- ARTICLES & ANNOUNCEMENTS (NATIONAL FOCUS)
- (1) “Pi Day” Activities
- (2) NUMB3RS–Weekly Episode Updates and Lesson Plans
- (3) “Mathematics, Mathematicians, and Mathematics Education” by Hyman Bass
- (4) “Professional Development for Mathematics and Science Teachers: Findings from a Decade of Local Systemic Change (LSC) Projects”
- (5) “Untying a Math Mystery” by Margaret Wertheim
- (6) Call for Volunteers: Algebra Diagnostic Assessment
ARTICLES & ANNOUNCEMENTS (NATIONAL FOCUS)
Contact: Gene Potter (PotterGene@msn.com); Mathematics Educators of Greater St. Louis
Mathematics Educators of Greater St. Louis (MEGSL) hosts a Pi Day (March 14) Web site with numerous informative and interesting links related to pi and to Sierpinski and Einstein, whose birthdays fall on March 14.
Pi Day Mission Statement:
Pi Day openly promotes the celebration of mathematics education, the collective enjoyment of mathematics, and the ageless, multicultural interest in pi.
Educators, students, and parents are encouraged to join together in a variety of public activities, expressing in imaginative ways their passion for the longstanding creative nature of mathematics.
300th Anniversary of Pi:
The sixteenth letter of the Greek alphabet was first used for the familiar value 3.1415… in the publication, “Synopsis Palmariorium Mathesios,” authored by William Jones in 1706. This year is thus the 300th Anniversary of the introduction of this mathematical symbol.
Pi Day Resources:
Download an extensive collection of pi facts, activities, and resources (the collection has been divided into two sections to speed download time and is in Microsoft Word format):
Source: Linda Beheler, Texas Instruments Education Support Team
The following information is from the weekly “We All Use Math Everyday” update from Texas Instruments. This online newsletter provides information about upcoming episodes of NUMB3RS and new classroom activities to accompany the mathematics in the programs.
(a) This Week on NUMB3RS:
“Mind Games” –Friday, March 10, 10 PM ET/PT on CBS
When a psychic (played by John Glover) leads authorities to a deadly crime scene in the wilderness, Charlie sets out to prove it is just a fluke.
(b) This Week’s Lesson Plans:
This activity explores the concepts of confidence interval and margin of error. Students can learn the basics of predicting a range of “plausible” results from an experiment.
“Right or Wrong”
This activity uses the binomial theorem to calculate the probabilities of different outcomes for a number of events. It includes binomial expansion, combinations, and Pascal’s Triangle.
This activity introduces the study of random walks. A random walk is a path in which each step could be in a variety of directions, each with its own probability. It also makes use of a calculator simulation for determining an approximate value of pi.
Visit http://www.cbs.com/numb3rs to see all available downloadable classroom activities for current and past episodes.
(c) Adding It Up–Part I: An Interview with Andrew Black
Andrew Black, math researcher for NUMB3RS, shares a behind-the scenes look at production of the show and how he helps to keep math center stage throughout the episodes’ plot twists and turns.
Question: Where do you get your story ideas for NUMB3RS and where does the math come in?
Answer: Usually a writer starts off with a strong FBI crime concept and then figures out how to implement up to three math twists throughout the story. That’s where I come in, to brainstorm with the writer. My assistant Matt and I put out what we call weekly “Math Tidbits” – these are usually 3-5 interesting math applications. For example, we summarized Classification and Regression Trees (C&RT), which is an interesting way to sort through and sift out meaningful/meaningless data. Sure enough, one of our writers seized on this and will make it the “Hero Math” in his episode.
The math itself comes from several places. First are books – textbooks and popular scientific non-fiction. Two examples include The Tipping Point by Gladwell, which helped inspire the episode “Sniper Zero,” and The Music of the Primes by du Sautoy, which helped inspire the episode “Prime Suspect.” We also rely heavily on arxiv.org, which provides us with a trove of white papers–many of the equations seen on the boards are inspired from here. Finally, I have five core consultants that help us out and watchdog the math–Dr. Gary Lorden (who does all the heavy lifting by adjusting the equations, making sure they match what’s going on in the story), Wolfram Research, Dr. Jordan Ellenberg, Dr. Alice Silverberg and Dr. Mark Bridger.
(Next week’s e-mail update will feature part two of a three-part interview with Andrew Black with a behind-the-scenes look at script development. To subscribe to the update,
(d) “Texas Instruments’ ‘NUMB3RS’ Every Day for a Hollywood Get-Away” Sweepstakes
Students (ages 13-19) can log onto http://www.cbs.com/primetime/numb3rs/ti/ from February 15 to March 15, 2006 for a chance to win an all expense paid vacation to Hollywood, plus a walk-on role on NUMB3RS for their teacher. To enter, students can simply click on the sweepstakes link, complete registration information and provide the name of their current math teacher.
In addition to getting an extra entry into the contest everyday by logging on to www.cbs.com/numbers, students can also earn extra credit by answering math questions, supplied by MATHCOUNTS.
