math

Plaschke: USC senior Jonah Mathews' dream comes true with some March magic

'To end it this way, you can't really ask for anything else,' USC's Jonah Mathews said of his game-winning three-pointer against UCLA on Senior Day.




math

How Peg + Cat can be a math class during coronovirus school closures

During coronavirus school closures PBS offers distance learning on TV and online for students.




math

Dean, Engineering, Math and Physical Sciences

The Dean of Engineering, Math and Physical Sciences is responsible for the leadership, organization and administration of the Division and provides oversight and support for all academic programs in the Division. There are thirteen (13) career programs and six (6) transfer programs housed within the




math

My most favorite math proof ever

Math is beautiful and, sometimes, math becomes even more beautiful with the help of a bit of computer science. My favorite proof of all time combines the two in just such a way. Goal: prove that the cardinality of the … Continue reading




math

New Study Confirms We Were Right: Reading, Math Scores Have Collapsed Thanks to Obama, Common Core

Conservatives had this Common Core thing all wrong, it was said. We’d be proven wrong by history. Common Core, pushed by President Barack Obama, was going to work. It wasn’t like all the other liberal education plans. A new study by the Pioneer Institute reveals that, no, we were right all along. The study, released…

The post New Study Confirms We Were Right: Reading, Math Scores Have Collapsed Thanks to Obama, Common Core appeared first on The Western Journal.




math

Biosecurity: Preparing for the Aftermath of Global Health Crises

9 January 2020

Professor David R Harper CBE

Senior Consulting Fellow, Global Health Programme

Benjamin Wakefield

Research Associate, Global Health Programme
The Ebola outbreak in the Democratic Republic of the Congo is a reminder that the security of samples taken during global health emergencies is a vital part of safeguarding biosecurity.

2020-01-09-DRC.jpg

A nurse prepares a vaccine against Ebola in Goma in August 2019. Photo: Getty Images.

The world’s second-largest Ebola outbreak is ongoing in the Democratic Republic of the Congo (DRC) and experts from around the world have been parachuted in to support the country’s operation to stamp out the outbreak. The signs are encouraging, but we need to remain cautious.

In such emergencies, little thought is usually given to what happens to the body-fluid samples taken during the course of the outbreak after the crisis is over. What gets left behind has considerable implications for global biosecurity.

Having unsecured samples poses the obvious risk of accidental exposures to people who might come into contact with them, but what of the risk of malicious use? Bioterrorists would have ready access to materials that have the characteristics essential to their purpose: the potential to cause disease that is transmissible from person to person, the capacity to result in high fatality rates and, importantly, the ability to cause panic and social disruption at the very mention of them.

Comparisons can be drawn with the significant international impact of the anthrax attacks in the US in 2001. Not only was there a direct effect in the US with five deaths and a further 17 people infected, but there was a paralysis of public health systems in other countries involved in the testing of countless samples from the so-called ‘white-powder incidents’ that followed.

Many laboratory tests were done purely on a precautionary basis to eliminate any possibility of a risk, no matter how remote. However, the UK was also hit when a hoaxer sent envelopes of white powder labelled as anthrax to 15 MPs.

The threat of the pathogen alone resulted in widespread fear, the deployment of officers trained in response to chemical, biological, radiological and nuclear incidents and the evacuation of a hospital emergency department.

We learned from the 2014–16 West Africa Ebola outbreaks that during the emergency, the future biosecurity implications of the many thousands of samples taken from people were given very little consideration. It is impossible to be sure where they all are and whether they have been secured.

It is widely recognized that the systems needed at the time for tracking and monitoring resources, including those necessary for samples, were weak or absent, and this has to be addressed urgently along with other capacity-building initiatives.

In Sierra Leone, for example, the remaining biosecurity risk is only being addressed after the fact. To help achieve this, the government of Canada is in the process of providing a secure biobank in the Sierra Leonean capital of Freetown. The aim is to provide the proper means of storage for these hazardous samples and to allow them to remain in-country, with Sierra Leonean ownership.

However, it is already more three years since the emergency was declared over by the then director-general of the World Health Organization (WHO), Margaret Chan, and the biobank and its associated laboratory are yet to be fully operational.

There are many understandable reasons for this delay, including the critical issue of how best to ensure the sustainability of any new facility. But what is clear is that these solutions take time to implement and must be planned for in advance.

