Mathematics Teaching

For the countless kids who sit through math class and wonder about the usefulness of algebra, geometry or calculus.Historically most "appealing" jobs haven't required mathematics ; rather, at most, only an ability to use calculators (old) and computers, internet (new). As a result, most kids see math as a giant bag of forgettable information used only to challenge them academically.In the wake of the Japanese earthquake or with all the recent flooding in parts of Canada, having effective evacuation plans are prepared by modelling..mathematical modelling is nothing new. The ancient Egyptians used geometry to model the world as they knew it and to predict when the Nile River would flood. At the height of the H1N1, or swine flu, outbreak in 2009, researchers from Toronto's St. Michael's Hospital used air traffic pattern data to accurately predict how the virus would spread around the world.it's important that the mathematics community showcase the role we are playing and use this to excite kids and the public on the power of mathematics.

Olympiad Programmes For Remote Regions

With nearly zero student representation in the international Olympiads from regions like Jammu and Kashmir, Himachal Pradesh, Uttaranchal and the north-East states, the Homi Bhabha Centre for Science Education (HBCSE) has decided to start exposure-cum-training camps for schools and colleges from these areas.HBCSE is the country’s nodal centre for Olympiad programmes in Mathematics, the Sciences and Astronomy. The programmes aim at promoting excellence in Science and Mathematics among pre-university students. HBCSE have decided to start a large number of exposure camps for school and college teachers of regions which are rarely represented in these competitions. HBCSE want students to consider a career in Science. Another objective is to drive up the higher secondary science education in our country by training science teachers.Teachers from schools and colleges in these areas lack in expertise and training required to handle tough competitions like the Olympiads. Some may not be even aware of this event. Another reason could be insurgency and violence in places like Jammu and Kashmir and some pockets of Assam.Another focus area will be interior regions in states like Bihar and Chhattisgarh. The camps will start by the end of November. Teachers will be exposed to the experimental programmes at HBCSE; training will be conducted and some of the experimental kits will be given to the teachers.The Olympiads have a rigorous, three-tier selection process, which includes a nationwide examination. Around 35 students are selected to participate in an intensive “orientation-cum-selection camp” at HBCSE, after which the final team is shortlisted.The HBCSE has written to the respective state education departments, Kendriya Vidyalayas, Indo-Tibetan schools and Sainik schools, asking them to help identify teachers to attend the camp.

Regional Mathematical Olympiad

The Regional Mathematical Olympiad , sponsored by the National Board for Higher Mathematics and coordinated by the Department of Mathematics, Cochin University of Science and Technology, will be held on December 5 at several centres in Kerala.The olympiad is meant for talented students from Class X to XII and is the first stage for selecting an Indian team for the International Mathematical Olympiad to be held in the Netherlands in July in 2011. The first five rank holders will get cash awards sponsored by KSCSTE and prizes from Prof C S Venkataraman Memorial. Applications with details such as name, class, address and email should be forwarded by principals of recognised schools, along with DD for `30 each entry in favour of Regional Coordinator, INMO, payable at any bank in Kochi, should reach P M Mathew, Department of Mathematics, St Joseph's College, Devagiri, Kozhikode 673008, before October 25. For an information brochure and old question papers, send a selfaddressed, `25stamped envelope of size 10 x 8 to A Vijayakumar, Regional Coordinator INMO, Department of Mathematics, Cusat, Kochi 22 or call 09447608851, or mail to vambat@gmail.com.

Perfect score

100 is a score that most students aim for in Mathematics. However, unlike last year when 707 students across the country had managed to achieve the score, only 160 managed to get full marks this year in the Central Board of Secondary Education (CBSE) class 12 exams.Of these, only 53 students in Delhi have scored 100 in Mathematics.The Board, however, said the figures do not reflect the overall performance of the students. Students who managed to score a perfect 100 said that though some questions were a little ‘tricky’, overall the paper was quite easy.Among others who scored the full marks in Mathematics are Sneha Aggarwal, a student of Rukmini Devi Memorial School, Pitampura and Vaishali Garga of DPS, R.K. Puram who are two of the three toppers in Delhi with a score of 97.2 per cent.Some of the other subjects in which the students scored the maximum marks are Geography, Economics, History, Physics, Chemistry, Biology, Business Studies, Accountancy and English Core.