Source: Bulletin of the American Mathematical Society – 23 June 2005 (via the 2/22/06 issue of “MSP News,” produced by Joni Falk)
Excerpt: “While university teaching is a substantial part of the academic mathematician’s professional life, recent years have seen many research mathematicians involved in school mathematics education as well. There has been much attention to the so-called “math wars,” an unfortunate term coined in the U.S. to describe the conflicts between mathematicians and educators over the content, goals, and pedagogy of the curriculum. Although these ‘wars’ attracted a great deal of attention, the involvement of mathematicians has a much longer history in our profession. And most of that history is not primarily a history of conflict. In what follows, I will offer some snapshots from that history to provide a more robust picture of our tradition of concern for pre-college mathematics education. That tradition is both edifying and inspiring…”
(4) “Professional Development for Mathematics and Science Teachers: Findings from a Decade of Local Systemic Change (LSC) Projects”
“Professional Development for Mathematics and Science Teachers: Findings from a decade of Local Systemic Change (LSC) Projects” presents major findings from a 10-year, large scale study of 75,000 mathematics and science teachers who participated in 88 LSC projects, with support from the National Science Foundation’s (NSF) Division of Elementary, Secondary, and Informal Education. The LSC projects provide valuable lessons in providing effective professional development to K-12 teachers to improve mathematics and science classroom instruction.
A PDF version of the 94-page pre-publication copy of this report is available for download at http://www.pdmathsci.net/findings/report/32
Overview of the Local Systemic Change Initiative
In 1995, the National Science Foundation (NSF) initiated the Local Systemic Change through Teacher Enhancement program. The initiative’s primary goal is to improve instruction in science, mathematics, and technology through teacher professional development within whole schools or school districts. NSF funded the first cohort of Local Systemic Change (LSC) projects in 1995, and an additional cohort of projects each year, for a total of 88 projects funded by 2002.
The LSC initiative distinguishes itself from former NSF-supported teacher enhancement efforts in two important ways. First, it targets all teachers in a jurisdiction for professional development; each targeted teacher is to participate in a minimum of 130 hours of professional development over the course of the project. Second, the LSC emphasizes preparing teachers to implement district-designated mathematics and science instructional materials in their classes.
In addition to providing professional development for teachers, the LSC initiative promotes efforts to build a supportive environment for improving science, mathematics, and technology instruction. LSC projects are expected to align policy and practice within targeted districts, and to engage in a range of activities to support reform, including:
• Building a comprehensive, shared vision of science, mathematics, and technology education;
• Conducting a detailed self-study to assess the system’s needs and strengths;
• Promoting active partnerships and commitments among an array of stakeholders;
• Designing a strategic plan that includes mechanisms for engaging teachers in high quality professional development activities over the course of the project; and
• Developing clearly defined, measurable outcomes for teaching, and an evaluation plan that provides formative and summative feedback.
The Core Evaluation
NSF’s solicitation for the LSC initiative indicated the Foundation’s interest from the outset in providing a framework for collecting data from LSC projects to evaluate their efforts. The goal of the evaluation activities was not only to assess individual projects, but also to aggregate data across projects to glean broader insights about the design, quality, and impact of the LSCs.
NSF contracted with Horizon Research, Inc. (HRI) in Chapel Hill, North Carolina to develop a data collection framework, to provide technical assistance in implementing evaluation activities, and to prepare cross-site analyses of evaluation results. Since the LSC’s inception, HRI has collaborated with NSF staff, LSC Principal Investigators (PIs), and project evaluators on the design and implementation of a core evaluation system. The system includes the collection of baseline data during an LSC’s first year of funding, and a range of data collection activities during subsequent years. Evaluators are asked to provide comprehensive evaluation reports in the second and final years of their projects, and less detailed reports in the interim years.
All of the evaluation activities are driven by a set of core evaluation questions:
– What is the overall quality of the LSC professional development activities?
– What is the extent of school and teacher involvement in LSC activities?
– What is the impact of the LSC professional development on teacher preparedness, attitudes, and beliefs about mathematics and science teaching and learning?
– What is the impact of the LSC on classroom practices in mathematics and science?
– To what extent are the district and school contexts becoming more supportive of the LSC vision for exemplary mathematics and science education?
– What is the extent of institutionalization of high quality professional development systems in the LSC districts?
Purpose of the Capstone Report
NSF’s Local Systemic Change program is in its final stages, with 18 of the 88 funded projects still active. Over the last decade, the initiative has left its mark on teachers, classrooms, schools, and districts. The purpose of the Capstone report is to look at the impact of the LSC from both a cross-site and longitudinal perspective. In particular, key findings from the analysis of core evaluation data provide some insights into topics relevant for other large-scale reform efforts__for example, the selection and preparation of professional development providers; designing effective interventions; reaching targeted audiences; and strategies for building stakeholder, policy, and “system” support for reforms. We believe that these findings will be of use to those who are designing and/or leading similar kinds of reforms that seek to influence classrooms and systems alike.
