBsTh/s640/20160923_104006.jpg" width="640" /></a></div>
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Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-84271413901587051362016-06-04T00:45:00.002-07:002020-02-11T20:10:54.452-08:00Claude Shannon Centenary and the 1-bit Maze (A-Maze-ing Dash Challenge)<span style="font-family: "verdana" , sans-serif;"><br /></span>
<span style="font-family: "verdana" , sans-serif;">The </span><span style="font-family: "verdana" , sans-serif;"><b><a href="http://www.cs.cityu.edu.hk/~cheewtan/sc/" target="_blank">Claude Shannon Centenary 2016 in Hong Kong</a></b> is a series of events held in Hong Kong to mark the life and legacy of <a href="https://en.wikipedia.org/wiki/Claude_Shannon">Claude Shannon</a></span><span style="font-family: "verdana" , sans-serif;">, an American mathematician and engineer, who was a visionary pioneer in the fields of computing, communications and artificial intelligence. </span><span style="font-family: "verdana" , sans-serif;">I chaired a seminar </span><span style="font-family: "verdana" , sans-serif;">on quantum information theory </span><span style="font-family: "verdana" , sans-serif;">given by t</span><span style="font-family: "verdana" , sans-serif;">he 2016 <a href="https://en.wikipedia.org/wiki/Alexander_Holevo" target="_blank">Shannon Award Lecturer Alexander Holevo</a> on May 6th. </span><span style="font-family: "verdana" , sans-serif;">A Claude Shannon Centenary workshop was also organised </span><span style="font-family: "verdana" , sans-serif;">on May 19th </span><span style="font-family: "verdana" , sans-serif;">by Professor Raymond Yeung at the CUHK Institute of Network Coding, where </span><span style="font-family: "verdana" , sans-serif;">I gave a talk titled "</span><i style="font-family: verdana, sans-serif;">To prove or to disprove: information inequalities and sparse optimization</i><span style="font-family: "verdana" , sans-serif;">". </span><br />
<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">I also delivered this as an invited talk at Tsinghua University in Beijing on May 14th ("纪念</span><span style="background-color: white; font-family: "verdana" , sans-serif; font-size: 16px;">Shannon诞辰一百周年学术论坛"</span><span style="font-family: "verdana" , sans-serif;">). My talk was on the automated generation of mathematical proof </span><span style="font-family: "verdana" , sans-serif;">to Shannon-type inequalities in information theory </span><span style="font-family: "verdana" , sans-serif;">using linear programming and cloud computing. Fancy that! A topic that would be impossible without </span><a href="https://en.wikipedia.org/wiki/A_Symbolic_Analysis_of_Relay_and_Switching_Circuits" style="font-family: verdana, sans-serif;">Shannon's Master thesis</a><span style="font-family: "verdana" , sans-serif;"> that engendered the birth of digital logic in 1938 and his </span><a href="https://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication" style="font-family: verdana, sans-serif;">seminal work on information theory</a><span style="font-family: "verdana" , sans-serif;"> in 1948, and these two seemingly-disparate subjects converge!</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkEXSLor_Wu_NQ1hBHsVL-IGp4HBRNssAD5VhohkybpVPXu3BFs91gf-BGJCgGRBLrvEipR0nlb2lH7ElJDEIQydLlkc-68FcuVz-gCW0QKdjzk1lZe0tD2i7LMOTJ6pJA8M24nqwml2Rx/s1600/13293332_10153778839777893_1579135062_n.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkEXSLor_Wu_NQ1hBHsVL-IGp4HBRNssAD5VhohkybpVPXu3BFs91gf-BGJCgGRBLrvEipR0nlb2lH7ElJDEIQydLlkc-68FcuVz-gCW0QKdjzk1lZe0tD2i7LMOTJ6pJA8M24nqwml2Rx/s200/13293332_10153778839777893_1579135062_n.jpg" width="200" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtknrps1uTwq0GLlpyIYAU2lYMD47DIRu2f4H4owN2cPhvSebqQHODK40SF5NHC65FaMSEY5WUp2xlGk_zmh1r7SC201Qhv9Btk-cwZ210zCNJsrzhIKBOvY3gHd_j8BiCBNq60fwPzP5X/s1600/IMG_1374-2.JPG" imageanchor="1" style="display: inline; margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtknrps1uTwq0GLlpyIYAU2lYMD47DIRu2f4H4owN2cPhvSebqQHODK40SF5NHC65FaMSEY5WUp2xlGk_zmh1r7SC201Qhv9Btk-cwZ210zCNJsrzhIKBOvY3gHd_j8BiCBNq60fwPzP5X/s200/IMG_1374-2.JPG" width="200" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAT_WbSVqgx1Kzx_XBzUHYuiAmUCDLFlahWJxzWlw-ft46_APrvuDrj9o80jgB81XGl3fVrBJw1quNzrljbN5ZbV5fSWhucEejDVlfrhqN09bz0L8TWSXLCjaS6Txy_HH0N38vCeNgwss7/s1600/IMG_1377.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAT_WbSVqgx1Kzx_XBzUHYuiAmUCDLFlahWJxzWlw-ft46_APrvuDrj9o80jgB81XGl3fVrBJw1quNzrljbN5ZbV5fSWhucEejDVlfrhqN09bz0L8TWSXLCjaS6Txy_HH0N38vCeNgwss7/s200/IMG_1377.JPG" width="200" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUdkHNSVzuUEpXNR3HV1gx2dLiWGFFCJEK9zQfSfqEszUJTi-gPWEa3FVDX1pyHNtuLr6-MJJYZH5x0bJyfAWauQ-QDXTgIOh32hdC8_2eIT00_lowyou-TtSsY2haehCKlYHDS99tqips/s1600/IMG_1381-2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUdkHNSVzuUEpXNR3HV1gx2dLiWGFFCJEK9zQfSfqEszUJTi-gPWEa3FVDX1pyHNtuLr6-MJJYZH5x0bJyfAWauQ-QDXTgIOh32hdC8_2eIT00_lowyou-TtSsY2haehCKlYHDS99tqips/s200/IMG_1381-2.JPG" width="200" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">A local outreach activity <b><a href="http://cschallenge.io/">Computer Science Challenge</a></b> was held on 21 May at the City University of Hong Kong for 180 middle school children (62 upper primary and 118 secondary school students) who formed teams to compete in three digital game </span><span style="font-family: "verdana" , sans-serif;">challenges. </span><span style="font-family: "verdana" , sans-serif;">The CS Challenge is part of the <a href="http://www.cs.cityu.edu.hk/~cheewtan/sc" target="_blank"><b>Claude Shannon Centenary, 2016 Hong Kong</b></a>. </span><span style="font-family: "verdana" , sans-serif;">During the CS Challenge, educational exhibits of Claude Shannon and replicates of his fun and thought-provoking robotic machines </span><span style="font-family: "verdana" , sans-serif;">—</span><span style="font-family: "verdana" , sans-serif;">Rubik-cube manipulators using Lego — were also on display</span><span style="font-family: "verdana" , sans-serif;">. </span><br />
