Alternative math is a short film in black comedy genre about mathematics and how some people want to change it to resolve their weakness in math. but it doesn’t work, do you want to know why? watch the movie:
Adapted from LinkedIn page of Jonathan J. Crabtree (Mathematics Historian: The Lost Logic of Elementary Mathematics)
(If you care, please share!)
In November I will be presenting a series of free presentations in Kolkata to relaunch Indian mathematics. You see, what young mathematics students get taught today is fundamentally flawed! Only by recompiling modern mathematics via Indian Laws and Logic will we ever truly understand mathematics. Alas, the elementary school mathematics pedagogies taught today are derived from 16th Century English mathematics, which in turn was based on a bad translation of ancient Greek mathematics. Just two digits are required to power all modern computation, 0 and 1. Yet the Greeks did not consider 1 a number and their mathematics had no concept of 0 or negative numbers. Thus, began an evolution of mathematics education that required constant and unnecessary workarounds, corrections and rules.
The sense of Brahmagupta’s laws of mathematics was never seen as the English exported their mathematical non-sense throughout their colonies and settlements of the British Empire. Had Indian laws and logic, rather than Greek mathematics been the starting point as the West transitioned from Roman Numerals to the numbers we use today, who knows, we might have cured cancer and colonised Mars by now! So, read on to discover a little about me and my quest to change mathematics and unlock its pure power and beauty; starting in India, for free, this November!
Fifty years ago, in 1968, I noticed the way we think about mathematics was wrong. Today, my area of research involves explaining how the rules and laws of mathematics taught in schools often lead to contradictions and paradoxes. Elementary mathematics SHOULD be intuitive and built upon a series of common sense insights – yet it isn’t.
Thirty-five years ago, in 1983, I set myself the goal of changing the way the western world teaches mathematics. Having studied economics at the University of Melbourne, I knew about the folly of making assumptions. No, we can’t assume either perfect market information, or that rational decisions are always made. People usually do NOT have all the information required to make a decision and people often make an irrational decision.
Unfortunately, mathematics educators have NOT had all the information they require to convey the intuitive beauty inherent in mathematics (that seamlessly connects to the physical world) and neither have they behaved rationally. To teach the same confusing mathematics lessons for centuries and keep expecting different results is NOT rational behaviour.
Notably, I failed mathematics at school and even repeated a year because of that fact. Yet, in 1984, a recruitment firm had me tested by psychologists to see if I would be a suitable employee for a management consulting firm. Yes, I got the job, yet I also got a shock! Upon resigning (to become a mathematics tutor), I was given a copy of my psychological appraisal. I had quit my management consulting career to teach children maths in a way that I thought was better than what I had been exposed to at school. Yes, I know that seems absurd, yet the test results in my hand revealed that I was in the top 1 percent of the population for mechanical reasoning and verbal logic! I had long felt stupid because I had once been really bad at mathematics, yet I did very clever analysis with numbers that the partners of the firm I worked at complimented.
Like many people seeking easy answers, I first turned to Vedic Mathematics. From Wikipedia, we read:
” Vedic Mathematics is a book written by the Indian monk Swami Bharati Krishna Tirtha and first published in 1965. It contains a list of mental calculation techniques claimed to be based on the Vedas. The mental calculation system mentioned in the book is also known by the same name or as “Vedic Maths”. Its characterization as “Vedic” mathematics has been criticized by academics, who have also opposed its inclusion in the Indian school curriculum.
Whilst there are some good mathematical shortcuts to be found in Vedic Mathematics for those interested in high-speed mental calculation, I eventually came to the conclusion (20 years later) that Vedic Mathematics is NOT Indian mathematics. (It is exactly what it is, the mathematics of Swami Bharati Krishna Tirtha.) After looking into the Trachtenberg Speed System of Mathematics, I was able to mentally multiply two 10-digit numbers on a blackboard to arrive at the 20-digit answer (with no visible workings) in a little over two minutes. Yet, my first few years attempting to fix mathematics were really a total waste of time. I was focussed on calculations, not concepts.