“LSC Research Updates” are 1-page summaries of key findings from the LSC studies that may be of interest to the K-12 education community. These updates can be downloaded from the LSC Web site: http://www.pdmathsci.net
Also see “NSF Educator-Training Effort Seen as Helpful” by Sean Cavanagh in today’s issue of Education Week: http://www.edweek.org/ew/articles/2006/03/08/26nsf.h25.html
Source: Los Angeles Times – 6 March 2006
(Note: Margaret Wetheim is the science columnist for the LA Weekly and director of the Institute for Figuring, which has recently been hosting a series of lectures on knot theory.)
You have to hand it to mathematicians; they can turn anything into a formal problem. Balls packed into boxes, folded paper, even bits of string become, in the hands of mathematical theorists, gateways to worlds of Byzantine complexity and beauty.
Take a piece of string–I mean literally, go get a piece of string and tie it into a knot. Now tape the two ends together so it makes a closed loop–necessary to fulfill the mathematical definition of a “knot.” How many different knot types do you think there are? The number is infinite, and the question of how to categorize these manifestations of loopiness has engaged some of the finest mathematical minds for a century.
We are nowhere near to having a complete taxonomy of knots, and some mathematicians view the problem as so inherently difficult that they think it is an impossible goal. Indeed, “knot theory” is an area of mathematics in which almost any generalized question you can think of is unlikely to be answered.
Although knots in math are essentially one-dimensional objects, understanding them has turned out to be a significant challenge. Moreover, knots provide mysterious links between the mathematical continents of topology, geometry and algebra, hinting that these enigmatic twists contain secrets to powerful, deep and general truths.
And yet this most esoteric branch of mathematics has also turned out to have immense application in the physical world. That’s because we now know that DNA and many other long molecules arrange themselves into knotted structures. Knot theorists are suddenly in demand from biologists, who want help understanding how clumps of DNA move through different mediums, how proteins fold up and how polymers behave. The specific knottiness of a piece of DNA, for example, determines whether certain enzymes can act on it, which has important implications for understanding diseases such as cancer.
Ken Millett, a knot theorist at UC Santa Barbara, is a leader in the application of this mathematics to DNA and other molecules. In the 1980s, inspired by UC Berkeley mathematician Vaughan Jones, Millett helped to revitalize knot theory when he was part of a team that discovered a strange new way of classifying knots. With this method, each knot can be associated with a particular equation that uniquely characterizes it. Still, mathematicians have no idea what the equations actually signify; they don’t seem to relate to any of the usual features of knots, such as shape and form. “Do they refer to some hidden structure within the knot?” Millett asks. “We really don’t know.”
Some physicists, however, think the equations are telling us something fundamental about the basic particles and forces of nature. They believe these arcane formulas may enable us to find the much-longed-for “theory of everything” under the umbrella of string theory. The equations also turn out to have application to the emerging field of quantum computing, which many scientists hope will usher in an era of new, more powerful computational devices.
The story of knots suggests that we never know from what areas of mathematics useful applications may spring. Although mathematics has no physical substance, it can be as precious as gold or oil, and ultimately as integral to our economy. As President Bush noted in January’s State of the Union speech, America’s place at the top of the global technological pyramid depends on a workforce that is well educated in math and science. Yet, nationally, our schools are understaffed in these critical areas. Which brings me to the importance of Millett’s other professional hat–math education. In addition to his knot research, Millett directs a program at Santa Barbara that recruits math and science undergraduates to become classroom teachers.
Given that a recent report by the National Academy of Sciences revealed that nearly 60% of American eighth-graders are taught math by teachers who did not major in math or pass any kind of certification exam, efforts such as Millett’s are critical. On Feb. 25, his work was honored in Washington with an award from the organization Quality Education for Minorities.
In the State of the Union address, the president pledged to train 70,000 math and science teachers to handle AP courses. But the plan does not call for hiring any new teachers, which is woefully shortsighted. Math education does not require expensive equipment, specialized buildings or fancy facilities; it just needs good teachers and a supportive learning environment.
The lessons of knot theory suggest that investing in this “arcane” subject will, in the long run, pay dividends.
Source: Helena Miranda — firstname.lastname@example.org (via the NCSM distribution list)
Through funding from the Institute of Education Sciences (IES), the Technology and Assessment Study Collaborative at Boston College (InTASC) is attempting to develop tests that will provide more diagnostic information about student learning than traditional standardized tests. The “algebra misconception” tests are designed to identify whether a given student’s achievement in algebra is being hindered by one or more common algebraic misconception.
The project is currently seeking teachers who are interested in helping to pilot this new approach to testing. Five tests available to teachers during this phase: linguistic, concept of a variable, concept of equality, graphing, and addends misconceptions. Each of these tests consists of 30 questions–each designed to diagnose one of the misconceptions–and should take approximately one class period (40 minutes) to complete.
Participating teachers may choose one or more of the five tests to administer to their students. Before taking the misconception tests, students will take a 20-item algebra ability test consisting of questions previously used on state tests and a short student questionnaire. All of these pilot tests will provide students and teachers with immediate feedback on students’ performance, a math ability score, and information about misconceptions that individual students may hold.
If you are interested, please visit the above Web site. Should you have any questions, please contact Helena Miranda at (617) 552-3646 or via email at email@example.com