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<span style="font-family: "verdana" , sans-serif;">One of the CS Challenge's tasks was to program a robot to solve a maze. This was inspired by </span><span style="font-family: "verdana" , sans-serif;">Shannon's <a href="http://techchannel.att.com/play-video.cfm/2010/3/16/In-Their-Own-Words-Claude-Shannon-Demonstrates-Machine-Learning" target="_blank">Maze-solving Theseus Mouse</a>, which was the world's </span><span style="font-family: "verdana" , sans-serif;">first digitally-programmed maze-solver </span><span style="font-family: "verdana" , sans-serif;">in 1951. Shannon's Theseus Mouse ushered in the age of machine intelligence when a computer (using telephone relays) is capable of searching for a solution by trial and error and then remembering the solution. It was also Shannon's Theseus Mouse that inspired <a href="http://ethw.org/Oral-History:Paul_Baran" target="_blank">Paul Baran, the Internet pioneer</a> </span><span style="font-family: "verdana" , sans-serif;">to come up with the </span><a href="http://insight.ieeeusa.org/insight/content/views/303552" style="font-family: verdana, sans-serif;" target="_blank">packet switching principle and dynamic routing</a><span style="font-family: "verdana" , sans-serif;"> underlying our Internet technologies.</span><br />
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<span style="font-family: "verdana" , sans-serif;">The maze in the </span><span style="font-family: "verdana" , sans-serif;">CS Challenge </span><span style="font-family: "verdana" , sans-serif;">for secondary school students was designed with <a href="http://www.science4all.org/article/shannons-information-theory" target="_blank">Shannon's entropy</a> </span><span style="font-family: "verdana" , sans-serif;">—</span><span style="font-family: "verdana" , sans-serif;"> a coin flip decides one of two possible maze entrances, i.e., t</span><span style="font-family: "verdana" , sans-serif;">he robot starts from the left entrance with a Head or otherwise from the right entrance with a Tail. The left and right entrances entail a left and right corner respectively, and the two passages meet at the intersection of a corridor to the exit. Now, a</span><span style="font-family: "verdana" , sans-serif;"> fair coin flip generates <a href="http://www.science4all.org/article/shannons-information-theory" target="_blank">one bit of information</a>. </span><span style="font-family: "verdana" , sans-serif;">In this way, as the coin is flipped only after the robot has been programmed, this 1-bit uncertainty prevents the participants from hard-coding the robot's movement (i.e., no dead reckoning); The robot has to hit an obstacle (i.e., the corner wall) and navigate its way by trial and error. </span><span style="font-family: "verdana" , sans-serif;">We hope that students know about Claude Shannon and his marvellous creations as they bravely enter the Maze as Theseus did. </span><span style="font-family: "verdana" , sans-serif;">Check out </span><a href="http://cschallenge.io/photo-gallery-%E7%9B%B8%E7%89%87/" style="font-family: verdana, sans-serif;">more pictures</a><span style="font-family: "verdana" , sans-serif;"> and the <a href="https://youtu.be/jAP7Os7dqbU" target="_blank">video</a> below on the 1-bit maze. </span><span style="font-family: "verdana" , sans-serif;">What a memorable and a-maze-ingly fun 2016 CS Challenge we had!</span><br />
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<span style="font-family: "verdana" , sans-serif;"><br /></span>Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-19770898653066964772016-02-20T23:11:00.001-08:002020-02-11T19:12:57.182-08:00Gamification for Learning Mathematics<span style="font-family: "verdana" , sans-serif;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiR6u1s14fWaBm-CPZ7pca8DulfxZXhp3TD41x0KwOthF3DidHtm7VI3xKbvXIT21ujuf5TV-vyGJrdFveisi0155vR7z-_H3VEm0kKXE8EKlYmO1JqKEEcbJWoxTvU6J8K8hD821N3Ns8U/s1600/cepie1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: "verdana" , sans-serif;"><img border="0" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiR6u1s14fWaBm-CPZ7pca8DulfxZXhp3TD41x0KwOthF3DidHtm7VI3xKbvXIT21ujuf5TV-vyGJrdFveisi0155vR7z-_H3VEm0kKXE8EKlYmO1JqKEEcbJWoxTvU6J8K8hD821N3Ns8U/s640/cepie1.jpg" width="640" /></span></a></div>
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<span style="font-family: "verdana" , sans-serif;">As seen by the popularity of Whitehouse's push for <a href="https://obamawhitehouse.archives.gov/blog/2016/01/30/computer-science-all" target="_blank">Computer Science For All</a>, gamification has been used very successful to promote basic computational thinking knowledge. There are indeed vast potentials in how gamification can be useful for teaching and learning of K-12 foundational subjects such as mathematics. This is simply because, digital games on a digital computer and ideas of computing (and mathematics) are intimately related. The level of public reception and enthusiasm in the <a href="https://obamawhitehouse.archives.gov/blog/2016/01/30/computer-science-all" target="_blank">Whitehouse's Computer Science for All</a> was reminiscent of the <a href="https://en.wikipedia.org/wiki/Nimrod_(computing)" target="_blank">Nimrod</a> when one of the earliest digital games (<a href="https://en.wikipedia.org/wiki/Nim" target="_blank">Nim</a>) was put into a digital computer and went on a whirlwind roadshow tour in 1951.</span><br />
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<span style="font-family: "verdana" , sans-serif;">Recently, we gave a talk on <i><b><a href="http://www.cityu.edu.hk/cepie/event/Matchimaking_Symposium_2016.pdf" target="_blank">Ed-tech on gamification for learning mathematics</a> </b></i>at a university's entrepreneurship symposium, sharing with the audience our <a href="http://www.algebragamification.com/" target="_blank"><b>Algebra Game</b></a> software and the idea of a <b>Mathematics Gamification Foundry</b>. This Gamification Foundry is a cloud-based data analytics platform that can serve as a new two-way educational technology in the era of personalized learning.</span><br />
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<span style="font-family: "verdana" , sans-serif;">With this Gamification Foundry, student players can:</span><br />
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<li><span style="font-family: "verdana" , sans-serif;">learn mathematics by playing brilliantly-crafted games.</span></li>
<li><span style="font-family: "verdana" , sans-serif;">“see” under the hood of the games and even remix them to create game variants to enhance problem-solving skills and computational thinking.</span></li>
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<span style="font-family: "verdana" , sans-serif;">Teachers are always in the loop. Educators can gain insights to these learning processes that can be analysed by big data analytics. Insights gained from students' online game-playing can be integrated with classroom teaching, and dedicated reports can be automatically generated for school teachers and parents. We are engineering this gamification foundry as a personalized way to learn mathematics and computer science. </span><br />