I had investigated many high-speed calculation books and ‘short-cut’ books, yet they all required more memorisation and meaning was missing. To be honest, it was only when I began investigating the history of mathematics, that I began to realise where mathematical ideas had been both formed and deformed.
Last year I made a bold decision. I would present some of my research, not to school teachers as I had previously been doing, but to a European audience comprised mostly of mathematics education professors and university department heads. My presentation, in effect, was an argument that many if not most mathematical foundations taken for granted by the eminent and expert mathematical audience, were in fact, false!
Despite my cheek having dared inform an audience of mathematics education professors that they did NOT understand elementary mathematics, my paper and presentation were gratefully received. Later, in a post-conference email to around 2000 mathematics educators, the organiser of the mathematics education conference* specifically thanked me for my paper and presentation.
Mathematics educators have the WRONG idea of multiplication. Mathematics educators have the WRONG idea of division. Mathematics educators have the WRONG idea of exponents. Mathematics educators have WRONG ideas of integer inequalities. Mathematics educators have WRONG ideas of negative numbers and Mathematics educators have WRONG ideas about introducing zero. For all the bad ideas in modern mathematics education, it’s a tribute to the human spirit that so many went so far in science with such a bad introduction to mathematics.
Why Indian School Teachers MUST attend a free presentation?
The great tragedy is, that despite India’s gift of zero as a number to the world, Indian mathematics education recently ranked second last out of 74 countries. I believe that only by teaching mathematics correctly, via the initial elementary ideas of Brahmagupta that I have spent years refining and extending, will India ever begin to transform into the prosperous powerhouse it deserves to be. Children deserve every chance to succeed in life and the keys of mathematics mastery open more doors than any other.
NEXT ARTICLE AT
I have only new information and ideas to share. I will not ask attendees to pay me money at any stage. All I ask is for you to open your mind to the new ideas my research has unlocked, so that you may join me in my quest to improve mathematics education in India.
For more information, please follow me here on LinkedIn or at https://twitter.com/jcrabtree
(If you care, please click like and share!)
Jonathan J Crabtree (Elementary Mathematics Historian, Melbourne Australia.)
* Dr. Alan Rogerson. D.Phil (Oxon), M.Sc., B.Sc., B.A. (Lon), Dip.Ed., Cert. Ed. (Cantab). Co-ordinator of the Mathematics Education for the Future Project
We talked about calculus two post ago in this blog and how it is both beautiful and vital for contemporary science and technology. Now I have decided to publish calculus problems regularly, not necessarily daily based. The reason that each problem is chosen is because it is learning us something.
So let’s begin with #1 problem:
From: Mathematical Institute of Oxford University
We are very sorry to hear of the death of Michael Atiyah. Michael was a giant of mathematics. He held many positions including Savilian Professor of Geometry here in Oxford, President of the Royal Society, Master of Trinity College, Cambridge, the founding Directorship of the Isaac Newton Institute and Chancellor of the University of Leicester. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004. Continue reading “Michael Atiyah 1929-2019”
Calculus has been always interesting for each of us in mathematics. No matter how advanced your field of research is, no matter how many years you have worked on different parts of mathematics, and even no matter how many times you have taught it to first semester students of science and engineering; again it is interesting and it has many different problems that you have never seen them before. Almost every mathematician has wrote a book or has had this idea to write a book on the subject. It may be the only part of mathematics with this amount of textbooks. Who can be so dare to claim that he could even review all of them in his lifetime? Continue reading “Calculus, oh dear calculus!”
As some of you may know, I have another blog in blogspot.com, in which is older than this blog. I have decided to publish “only math” contents here in this blog. All my other daily notes will be published in my blogger blog:
Thank you all in advance because of you attention.
How a corrosive culture keeps women out of leadership positions on math
As soon as mathematician Chad Topaz ripped the plastic off his copy of the American Mathematical Society’s magazine Notices, he was disappointed. Staring back at him from the cover were the faces of 13 of his fellow mathematicians—all of them men, and the majority of them white. “Highlighting all this maleness and whiteness—what is the message that is being sent to the membership?” he wondered. Continue reading “Why Are There So Few Women Mathematicians?”
