The 2001 Mathematics Instructional Materials Adoption Report (California) and other information about the 2001 mathematics adoption can be found at http://www.cde.ca.gov/cfir/index.html#2. The Adoption Report is available as a pdf file: http://www.cde.ca.gov/cfir/math/mathrpt.pdf
This May, master teacher Jaime Escalante will bring the subject of algebra to life for California math teachers in two one-day institutes titled "Algebra in the Real World."
Escalante, who gained national attention for his ability to inspire inner city students to master advanced mathematics, will share strategies for motivating students who "hate math." Teachers will also leave the institute armed with engaging multimedia resources that answer the question, "Why do I need to learn algebra?"
"Algebra is the key to higher math," commented Mr. Escalante. "But we won t get improved performance in algebra just by saying that we want it. We need to give teachers better tools and better training."
The workshop is being sponsored by The Futures Channel, a producer and publisher of digital resources for math, science, technology and arts education. The Futures Channel offers teachers an extensive archive of video and lesson materials that connect curriculum topics to their real world applications; it supports these tools with professional development services.
Each participant will receive a binder containing two video tapes and a CD-ROM containing algebra-related "micro-documentaries "drawn from The Futures Channel's award-winning archive, as well as 30 classroom projects that are linked to algebra curriculum topics and support algebra standards.
Locations and dates for the institutes will be: May 5, Santa Clara and May 12, Los Angeles. For exact location and registration details, contact: Jason Dean, 877.937.7515, ext. 238 (toll free). Email: email@example.com (You may register until the day of the event, but please call Jason to let him know of your interest in attending.)
Note: The first four books in the National Council of Teachers of Mathematics' Navigations series (an extension of NCTM's Principles and Standards for School Mathematics) focus on algebra and were released earlier this month: http://www.nctm.org/meetings/annuals/orlando/daily/wednesday.htm#navigations
(1) "Don't Allow 'New Math' To Multiply, Regent Says" by Kenneth Lovett, Carl Campanile and Ikimulisa Sockwell-Mason
A top state education official yesterday threw cold water on efforts to impose the controversial "New Math" program throughout the city. "This seems to be a very dangerous time to be messing around with an entire math curriculum," said Merryl Tisch, a member of the state Board of Regents and a former teacher...
Critics deride constructivist math as "fuzzy math." But its supporters say it makes it easier for kids to understand arithmetic...
"The fact that the class sizes in New York are so large makes it much more difficult to teach with a constructivist philosophy," Tisch said. And she added that instructing students this way requires massive retraining of teachers.
But supporters claim that when teachers are retrained to teach the New Math, students do better. Professors at City College and the Freudenthal Institute in the Netherlands retrained more than 400 teachers in Districts 2 through 6 in Manhattan. Their analysis shows that students taught the New Math scored better on city and state standardized tests in 1999.
The study compared 454 students being taught the new way with 1,450 students instructed the traditional way. In grades 4 and 5, students in constructivist math scored at least 10 points higher. And the gap widened in classes with teachers who underwent the most extensive training, said City College Professor Catherine Twomey Fosnot, a co-author of the study. The results should puncture the arguments of critics who are using "scare tactics" to scuttle needed reform, Fosnot said...
Schools Chancellor Harold Levy said yesterday schools will continue to teach most students traditional math - not the new arithmetic that critics brand "fuzzy" math.
"For the vast bulk of students, the traditional program is the one that should be used," he said. "I want to make sure there are good, solid, traditional math programs all throughout the city . . . Children have to be able to add, subtract, multiply and divide numbers"...
Levy stressed he would not impose a "one-size fits all" curriculum on school district superintendents, and would continue to allow experiments with "alternative" math programs, as long as they're "standards-based" and sanctioned by the state. "In the rare exceptions where the superintendents make the decision that an alternative program is superior," he said, "they should be given the flexibility to innovate."
The "constructivist" movement has already riled at least one state education official. Merryl Tisch, a member of the state Board of Regents and former teacher, warned earlier this week that city education officials should "hunker down and focus on the basics."
But the chancellor insisted the new math has worked well in Manhattan's District 2 schools, despite criticism from some parents. He pointed out teacher training is crucial - and failing that, there will be problems no matter what curriculum is being taught.
"There's nothing in here that's fuzzy math," said District 2 Supt. Shelley Harwayne, who noted that 76 percent of her students meet or exceed state math standards. "Our program is aligned with the state standards"...
The chancellor has created a commission of experts that will soon issue a report on how mathematics should be taught in schools.
Tony Snow interviewed Lee Stiff, President of the National Council of Teachers of Mathematics, and Merryl Tisch, member of the New York State Board of Regents.