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<span style="font-family: "verdana" , sans-serif;">Beyond enhancing numeracy and computational thinking skills, we also hope to explore whether our <a href="http://www.algebragamification.com/" target="_blank"><b>Algebra Game</b></a> software can be useful to children with dyscalculia – a math disability in learning or comprehending arithmetic (estimated to be one in twenty). It was suggested that computer games can diagnose and treat dyscalculia in a recent Nature article <a href="http://www.nature.com/news/dyscalculia-number-games-1.12153" target="_blank">Dyscalculia: Number games, Nature 493, 150–153 (10 January 2013)</a>.</span><br />
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Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-49838444154610524452016-01-02T06:51:00.000-08:002017-03-07T18:18:40.254-08:00Oh Hooray! Another Hour of Algebra (OHAHOA)<span style="font-family: "verdana" , sans-serif;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGaj2wqgaryuoQb8Z8lDZV5nj2UsP9Zrm0TgQfnhbX6w33eODuR7kDxCAB3-RIGFBV-DEuxt2-csSD1kIKnUNMZ20oSd2gMcF51EtdX5vj-kKoP0jHkUhBhlyc1lEGQeUhpyzEl5Mo0IcJ/s1600/PC170090.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: "verdana" , sans-serif;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGaj2wqgaryuoQb8Z8lDZV5nj2UsP9Zrm0TgQfnhbX6w33eODuR7kDxCAB3-RIGFBV-DEuxt2-csSD1kIKnUNMZ20oSd2gMcF51EtdX5vj-kKoP0jHkUhBhlyc1lEGQeUhpyzEl5Mo0IcJ/s640/PC170090.JPG" width="640" /></span></a></div>
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<span style="font-family: "verdana" , sans-serif;">We celebrated the first <b>OHAHOA Day</b> in December 2015 during the Hour of Code Week at a primary school in Hong Kong. While the children gets to learn some very basic ideas of computer, we had a play-testing trial of the <a href="http://www.algebragamification.com/" target="_blank">Algebra Maze game</a> for a hundred and fifty Year-3 primary school students (2nd Grade in the US school system) as they not only had an hour of computer but merrily "<b>Oh Hooray! Another Hour of Algebra (OHAHOA)</b>" <a href="https://www.facebook.com/algebragame" target="_blank">playing our Algebra Maze game</a> (Facebook photos)!</span><br />
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<span style="font-family: "verdana" , sans-serif;">OHAHOA is a <a href="http://acronyms.thefreedictionary.com/OHAHOA" target="_blank">wickedly funny mnemonic</a> for remembering three formulas in trigonometry. The monograph "<a href="http://www.cambridge.org/hk/academic/subjects/mathematics/recreational-mathematics/twenty-years-blackboard?format=PB&isbn=9780883855256" target="_blank">Twenty Years Before the Blackboard</a>" contains some remarkably funny ones of OHAHOA:</span><br />
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<span style="font-family: "verdana" , sans-serif;">- <b>O</b>h <b>h</b>eck! <b>a</b>nother <b>h</b>our <b>o</b>f <b>a</b>lgebra (that dates back to 1972 in the Dictionary of Mnemonics)</span><br />
<span style="font-family: "verdana" , sans-serif;">- Some <b>o</b>f <b>h</b>er children <b>a</b>re <b>h</b>aving trouble <b>o</b>ver <b>a</b>lgebra (that dates back to pre-1968)</span><br />
<span style="font-family: "verdana" , sans-serif;">- Sin - <b>oh</b>! Cos - <b>ah</b>! Tan - <b>o</b>h/<b>a</b>h! (1928)</span><br />
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<span style="font-family: "verdana" , sans-serif;">All these, especially the first one, express a deep sense of frustration in learning mathematics. We hope that OHAHOA Day will evolve into multi-pronged learning: Learning to use a computer to learn mathematics. We want to turn frustration into fun.</span>Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-48990084816802480042015-10-03T22:42:00.001-07:002020-02-11T22:17:46.984-08:00Starting Up our Algebra Game<span style="background-color: white; font-family: "verdana" , sans-serif;">
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<span style="background-color: white; font-family: "verdana" , sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-Yq4IwAWTz298wzHAwv3kAImP9K96aqHq533ozdzfggV_AoK1s8cRbsrJD0UpydlU8jG6XRYCeQEwJRv00Vo3d7G4XZlg_Tv4RFN87_wfzTk_9p1D4_7nJ3BzTgP60OtvV8jQCoL2jP9O/s1600/poster-1%255B1%255D.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="436" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-Yq4IwAWTz298wzHAwv3kAImP9K96aqHq533ozdzfggV_AoK1s8cRbsrJD0UpydlU8jG6XRYCeQEwJRv00Vo3d7G4XZlg_Tv4RFN87_wfzTk_9p1D4_7nJ3BzTgP60OtvV8jQCoL2jP9O/s640/poster-1%255B1%255D.png" width="640" /></a></span></div>
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<span style="background-color: white; font-family: "verdana" , sans-serif;">Software is eating the world. Yet, it is a marvel of how readily the younger generation eats up software like Angry Bird, Storybird, Youtube, mobile app games etc.</span><br />
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<span style="background-color: white;">We have learned an enormous insight to the <a href="http://algebragame.blogspot.hk/2015/07/terence-taos-algebra-game.html" target="_blank">Terence Tao's algebra game</a> and want to make this fun game accessible to more people especially the younger generation. </span></span><span style="background-color: white; font-family: "verdana" , sans-serif;"><span style="background-color: white;">In the next few months, as we launch some of the mobile app software revolving around the <b><a href="http://www.algebragamification.com/" target="_blank">Algebra Game</a></b>, I hope that this is one small step towards developing learning technologies that make an impact no matter how small. T</span></span><span style="background-color: white; font-family: "verdana" , sans-serif;">o make </span><i style="background-color: white; font-family: verdana, sans-serif;"><a href="http://www.engineeringchallenges.org/challenges/learning.aspx" target="_blank">Advance Personalized Learning</a></i><span style="background-color: white; font-family: "verdana" , sans-serif;"> at scale possible,</span><span style="background-color: white; font-family: "verdana" , sans-serif;"><span style="background-color: white;"> we want </span></span><span style="background-color: white; font-family: "verdana" , sans-serif;"><span style="background-color: white;">to make learning mathematics and computer science a cool thing for everyone. </span></span><br />