The difficulties of responding to an outbreak in a conflict zone have been well documented, and the frequent violence in DRC has undoubtedly caused delays in controlling the outbreak. According to figures from WHO, during 2019 approximately 390 attacks on health facilities in DRC killed 11 and injured 83 healthcare workers and patients.

Not only does the conflict inhibit the response, but it could also increase the risk posed by unsecured samples. There are two main potential concerns.

First is the risk of accidental release during an attack on a health facility, under which circumstances sample containers may be compromised or destroyed. Second is that the samples may be stolen for malicious use or to sell them to a third-party for malicious use. It is very important in all outbreaks to ensure the necessary measures are in place to secure samples; in conflict-affected areas, this is particularly challenging.

The sooner the samples in the DRC are secured, the sooner this risk to global biosecurity is reduced. And preparations for the next emergency must be made without further delay.

The following steps need to be taken:

  • Affected countries must ‘own’ the problem, with clear national government commitment to take the required actions.
  • Funding partners must coordinate their actions and work closely with the countries to find the best solutions.
  • If samples are to be kept in-country, secure biobanks must be established to contain them.
  • Sustainable infrastructure must be built for samples to be kept secure into the future.
  • An international agreement should be reached on the best approach to take to prepare for the aftermath of global health emergencies.




math

Biosecurity: Preparing for the Aftermath of Global Health Crises

9 January 2020

Professor David R Harper CBE

Senior Consulting Fellow, Global Health Programme

Benjamin Wakefield

Research Associate, Global Health Programme
The Ebola outbreak in the Democratic Republic of the Congo is a reminder that the security of samples taken during global health emergencies is a vital part of safeguarding biosecurity.

2020-01-09-DRC.jpg

A nurse prepares a vaccine against Ebola in Goma in August 2019. Photo: Getty Images.

The world’s second-largest Ebola outbreak is ongoing in the Democratic Republic of the Congo (DRC) and experts from around the world have been parachuted in to support the country’s operation to stamp out the outbreak. The signs are encouraging, but we need to remain cautious.

In such emergencies, little thought is usually given to what happens to the body-fluid samples taken during the course of the outbreak after the crisis is over. What gets left behind has considerable implications for global biosecurity.

Having unsecured samples poses the obvious risk of accidental exposures to people who might come into contact with them, but what of the risk of malicious use? Bioterrorists would have ready access to materials that have the characteristics essential to their purpose: the potential to cause disease that is transmissible from person to person, the capacity to result in high fatality rates and, importantly, the ability to cause panic and social disruption at the very mention of them.

Comparisons can be drawn with the significant international impact of the anthrax attacks in the US in 2001. Not only was there a direct effect in the US with five deaths and a further 17 people infected, but there was a paralysis of public health systems in other countries involved in the testing of countless samples from the so-called ‘white-powder incidents’ that followed.

Many laboratory tests were done purely on a precautionary basis to eliminate any possibility of a risk, no matter how remote. However, the UK was also hit when a hoaxer sent envelopes of white powder labelled as anthrax to 15 MPs.

The threat of the pathogen alone resulted in widespread fear, the deployment of officers trained in response to chemical, biological, radiological and nuclear incidents and the evacuation of a hospital emergency department.

We learned from the 2014–16 West Africa Ebola outbreaks that during the emergency, the future biosecurity implications of the many thousands of samples taken from people were given very little consideration. It is impossible to be sure where they all are and whether they have been secured.

It is widely recognized that the systems needed at the time for tracking and monitoring resources, including those necessary for samples, were weak or absent, and this has to be addressed urgently along with other capacity-building initiatives.

In Sierra Leone, for example, the remaining biosecurity risk is only being addressed after the fact. To help achieve this, the government of Canada is in the process of providing a secure biobank in the Sierra Leonean capital of Freetown. The aim is to provide the proper means of storage for these hazardous samples and to allow them to remain in-country, with Sierra Leonean ownership.

However, it is already more three years since the emergency was declared over by the then director-general of the World Health Organization (WHO), Margaret Chan, and the biobank and its associated laboratory are yet to be fully operational.

There are many understandable reasons for this delay, including the critical issue of how best to ensure the sustainability of any new facility. But what is clear is that these solutions take time to implement and must be planned for in advance.

