In This Issue...
Source: The Center for the Future of Teaching and Learning,
via Susie Hakansson (Executive Director, California Mathematics
The Center for the Future of Teaching and Learning recently released a survey of more than 5,200 California teachers that examines their experiences, challenges and professional development needs in teaching the state's more than 1.6 million students designated as English learners.
The report, Listening to Teachers of English Language Learners, was a collaborative project of Policy Analysis for California Education (PACE), the University of California Linguistic Minority Research Institute (UC LMRI) and the Center for the Future of Teaching and Learning. This survey of teachers finds little participation in professional development activities and a lack of time and instructional resources needed to effectively teach their English learning students. The teachers surveyed state their efforts are often complicated by their struggle to effectively communicate with the parents and families of these students. Among the report,s key finding of those surveyed:
43% of teachers with 50% or more English learners in their classrooms had received no more than one in-service that focused on the instruction of English learners.
Lack of time and appropriate tools and materials were commonly cited challenges. Many teachers said that they did not have textbooks written in a way that made the material accessible to English learners.
27% of K-6 teachers said they struggled to communicate with students, families and communities. Seventh-12th grade teachers most often mentioned communicating with, understanding, and connecting with students as the greatest challenge they faced.The report, Listening to Teachers of English Language Learners, and is now available online at our Web site: http://www.cftl.org/whatsnew.php
(1) How Can Universities Improve Schoolteachers in Math and Science? A Live Discussion with The Chronicle of Higher Education
Source: Evan Goldstein (Chronicle of Higher
Education) via Linda Gojak, President, National Council of
Supervisors of Mathematics - 20 May 2005
A story in this week's issue of The Chronicle of Higher Education (CHE) looks into the debate of how much and what kind of role university researchers should play in improving math and science education.
Gordon A. Kingsley, an associate professor in the school of public policy at the Georgia Institute of Technology, will be the guest in a live Colloquy on The Chronicle's Web site on Thursday, May 26, at 2 p.m. (EDT; 11 a.m. PDT). Mr. Kingsley's teaching and research focus on science and technology policy and organizational theory. To read the complete story, submit questions and comments in advance, and to participate live on Thursday, go to http://chronicle.com/colloquy.
More about the issue:
In this year's budget, Congress cut spending for a National Science Foundation program in which universities and school districts collaborate to improve schoolteachers' knowledge of mathematics and science. Congress increased by the same amount funds for a version of the program that is run by the U.S. Department of Education. That program, though it reaches schools in all 50 states, is more narrowly focused on helping teachers prepare students to pass state tests on mathematics that are required by the No Child Left Behind Act.
Supporters of the shift in funds say that the Education Department is in a better position to work with school districts, and that the NSF is a research agency, not an education agency. But advocates of strengthening the NSF program, called the Math and Science Partnerships, argue that not enough is known about how to improve student performance in math and science, and that the NSF program is better designed to provide answers. Without such understanding, they say, giving schoolteachers more training in those subjects may not produce significant progress.
What role should university researchers play in improving elementary and secondary education? Should the emphasis be on improving teachers' knowledge of their subject or on their teaching methods? Or, as some critics suggest, are universities not necessarily the best partners in school reform? Can college professors, in turn, learn a lot about math and science instruction from schoolteachers -- and are they willing to listen? Join CHE this Thursday to discuss these questions and more.
It is oversimplified, unrealistic, and unfair to try to raise students' achievement in mathematics simply by putting pressure on teachers to "try harder." To assume that teachers aren't already "trying hard enough" is grossly inaccurate.
Across the board, teachers want students to achieve at high levels, and they do whatever they can to help them learn. But to accomplish the ambitious goal of a high-quality mathematics education for every student, educators, policymakers, and communities will have to make significant, fundamental changes in the educational system, not just exhort teachers to "try harder."
* What do you think are the most important changes school systems should make to improve students' learning?
* What are the challenges you face in making improvements in teaching and learning?
Read the NCTM President's Message at http://nctm.org/news/president/2005_05president.htm and submit your comments prior to the Web chat. Then join Cathy Seeley today for a live Web chat at 4:00 EDT (1:00 PDT).
All Presidential chats are archived at http://nctm.org/news/chat_archive.htm
Teachers all over the world--including at least one U.S. Army soldier stationed in Iraq--are using the Department's new professional development tools via the Web. This online professional development is a convenient way for teachers to satisfy state professional development requirements. Florida's Panhandle Area Educational Consortium e-newsletter recently ran a story about this soldier, a high school algebra and calculus teacher from Texas. To read more, see: http://www.paec.org/newsletterdetail.asp?ID=10&sID=S1
Thirty-two states (including California) and the District of Columbia now give or allow local districts to give teachers credit for participating in Teacher-to-Teacher conferences and free e-Learning digital workshops. To learn more, visit the Department's Teacher Initiative Web site: http://www.ed.gov/teachers/how/tools/initiative/index.html. Click on the link "Get Professional Development Now." The initiative has just added a U.S. map to assist teachers in finding out how they can receive credit for e-Learning workshops. Teachers can click on the link for their states to find out more.