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<span style="font-family: "verdana" , sans-serif;"><span style="background-color: white;">Check us out </span></span><span style="font-family: "verdana" , sans-serif;">at </span><a href="http://www.algebragamification.com/" style="font-family: Verdana, sans-serif;">http://www.algebragamification.com</a><span style="font-family: "verdana" , sans-serif;">. </span><span style="background-color: white; font-family: "verdana" , sans-serif;">We will post pictures of our learning endeavours on <a href="https://www.facebook.com/algebragame" target="_blank">our Algebra Game Facebook Page</a> and hope to release more fun software in the future </span><span style="background-color: white; font-family: "verdana" , sans-serif;"> — stay tuned!</span><br />
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</span>Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-48733178100573581642015-07-11T00:19:00.001-07:002020-02-12T17:48:40.221-08:00Terence Tao's Algebra Game<span style="font-family: "verdana" , sans-serif;"><a href="https://www.math.ucla.edu/~tao" target="_blank">Terence Tao</a>, a famous mathematics professor at the UCLA, blogged about various issues on <a href="https://terrytao.wordpress.com/2012/04/15/gamifying-algebra" target="_blank">Gamifying High-School Mathematics</a> in 2012. He also introduced an interesting mathematical puzzle to gamify elementary algebra, i.e., solving a single linear algebra equation with one variable, on his blog.</span><br />
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<span style="font-family: "verdana" , sans-serif;">The idea of Tao's algebra game is to reduce a given linear algebra equation to "x = numerical_solution" through a selection of a finite number of given clues. This algebra game was created using the <a href="http://scratch.mit.edu/" target="_blank">MIT Scratch</a> software tool and can be played <a href="https://scratch.mit.edu/projects/2477436/" target="_blank">here</a> (requires Java). Let's give an example using a screenshot of the game (taken from Tao's blog) as shown below. Initially, the puzzle is the algebra equation "5x + 3 = x + 11" and the given clues are the three possibilities "Subtract 1", "Divide by 2" and "Subtract x". A player chooses one of the possibilities by clicking on the avatar icon. Say, suppose the player chooses "Subtract 1", the algebra equation changes to "5x + 2 = x + 10" (since both sides of the original equation "5x + 3 = x + 11" get subtracted by one).</span><br />
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<span style="font-family: "verdana" , sans-serif;">Of course, one possible "solution" to the puzzle below is the sequence of "Subtract 1" then "Subtract x" then "Divide by 2" then "Subtract 1"and then finally "Divide by 2" to yield "x = 2". A total of five moves to reach the desired state. What matters is not the final value of x (which can be eye-balled easily), rather, it is the inquisitive problem-solving process while playing.</span><br />
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<span style="font-family: "verdana" , sans-serif;">Tao's algebra game is absolutely fun (and some of the higher levels are fairly challenging, even for an adult like me). The benefit is obvious: children learn a real subject (e.g., elementary algebra) while playing. Particularly pleasant is the mathematical depth behind the game. The twelve levels (from easy to hard) in Tao's Scratch mock-up version were <i>cleverly </i>hand-crafted. Yet, there are a few intriguing questions: First, how to engineer the difficulty level of the game automatically? Second, how does a computer (<i>not human player</i>) solve a given puzzle efficiently, i.e., with the fewest number of moves? Third, how to engage the human players in an entertaining manner so that they keep on playing it and, unknowingly, develop a better number sense or mathematical intuition and that such an improvement can be measured?</span><br />
<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Another practical question is the means by which these kind of educational games can be readily deployed on existing computing platforms to reach the target audience players (in this case, the target audience is presumably 8 to 12 years old primary school students, and why not adults? I like playing it too). The <a href="http://scratch.mit.edu/" target="_blank">MIT Scratch</a> software tool is relatively easy (even for 6 years-old) to create games and animations on desktop PC's and laptops, and accessible only through a web browser. If this were a Facebook game, can it reach K12 students since Facebook requires users to be older than 13? If this were a mobile app game, can it reach the target audience who may not have personal mobile devices or audience who only have desktop PC's and laptops?</span>Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-56841401644448617252015-06-26T18:50:00.000-07:002020-02-11T18:46:21.809-08:00Claude Shannon: Centennial and Machines<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiA7HbC6QQI8wXpgQSWhgry2Tg3Mf6Dwf2b-7odN_L3_MXsDZmkyMTjz_DTW4fY7osIIY6QniKUp-NZ011nbx_0LLZqJiD4xK1X9-iagcJCe5WZ0MdyduvW_SL7idIkp1Te4UzI3kryUjrX/s1600/shannon_mouse_lg.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: "verdana" , sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiA7HbC6QQI8wXpgQSWhgry2Tg3Mf6Dwf2b-7odN_L3_MXsDZmkyMTjz_DTW4fY7osIIY6QniKUp-NZ011nbx_0LLZqJiD4xK1X9-iagcJCe5WZ0MdyduvW_SL7idIkp1Te4UzI3kryUjrX/s1600/shannon_mouse_lg.jpg" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: "verdana" , sans-serif;">Claude Shannon and his electromechanical mouse Theseus. Retrieved from http://www.kerryr.net/pioneers/gallery/ns_shannon5.htm</span></td></tr>
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<a href="https://en.wikipedia.org/wiki/Claude_Shannon" target="_blank">Claude Elwood Shannon</a> (April 30, 1916 – February 24, 2001) was a distinguished American electrical engineer and mathematician who founded the field of Information Theory when he published his landmark paper "A Mathematical Theory of Communication" in 1948. He worked on anti-aircraft and cryptography systems during World War II, and later on had a career at the AT&T Bell Labs and as a Professor at MIT. The MIT Technology Review Magazine ran an article on this <a href="http://www.technologyreview.com/featuredstory/401112/claude-shannon-reluctant-father-of-the-digital-age" target="_blank">Reluntant Father of the Digital Age</a> shortly after his death.</span><br />
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In fact, while Shannon was still a student at MIT, he wrote what has been touted as <i>the Most Important Master's Thesis of the Twentieth Century</i> (putting forward the idea that <i>Boolean algebra</i> can be used for computing). Many technological fields that we know of now (such as the digital revolution, secrecy and cryptography, artificial intelligence, wearable computing) can all be traced back to Shannon's pioneering ideas and work.</span><br />