Madhukar Daftary

Madhukar Daftary, a sexagenarian from Vadodara, is a leader in his own right. The retired chemical engineer spends four hours every day solving maths and physics problems posted online by people who usually want 'urgent homework help'. After having meticulously tackled over 8,296 questions in two years, the silver-haired answer guru is India's 'top contributor' in the mathematics section of 'Yahoo Answers', the community-driven Q & A website.

Ngo Bao Chau

Mathematician Ngo Bao Chau, who made one of Time magazine’s top 10 scientific discoveries of 2009, has accepted a faculty appointment at the University of Chicago. Ngô will become a professor of mathematics, effective Sept. 1, 2010.Ngo, 37, came to Time’s attention for decisive advances he recently made in two central areas of modern mathematics: number theory and representation theory.He proved a basic result, a matching conjecture called ‘the fundamental lemma,’ so named because it represents the central gate for progress in the Langlands program. Native of Hanoi, North Vietnam, Ngô received his doctoral degree from Université Paris-Sud in 1997. Currently a member of the Institute for Advanced Study in Princeton, N.J., Ngô received the Oberwolfach Prize in 2007, the Prix Sophie Germain de l’Académie des Sciences de Paris in 2007 and the Clay Research Award in 2004.In 1979 the Canadian-American mathematician Robert Langlands developed an ambitious and revolutionary theory that connected two branches of mathematics called number theory and group theory. In a dazzling set of conjectures and insights, the theory captured deep symmetries associated with equations that involve whole numbers, laying out what is now known as the Langlands.The lemma is a conjectured identity between orbital integrals for two groups, e.g., the unitary groups U(n) and U(p)xU(q), where p+q = n. Combined with the Arthur-Selberg trace formula, it enables one to prove relations between automorphic forms on different groups and is a key step towards proving links between certain automorphic forms and Galois representations. This is one of the aims of the Langlands program, which seeks a far-reaching unification of ideas in number theory and representation theory. The result of Laumon and Ngô uses the equivariant cohomology approach introduced by Goresky, Kottwitz, and MacPherson, who proved the lemma in the split and equal valuation case. The proof for the unitary case, which is significant for applications, requires many new ideas, including Laumon's deformation strategy and Ngô's purity result which is based on a geometric interpretation of the endoscopy theory of Langlands and Kottwitz in terms of the Hitchin fibration. 1. Short curriculum vitae of Ngo Bao Chuoa•1972 born in Hanoi, Vietnam•1990 moves to France•1992-1995 student at the ENS, rue d’Ulm•1993-1997 doctoral studies at U. de Paris Sud, with G. Laumon•1997 dissertation ‘Le lemme fondamental de Jacquet et Ye’•1998-2004 charg´ de recherches au CNRS, at Univ. de Paris Norde•2004 Habilitation•2004– Professor U. de Paris-Sud•2006– IAS, Princeton•distinctions: Clay Research Award 2004, Speaker at ICM 2006.The conjecture of Langlands and Shelstad lies in the field of automorphic forms. Inthe beginning of the 20th century this theory was the theory of modular forms, i.e., ofholomorphic functions on the upper half plane transforming in a prescribed way under theaction of discrete groups of conformal motions. It was only in the 1950’s, under the influ-ence of I. Gelfand and Harish-Chandra, that the theory of automorphic forms on arbitrarysemi-simple Lie groups, or semi-simple algebraic groups, was developed. In the 1960’s thetheory was dramatically refocused through the introduction by R. Langlands of his func-toriality principle. This principle is a conjecture that stipulates correspondences betweenautomorphic forms on semi-simple groups which are related by a homomorphism betweentheir Langlands dual groups. This principle is surely among the most ingenious ideas ofthe last century and constitutes the deepest statement about automorphic forms known today.