SNOW: About half the public schools in New York City are practicing a controversial teaching method called constructivist math. The method assumes that, one, children learn better from peers than teachers; two, retain information better if they discover it themselves; and, three, that most respond poorly to rote memorization...
Mr. Stiff, first let me start with the theory here. Do you really believe kids learn better from kids than teachers?
LEE STIFF...: As president of the National Council of Teachers of Mathematics, we propose [Standards-based] mathematics, which is not exactly the same as what you're talking about.
So, we don't think kids learn better from kids per se. Kids learn better from using materials and talking about ideas and having teachers direct them and help them, facilitating the instruction.
SNOW: Facilitating the instruction, how does that differ from standing up and saying, "OK, here are the times tables. Memorize them"?
STIFF: Well, ... it allows young people to see what the problems are all about. So by using manipulatives, we would call them, or those objects, they can actually cut and divide in ways that they can actually see what the amounts are and reason the answer.
SNOW: Ms. Tisch, what's wrong with that?
MERYLL TISCH...: There is absolutely nothing wrong with what the professor is saying. But what I really am seeing across New York State is a balance. And we believe very firmly that children need to learn to walk before they can run...They need to have the basics so that discovery and inquiry, which are part of the analytical reasoning that I think the professor is alluding to, becomes a natural process.
But we have found that as students are acquiring the basics, they are more able to enter into those discovery and inquiry exercises. And without the basics, we find that they are starting with a deficit...
STIFF: ...We want kids to learn the basics. We want kids to be able to add, subtract, multiply and
divide. We want kids to understand how that all works as well. So in addition to just being able to put down two and carry one, we want them to understand what the one represents. And we do this in a variety of ways.
So, when we talk about [Standards-based] mathematics, when we talk about young people having the opportunity to reason and do problem solving, we want to engage them at the very beginning. Basics are needed to solve problems, but the facility of solving problems happens with doing it, not waiting to some threshold moment in time where you all of a sudden begin to solve problems.
SNOW: But is there not a point at which doing it becomes impractical when you're dealing with large sums or where you start doing more complicated mathematical operations, when you start doing integration, for instance, to sort of...
STIFF: That's the power of the approach. We begin with reasonable sums so that young people understand the relationships. And then as they encounter larger sums that you spoke of, then they're better able to understand and see through that because they've had the experience with more manageable situations... So that in the situation that you showed in your problem to begin with, that was a very manageable situation of division and multiplying of fractions. So when it comes to a problem that involves larger numbers or more complex situation, they have something to look back on to inform them on how to handle a more complex situation...
It's "education week" in the U.S. Senate in the next several days, and lawmakers are set to debate various bills aimed at changing the American public school system. With George W. Bush eager to be known as the "education president," the work of Congress in this area is getting close scrutiny from the new administration.
Last week he touted an idea that he and lawmakers are working on to let youngsters shift from consistently poor schools to higher-performing ones in the public system.
Another hot topic up for debate is uniform annual testing of pupils.
Republicans and Democrats agree they need to close the yawning gap in test scores between lower- and upper-income pupils and to ensure that American students are academically competitive in a global economy.
Bush reiterated last week that he wants to hold public schools accountable for academic results by requiring annual state testing in the third through eighth grades.
In return for their taxpayers' money, "the local folks ought to develop accountability measures that tell us all whether or not children are learning to read and write and add and subtract," he said.
Bush also wants to require states to administer to a sampling of students in the fourth, eighth and 12th grades a national test, the National Assessment for Educational Progress, as a benchmark to measure school performance. The test is now voluntary.
Some powerful Democrats support the national testing idea, including Sen. Edward M. Kennedy, D-Mass., who says uniform standardized tests are necessary "so we have a reality check as to what's happening."
But Kennedy and Sen. Joseph Lieberman, D-Conn., say testing isn't enough. They and a number of centrist lawmakers have been negotiating with the White House to provide more money for private tutors and for training of teachers and principals to serve in the lowest-performing public schools.
Bush has proposed spending about $9.1 billion for services to schools that serve poor students, but Democrats are pressing for $15 billion. Senate Democrats also want $3.4 billion to hire and train teachers next year, while Bush's budget includes $2.6 billion.
"We don't want the testing to find out the need and leave the children wanting," Kennedy said. "Tests are not reforms. We need to get the help for the child when the child needs it."
Sen. Paul Wellstone, D-Minn., warns that too much standardized testing prompts teachers to narrow their focus and prepare students only to score well on exams -- at the expense of teaching broader and more important subject matter. Wellstone said that "over-emphasis on tests appeals to the least common denominator in education and is not most parents' idea of a quality education."