For two millennia, Euclid’s Elements, the foundational ancient work on geometry by the famed Greek mathematician, was required reading for educated people. (The “classically educated” read them in the original Greek.) The influence of the Elements in philosophy and mathematics cannot be overstated; so inspiring are Euclid’s proofs and axioms that Edna St. Vincent Millay wrote a sonnet in his honor. But over time, Euclid’s principles were streamlined into textbooks, and the Elements was read less and less. Continue reading “A Beautifully-Designed Edition of Euclid’s Elements from 1847 Gets Digitized: Explore the New Online, Interactive Reproduction”
Le dernier séminaire Aromaths du semestre aura lieu le mercredi 19 décembre à 14h dans la salle 24-34-207 et sera présenté par Zindine Djadli.
Sujets abordés : courbes dans le plan • courbure • analyse réelle
Le but de l’exposé est de présenter un procédé naturel de déformation des courbes planes. De façon imagée, il s’agit de rendre la courbe moins “courbée” là où elle l’est le plus et de la rendre plus “courbée” là où elle l’est le moins. Grâce à quelques vidéos, on se rendra compte de l’effet obtenu : une courbe convexe se transforme immanquablement en
cercle ! Il est à noter, et ce sera l’un des points abordés dans l’exposé, que ce sont des techniques similaires qui ont permis à Perelman de donner une démonstration de la fameuse conjecture de Poincaré au début des années 2000.
Scientists have created a “map” of odor molecules, which could ultimately be used to predict new scent combinations
The human nose finds it simple to distinguish the aroma of fresh coffee from the stink of rotten eggs, but the underlying biochemistry is complicated. Researchers have now created an olfactory “map”—a geometric model of how molecules combine to produce various scents. This map could inspire a way to predict how people might perceive certain odor combinations and help to drive the development of new fragrances, scientists say. Continue reading “Unraveling the Mathematics of Smell”
Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.
By: Kevin Hartnett https://www.quantamagazine.org
Philip Gibbs is not a professional mathematician. So when he wanted a problem to chew on, he looked for one where even an amateur could make a difference. What he found was a challenge that could drive even the most exacting minds mad. In a paper completed earlier this year, Gibbs achieved a major advance on a 100-year-old question that hinges on the ability to accurately measure area down to the atomic scale. Continue reading “Amateur Mathematician Finds Smallest Universal Cover”
By Perri Klass, M.d.
April 24, 2017
My mother was what we would now call math anxious, if not phobic. My daughter, on the other hand, was a math major, which always left me feeling like the transitional generation, capable of mastering standardized-test math problems and surviving college calculus (it’s one of the pre-med requirements) but never really connecting to the beauty or power of the subject. Continue reading “Fending Off Math Anxiety”
The 10th World Mathematics Invitational (WMI) took place at Yonsei University in Incheon, South Korea Zahra Zavieh, a student at Urmia University northwest Iran, the provincial capital of west Azerbaijan, won a gold medal for Iran, in a competition that brought together the world’s best math students.
the tournament was held in South Korea at the end of July and 54 students took part, with Iran placing 2nd in the tournament with 5 gold, 18 silver and 17 bronze medals, as well as 14 diplomas
In the latest issue of NOTICES of AMS you find an extended article about life and works of Iranian mathematician late Maryam MIRZAKHANI. Here is the link (PDF):
“As mathematicians, we know one of our first rules is no math in public. We want people to think we know how to do it without having to show them we can do it.”