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Despite all these achievements, Shannon is surprisingly little known. Next year 2016 is <b>Shannon's centenary</b>. To get the public know more about Shannon, the Information Theory Society is on a drive <a href="http://www.itsoc.org/people/bog/bog-meeting-isit-2015-hong-kong/Shannon_Centennial.pdf" target="_blank">to make a movie </a>about this scientific genius of the twentieth century. Incidentally, Shannon did appear in a movie once - back in 1961 - in a MIT Centennial Film called <a href="http://video.mit.edu/watch/the-thinking-machine-1961-mit-centennial-film-6712/" target="_blank">The Thinking Machine</a>. At 50:09 mins of the film, he shared his vision of a <i>future </i><i>machine capable of learning by experience</i>. The Information Theory Society also aims to organize events worldwide to celebrate the Shannon's centenary. </span><br />
<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">I wonder: <i>What <a href="http://www.theguardian.com/science/2014/jun/22/shannon-information-theory" target="_blank">little bits</a> of things can we do to celebrate Shannon's centenary?</i></span><br />
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Worth noting is Shannon's fun-loving and unconventional side: To amuse himself, Shannon created very clever mechanical and electrical toys -- a juggling robot, a flame-throwing trumpet, a maze-solving mouse, a chess-playing machine, a mind-reading machine, a manipulator to solve the Rubik's cube game etc. The <a href="https://en.wikipedia.org/wiki/Useless_machine" target="_blank">Ultimate Machine</a> is another such curiously uncanny toy -- we have one built from a small motor, off-the-shelf electronics and recyclable. See video below.</span><br />
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In a 1987 interview, the Omni Magazine asked Shannon: <i>Do you find it depressing that chess computers are getting so strong? </i></span><br />
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Shannon replied: <i>I am not depressed by it. I am rooting for the machines! I have always been on the machines' side. Ha-ha! </i></span><br />
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<span style="font-family: "verdana" , sans-serif;"><br /></span>Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-17961976332677844242015-06-16T07:46:00.003-07:002016-02-21T19:14:45.103-08:00Googling Arithmetic Limerick<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV89VZ_e3N7vAed6KQ2rQ00MdgZHA8zm9V8Lft5WLBPKmfhGWlOfgvUfaoQ47wj-v_iyhZZkn6Qqs1t_Tm3aQNVurfc5vNIE-Tm2UCwTFBdJugfx7q5-wf1ai5bseyHzsSOq_tNUUaOC-M/s1600/math.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV89VZ_e3N7vAed6KQ2rQ00MdgZHA8zm9V8Lft5WLBPKmfhGWlOfgvUfaoQ47wj-v_iyhZZkn6Qqs1t_Tm3aQNVurfc5vNIE-Tm2UCwTFBdJugfx7q5-wf1ai5bseyHzsSOq_tNUUaOC-M/s1600/math.png" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">While using Google to scour the Internet for poems on arithmetic and algebra, </span><span style="font-family: "verdana" , sans-serif;">I came across the following three limericks. </span><span style="font-family: "verdana" , sans-serif;">The first is similar in spirit to the <a href="http://algebragame.blogspot.hk/2015/05/carrollian-algebra.html" target="_blank">Carroll's poem</a> and the next two are similar to </span><span style="font-family: "verdana" , sans-serif;"><a href="http://algebragame.blogspot.hk/2015/06/diophantus-puzzle.html" target="_blank">Diophantus puzzle</a></span><span style="font-family: "verdana" , sans-serif;"> in my earlier posts. </span><br />
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<span style="font-family: "verdana" , sans-serif;"><a href="https://en.wikipedia.org/wiki/Leigh_Mercer" target="_blank">Leigh Mercer</a>, a noted British wordplay, wrote the following (excerpt from Word Ways, 1980, pp. 36):</span><br />
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<dd style="background-color: white; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;"><span style="line-height: 17.92px;">A dozen, a gross, and a score </span></span></dd><dd style="background-color: white; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;"><span style="line-height: 17.92px;">Plus three times the square root of four </span></span></dd><dd style="background-color: white; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;"><span style="line-height: 17.92px;">Divided by seven </span></span></dd><dd style="background-color: white; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;"><span style="line-height: 17.92px;">Plus five times eleven </span></span></dd><dd style="background-color: white; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;"><span style="line-height: 17.92px;">Is nine squared and not a bit more.</span></span></dd><dd style="background-color: white; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><br /></dd><span style="font-family: "verdana" , sans-serif;">Interestingly, Google's omnipotent search engine can <i>"solve"</i> this limerick automatically by entering the following<i> slightly modified verse</i> into the Google search bar:</span><br />
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<span style="background-color: white; font-family: "verdana" , sans-serif;"><i><b>(a dozen, and a gross, and a score plus three times the square root of four) divided by seven plus five times eleven</b></i></span><br />
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<span style="font-family: "verdana" , sans-serif;">The following two are by <a href="http://www.pleacher.com/" target="_blank">David Pleacher</a>, a retired mathematician:</span><br />
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<span style="font-family: "verdana" , sans-serif;">Said a certain young lady named Gwen </span><br />
<span style="font-family: "verdana" , sans-serif;">of her tally of smitten young men, </span><br />
<span style="font-family: "verdana" , sans-serif;">"One less and three more </span><br />
<span style="font-family: "verdana" , sans-serif;">Divided by four </span><br />
<span style="font-family: "verdana" , sans-serif;">Together give one more than ten." </span><br />
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<span style="font-family: "verdana" , sans-serif;">How many boyfriends had she? Answer <a href="http://www.pleacher.com/mp/mpoetry/limrik1.html" target="_blank">here</a>.</span><br />
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<span style="font-family: "verdana" , sans-serif;">Some freshmen from Trinity Hall </span><br />
<span style="font-family: "verdana" , sans-serif;">Played hockey with a wonderful ball; </span><br />
