Source: Kay Garcia, NBCT, California Department of Education - 916-323-5832
The November 2002 announcement of 651 newly certified National Board Certified Teachers (NBCTs) in California included 42 math teachers. Each of these accomplished teachers spent the last school year compiling a portfolio of their practice in addition to taking a three-hour exam. Now comes the fiscally rewarding part: these teachers will be applying for a $10,000 incentive award from the state. Those working in low-performing schools may apply for an additional $20,000 award.
For information about the National Board certification process, the incentive awards, and support that is available for California teachers, please visit http://www.cde.ca.gov/pd/nbpts/ For a list of NBCTs, visit http://www.nbpts.org/nbct/directory.cfm where you can search by name, certificate, state, and year. Two separate certifications are available for math teachers: Middle Childhood through Early Adolescence/Mathematics and Adolescence and Young Adulthood/Mathematics.
On 3 December 2002, California Governor Gray Davis stated, "National Board Certification is a powerful professional development tool that signifies a teacher has achieved excellence in the classroom. I offer my sincere congratulations to all the teachers who have received this prestigious designation. This process will strengthen the teaching profession and ultimately lead to greater academic achievement among all of California's students."
Source: The Boston Globe - 8 December 2002
For the past few years, Massachusetts educators have worried as students' MCAS math scores have lagged stubbornly behind gains in English. When results released this fall revealed a yawning gap between the two subjects, the state's education chief--himself a former math teacher--called for a math "revolution."
Most educators agree any efforts must go beyond fine-tuning teaching methods or making more time for tutoring, to a radical alteration of the way schools and society approach a subject that has tripped up students for years. Many Massachusetts school districts are grappling with how to launch that effort as students who have repeatedly failed the MCAS, many of them just the math portion, prepare to take a retest this week.
The move has taken on new urgency: Across the state, universities are unveiling math projects with local schools to bring the subject to life, while other districts are insisting teachers cooperate across grades to help students tackle increasingly difficult concepts. Some schools are aggressively analyzing student data to target weaknesses, and still others are taking their cues from programs hailed in other countries as a key to accelerating students' grasp of math. Some communities are simply focused on making students feel good about math, working to make it more fun and friendly, dispel phobias about it, and encourage all students to embrace it.
And in a state where education leaders rarely weigh in on how schools should go about teaching students, state officials are drumming up support for pilot projects using "Singapore math," a curriculum they say could be the answer for some districts. On Friday, it was introduced to 70 educators.
Piloted locally in North Middlesex Regional Schools, the program was developed in Singapore, where in 1999, eighth-graders earned first place in the Third International Mathematics and Science Study [TIMSS], while US students' scores put them far down in the pack. Singapore math relies heavily on visuals and employs increasingly complex word problems to teach skills. It focuses on finding different ways to solve and express problems, not simply formulas taught by a teacher.
"I don't consider Singapore math to be the be-all and end-all," said state Education Commissioner David Driscoll. "But I think there are too many people out there who don't even know how to get started. They need a hook; they need a program."
Massachusetts is not the only state struggling with a math problem--or realizing it must find a solution. Vermont, for example, is retraining elementary teachers to incorporate algebra concepts as early as kindergarten.
Some argue the Bay State is not even so bad off. On tests such as the National Assessment of Educational Progress, known as the Nation's Report Card, Massachusetts students outperform most of their counterparts in other states. But Driscoll notes that when two other measures are considered, the picture is not so rosy: The United States is outperformed by many countries in the international survey, and the MCAS shows that math performance among Bay State students appears to have plateaued.
And in Massachusetts, the MCAS is king. Students must pass the 10th-grade MCAS in both math and English to graduate (25 percent of 10th-graders in 2002 failed the math test, compared with 14 percent who failed the English). The state's test is also the gauge used by the federal government under the new "No Child Left Behind Act" to measure whether Massachusetts schools are making the progress they should.
State education officials are bothered by more than the simple fact that large numbers of students in some grades are still failing MCAS math--including one-third of eighth-graders last spring, for example. The number of students scoring in the advanced and proficient levels--the top two tiers of a four-tier scoring system--has hardly changed in five years in some grades.
"The real issue for me is not just getting kids out of the basement," said Sandra Stotsky, a state associate commissioner of education. "The issue is why aren't we improving in the number of kids in the top two categories?"