Michael Green -Lucasian Professor of Mathematics

Professor Michael Green, one of the world's leading theoretical physicists is to become the 18th Lucasian Professor of Mathematics at Cambridge University.He was elected by senior university staff to one of the world's most famous academic titles after Professor Stephen Hawking decided to shed the title. Prof Green is a professor of theoretical physics at Cambridge and the university said he was a pioneering scientist.Prof Hawking stepped down in September after holding the title for 30 years but continues to work at the university. Previous holders of the title, founded by MP Henry Lucas in 1663, include Sir Isaac Newton, Charles Babbage, Sir Joseph Larmor and Sir James Lighthill.Michael Green is one of the founders of string theory, which he pioneered from the early seventies onwards. Apart from original research in the area, his contributions include the a textbook co-authored with Edward Witten and John Schwarz, which for many years remained the only string theory text book around.
Michael Green, together with John Schwarz of the California Institute of Technology, laid the foundations for string theory, which is being heralded as the unifying link between Einstein’s Theory of Relativity and quantum mechanics. String theory has the potential to better explain all kinds of forces in the physical world, from electromagnetic forces and the forces of attraction in the nucleus of an atom, to gravity. The eighteenth Professor to take up this position carries forward the very distinguished tradition of the post.Green and Schwarz have been working on string theory since the early nineteen seventies, a time when physicists were baffled by inconsistencies and anomalies in the theory and easily gave up working on it. The duo’s first breakthrough came in 1984, when they made their first breakthrough in the field and convinced the theoretical physicists of the world of the viability of string theory.
The Chair was deeded in December 1663 as a gift to the University of Cambridge from Henry Lucas, who was a Member of Parliament for the University. It was a time when many of the fundamental mathematical tools used today, such as calculus, had yet to be developed. Professors who have held the chair have made contributions, not just to mathematics, but also to the fields of theoretical and applied physics, fluid mechanics, chemistry, astronomy, and even computing.
The Chair never got quite as much media attention until it was held by Stephen Hawking, well known theoretical physicist and author of A Brief History of Time.

RSA-768

A team of researchers has successfully factored a 232-digit number into its two composite prime-number factors, but too late to claim a $50,000 prize once attached to the achievement. The number, RSA-768, was part of a cryptography challenge that technically ended in 2007 that had been sponsored by RSA Laboratories, a prominent computer-security firm. RSA-768, so named because its binary representation is 768 bits long, is the largest number from the now-defunct challenge to be cracked. Thorsten Kleinjung of the Swiss Federal Institute of Technology in Lausanne, Switzerland, and his colleagues announced their result and posted to the Cryptology ePrint.Public key encryption works because it's easy to multiply two large numbers together, but very hard to calculate the factors of a large number. Doing so is largely a brute force process taking an enormous amount of computing power.