Here we go to have a real surprise, as they say the smoke arise from the big logs. (it is a Persian proverbs showing the importance of experience of elders rather energy of youths)
One of the most important unsolved problems in mathematics may have been solved, retired mathematician Michael Atiyah is set to claim on Monday. In a talk at the Heidelberg Laureate Forum in Germany, Atiyah will present what he refers to as a “simple proof” of the Riemann hypothesis, a problem which has eluded mathematicians for almost 160 years. Continue reading “Famed mathematician claims proof of 160-year-old Riemann hypothesis”
Calculus is almost the most known branch of mathematics in which over the university students in each discipline from economy to physics would face with it during their study at university.
here you will watch a documentary about its roots and the time it was born. It is an excellent scientific video, although it is an old B.B.C production. Generally they are far away pretentious in compare with today’s scientific documentaries, I think. I hope you enjoy the video: Continue reading “The Birth Of Calculus (1986)”
In a report posted online today, Peter Scholze of the University of Bonn and Jakob Stix of Goethe University Frankfurt describe what Stix calls a “serious, unfixable gap” within a mammoth series of papers by Shinichi Mochizuki, a mathematician at Kyoto University who is renowned for his brilliance. Posted online in 2012, Mochizuki’s papers supposedly prove the abc conjecture, one of the most far-reaching problems in number theory.
The fourth video in the Non-linear algebra series is now online!
In this lecture, Mateusz Michałek discusses two fundamental examples of algebraic varieties: linear spaces and Grassmannians.
From nature.com |
An algebra pioneer who faced discrimination deserves wider recognition on the centenary of her namesake theorem.
Emmy Noether was a force in mathematics — and knew it. She was fully confident in her capabilities and ideas. Yet a century on, those ideas, and their contribution to science, often go unnoticed. Most physicists are aware of her fundamental theorem, which puts symmetry at the heart of physical law. But how many know anything of her and her life?
A conference in London this week, the Noether Celebration, hopes to change that. It’s a welcome move. In a world where young scientists look for inspirational female role models, it is hard to think of a more deserving candidate.
Noether was born in 1882 in Erlangen, Germany. Her parents wanted all their children to get doctorates, so although many universities at the time did not formally accept women, she went. After graduation, sexist regulations prevented Noether from getting jobs in academia. Undaunted, for many years she lectured in Erlangen and, from 1915, at the University of Göttingen — often for free.
At the time, that city was the centre of the mathematical world, largely due to the presence of two of its titans — Felix Klein and David Hilbert. But even when Noether was being paid to teach at Göttingen and making her most important contributions, fate and further discrimination intervened: Hitler took power in 1933 and she was fired for being Jewish. She escaped to the United States and taught at Bryn Mawr College in Pennsylvania, until she died in 1935, at the age of just 53.
Noether devoted her career to algebra and came to see it in a striking new light. “All of us like to rely on figures and formulas,” wrote Bartel van der Waerden, her former student, in his obituary of Noether. “She was concerned with concepts only, not with visualization or calculation.”
Noether saw maths as what are now called structures. To her, the characteristics of a structure’s components — be they numbers, polynomials or something else — mattered less than the networks of relations among an entire set of objects. This enabled her to give proofs that applied to more general structures than the original ones, and which revealed unseen connections.
It was a new and elegant approach that changed the face of algebra. And Noether realized that it could influence other parts of maths. One was topology, a field in which “she published half a sentence and has an everlasting effect”, one mathematician wrote. Before Noether, topologists had been counting holes in doughnuts; she brought to bear the full power of her structures to create something called algebraic topology.
The results that Noether published 100 years ago were, for her, a rare foray into physics, in which she was not particularly interested. Albert Einstein had just developed his general theory of relativity, and was struggling to understand how energy fitted into his equations. Hilbert and Klein were working on it, too, and asked Noether for help.
That she did help is an understatement. Noether’s expertise in symmetry led her to discover that the symmetries of a physical system are inextricably linked to physical quantities that are conserved, such as energy. These ideas became known as Noether’s theorem (E. Noether Nachr. d. Ges. d. Wiss. zu Göttingen, Math.-phys. Kl. 1918, 235–257; 1918).