Some conservatives, such as Sen. Jesse Helms, R-N.C., who normally side with the president, oppose Bush's idea to force states to administer the National Assessment for Educational Progress. They argue that states, not the federal government, should determine which tests to use.
Several voucher proposals also are expected to spark heated debate.
Sen. Judd Gregg, R-N.H., plans to push one that would give parents of students in poorly performing public schools $1,500 vouchers each toward tuition at private schools, including religious ones. He and other Republicans are also expected to offer measures to create pilot programs allowing youngsters in public schools deemed "unsafe" to use vouchers to help them attend a private school.
But leaders of teachers unions, who vigorously oppose such voucher ideas, say they have mustered enough votes to kill them.
Randall Moody, a lobbyist for the National Education Association, says vouchers "are unacceptable because they drain money from public schools and violate the separation of church and state"...
The compromise idea Bush mentioned last Wednesday could gain strength on the Senate floor this week. It would allow parents of children in public schools that rank as failures for three or four years in a row to send their child to a higher-performing public school. Or the parent could choose to use some school funds to hire tutors or pay for summer school or outside-school academic programs from a list of state-approved providers.
As the Senate prepares to debate President Bush's education proposal, the White House and Senate Democrats remain at odds over a crucial element of the plan: the amount of money the government should spend to improve schools...
The difficult negotiations are threatening to undermine progress on an initiative that until recently seemed to have broad bipartisan support. Already, the stalemate has prompted Senate Majority Leader Trent Lott (R-Miss.) to postpone the start of the education debate on the floor, initially set to begin Monday, to Wednesday at the earliest, in hopes that an agreement can be reached...
Nowhere is the difference between Democrats and Republicans more glaring than in the amounts both sides envision spending on Title I, the federal government's main remedial education program.
Democrats say Title I spending should be increased next year by $15 billion, arguing that the subsidies reach only one-third of eligible schools. Bush favors a $9.1 billion increase...
Beyond the debate over money, a wide range of interest groups have concerns with the bill, which would consolidate scores of education programs, require annual tests in grades three through eight and allow as many as seven states to receive the education funding as a block grant in return for strict accountability provisions...
Amy Wilkins, co-partner of the Education Trust, an education lobbying group that initially supported the Bush plan, complained that the measure's student testing provisions are being watered down. Rather than requiring states to offer the same standardized test, the bill would allow school districts to offer different tests from year to year. "If the bill goes through as is, it will be nothing more than a cheap political victory for Bush," Wilkins said. "Tests need to be comparable over time."
The education plan is expected to face an even more difficult course in the House. Some GOP House members oppose a part of Bush's plan that would require a sample of students in each state to take the National Assessment of Educational Progress (NAEP) test. Bush envisions the nationwide test as a benchmark for state exams, an idea that conservatives and others resist because they see it as the first step toward a national curriculum.
"It is true that all 50 states do not have high-quality rigorous exams based on their standards," said Bruce Hunter, public policy director for the American Association of School Administrators. "But you can tell that without using NAEP as a benchmark. Our position is that we don't want a national test"...
The disagreements over federal education policy parallel past fights. In particular, Democrats are eager to continue initiatives launched under former president Bill Clinton to allot federal money to reduce class sizes and build schools, whereas Republicans are interested in freeing local school districts to spend federal aid as they see fit while imposing stricter rules to hold school systems accountable for student performance...
The tests that are playing an increasingly central role in education need to be changed substantially to reflect new knowledge about how people think and learn, a report released last week asserts.
The report, by a committee of the National Research Council, argues that the combination of new research about cognition and advances in technology and measurement provides an "opportune time" to rethink the theoretical underpinnings of assessments.
"One of the central dilemmas in testing policy in the United States has been the collision between tests used for accountability purposes and the same tests' being used to inform instruction," said Michael J. Feuer, the executive director of the NRC's Center for Education. "What this report gives us is a road map that would go a long way to connecting tests that can be useful for accountability but that can also provide information for teachers and students."
Many existing tests, the report notes, focus on discrete bits of knowledge and skill rather than on the most complex aspects of student achievement. They do not chart students' progress over time, nor do they provide adequate insights into students' thinking strategies, the nature of their misunderstandings in particular subjects, or the types of help that could best improve learning.
The council's 17-member Committee on the Foundations of Assessment proposes a "major program of research" that would synthesize current thinking about cognition and measurement in order to design new tests that could yield fairer and more accurate information about students.
It also recommends that states and districts sample a broader range of student competencies and understandings by using a variety of testing techniques or multiple measures of student performance.
"One of the things that we're pushing for is more coordinated systems of assessments," which might include such alternative measures as portfolios and tasks that students complete during the course of ongoing classroom instruction, said Naomi Chudowsky, the study's director.