51th Mathematical Olympiad

The 51st International Mathematical Olympiad will take place in Astana, Republic of Kazakhstan from the 6th until the 12th of July, 2010.A Mathematical Olympiad is a problem solving competition open to all "mathletes". The aim of the competition is to test innate problem solving skills. The problems are restricted to those that require minimal background and high ingenuity. Since one of the goals of such olympiads is to identify talent at a young age, these olympiads are usually restricted to students not yet admitted to any undergraduate programme.The content ranges from extremely difficult precalculus problems to problems on branches of mathematics not conventionally covered at school and often not at university level either, such as projective and complex geometry, functional equations and well-grounded number theory, of which extensive knowledge of theorems is required. Calculus, though allowed in solutions, is never required, as there is a principle at play that anyone with a basic understanding of mathematics should understand the problems, even if the solutions require a great deal more knowledge. Supporters of this principle claim that this allows more universality and creates an incentive to find elegant, deceptively simple-looking problems which nevertheless require a certain level of ingenuity.The selection process differs by country, but it often consists of a series of tests which admit fewer students at each progressing test. Awards are given to a top percentage of the individual contestants. Teams are not officially recognized—all scores are given only to individual contestants, but team scoring is unofficially compared more so than individual scores. Contestants must be under the age of 20 and must not be registered at any tertiary institution. Subject to these conditions, an individual may participate any number of times in the IMO.
Scoring and format
The paper consists of six problems, with each problem being worth seven points, the total score thus being 42 points. No calculators are allowed. The examination is held over two consecutive days; the contestants have four-and-a-half hours to solve three problems per day. The problems chosen are from various areas of secondary school mathematics, broadly classifiable as geometry, number theory, algebra, and combinatorics. They require no knowledge of higher mathematics such as calculus and analysis, and solutions are often short and elementary. However, they are usually disguised so as to make the process of finding the solutions difficult. Prominently featured are algebraic inequalities, complex numbers, and construction-oriented geometrical problems.Each participating country, other than the host country, may submit suggested problems to a Problem Selection Committee provided by the host country, which reduces the submitted problems to a shortlist. The team leaders arrive at the IMO a few days in advance of the contestants and form the IMO Jury which is responsible for all the formal decisions relating to the contest, starting with selecting the six problems from the shortlist. As the leaders know the problems in advance of the contestants, they are kept strictly separated and observers.Each country's marks are agreed between that country's leader and the deputy leader and coordinators provided by the host country (the leader of the team whose country submitted the problem in the case of the marks of the host country), subject to the decisions of the chief coordinator and ultimately a jury if any disputes cannot be resolved.
Selection process
The selection process for the IMO varies greatly by country. In some countries, especially those in east Asia, the selection process involves several difficult tests of a difficulty comparable to the IMO itself. The Chinese contestants go through a camp, which lasts from March 16 to April 2. In others, such as the USA, possible participants go through as series of easier standalone competitions that gradually increase in difficulty. In the case of the USA, the tests include the American Mathematics Competitions, the American Invitational Mathematics Examination, and the United States of America Mathematical Olympiad, each of which is a competition in its own right. For high scorers on the final competition for the team selection, there also is a summer camp, like that of China.
The former Soviet Union and other eastern European countries' selection process consists of choosing a team several years beforehand, and giving them special training specifically for the event. However, such methods have been discontinued in some countries.
Awards
The participants are ranked based on their individual scores.
• Subsequently the cutoffs (minimum score required to receive a gold, silver or bronze medal) are chosen such that the ratio of medals awarded approximates 1:2:3.
• Participants who do not win a medal but who score seven points on at least one problem get an honorable mention.
• Special prizes may be awarded for solutions of outstanding elegance or involving good generalisations of a problem. This last happened in 2005, 1995 and 1988, but was more frequent up to the early 1980s.
• The rule that at most half the contestants win a medal is sometimes broken if adhering to it causes the number of medals to deviate too much from half the number of contestants. This last happened in 2006 when the choice was to give either 188 or 253 of the 498 contestants a medal.
The selected students in first round will now participate in the second stage Indian National Mathematical Olympiad (INMO). Homi Bhabha Centre for Science Education is the nodal centre of the country for olympiad programmes in mathematics and science, including astronomy.The mathematics olympiad is conducted in five stages under the aegis of the National Board of Higher Mathematics (NBHM) for class 11th & 12th. Students from 23 places will participate in the second stage on the basis of the results of RMO. Each participating country, other than the host country, may submit suggested problems to a Problem Selection Committee provided by the host country, which reduces the submitted problems to a shortlist. The team leaders arrive at the IMO a few days in advance of the contestants and form the IMO Jury which is responsible for all the formal decisions relating to the contest, starting with selecting the six problems from the shortlist. As the leaders know the problems in advance of the contestants, they are kept strictly separated and observed.

Zohaib Ahmed

A schoolboy has become the youngest person ever to pass A level maths with a Grade A at the age of 9. Zohaib Ahmed grabbed top marks in Mathematics despite sitting his exams an incredible nine years early.Zohaib, who goes to primary school, was still only eight when he took the first of his A-level papers in January.He scored 90 per cent across all six modules to land his A-grade.Now he plans to take A-level further maths, doing three modules in the summer and then three in January. He aims to head off to university by the time he is 14.Last August Zohaib scooped an A* (A star) in his GCSE maths at the age of just eight.Zohaib's 11-year-old brother Wajih is also celebrating getting an A-grade at A-level further maths with a 96 per cent pass.Last summer he had achieved a top grade A in his maths A-level while aged 10.The brothers share the same ambition of working in the city as an actuary in the finance sector.

International Conference on Recent Trends in Mathematical Sciences

Sixty-five mathematicians from 15 countries will take part in the first international conference on mathematics.The three-day International Conference on Recent Trends in Mathematical Sciences is organised by Bahrain University's mathematics department.Mathematicians will present lectures on their recent research on various topics, including statistics and operations research.The topics also include quantum information and mathematical modelling, computational mathematics, differential equations, algebra, number theory, history and foundation.The keynote speakers are Cardiff University professor Michael Eastham, Frankfurt Institute of Natural Sciences Professor M S Alnachaii and Russian Academy of Sciences Professor R Nagmaatulin.