The difficulties of responding to an outbreak in a conflict zone have been well documented, and the frequent violence in DRC has undoubtedly caused delays in controlling the outbreak. According to figures from WHO, during 2019 approximately 390 attacks on health facilities in DRC killed 11 and injured 83 healthcare workers and patients.

Not only does the conflict inhibit the response, but it could also increase the risk posed by unsecured samples. There are two main potential concerns.

First is the risk of accidental release during an attack on a health facility, under which circumstances sample containers may be compromised or destroyed. Second is that the samples may be stolen for malicious use or to sell them to a third-party for malicious use. It is very important in all outbreaks to ensure the necessary measures are in place to secure samples; in conflict-affected areas, this is particularly challenging.

The sooner the samples in the DRC are secured, the sooner this risk to global biosecurity is reduced. And preparations for the next emergency must be made without further delay.

The following steps need to be taken:

  • Affected countries must ‘own’ the problem, with clear national government commitment to take the required actions.
  • Funding partners must coordinate their actions and work closely with the countries to find the best solutions.
  • If samples are to be kept in-country, secure biobanks must be established to contain them.
  • Sustainable infrastructure must be built for samples to be kept secure into the future.
  • An international agreement should be reached on the best approach to take to prepare for the aftermath of global health emergencies.




math

Working It Out. Math solves a mystery about the opening of "A Hard Day's Night."

The music of most hit songs is pretty well known, but sometimes there are mysteries. One question that remained unanswered for over forty years is: What instrumentation and notes make up the opening chord of the Beatles. "A Hard Day.s Night"? Mathematician Jason Brown - a big Beatles fan - recently solved the puzzle using his musical knowledge and discrete Fourier transforms, mathematical transformations that help decompose signals into their basic parts. These transformations simplify applications ranging from signal processing to multiplying large numbers, so that a researcher doesn.t have to be "working like a dog" to get an answer. Brown is also using mathematics, specifically graph theory, to discover who wrote "In My Life," which both Lennon and McCartney claimed to have written. In his graphs, chords are represented by points that are connected when one chord immediately follows another. When all songs with known authorship are diagrammed, Brown will see which collection of graphs - McCartney.s or Lennon.s - is a better fit for "In My Life." Although it may seem a bit counterintuitive to use mathematics to learn more about a revolutionary band, these analytical methods identify and uncover compositional principles inherent in some of the best Beatles. music. Thus it.s completely natural and rewarding to apply mathematics to the Fab 4 For More Information: Professor Uses Mathematics to Decode Beatles Tunes, "The Wall Street Journal", January 30, 2009..




math

Thinking Outside the Box Score - Math and basketball: Part 1

Muthu Alagappan explains how topology and analytics are bringing a new look to basketball.




math

Making Beautiful Mathematics

Rob Schneiderman talks about the metaphorical connections between math and music




math

Analytic Trends in Mathematical Physics

Houssam Abdul-Rahman, Robert Sims and Amanda Young, editors. American Mathematical Society, 2020, CONM, volume 741, approx. 208 pp. ISBN: 978-1-4704-4841-7 (print), 978-1-4704-5388-6 (online).

This volume contains the proceedings of the Arizona School of Analysis and Mathematical Physics, held from March 5–9, 2018, at the University of...




math

I’m Just Not a Math Person…

We as mathematicians seem practically hell-bent on removing the phrase “I’m just not a math person” from students’ vocabularies. Maybe that’s why they scream it so loudly and defiantly? Math has so many tactical advantages over sports and the arts. … Continue reading




math

Top ways to use free AMS math content




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"Mathematics and the Family Tree of Sars-Cov-2," the May Feature Column by Bill Casselman




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Math in the Media - May 2020:John Conway, "magical mathematician", Topological analysis of zebrafish, teaching online...




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2020 Mathematical Art Exhibition gallery on AMS Mathematical Imagery




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<strong>UPDATED:</strong> Access MathSciNet and other AMS content during COVID-19 closures

updated April 1, 2020

In response to current challenges that colleges and universities face as a result of the spread of COVID-19, the American Mathematical Society is offering libraries and institutions additional support, in line with recommendations in the ICOLC Statement on the Global COVID-19 Pandemic and Its Impact on Library Services and Resources.