The Department now has 23 free e-Learning sessions available. To view any of the math, reading, English, language arts, or science sessions, visit http://www.ed.gov/teachers/how/tools/initiative/index.html. The site also has information about using data in the classroom and the basics of the No Child Left Behind Act.
The e-Learning professional development website is part of the U.S. Department of Education's Teacher-to-Teacher Initiative, which also supports teachers through workshops, email updates, and the American Stars in Teaching recognition project.
If you would like to receive electronic Teacher Updates from the U.S. Department of Education, visit http://www.ed.gov/teachers/how/tools/initiative/index.html.
A baker knows when a loaf of bread is done, and a builder knows when a house is finished. Yogi Berra told us "it ain't over till it's over," which implies that at some point it is over. But in mathematics, things aren't so simple. Increasingly, mathematicians are confronting problems wherein it is not clear whether it will ever be over.
People are now claiming proofs for two of the most famous problems in mathematics--the Riemann Hypothesis and the Poincare Conjecture--yet it is far from easy to tell whether either claim is valid. In the first case, the purported proof is so long and the mathematics so obscure no one wants to spend the time checking through its hundreds of pages for fear they may be wasting their time. In the second case, a small army of experts has spent the last two years poring over the equations and still doesn't know whether they add up.
In popular conception, mathematics is the ultimate resolvable discipline, immune to the epistemological murkiness that so bedevils other fields of knowledge in this relativistic age. Yet Philip Davis, emeritus professor of mathematics at Brown University, has pointed out recently that mathematics also is "a multi-semiotic enterprise" prone to ambiguity and definitional drift.
Earlier this year, Davis gave a lecture to the mathematics department at the University of Southern California titled, "How Do We Know When a Problem Is Solved?" Often, he told the audience, we cannot tell, for "the formulation and solution of problems change throughout history, throughout our own lifetimes, and even through our rereadings of texts."
Part of the difficulty resides in the notion of what we mean by a solution, or as Davis put it: "What kind of answer will you accept?"
Take, for instance, the task of trying to determine whether a very large number is prime--that is, it cannot be split evenly into the product of any smaller components, except 1. (Six is the product of 2 by 3, so it is not prime; 7 has no smaller factors, so it is.) Determining primeness has huge practical consequences--prime numbers are widely used in computer security codes, for instance--yet when the number is large it can take an astronomical amount of computer time to determine its primeness unequivocally. Mathematicians have invented statistical methods that will give a probabilistic answer that will tell you, for instance, a given number is 99.99 percent certain to be prime. Is it a solution? Davis asked.
Other problems also can be addressed by brute computational force, but many mathematicians feel intrinsically uncomfortable with this approach. Said Davis: "It is certainly not seen as an aesthetic solution." A case in point is the four-color map theorem, which famously asserts that any map can be colored with just four colors (no two adjoining sections may be the same color).
The problem was first stated in 1853 and over the years a number of proofs have been given, all of which turned out to be wrong. In 1976, two mathematicians programmed a computer to exhaustively examine all the possible cases, determining that each case does indeed hold. Many mathematicians, however, have refused to accept this solution because it cannot be verified by hand. In 1996, another group came up with a different (more checkable) computer-assisted proof, and in December this new proof was verified by yet another program. Still, there are skeptics who hanker after a fully human proof.
Both the Poincare Conjecture (which seeks to explain the geometry of three-dimensional spheres) and the Riemann Hypothesis (which deals with prime numbers) are among seven leading problems chosen by the Clay Mathematics Institute for million-dollar prizes. The institute has its own rules for determining whether any one of these problems has been solved and hence whether the prize should be awarded. Critically, the decision is made by a committee, which, Davis said, "comes close to the assertion that mathematics is a socially constructed enterprise."
Another of the institute's million-dollar problems is to find solutions to the Navier-Stokes equations that describe the flow of fluids. Because these equations are involved in aerodynamic drag, they have immense importance to the aerospace and automotive industries.
Yacht designers must also wrestle with these legendarily difficult equations. Over lunch, Davis told a story about yacht racing. He had recently talked to an applied mathematician who helped design a yacht that won the America's Cup. This yachtsman couldn't have cared less if the Navier-Stokes equations were solved; what mattered to him was that, practically speaking, he could model the equations on his computer and predict how water would flow around his hull. "Proofs," Davis said, "are just one of the tools that mathematicians now use."
We may never fully solve the Navier-Stokes equations, but, according to Davis, it will not matter. Like so many other fields, mathematics is becoming less about some Platonic ideal of ultimate answers, and more a functional project of computational simulation and communal negotiation. Dare we say it: Math is becoming postmodern.
COMET is sponsored in part by a grant from the California Mathematics Project.
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