MATH LAB

The Central Board of Secondary Education (CBSE) has issued a circular to its affiliated schools to establish a mathematics laboratory in order to promote learning among students through work activities. It was suggested that the concept would likely to be introduced from class third till eight.This new concept would not only help the children but also the teacher to visually explain some abstract concepts by using three-dimensional models.The laboratory would help a student learn the subject with the help of concrete objects and verify and discover certain geometric properties using models and measurements.The board has directed the schools to emphasize on the tools and equipment’s to be used in the laboratory, should be made locally designed by innovative methods.

project evaluation committees for UPTU

Uttar Pradesh Technical University (UPTU) will now have to work on their final year projects from the beginning of the session. The university has decided to monitor the progress of the projects on a monthly basis so that students take their assignments seriously.The UPTU has started to set up project evaluation committees, which will be functional from the current academic session. The committees are being set up at three levels. The state level committee, which has already been constituted, comprises the vice-chancellor, additional examination controller and six professors — from university and engineering and management institutes.The other two types of committees will be set up by each of the institutions. While one will comprise selected faculty members headed by the concerned college director, the other will comprise senior teachers of different engineering and managements streams of the same college.

Hawking to retire as Lucasian Professor

British astrophysicist Stephen Hawking will next year retire as Cambridge University's Lucasian Professor of Mathematics, a position once held by Isaac Newton.it was policy for the title holder to retire at 67. Hawking, who has held the position since 1979 and has worked at Cambridge since 1962, will be 67 in January.The scientist, whose books including "A Brief History of Time" have sought to popularise study of stellar physics, will stay at the university but a new Lucasian professor will be appointed.Isaac Barrow became the first holder of the post in 1664, and notable successors have included Charles Babbage, Sir Joseph Larmor and Sir James Lighthill.Despite being almost completely paralysed by motor neurone disease, Prof Hawking became one of the world's leading experts on gravity, black holes, and the origins of the universe.

Regional Mathematical Olympiad

The Regional Mathematical Olympiad will be held on November 9 between 1 p m and 4 p m in Thiruvananthapuram, Kollam, Kottayam, Alappuzha, Adoor,Ernakulam, Irinjalakuda, Thrissur, Palakkad, Kozhikode, Kannur and Kasargod. The students from Class XI/XII and exceptional students of Class X can apply.There is no prescribed syllabus for the Olympiad.The five toppers will win a cash prize of Rs 2000 and Prof C S Venkataraman memorial prizes.Twenty toppers candidates (six from class XII) will be selected for the Indian National Mathematical Olympiad (INMO) to be held at CUSAT on February 2009.Thirty INMO awardees will be invited for a training camp to select an Indian team for the International Mathematical Olympiad (IMO) 2009.IMO-2008 was held in Spain and India was placed 31 with 5 bronze medals.There is no application form for participating in the Olympiad.Principals can forward the list of the candidates with student’s name, medium of instruction,class, residential address,phone numbers, email-ids and requested centre with a registration fee of Rs 30 by Cash/MO/DD drawn in favour of Regional Coordinator, INMO payable at State Bank of Travancore, Cochin University.The last date for filled in application is October 10. For old question papers and information brochure, send in an application with a 10*8 self-addressed envelope affixed with Rs 25 stamps to Dr A Vijayakumar, Regional coordinator, INMO, Dept of Maths, CUSAT- 22.For further details, call 0484-2577518 or logon on maths.cusat.ac.in/olympiad.

Mathematics Olympiad-2008

the Central Board of Secondary Education (CBSE) will be organising Mathematics Olympiad-2008 for the students studying in the CBSE schools on November 9 at Jawaharlal Nehru School, Habibganj Bhopal.The examination will commence at 1 pm and the duration of the examination will be 3 hours. Candidates should report to the school at 12 noon or even before that.the students of standard IX, X, XI and XII can participate in this examination. Any school affiliated to CBSE can sponsor a maximum of five students for the same. The five students should be selected strictly on the basis of the screening test conducted by the school itself.The head of the institution will forward the names of 5 students to the co-ordinator (Madhya Pradesh and Chhattisgarh) V Vijay Kumar, Principal of Jawaharlal Nehru School, Bhopal (Phone Numbers as office -0755-2485026, 2505375, Residence- 0755-2423390).The list of students along with the entry fee of Rs 35 per candidate, the latter through Demand Draft, drawn on any Nationalised Bank only, payable at Bhopal in favour of "Principal, Jawaharlal Nehru School" should reach the state co-ordinator by October 10, 2008.The admit card would be issued by the sponsoring school should have complete information about the students. The admit card should also carry the signature of the student and his/her latest photograph attested by the Principal of the school.Roll numbers will be allotted to the candidates at the time of examination. Any student will not be allowed without admit card issued by the sponsoring school. Syllabus and pattern of examination will be as there is no specific syllabus for the examination.Areas of school mathematics such as geometry, basic number theory, trigonometry, arithmetic, combination etc are to be prepared for the test. For further clarifications if any may contact the co-ordinator on the above mentioned telephone numbers.Central Board of Secondary Education (CBSE), Delhi has been conducting CBSE Group Mathematics Olympiad for the students of affiliated schools to identify, encourage, promote and nurture the talent in mathematics.Top 30 students from CBSE Group are then allowed to participate in Indian National Mathematics Olympiad conducted by National Board of Higher Mathematics.Student selected at the national level will participate in the International Mathematics Olympiad.