The AMS is also participating in the Copyright Clearance Center Education Continuity License program, providing access to our content for distance learning and other educational uses at no cost to the user.

We are extending grace access for content hosted on our platforms (including MathSciNet) through the end of May for our existing customers. We will re-evaluate this timing as needed.

As courses transition to online, we can provide instructors with complimentary electronic “reserve” copies of our textbooks for cases in which students do not have access to their print copies.

E-books purchased through the perpetual access model on the AMS platform are always available DRM-free with unlimited simultaneous use. In addition, we are partnering with ProQuest to allow multi-user access through mid-June to all e-books purchased on their platforms. Read ProQuest’s statement.

We are providing remote access to all our content, including MathSciNet. In normal circumstances, this remote access can be set up while on campus or while connected via institution VPN (in order to validate IP-based access). We realize many students, faculty, and researchers did not have an opportunity to initiate this access before leaving campus, so we have given instructions to our library partners on how patrons can connect to our content. Please contact your librarian for assistance.

Libraries: if you have not received instructions to share with your patrons, please email us at cust-serv@ams.org or be in touch about any other of your library’s needs.

Review all AMS Resources & Updates.




math

European Congress of Mathematics: Krakow, July 2-7, 2012

Rafal Latala, University of Warsaw, Andrzei Rucinski, Adam Mickiewicz University, Pawel Strzelecki, University of Warsaw, Jacek Swiatkowski, University of Wroclaw, and Dariusz Wrzosek and Piotr Zakrzewski, University of Warsaw, Editors - A publication of the European Mathematical Society, 2013, 824 pp., Hardcover, ISBN-13: 978-3-03719-120-0, List: US$128, All AMS Members: US$102.40, EMSEMC/2012

The European Congress of Mathematics, held every four years, has become a well-established major international mathematical event. Following those in...




math

Pearls from a Lost City: The Lvov School of Mathematics

Roman Duda, University of Wroclaw - Translated by Daniel Davies - AMS, 2014, approx. 216 pp., Hardcover, ISBN-13: 978-1-4704-1076-6, List: US$39, All AMS Members: US$31.20, HMATH/40

The fame of the Polish school at Lvov rests with the diverse and fundamental contributions of Polish mathematicians working there during the interwar...




math

Interview with mathematician and book author Kit Yates

"In his new book--The Math of Life & Death: 7 Mathematical Principles that Shape Our Lives--mathematician Kit Yates makes complex mathematical concepts easily accessible to anyone, and which can improve decision making in an increasingly quantitative society. In this Q&A, Yates discusses why math is relevant to everyday life." See "Mathematician Kit Yates on Anti Vaxxer Movement, Air Travel Germs and Samoa's Measles Outbreak," by Meredith Wold Schizer, Newsweek, December 23, 2019.




math

Math Students + Habitat for Humanity build homes

Students in a math class at Columbine High School in Colorado used geometry to work with Habitat for Humanity to build homes for those in need. See the video segment at "Students Build Houses For Families In Need...In Math Class," by Shaun Boyd, CBS4 Denver TV, December 23, 2019.




math

Mathematics from arts?




math

Quanta hosts a new podcast series on mathematics

"[W]hen the editors at Quanta Magazine invited me to host a podcast for them, I jumped at the chance...Through this podcast, I've been learning about the inner lives of some of the most intriguing mathematicians and scientists working today. [I]n every case, I wanted to know what makes them tick. I wanted to know why they do what they do, what they’ve discovered, and why it matters to them and to the world." Read "Why I'm Hosting The Joy of x Podcast," by Steven Strogatz, Quanta Magazine, January 14, 2020.




math

Mathematician Emily Riehl earns President's Frontier Award

Emily Riehl, Johns Hopkins University, received the university's $250,000 President's Frontier Award, whose purpose is to nurture individuals at Johns Hopkins University who are breaking new ground and poised to become leaders in their field. Riehl studies category theory and says that "I just thought the proofs were the most beautiful of any of the other areas I've encountered. ... It was sort of love at first sight and I am lucky to be able to do what I love." The award is considered a "$250,000 investment in doing more of what she loves."

Also see and hear this coverage: "Johns Hopkins Mathematician from B-N [Bloomington-Normal, IL] Breaks Barriers and Wins Research Grant, by Jolie Sherman, WGLT, February 27, 2020.