As part of that effort, the report advocates shifting more attention and resources toward the classroom assessments given by teachers and away from high-stakes, large-scale exams.
"The current educational assessment environment in the United States assigns much greater value and credibility to external, large- scale assessments of individuals and programs than to classroom assessment designed to assist learning," the report says. "A vision for the future is that assessments at all levels-from classroom to state-will work together in a system that is comprehensive, coherent, and continuous."
Although creating such coherent assessment systems would require more time and money, Mr. Feuer said, doing so is not unrealistic. He noted that the U.S. Senate has proposed $400 million in fiscal 2002 to help states create new tests. "Even on Capitol Hill, they know if they're going to get this next round of testing right, it's going to require a sizable investment," he said.
The National Research Council's report, "Knowing What Students Know: The Science and Design of Educational Assessment," argues that in the past four decades, studies of the human mind have provided considerable insight into how children develop conceptual understanding, how people acquire expertise in particular subjects, and which thinking processes are associated with competent performance.
At the same time, advances in measurement technology mean it's now possible to characterize student achievement in terms of multiple aspects of proficiency rather than a single test score, to track students' growth over time, and to analyze which factors contribute to student learning.
Despite such advances, the report says, most tests remain mired in the past, reflecting earlier theories of learning characterized as the step-by- step accumulation of facts, procedures, and definitions.
"What we have is an approach which literally takes bits and pieces of information and treats them as largely substitutes for one another, and doesn't do justice to the nature of knowledge and understanding," said James W. Pellegrino, a co-chairman of the NRC committee and a professor of cognitive studies at Vanderbilt University.
Although current tests do a reasonable job of measuring students' knowledge of basic facts and procedures, the report says, they provide very limited information that educators can use to identify why students do not perform well or how teachers can best modify instruction.
The committee, whose work was supported by the National Science Foundation, suggests crafting a new generation of assessments founded on advances in cognitive research, technology, and measurement.
"If we would spend more time on careful, thoughtful crafting of the assessments and getting them to the point where they could answer the kinds of questions we want answered," said Mr. Pellegrino, "then ultimately, these instruments would be far more valuable, and the investments would have a far greater return."
The committee recommends basing assessments on an underlying theory of how student understanding develops in a content area. That theory, in turn, should be based on empirical studies and models of how people learn and exhibit expertise in a particular subject, such as geometry.
Such assessments should focus less on isolated facts and skills and more on how students organize factual and procedural knowledge in a subject, the report argues. Tests also should probe how students monitor or reflect on their own thinking-a process known as "metacognition" that is one of the hallmarks of expertise. And tests should examine the specific strategies that children use to solve problems.
To make assessments fairer, the committee also urges that students' opportunities to learn the material being tested be taken into account both in designing tests and in interpreting children's responses.
Too often, the report says, teachers' classroom-based assessments mirror the same testing formats and scoring practices found in large-scale tests. The report advocates that instruction about assessments and about how students learn become a required part of teacher-preparation and professional-development programs. Such education should be linked to actual experiences in classrooms, both in assessing students and interpreting their development of competence, the report says. And it suggests that states require such teacher education through their licensing and accreditation standards.
In addition, the report calls for new ways of reporting test results that focus less on ranking students and schools and more on tracking students' development of competence within a subject. Such reporting would include specific benchmarks and examples of where students stand on a continuum of learning.
The panelists argue that alternatives to on-demand, standardized testing of every child already exist. If individual scores are needed, their report says, much richer information about children's learning could be extracted from classroom work produced during the course of instruction, through such means as portfolios and tasks that students complete while learning the curriculum, but that are common across schools or districts.
If the primary purpose of the tests is program evaluation or accountability, the committee says, it may not be necessary to test every student.
The report is particularly optimistic that new advances in technology could help remove some of the constraints that have limited testing practices in the past. Sophisticated computer-based programs, for example, can track the sequence of actions students take to solve problems, analyze patterns of correct and incorrect reasoning, and provide rapid and informative feedback to students and teachers, while also serving accountability purposes.
One of the best examples, Mr. Pellegrino said, is "intelligent tutoring" systems, such as those used in algebra. Students answer questions on a computer, which matches their responses to a cognitive map of how student thinking in algebra develops over time.
When a student asks for help, the computerized "tutor" can estimate where the student is in his or her development and provide hints that are tailored to the student's particular approach to the problem.
Bringing together scientists, educators, task designers, and psychometricians to work on such efforts, the report argues, could result in a "significant leap forward in the field of assessment."
COMET is sponsored in part by a grant from the California Mathematics Project.
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