As well as answering a conundrum in general relativity, this theorem became a guiding principle for the discovery of new physical laws. For example, researchers soon realized that the conservation of net electric charge — which can neither be created nor destroyed — is intimately related to the rotational symmetry of a plane around a point. The impact was profound: those who created the standard model of particle physics, and the researchers who attempt to extend it, think in terms of Noether’s symmetries.
Some biographies inaccurately portray Noether as a somewhat helpless genius at the mercy of men’s charitable actions. In reality, she was an assertive personality, recognized leader and the first female plenary speaker at the renowned International Congress of Mathematicians.
The status of women in mathematics and science has improved since Noether’s time, but bias and discrimination remain. Too few leading female mathematicians receive the recognition they deserve. (Only one woman, Maryam Mirzakhani, has received the Fields Medal, and none has won the Abel Prize — the field’s top awards.) Noether is an inspiration: including to UK mathematician Elizabeth Mansfield, who co-organized the London meeting and works on modern extensions of Noether’s work.
We don’t know how many potential Emmy Noethers have been unfairly denied the chance to show their talents. More people should know — and should celebrate — one who changed the scientific world against the odds.
Among all dreadful news we receive every day, which make us feel pain in our hearts, sometimes there are good news that turn the light of hope in my heart. Among them are the good news correspondent to the situation of women of Middle East. The Area is by itself a dilemma and only few people of habitant of the Area really know what is happening here. Women’s situation has deeply changed, although there are so many unseen and ignored rights. I just read this news from Tehran Times and I felt happy. You cannot modernize a society without literate women. You cannot reform the culture and restructure the economy with illiterate women in which are nearly more than the half population of the society:
TEHRAN – Literacy gap between women and men is decreasing in Iran, reaching to 12 percent compared to 40 percent three decades ago.
According to the latest statistics released by the Statistical Center of Iran, in the Iranian calendar year 1395 (March 2016-March 2017), the number of illiterate women was 5,569,035 while the number of illiterate men was 3,226,518.
However, the number of literate women in the same year was 29,753,843 and the number of literate man stood at 32,912,917.
Although the number of literate people, both men and women are equal at Iranian cities, there is a great gap of illiteracy between men and women in rural areas, head of the Literacy Movement Organization Ali Baqerzadeh has said.
Currently there exists about 1,800,000 illiterate women in Iran, he noted, adding that two thirds of illiterate people are women in the world.
A large number of illiterate children below the age of seventeen are depriving from a literate mother, i.e. there exists a direct and meaningful relation between parent’s literacy and children’s lack of education, Baqerzadeh explained.
The diagram of under-three-year-old children’s mortality rate proves that children’s mortality rate has a direct relationship with the education level of mothers, he added.
I just don’t understand the two last paragraphs of the statement: “there exists a direct and meaningful relation between parent’s literacy and children’s lack of education, Baqerzadeh explained. The diagram of under-three-year-old children’s mortality rate proves that children’s mortality rate has a direct relationship with the education level of mothers, he added.”
Why? do you have any idea?
Reference: Tehran Times | September 10, 2018 |
Teachers who coach teams in a mathematical modeling challenge share ideas for helping students develop more confidence.
What does it take to improve student success and interest in math? The Philadelphia-based Society for Industrial and Applied Mathematics (SIAM) asked more than 400 U.S. high school math teachers for their advice related to teaching and learning mathematics.
“The good news is that students can have success in math class with the right effort, attitude, and behavior, regardless of a natural affinity or being ‘good at math,’” said Michelle Montgomery, project director of the MathWorks Math Modeling (M3) Challenge at SIAM. “Using quantitative skills to solve real, open-ended problems by employing the mathematical modeling process is a great way to get started.”
The teachers surveyed were all coaches of student teams that participated in the M3 Challenge, a national, internet-based contest with no registration or participation fees. Thousands of high school juniors and seniors spend a weekend in March coming up with a solution to a real-world problem using mathematical modeling. To add a bit of pressure, when the students download the problem, they have only 14 hours to work on it. The 2018 event was the 13th annual contest.
WHAT THE TEACHERS RECOMMEND
1. Build confidence. More than two-thirds of respondents (68 percent) cited lack of confidence as a problem that prevents their students from succeeding in mathematics.