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2020 Mathematical Art Exhibition Awards

The 2020 Mathematical Art Exhibition Awards were made at the Joint Mathematics Meetings last week "for aesthetically pleasing works that combine mathematics and art." The chosen works were selected from the exhibition of juried works in various media by over 90 mathematicians and artists from around the world.

"Suspended Helical Stair," by Mark Donohue (California College of the Arts, San Francisco, CA), was awarded Best textile, sculpture, or other medium. "A unique cable system to suspend a stair was developed in collaboration with a leading structural engineer. The suspended cables form a double helicoid nested within an ascending spiral hyperboloid to create the necessary points of support for the gravity loads and lateral bracing for the seismic loads. Each concrete stair tread was designed as an independent element that is strung together with the stairs above and below it to form a single spiral stair when the steel cables that run through them are post tensioned. The entire stair tread and suspension cable system can be understood as a play of ruled surfaces with each part related to the other through their shared geometric lineage." The work is string and plywood,45 x 23 x 23 cm, 2018.

2018

"A Unit Domino," by Douglas McKenna (Mathemaesthetics, Inc., Boulder, CO), was awarded Best photograph, painting, or print. "This piece is based upon an artist-discovered "half-domino" space-filling curve. The drawing comprises some half-million connected line segments, arranged in two perfectly recursive levels of double-spiral pairs, slowly changing color, in a single, over-one-mile-long self-avoiding path from lower left to lower right (the lower right square that sticks out is an integral part of its self-negative structure). The limiting curve covers a self-similar gasket tile with an infinitely long, almost-everywhere linear border. With an upside-down copy of itself, two such gaskets of unit area exactly cover a 1x2 domino, without overlap. The artist's app/eBook "Hilbert Curves" for iPad/iPhone explains how he discovered these beautiful constructions." The work is a glicée print,106 x 66 cm, 2015.

"Computational Wings," by David Bachman (Pitzer College, Claremont, CA), received Honorable Mention. "The body of this dragonfly is taken from a photograph, while the wings were computationally generated. A variety of algorithms were used to create them. First, a set of points were randomly populated across each wing and moved by a circle packing algorithm, where the radius of each circle was inversely proportional to the distance from the body. Next, those points were used to create a Voronoi diagram. Main veins were located by a shortest walk algorithm through the edges of this diagram, and those veins were given a variable thickness according to the distance travelled as you traverse them outward from the body." The work is laser etched acrylic, 23 x 35 x 3 cm, 2019.

(Click on the thumbnails to see larger versions of the images.)

The Mathematical Art Exhibition Award "for aesthetically pleasing works that combine mathematics and art" was established in 2008 through an endowment provided to the American Mathematical Society by an anonymous donor who wishes to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form. The awards are $400 for Best photograph, painting, or print; $400 for Best textile, sculpture, or other medium; and $200 for Honorable Mention. The Mathematical Art Exhibition of juried works in various media is held at the annual Joint Mathematics Meetings of the American Mathematical Society (AMS) and Mathematical Association of America (MAA). a gallery of works in the 2020 exhibition will be on AMS Mathematical Imagery.

Find out more about the Mathematical Art Exhibition Award and see past recipients.

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The American Mathematical Society is dedicated to advancing research and connecting the diverse global mathematical community through our publications, meetings and conferences, MathSciNet, professional services, advocacy, and awareness programs.




math

2020 AMS Math Poetry Contest winners

Congratulations to the 2020 AMS Math Poetry Contest Winners in the middle school, high school, and college categories: Sabrina Little, Mackintosh Academy, Boulder, for "Outlier;" Austen Mazenko, Cherry Creek High School, for "The Number Won; and Chenyu Lin, Colorado Christian University, for "x2 + y2 = 1(ife)." The poems were read during Mathemati-Con at the 2020 Joint Mathematics Meetings in Denver, CO. Read the poems and learn about the contest and Math and Poetry. (Photo: (left to right) Austen Mazenko, Sabrina Little, poetry contest judge Gizem Karaali, and Chenyu Lin.