Infosys Mathematics Prize.

Professor Manindra Agarwal of the Indian Institute of Technology-Kanpur (IIT-K) has been chosen as the first recipient of the Infosys Mathematics Prize. Agarwal completed his BTech in computer sciences from IIT-K in 1986, and his PhD in 1991. Over the years,he has been working on Complexity Theory, a branch of mathematics.The head of the computer science and engineering department at IIT-K, Agarwal has been selected for the award Dr Manindra Agrawal has been awarded for his outstanding work in Complexity Theory, the branch of mathematics concerned with the study of algorithms for solving mathematical and related scientific problems, especially their efficiency and running times. Dr Agrawal is best known for the discovery of a deterministic polynomial time algorithm, for primality testing in his joint paper with his former students. This discovery resolved a long-standing problem of a fast test of primality, which had been the subject of intense study in the field of mathematics and computer science research.The Infosys Mathematics Prize was jointly instituted by Infosys and NIAS earlier this year to encourage and foster an interest in mathematics.

Henri Cartan

world has lost one of the greatest scientists of the twentieth century. Henri Cartan a legendary figure in mathematics died inParis on 13 August, at the age of 104 years.
Almost all of Dr. Cartan's career was spent in France, and he was acclaimed for his research in areas of pure mathematics, including algebra, topology and analytic functions of complex variables. He was also an influential writer and teacher.At least two of his pupils won Nobel prizes, one in economics and one in physics. Two others received the Fields Medal, which is awarded for accomplishment in mathematics and is regarded as the mathematics equivalent of the Nobel Prize.In 1980, Dr. Cartan received the Wolf Prize, one of the highest honors in mathematics.Apart from his professional achievements.Henri Cartan will be remembered for his personal qualities.He was generous to students,colleagues and friends, and a vigorous defender of Human Rights.

Science subjects really hard

A new research has shown that school kids studying science and technology subjects like Maths, Physics and Chemistry find it much harder to achieve the top exam grades than candidates of similar ability studying subjects like Media Studies and Psychology.For the study, researchers at Durham University analysed and compared data from nearly one million schoolchildren sitting GCSE and A-level exams and reviewed 28 different studies of cross subject comparison conducted in the UK since 1970.They found significant differences in the relative difficulty of exams in different subjects with the sciences among the hardest.On average, subjects like Physics, Chemistry and Biology at A-level are a whole grade harder than Drama, Sociology or Media Studies, and three-quarters of a grade harder than English, RE or Business Studies.Researchers voice concerns that students will be more likely to choose to study ‘easier’ subjects and will not opt to study science subjects that are desperately needed by employers in the knowledge economy.

Girls just as good as boys in math

The long held belief that boys are better at maths than girls has been refuted by a new study.Based on the test results of seven million students in the US, researchers at UC Berkeley have found that boys and girls in grades two to 11 scored the same in maths.Previous studies have shown that girls are just as capable at math as boys, but the new research was the first to cover such a massive sample of students across the country - taking advantage of the standardized test scores now required by No Child Left Behind. The study was led by American psychologist Janet S. Hyde, from the Department of Psychology at the University of Wisconsin (Madison). Her colleagues are Sara M. Lindberg, also from the Department of Psychology at the University of Wisconsin, Marcia C. Linn, from Education in Mathematics, Science, and Technology at the University of California at Berkeley, and Amy B. Ellis and Caroline C. Williams, both from the Department of Curriculum and Instruction at the University of Wisconsin.