<span style="font-family: "verdana" , sans-serif;">They found that two times its weight, </span><br />
<span style="font-family: "verdana" , sans-serif;">Plus weight squared, minus eight, </span><br />
<span style="font-family: "verdana" , sans-serif;">Gave "nothing" in ounces at all. </span><br />
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<span style="font-family: "verdana" , sans-serif;">What was the weight of the ball? Answer <a href="http://www.pleacher.com/mp/mpoetry/limrik2.html" target="_blank">here</a>.</span><br />
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Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-67978301441198160442015-06-12T21:27:00.001-07:002020-02-12T23:33:55.532-08:00Learning and Testing<div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2eO-zanRT2NsPl3ZrDzUrbViGrKkRQF6xbYKfvlEZ60BqVM71Vc7k3iK67ZePvmR-Cwh7UjvIf_DHezn1an3LO78gcOrDunMIj2eZ-oFVSgy9ETfWlJ0ue7NcSD7aqEXDd7dJzqdSBOOi/s1600/test.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2eO-zanRT2NsPl3ZrDzUrbViGrKkRQF6xbYKfvlEZ60BqVM71Vc7k3iK67ZePvmR-Cwh7UjvIf_DHezn1an3LO78gcOrDunMIj2eZ-oFVSgy9ETfWlJ0ue7NcSD7aqEXDd7dJzqdSBOOi/s400/test.jpg" width="400" /></a></div>
<span style="font-family: "verdana" , sans-serif;">In many Asian countries, standardized testing is the hallmark of primary and secondary school education. Outside of regular schools, numerous after-school coaching activities, preparation schools and commercial tuition centers thrive in training young students to excel in standardized testing. This is big business - involving enormous education spending in the hope of getting a good enough grade for these </span><span style="font-family: "verdana" , sans-serif;">pressure-cooker standardized </span><span style="font-family: "verdana" , sans-serif;">tests.</span><br />
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<span style="font-family: "verdana" , sans-serif;">In places like Hong Kong and Singapore, </span><span style="font-family: "verdana" , sans-serif;">primary and secondary </span><span style="font-family: "verdana" , sans-serif;">school students </span><span style="font-family: "verdana" , sans-serif;">sit en masse for UK-style standardized exams (O-level, AS-level, A-level). T</span><span style="font-family: "verdana" , sans-serif;">he sense of anxiety and dread often lingers among these students </span><span style="font-family: "verdana" , sans-serif;">in the lead-up to the public exams. </span><span style="font-family: "verdana" , sans-serif;">I</span><span style="font-family: "verdana" , sans-serif;">n the hot summer month of June </span><span style="font-family: "verdana" , sans-serif;">in mainland China, massive number of students travel across the country to sit for the national higher education entrance examination - a high-stakes game - that requires gadgets like </span><span id="goog_27164969" style="font-family: "verdana" , sans-serif;"></span><a href="http://time.com/3914087/china-drones-cheating-exams" style="font-family: Verdana, sans-serif;" target="_blank">multi-rotor drones as invigilators</a><span style="font-family: "verdana" , sans-serif;">.</span><br />
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<span style="font-family: "verdana" , sans-serif;">I recently came across an Edweek article "<a href="http://blogs.edweek.org/edweek/education_futures/2014/09/rethinking_the_emphasis_on_standardized_testing.html" target="_blank">Rethinking the Emphasis on Standardized Testing</a>" on the traditional standardized testing in Asia and how it affected mathematics proficiency and even the lifetime success of a student. The article's author started a </span><span style="font-family: "verdana" , sans-serif;">First-in-Math venture</span><span style="font-family: "verdana" , sans-serif;"> to host math tournaments in the United States to play </span><a href="http://www.4nums.com/" style="font-family: verdana, sans-serif;" target="_blank">24 Game</a><span style="font-family: "verdana" , sans-serif;"> - in fact a card game that originates from China in the 1960's. Have a go at the <a href="http://www.4nums.com/">24 Game</a> to test your reflex and sharpen your mind (The game at </span><span style="font-family: "verdana" , sans-serif;"><a href="http://www.4nums.com/">http://www.4nums.com</a> is free</span><span style="font-family: "verdana" , sans-serif;">)! Public examination and standardized testing</span><span style="font-family: "verdana" , sans-serif;"> in Asia</span><span style="font-family: "verdana" , sans-serif;"> are big business indeed - going by the government spending </span><span style="font-family: verdana, sans-serif;">of 3-4% of GDP </span><span style="font-family: verdana, sans-serif;">on education.</span></div>
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<span style="font-family: "verdana" , sans-serif;">One interesting takeaway from the Edweek article is that:</span><br />
<span style="font-family: "verdana" , sans-serif;"><i>Testing has its place as long as it doesn’t push kids away from a sense of wonder and fascination for the world around them.... </i><i>A far more worthy goal would be to create a system wherein the whole individual is addressed, developed, and encouraged to thrive in the pursuit of a better life. </i></span><br />
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<span style="font-family: "verdana" , sans-serif;">I think this pretty much sums up personalized learning as the next frontier in education. What truly amazing technological innovations can we invent in this quest to <i>advance personalized learning</i>? Will that be a</span><span style="font-family: "verdana" , sans-serif;">n ecosystem of mobile digital tutors, an Internet of peer learning, automated software to individualize learning, learning analytics at scale, smarter interactive computer tests </span><span style="font-family: "verdana" , sans-serif;">driven by </span><span style="font-family: "verdana" , sans-serif;">computational neuroscience</span><span style="font-family: "verdana" , sans-serif;">, AI,</span><span style="font-family: "verdana" , sans-serif;"> cloud computing and machine learning?</span><span style="font-family: "verdana" , sans-serif;"> Or will it be more powerful surveillance drones?</span></div>
