# Arama Sonuçları

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## Blog Yazıları (14)

- Christmas Lectures by Royal Institution
Started by Michael Faraday in 1825, and now broadcast on UK national television every year, the CHRISTMAS LECTURES are the UK's flagship science series. The CHRISTMAS LECTURES are repeated in a number of countries across the world like Singapore and Japan. This year's lecture is given by Mathematician Dr Hannah Fry (@FryRsquared) - Secrets and lies: The hidden power of maths. Hannah Fry revealed a hidden layer of maths that now drives everyday life in powerful and surprising ways. Life’s most astonishing miracles can be understood with probability, big data dictates many of the trends we follow, and powerful algorithms secretly influence even our most important life choices. Broadcasted on BBC 4 at 8pm on 26, 27 and 28 December and now on the Youtube. Yesterday the final lecture has been uploaded the RI channel. Part 3: How Can We All Win? The final lecture is about why maths can fail and asks what the limits of maths are. Part 2: How to Bend the Rules It is about how data-gobbling algorithms have taken over our lives and now control almost everything we do without us even realising. Part 1: How to Get Lucky It is about how mathematical thinking and probability can allow us to understand and predict complex systems - even helping us to make our own luck. To watch all the videos by Hannah Fry you can visit her website You can watch the past lectures to catch up with past CHRISTMAS LECTURES in full and for free on RI's online archive. There are three books related with Christmas Lectures - 13 journeys through space and time by Colin Stuart - 11 Explorations into Life on Earth by Helen Scales - 10 Voyages Through the Human Mind by Cat de Lange You can support and donate for the Christmas lectures here Click here for the Royal Institution Youtube Channel

- Quanta Magazine
I would like to introduce you "Quanta Magazine" https://www.quantamagazine.org/ Quanta Magazine is an editorially independent online publication launched by the Simons Foundation to enhance public understanding of science. Why Quanta? Albert Einstein called photons “quanta of light.” Our goal is to “illuminate science.” You can find articles about physics, biology, mathematics as well as the computer science It has been already but with the latest addition to the magazine, it becomes a must-to-read resource for every math-lover. The Map of Mathematics The writers define the map as "From simple starting points — Numbers, Shapes, Change — the map branches out into interwoven tendrils of thought. Follow it, and you’ll understand how prime numbers connect to geometry, how symmetries give a handle on questions of infinity. And although the map is necessarily incomplete — mathematics is too grand to fit into any single map — we hope to give you a flavor for the major questions and controversies that animate the field, as well as the conceptual tools needed to dive in." You will not be able to leave the platform when navigating on this map. Another great math article from the magazine is "Solution: ‘Natural Law and Elegant Math’" addresses Eugene Wigner’s famous article “The Unreasonable Effectiveness of Mathematics in the Natural Sciences and asks if it is that the way nature really works? Since launching as Quanta on July 16, 2013, the magazine has attracted a loyal and rapidly growing audience through its core news features as well as interviews, columns, blog posts, videos, puzzles and podcasts. The magazine’s seven-minute planetarium show, titled “Journey to the Birth of the Solar System,” has been picked up by 14 planetariums and counting. Picture is teken from the article "How Simple Math Can Cover Even the Most Complex Holes" Two Quanta Magazine writers have been recognized for their recent work covering physics and mathematics. Natalie Wolchover, Quanta’s senior physics writer, won the American Institute of Physics’ 2017 Science Communication Award in the articles category for her story “What No New Particles Means for Physics.” Kevin Hartnett, Quanta’s senior math writer, will be featured in The Best Writing on Mathematics 2017 for his feature “A Unified Theory of Randomness.” Have a good read! Do not forget to come back for funmathfan :)