2. Encourage questioning and make space for curiosity. Sixty-six percent of respondents said their best piece of advice for students looking to do well in math was to not only pay attention in class but also ask for clarification when they need to better understand something.
3. Emphasize conceptual understanding over procedure. Three out of four respondents (75 percent) emphasized that working hard to understand math concepts and when to apply them versus simply memorizing formulas is essential to doing well.
4. Provide authentic problems that increase students’ drive to engage with math. Sixty-three percent of participants pointed to students’ desire, initiative, and motivation to succeed in math as being critical, and the majority of them (80 percent) said that applying math to real-world problems helps increase both student interest and understanding.
5. Share positive attitudes about math. Teachers suggest that parents avoid talking negatively about math, and especially avoid saying that it is hard or useless (74 percent)—instead they should encourage their kids not to give up, and help them find math mentors when they’re not able to answer questions (71 percent).
It’s no coincidence that these teaching practices are a regular part of facilitating math modeling. Through modeling, students tackle relevant, authentic, real-world problems. According to Lauren Tabolinsky, academic program manager at MathWorks, making math relevant for students and careers is the reason MathWorks sponsors the M3 Challenge.
SIAM’s Montgomery adds that “inherent in modeling work are things like motivation, identification of variables that affect the issue (no spoon feeding of data or approaches), gut checking of answers, and justifying solutions offered. The result? Interest and enthusiasm for working a problem, and the understanding that being able to use skills in your math toolbox can provide insight into relevant issues facing communities and the world today.”
For example, the 2018 M3 Challenge problem was called “Better ate than never: Reducing wasted food.” Students addressed an issue identified by the Food and Agriculture Organization of the United Nations: Approximately one-third of all food produced in the world for human consumption every year goes uneaten.
In the first part of the problem, student teams used mathematics to predict whether the food waste in a given state could feed all of the food-insecure people living there. In the second part, teams created a mathematical model that could be used to determine the amount of food waste a household generates in a year based on their traits and habits. They were given four different types of households to consider.
Finally the teams were challenged to make suggestions about how wasted food might be repurposed. They used mathematical modeling to provide insight into which strategies should be adopted to repurpose the maximal amount of food at the minimum cost, and they accounted for the costs and benefits associated with their strategies.
Because such problems are realistic, big, and messy, student teams have plenty of opportunity to make genuine choices about how they want to go about solving them, which mathematical tools they will apply to develop and test their models, and how they will communicate their solution. There’s plenty of work to go around, so all team members can contribute.
If you relate this M3 Challenge modeling problem to the advice from the teacher coaches above, you can see why participation in math modeling competitions as a team sport can help students develop more mathematical confidence, competence, and interest.
Photo from edutopia.com
Jo Boaler, Michaela Epstein and Michelle Fry on Maths Education, and Saudi Arabia’s bold new education reforms
In this month’s Talking Teaching, Sophie Murphy interviews Stanford University’s Jo Boaler who argues that the latest neuroscience explains what she has always argued – that anyone can do maths. Kerry Elliott talks to Michaela Epstein and Michelle Fry about how on-line maths learning is engaging students and producing impressive results. And finally, Maxine discusses the radical educational reforms being undertaken through the extraordinary partnership between the Melbourne Graduate School of Education and Saudi Arabia.
Comment définir le vivant ? Comment la vie est-elle apparue sur Terre ? Y a-t-il d’autres formes de vie dans l’Univers ? Découvrez où en est la recherche sur toutes ces questions dans ce nouveau dossier multimédia de la collection Sagascience du CNRS : Les origines de la vie
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Dans une enquête, M6 met en lumière ce phénomène de prostitution étudiante à travers le témoignage d’une jeune fille et celui d’un “Daddy”. La France compterait 40.000 Sugar Babies, dont plus de 7.000 seraient étudiantes. Continue reading “Sugar Babies : "Un échange jeunesse, corps, sexe et argent", résume un daddy”