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Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-26725603304290241702015-06-01T07:23:00.002-07:002015-12-16T23:21:09.289-08:00Diophantus Puzzle<span style="background-color: white; color: #252525; line-height: 17.92px;"><span style="font-family: "verdana" , sans-serif;">Diophantus was a Greek mathematician whose work laid down important foundation for the development of algebra. Listed on Wikipedia is an interesting <a href="http://en.wikipedia.org/wiki/Diophantus">puzzle</a></span></span><a href="http://en.wikipedia.org/wiki/Diophantus"><span style="background-color: white; color: #252525; font-family: "verdana" , sans-serif; line-height: 17.92px;"> to guess the age of </span><span style="background-color: white; color: #252525; font-family: "verdana" , sans-serif; line-height: 17.92px;">Diophantus</span></a><span style="background-color: white; color: #252525; font-family: "verdana" , sans-serif; line-height: 17.92px;">:</span><br />
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<dl style="background-color: white; color: #252525; line-height: 17.92px; margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;">'Here lies Diophantus,' the wonder behold.</span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;">Through art algebraic, the stone tells how old:</span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;">'God gave him his boyhood one-sixth of his life,</span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;"><br /></span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;">One twelfth more as youth while whiskers grew rife;</span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;">And then yet one-seventh ere marriage begun;</span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;">In five years there came a bouncing new son.</span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;"><br /></span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;">Alas, the dear child of master and sage</span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;">After attaining half the measure of his father's life chill fate took him. </span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;">After consoling his fate by the science of numbers for four years, he ended his life.'</span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span style="font-family: "verdana" , sans-serif;"><br /></span></dd></dl>
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<span style="color: #252525; font-family: "verdana" , sans-serif; line-height: 17.92px;">This Diophantus puzzle has a similar flavor to the <a href="http://algebragame.blogspot.hk/2015/05/carrollian-algebra.html" target="_blank">Carroll's puzzle in my previous post</a>. Here, however, a finite sequence of moves (in fact, events in the timeline) is applied to an unknown - </span><span style="color: #252525; font-family: "verdana" , sans-serif; line-height: 17.92px;">Diophantus's age. </span><br />
<span style="color: #252525; font-family: "verdana" , sans-serif; line-height: 17.92px;">How long did </span><span style="color: #252525; font-family: "verdana" , sans-serif;"><span style="line-height: 17.92px;">Diophantus live</span></span><span style="color: #252525; font-family: "verdana" , sans-serif; line-height: 17.92px;">?</span></div>
Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-15581592519327488882015-05-29T09:20:00.000-07:002015-10-27T20:08:17.140-07:00Carrollian Algebra<div style="padding: 0.6em 0px 0.5em;">
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMqmix_p9TWdlQQ76xsj_QMzbUzaVD-5GFNWZSqf8jzbfFgub_qbxzW5YP9XKAHM1SFRT8Gbw4Flce7MsffW9Rvj_jJA8JdM7weqO_cnLOy94cMj8lGMW2du6NuqrxVKVV3YqC1o_Qmgnf/s1600/86queens.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMqmix_p9TWdlQQ76xsj_QMzbUzaVD-5GFNWZSqf8jzbfFgub_qbxzW5YP9XKAHM1SFRT8Gbw4Flce7MsffW9Rvj_jJA8JdM7weqO_cnLOy94cMj8lGMW2du6NuqrxVKVV3YqC1o_Qmgnf/s1600/86queens.jpg" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: 12.8px;">Alice</span><span style="font-size: 12.8px;"> talking to </span><span style="font-size: 12.8px;">White and Red Queens</span></td></tr>
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;"><i>Alice's Adventures in Wonderland</i> and its sequel <i>Through the Looking Glass</i> are some of the well-known children's classic tales written by <b>Lewis Carroll</b>, whose real name is <i>Charles Lutwidge Dodgson</i>, a mathematics lecturer at Oxford University. </span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">There are various <i>algebra games designs</i> embedded in Carroll's work. </span></span><span style="font-family: Verdana, sans-serif; line-height: 17.54px;">Let's use a few examples to illustrate. </span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">The first example is <b>quiz-based design</b> that comes from an excerpt in <i>Through the Looking Glass</i>, by Lewis Carroll:</span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">'Can you do Addition?' the White Queen asked. 'What's one and one and one and one and one and one and one and one and one and one?'</span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">'I don't know,' said Alice. 'I lost count.'</span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">'She can't do Addition,' the Red Queen interrupted, 'Can you do Subtraction? Take nine from eight.'</span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">'Nine from eight I can't, you know,' Alice replied very readily: 'but—'</span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">'She can't do Subtraction,' said the White Queen. 'Can you do Division? Divide a loaf by a knife—what's the answer to that?'</span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">----</span></span><br />
<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;"><br /></span></span><span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">Both Alice and the reader are entertainingly quizzed by the Queens. Try arguing with arithmetic!</span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">The second example is <b>puzzle-based design</b> that comes from an excerpt in <i>The Hunting of the Snark</i>, by Lewis Carroll: </span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">Taking Three as the subject to reason about --</span></span><br />
<span style="font-family: Verdana, sans-serif; line-height: 17.54px;"> A convenient number to state--</span><br />
<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">We add Seven, and Ten, and then multiply out </span></span><br />
<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;"> By One Thousand diminished by Eight.</span></span><br />
<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;"><br /></span></span>
<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">The result we proceed to divide, as you see, </span></span><br />
<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;"> By Nine Hundred and Ninety and Two:</span></span><br />
<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">Then subtract Seventeen, and the answer must be </span></span><br />