- Adaptive Learning
When Bloom published the two-sigma problem in 1984, he shared two fundamental findings. The first one is that “everyone can achieve” and the second one is “a student taught 1-1 using mastery learning methods performed above 98% (2 standard deviations) better than a student taught in a conventional class setting. These results are not very surprising since the lower teacher to student ratio always leads to better results in learning. On the other hand, providing a private tutor for every student is too expensive and well there is not enough teachers to do that .. So, the question becomes; Is there a way to achieve the 1-1 teaching? Educators all over the world research to find an answer to this 30-year-old problem. Everyone is thinking about if the use of technology in the classroom can solve this problem. Despite all the efforts and progress, technology still has not reach to the level of 1-1 tutoring. What about Artificial Intelligence? Can AI respond the unique needs of each individual by using learning theories, predictive analysis, cognitive science and machine learning? Adaptive Learning is defined as “The field—which uses artificial intelligence to actively tailor content to each individual’s needs—draws upon knowledge domains as diverse as machine learning, cognitive science, predictive analytics, and educational theory—to make this learner-centered vision of education a reality.” Adaptive courses are personalized to each learner. Individuals’ learning paths are determined by learner inputs, such as performance, prior knowledge, and engagement, that drive an adaptive algorithm. Bite-size modules with granular learning objectives are very important for adaptive learning. Granular LOs allow the algorithm to pin-point specific concepts a learner may be struggling with, and then provide immediate remediation to target their specific knowledge gaps. Adaptive Learning uses the mastery-based” learning idea. Learners must achieve proficiency in order to progress and complete the course; learners can spend however long they need to master concepts. Adapting Learning also requires adapting testing. Different types of assessments engage different types of learners. Providing assessments in a variety of formats leverages the available diversity in order to better assess a learner’s mastery of the content. Adaptive testing is figuring out each learner’s proficiency or skill-level in as few questions as possible. Item Response Theory” and “Knowledge Space Theory” are used in both adaptive learning and adaptive testing. HOW IT WORKS? Adaptive learning provides “Individualized mastery-based” learning by using four theories. >> Metacognitive theory (The learners learn best when they know what they don’t know.) >> . Theory of Game Design ( where the idea of levels of the games must be engaging as well as challenging enough so that you continue to work on it but it has to be still archivable so that you cannot loose all the time which means you lose your motivation to continue) >> . Ebbinghaus Forgetting Curve (AI simply decides the number of repetitions you need to put a skill or a knowledge to your long-term memory and it provides that repetition just before you forget something) >> Theory of Deliberate (Deep) Practice. Practice and practice until it become a part of the automaticity. Remember, Erickson claims that it takes 10 000 hours of practice to become an expert on something so it rephrases the belief of “experts are always made, not born”. Intentional focus (practice has to have a specific target) Challenge exceeds skills Immediate feedback Repetition to Automaticity Since modules of the adaptive learning are bite-size, It gives the insight down to the granular level of the each learning objective and how the learner interacts with it. AI can use this data to find out what’s working, what's not, what the patterns are across the group and most importantly, use to optimize each learners path to mastery. Since time is the most valuable asset of us, adaptive learning achieves efficiency in time by showing to each learner only what they need to see at only when they need to see it. Mc Graw Hill is one of the leading publishers becomes a pioneer in adaptive learning with ALEKS. Assessment and LEarning in Knowledge Spaces is a Web-based, artificially intelligent assessment and learning system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. You can try ALEKS by checking the Mc Graw Hills website Overall, I really liked the idea of AI provides individualized mastery-based learning, I have tried to sample adaptive learning module as well, I particularly liked the way it asks the confidence level of the learner at each question. Being able to collect data about accuracy, time spend, and confidence of the learners can give you a great insight to revise your instruction as well. On the other hand, creating bite-size modules by using granular LO's requires a very detailed work and very long time, and I wonder what happens if the task or the problem involves or requires using more than one objective or higher-level objectives. I wonder how you think? Resources: - https://prod-edxapp.edx-cdn.org/assets/courseware/v1/5bd9250eceebea4202f2e042c5e7568b/asset-v1:USMx+LDT200x+3T2019+type@asset+block/Universal_Design_for_Learning.pdf - https://hbr.org/2007/07/the-making-of-an-expert - https://www.mheducation.com/ideas/what-is-adaptive-learning.html.html.html.htm