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International study shows Hong Kong students' good performance in reading, mathematical and scientific literacy




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Mathematical light shines blindly on us

By William Yslas Vélez Professor Emeritus University of Arizona “When I go to a Mexican restaurant I would gladly pay the musicians to stop playing.” John (not his real name) did not like the noise level. This statement came up … Continue reading




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A mathematician’s mission statement

By Pamela E. Harris and Julianne Vega Companies and organizations are driven by their mission statements. These mission statements provide a concrete summary of what they value and what they work to achieve. Take for example the following mission statements: … Continue reading




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Mathematical Reviews at JMM 2020 in Denver

Mathematical Reviews will be at the JMM in Denver, January 13-18, 2020. The Joint Mathematical Meetings is the largest gathering of mathematicians in the world.  There are lots of great activities:  invited lectures, special sessions, editorial meetings, exhibits, and the chance to … Continue reading




math

Mathematics and epidemiology

Mathematics is a useful tool in studying the growth of infections in a population, such as what occurs in epidemics.  A simple model is given by a first-order differential equation, the logistic equation, $frac{dx}{dy}=eta x(1-x)$ which is discussed in almost any … Continue reading



  • Mathematics in the news

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A short video about MathSciNet

There is a three-minute video about MathSciNet now available online on Vimeo. It is also available as part of a blog post from EBSCO, which mostly discusses Mathematics and Statistics Awareness Month and the really neat book Living Proof: Stories … Continue reading




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Rammya Mathew: Liquid diets offer promise, but we still need upstream solutions




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What math professors and k-12 teachers think of each other

By Michael Pershan, St. Ann’s School I. What do primary/secondary math educators think of the teaching that happens in colleges? And — the other way around — what do mathematics professors think of primary and secondary math teaching? I’m nearing … Continue reading




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The Future of Enrichment: Math Contests or Math Circles?

by Doug O’Roark Executive Director, Math Circles of Chicago The New York Times recently published an article entitled “The Right Answer? 8,186,699,633,530,061 (An Abacus Makes It Look Almost Easy)”. Its lead photograph features over 100 children seated at desks, facing … Continue reading




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Teaching math in prison

By: Kristin Pfabe, Nebraska Wesleyan University “I am sad this class is going to be over,” said one student. “What am I going to do with myself?” asked another during the last week of an Intermediate Algebra class that I … Continue reading




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A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves

Mary M Tai
Feb 1, 1994; 17:152-154
Short Report




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Spain’s Labor Migration Policies in the Aftermath of Economic Crisis

A relatively new destination for immigrants, Spain has developed a labor migration system that builds on longstanding relationships with countries outside the European Union and that actively involves employers, trade unions, and regional governments. This report examines how this legal framework has evolved in recent decades, and how it could serve as a model for EU policymakers in admitting non-EU workers.




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Mathematics at 2019 SACNAS

Below I share some details about SACNAS and some of the mathematical events that happened at this year’s SACNAS National Conference.  I hope that this may also serve as an invitation/motivation for anyone interested in diversity and mathematics to participate … Continue reading





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Mathematical Metaphors


Theories in all areas of science tell us something about the world. They are images, or models, or representations of reality. Theories tell stories about the world and are often associated with stories about their discovery. Like the story (probably apocryphal) that Newton invented the theory of gravity after an apple fell on his head. Or the story (probably true) that Kekule discovered the cyclical structure of benzene after day-dreaming of a snake seizing its tail. Theories are metaphors that explain reality.

A theory is scientific if it is precise, quantitative, and amenable to being tested. A scientific theory is mathematical. Scientific theories are mathematical metaphors.

A metaphor uses a word or phrase to define or extend or focus the meaning of another word or phrase. For example, "The river of time" is a metaphor. We all know that rivers flow inevitably from high to low ground. The metaphor focuses the concept of time on its inevitable uni-directionality. Metaphors make sense because we understand what they mean. We all know that rivers are wet, but we understand that the metaphor does not mean to imply that time drips, because we understand the words and their context. But on the other hand, a metaphor - in the hands of a creative and imaginative person - might mean something unexpected, and we need to think carefully about what the metaphor does, or might, mean. Mathematical metaphors - scientific models - also focus attention in one direction rather than another, which gives them explanatory and predictive power. Mathematical metaphors can also be interpreted in different and surprising ways.