<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;"> Exactly and perfectly true.</span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">----</span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">In a way, the Carroll's puzzle-based design is similar to the <a href="http://dynamicmathclassroom.blogspot.com/2013/06/the-famous-jinx-puzzle.html">Jinx Puzzle</a> introduced by Harold Jacob in his book<i> Elementary Algebra (1979)</i>. </span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">In Carroll's puzzle game, an initial number (can be any and need not be Three) first gets manipulated through a finite sequence of arithmetic moves (the above first stanza) to become another numerical result. A second finite sequence of arithmetic moves (the above second stanza) is then carefully chosen to go from this numerical result back to the initial number. Thus, the two finite sequences are essentially inverse of each other.</span></span><br />
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<span style="line-height: 17.54px;"><span style="font-family: Verdana, sans-serif;">In Jacob's Jinx Puzzle game, an initial number (can be chosen from a few possibilities) goes through a carefully-crafted finite sequence of arithmetic moves to become a particular desired numerical result, giving the impression that <i>All roads lead to Rome</i>.</span></span></div>
Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-63339229890041301702015-05-16T21:50:00.002-07:002020-02-11T22:12:09.920-08:00Exploring Algebra Games<span style="font-family: "verdana" , sans-serif;">Maria Andersen recently wrote a <a href="http://busynessgirl.com/level-up-video-games-for-learning-algebra" target="_blank">blog article with a nicely-made Prezi video</a> giving an overview of existing games out there in the market to learn elementary school algebra.</span><br />
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<span style="font-family: "verdana" , sans-serif;">Many of these games are commercial and they seem to have good and catchy graphics. It seems that most of the game design are primarily quiz-based. There are also a few puzzle-like ones that require players to develop a playing strategy. It will be interesting to think of different game design for learning algebra. </span></div>
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<span style="font-family: "verdana" , sans-serif;">Another observation is that many of these games are mobile apps that run on smartphones or tablets. </span><span style="font-family: "verdana" , sans-serif;">Imagine the super duper ease of getting </span><span style="font-family: "verdana" , sans-serif;">the games</span><span style="font-family: "verdana" , sans-serif;"> off-the-shelf from Google Play and Apple app stores and playing them instantly. </span><span style="font-family: "verdana" , sans-serif;">Mobile app platforms have thus made mathematical games more accessible for many people. </span><span style="font-family: "verdana" , sans-serif;">One wonders the possibility of a math teacher deploying these apps in a real classroom, and how would such math games complement the teaching curriculum? </span><br />
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<span style="font-family: "verdana" , sans-serif;">In the first place, teachers have to vet these games and find one that suits the curriculum. </span><span style="font-family: "verdana" , sans-serif;">Given that teachers are busy, it is not easy to get real statistics or data to show how useful the mobile games are as a teaching aid and whether the students actually learn. But suppose a teacher picks a mobile game, then what game design might attract the teacher <i>and the students</i>? </span><br />
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<span style="font-family: "verdana" , sans-serif;">Quiz-based games in some sense "digitize" the paper-and-pencil approach to working on a fixed set of questions, possibly providing hints in the form of multiple choice. Quiz-based games can certainly be useful for drilling. On the other hand, puzzle-type games are typically harder to design, because it involves the element of strategic thinking. If we can instil in students the idea that learning mathematics is to think strategically, then this can be a more </span><span style="font-family: "verdana" , sans-serif;">efficient way for students to build self-motivation and take on challenging problems as compared to the quiz-based game design.</span></div>
Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0tag:blogger.com,1999:blog-2332072973434908889.post-26914801772924303112015-05-03T08:08:00.001-07:002020-02-11T17:34:51.453-08:00Explorer - The First Step<span style="font-family: "verdana" , sans-serif;">Yes, that's you - you're the explorer.</span><br />
<span style="font-family: "verdana" , sans-serif;">"Explorer?"</span><br />
<span style="font-family: "verdana" , sans-serif;">[ From the Preface: <a href="https://www.artofmathematics.org/books/games-and-puzzles">Games & Puzzles, Discovering the Art of Mathematics</a> by V. Ecke and C. von Renesse with J. F. Fleron and P. K. Hotchkiss, 2015 ]</span><br />
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<span style="font-family: "verdana" , sans-serif;">In 2008, the National Academy of Engineering (NAE) made <a href="http://engineeringchallenges.org/9127.aspx">Advance Personalized Learning</a> as one of the fourteen grand challenges for engineering in the 21st century. Since then we have witnessed the emergence of amazing technologies for learning such as mobile tech, MOOC, flipped classroom, social learning networks, Youtube, gamification, .... Everyone learns mathematics differently. Can a math teacher cater to the different learning style of each and every student?</span><br />
<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Perhaps, we can start by teaching children, K12 students and even adults to see mathematics as not just arithmetic or algebra. Mathematical skills and knowledge can be shaped </span><span style="font-family: "verdana" , sans-serif;">through playing. </span><span style="font-family: "verdana" , sans-serif;">This is the journey to explore the less trodden paths of </span><span style="font-family: "verdana" , sans-serif;">personalized </span><span style="font-family: "verdana" , sans-serif;">learning</span><span style="font-family: "verdana" , sans-serif;"> through</span><span style="font-family: "verdana" , sans-serif;"> innovations in </span><span style="font-family: "verdana" , sans-serif;">computer science.</span>Algebra Gamehttp://www.blogger.com/profile/00099090203216489094noreply@blogger.com0