## Sayfalar (30)

- Blog | MATH FAN
Eda Aydemir The Number of Lattice Squares* There are many puzzles about the number squares you can draw by using the grid points ( lattice points) on a given grid. Here is an... Eda Aydemir Atatürk ve Matematik Bu 10 Kasımda, O'nun fikirlerinin temellerini oluşturan kitaplara bir göz atalım. Eda Aydemir FLEXTANGLES Flextangles are paper models with hidden faces. Flextangles, gizli yüzleri ortaya çıkarmak için esnetilebilen kağıt modellerdir. Eda Aydemir Net of a Sphere, Different Map Projections, Codex Atlanticus, and a Library in Italy We know that it is not possible to draw the net of a sphere like cylinders, cones, or polyhedra. So, how we can represent a 3D sphere on... Eda Aydemir Kürenin Açınımı, Farklı Haritalama Teknikleri ve Milano'da bir kütüphane; Milano'daki Ambrosiana Kütüphanesi, Matematikçiler için kutsal yerlerden bir olabilir. Eda Aydemir Create Your Own Math Clock A blank wall clock turns to a STEM activity with science, history and many different mathematical concepts like fractions, circles, angles, Eda Aydemir Çarpım Tablosunun Resmini Çizelim! Vedic Kareleri & Vedic Kurtçukları ve Spirolaterals Aşağıdaki görsellerin çarpım tablosunun kendisi olduğunu söylesem? Şimdi kendi çarpım... Eda Aydemir Vedic Squares & Vedic Worms, Spirolaterals IDENTIFYING THE PATTERNS OF MULTIPLICATION TABLE Can you draw the picture of the multiplication table? What if I tell you the images... Eda Aydemir Matematik & Sanat; İlhan Koman Sanatı ve matematiği harmanlayarak en etkileyici örneklerini yaratan ünlü heykeltıraşımız İlhan Koman’ın seneye doğumunun 100. yılını... Eda Aydemir Açık Eğitim Hareketi (Open Education Movement & Resources "OER") Eğitimcilerin, öğrencilerinin ihtiyaçlarına göre sürekli olarak hazırladıkları ve yeniledikleri eğitim materyalleri, aktif ders saatleri... Eda Aydemir Matematiğin Peşinde Ekibi Utku Aytaç, Can Ozan Oğuz Eda Aydemir MATH & SCIENCE DAYS TO CELEBRATE Celebrating birthdays of the great mathematicians and scientists as well as the national and global days related with math & science can... Eda Aydemir Profesyonel Gelişim (Professional Development ‘PD’) Funmathfan platformu online olduğundan beri en çok gelen ve en sevindirici mailer, mesleğe yeni adım atacak olan öğretmenlerin, okul... Eda Aydemir 14 Mart Uluslararası Matematik Günü Unesco'nun Kasım 2019'da, Pi günü olarak kutlanan 14 Mart gününü Uluslararası Matematik Günü ilan etmesi ile dünyanın dört bir yanındaki... Eda Aydemir SPIROGRAPH As we all know through play, kids learn different things without even realizing it! Playing with a spirograph, experimenting and trying... Eda Aydemir Adaptive Learning When Bloom published the two-sigma problem in 1984, he shared two fundamental findings. The first one is that “everyone can achieve” and... Eda Aydemir Activities Section of Mathigon Mathigon, one of the best mathematical sources of the web, also has another treasure "activities" In this section, you can find an... Eda Aydemir Virtual STEAM Museums As you all know there are great math, science and technology museums all around the world. I have listed a few of them under the STEAM... Eda Aydemir The Year Game from NCTM As a part of NCTM ’s year-long 100th birthday celebration, they have created a year game for 2020. The Game is how many expressions you... Eda Aydemir Christmas Lectures by Royal Institution Started by Michael Faraday in 1825, and now broadcast on UK national television every year, the CHRISTMAS LECTURES are the UK's flagship... Eda Aydemir Quanta Magazine I would like to introduce you "Quanta Magazine" https://www.quantamagazine.org/ Quanta Magazine is an editorially independent online... Eda Aydemir Secrets of the Surface The world premiere screening of Secrets of the Surface: The Mathematical Vision of Maryam Mirzakhani will take place on Friday, January... Eda Aydemir Math Letters to Parents ✉️ Recently, I have seen a great way of reaching out to parents on mathematical notes via a website called Big Ideas Maths. All of these...