Some mathematical models are very accurate metaphors. For instance, when Galileo dropped a heavy object from the leaning tower of Pisa, the distance it fell increased in proportion to the square of the elapsed time. Mathematical equations sometimes represent reality quite accurately, but we understand the representation only when the meanings of the mathematical terms are given in words. The meaning of the equation tells us what aspect of reality the model focuses on. Many things happened when Galileo released the object - it rotated, air swirled, friction developed - while the equation focuses on one particular aspect: distance versus time. Likewise, the quadratic equation that relates distance to time can also be used to relate energy to the speed of light, or to relate population growth rate to population size. In Galileo's case the metaphor relates to freely falling objects.

Other models are only approximations. For example, a particular theory describes the build up of mechanical stress around a crack, causing damage in the material. While cracks often have rough or ragged shapes, this important and useful theory assumes the crack is smooth and elliptical. This mathematical metaphor is useful because it focuses the analysis on the radius of curvature of the crack that is critical in determining the concentration of stress.

Not all scientific models are approximations. Some models measure something. For example, in statistical mechanics, the temperature of a material is proportional to the average kinetic energy of the molecules in the material. The temperature, in degrees centigrade, is a global measure of random molecular motion. In economics, the gross domestic product is a measure of the degree of economic activity in the country.

Other models are not approximations or measures of anything, but rather graphical portrayals of a relationship. Consider, for example, the competition among three restaurants: Joe's Easy Diner, McDonald's, and Maxim's de Paris. All three restaurants compete with each other: if you're hungry, you've got to choose. Joe's and McDonald's are close competitors because they both specialize in hamburgers but also have other dishes. They both compete with Maxim's, a really swank and expensive boutique restaurant, but the competition is more remote. To model the competition we might draw a line representing "competition", with each restaurant as a dot on the line. Joe's and McDonald's are close together and far from Maxim's. This line is a mathematical metaphor, representing the proximity (and hence strength) of competition between the three restaurants. The distances between the dots are precise, but what the metaphor means, in terms of the real-world competition between Joe, McDonald, and Maxim, is not so clear. Why a line rather than a plane to refine the "axes" of competition (price and location for instance)? Or maybe a hill to reflect difficulty of access (Joe's is at one location in South Africa, Maxim's has restaurants in Paris, Peking, Tokyo and Shanghai, and McDonald's is just about everywhere). A metaphor emphasizes some aspects while ignoring others. Different mathematical metaphors of the same phenomenon can support very different interpretations or insights.

The scientist who constructs a mathematical metaphor - a model or theory - chooses to focus on some aspects of the phenomenon rather than others, and chooses to represent those aspects with one image rather than another. Scientific theories are fascinating and extraordinarily useful, but they are, after all, only metaphors.




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New Study Shows 1-to-1 Technology Improves Student Achievement in Math Over Time

A new study published in the Educational Evaluation and Policy Analysis journal found that there is potential for 1-to-1 technology programs to increase achievement in the short term, but more so in the medium term.




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Getting Students to Talk About Math Helps Solve Problems

Math discourse is a technique that works as well virtually as it does on paper or in face-to-face classrooms, according to experts.




math

Stop Giving Inexperienced Teachers All the Lower-Level Math Classes, Reformers Argue

“Detracking” math teachers is tough because many educators resist upending their routines or challenging informal hierarchies, and PD initiatives to make it happen are limited.




math

Are Math Coaches the Answer to Lagging Achievement?

A sizable body of research shows that intensive, one-on-one coaching can improve instructional practice and student achievement more than other professional development offerings for teachers.




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How to Teach Math to Students With Disabilities, English Language Learners

Experts recommend emphasizing language skills, avoiding assumptions about ability based on broad student labels, and focusing on students’ strengths rather than their weaknesses.




math

Who's Afraid of Math? Turns Out, Lots of Students

A program in Howard County, Md., is built on the insight that children can have strong emotions around academics, and those emotions can sabotage learning.




math

How Schools Are Putting Equity First in Math Instruction

Educators are changing instructional priorities, altering lessons, and working on ways to help teachers grow professionally, all in an effort to raise math achievement.




math

Who's Afraid of Math? Turns Out, Lots of Students

A program in Howard County, Md., is built on the insight that children can have strong emotions around academics, and those emotions can sabotage learning.




math

New York Set to Revise Common-Core Reading and Math Standards

New York state is considering adopting a new set of K-12 reading and math standards that differ somewhat from the Common Core State Standards, which have had rocky reception in the state since they went into place in 2010.