- Online Games | MATH FAN
Online Games and Puzzles with Polypad Single Cuts Square Puzzle Star Wars Battleship LS Star Wars Battleship DS Geomagic Squares Isometric Puzzle Orange Game SUDOKU Magic Squares Hexagon Puzzle Number of Triangles Geomagic Rhombuses Square puzzle Sticky Numbers Geomagic squares 3 Pentomino Pairs HEX Mastermind Game HIP Game

- Lattice Squares | MATH FAN
The Number of Lattice Squares* There are many puzzles about the number squares you can draw by using the grid points ( lattice points) on a given grid. Here is an example ; The correct answer is not 9 (the number of 1x1 squares). There are many other squares you can create using the given points. These hard to catch tilted squares makes these puzzles interesting! Now we have a harder puzzle to work on! What is the total number of squares that can fit into an n x n grid? *Lattice squares are the squares whose vertices are on the grid points. There are two types of lattice squares, grid ones and the tilted ones. Let’s define a "grid square" as a square whose vertices are lattice points and sides are along the axis. (vertical squares). They are easy to create and have square number areas. A "tilted square" is a square whose vertices are still lattice points, but its sides are not along the axis. Tilted squares have whole number areas. The side length of a tilted square can easily be found by using the Pythagorean Theorem. Now, let’s have a look at a 3 x 3 squares and find the total number of grid and tilted squares that can be drawn using the lattice points. The number of grid squares that can be drawn is 9 +4 +1 = 14 Now, let’s find the number of tilted squares The number of tilted squares that can be drawn is 4 + 2 = 6. Then, the total number of lattice squares is 14 + 6 = 20 by using the points of a 3 x 3 grid. One may wonder if there is a short way of finding the number of squares for an n x n square. The questions we need to answer are; The number of grid squares in a n x n square The side length of the biggest tilted square that can be drawn in an n x n square The number of tilted squares in a n x n square The total number of lattice squares in an n x n square. Any relation among the number of tilted squares and grid squares We need to investigate all the possible squares carefully and record our findings systematically to be able to find answers to these questions. Here is a Polypad file you can work on to make drawings; You may need more grids to highlight to create different squares. Good luck! ------ ***------ SOLUTION We can start solving this puzzle by remembering another one! Famous" Checkerboard Puzzle ". The answer of the Checkerboard Problem gives us the number of grid squares. To be able to find the total number of squares on a checkerboard, we need to consider that the board has 2 x 2 squares, 3 x 3 squares, 4 x 4 squares and so on other than 64 unit squares. If we organize our findings in a table. We may easily see that they follow the pattern of square numbers. Number of Grid squares in a n x n square; So for an n x n grid, the number of normal grid squares is simply the sum of the square numbers. One way to express the number of grid squares in an n x n grid is; When it comes to find the number of the tilted squares, we may discover different patterns. If you need an extra help for finding the side lengths of the tilted squares, you may have a look at the Square Areas on Grid Polypad Activity . When we organize the data for the tilted squares, one particular pattern can catch your eye. The number of √2 x √2 squares also follows the pattern of square numbers and so does 2√2 x 2√2 and 3√2 x 3√2 … The other tilted squares with the side lengths √5, √10, √13 … can be tricky to count. Be aware the symmetry of the square can make a different square now! √5 x √5 Example in a 4 x 4 grid square; There are 8 of them. If we have a closer look to 4 x 4 grid square, we see that there are 20 tilted square and 30 grid squares. Now, let’s have a look at the 5x5 case; Now there are 50 tilted squares and 55 grid squares. If you repeat the same steps for a 6 x 6 grid; We see that there are 105 tilted squares. You may realize that; In a n x n grid, the total number of grid squares and tilted squares, is equal to the number of tilted squares in a (n+1)×(n+1) grid. Now, let’s try to figure out the side length of the biggest tilted square that can fit into an n x n grid. Let “c” be the side length of the tilted square in a grid. By Pythagorean theorem a^2+b^2=c^2 and we also know that a+b can be at most n units long. a+b <= n For example in a 5 x 5 grid; you may draw “a+b” can never exceed the value of n. Let’s now try to write the side lengths of the tilted squares which will be added to the list for an 7x 7 grid. Find a + b <=7 the new values will be 6 +1 , 5+2 and 4+3 Now, let’s organize our findings about the tilted squares for each n x n grid; Here you may want to double check your results by comparing the patterns you have discovered before. Try to write the new values for 7x7 One way to express the number of tilted squares in a n x n square So the total number of lattice squares in a n x n grid can be found by These expressions can also prove our previous discovery about the total number of lattice squares in a n x n grid, the number of tilted squares in a (n+1)×(n+1) grid. One of the best outcomes of working on a problem like this is the beauty of the solution ! Extension: Can we derive a formula for the total number of lattice squares in an n x m rectangular grid where n>m?