Recently, the Education Department launched a study into how schools performed on the eighth-grade math MCAS to identify why some have successfully pushed more students into the higher-scoring levels. Do they have smaller classes? Work in groups? Use a particular program? Spend more class time on math?
"We are really quite concerned to find out what is going on in schools that seem to be able to move kids across whole category levels," Stotsky said.
Math specialists and teachers blame a variety of things for the lack of US progress in math, including a culture that does not appreciate math and fosters a fear of the subject. Some say that wars over the best way to teach math--similar to battles over teaching reading that were waged in the last two decades--have moved many educators and specialists toward extreme ends of the philosophical spectrum and muddied the discussion.
Tom Fortmann, a math consultant to Mass Insight Education, says students have been "drilled in certain procedures, such as how to do long division or multiplication, but they frequently don't know what they're doing. Many of them don't know what multiplication is," he said. "They were conditioned into the mode, where a teacher shows them how to do something and they repeat it."
A core problem, according to some specialists, is that many teachers--particularly in elementary and middle school, where many of them are trained as generalists--don't know math themselves well enough. Some are simply intimidated.
"Teachers are not taught enough math, and not enough students with mathematical aptitude go into teaching," said Wilfried Schmid, a Harvard professor of mathematics who helped draft the state's most recent K-12 math curriculum guidelines. "This is a worldwide phenomenon. You hear this everywhere."
Others say some teachers with a good grasp of math haven't been shown effective ways of teaching it. State officials are hoping that some newly strengthened teacher licensing requirements that kick in next fall will help prepare incoming teachers. In the meantime, some districts are trying to boost the know-how of current teachers and give them programs and training that work, all in hopes of improving future math MCAS scores.
Two years ago, North Middlesex schools teamed up with Fitchburg State College to begin training teachers in Singapore math. Now found in 80 schools nationwide, the program expects students to master skills early and continue to use them as courses grow more advanced. "It created a belief system among us that kids can learn more math," said Mary Waight, associate superintendent for curriculum. "We're no longer marching through the math textbook."
All eighth-graders in the district are now enrolled in algebra--up from only 25 percent a few years ago, Waight said...
"They're seeing things that are challenging and difficult and they can do it," said Karin Pillion, a 17-year veteran teacher, who says she is teaching difficult math concepts earlier. She has used Singapore math in her fourth-grade classroom since the district decided to test it out.
Singapore math is now in 55 classrooms in North Middlesex--or about a third of them. And already district officials say they're seeing results. About 78 percent of sixth-graders who used it for at least a year scored in the proficient or advanced categories of the math MCAS in 2002, compared with 53 percent of students in other math programs.
"They've really risen to the challenge," Pillion said. "They're really involved in the math thinking."
(2) "A Coherent Curriculum--The Case of Mathematics" by William Schmidt, Richard Houang, and Leland Cogan
Source: American Educator - Summer 2002
William Schmidt is the director of the U.S. National Research Center for the Third International Mathematics and Science Study (TIMSS), where Richard Houang is the associate director and Leland Cogan is a senior researcher... Sections of this article were adapted from "Curriculum Coherence: An Examination of U.S. Mathematics and Science Content Standards from an International Perspective," a research paper that is being prepared for publication, and from "The Implications of TIMSS for Teacher Quality," a speech delivered by Dr. Schmidt at the AFT/NEA Conference on Teacher Quality. The article is also based on research first described in Why Schools Matter, Facing the Consequences, and A Splintered Vision.
... A new analysis of data from the Third International Math and Science Study (TIMSS) provides evidence that American students and teachers are greatly disadvantaged by our country's lack of a common, coherent curriculum and the texts, materials, and training that match it.
Some people think that the purpose of an international comparison is to see which country is best and then get the U.S. to emulate its practices. That idea is na¥ve. You cannot lift something from one cultural context and expect it to work in another. But international research can cause us to challenge some of our common assumptions about education and consider alternatives to what we are doing. First, let us briefly review what TIMSS is and the TIMSS findings to date, which have been published in a series of previous reports. Then we will turn to our more recent findings in grades one through eight mathematics curricula, in which we can see that high-performing countries teach a very similar, very coherent, core math curriculum to all of their students--and we, decidedly and clearly, do not. Lastly we will look at the importance of this finding by examining the cascade of benefits that flow from attaining a coherent, common curriculum.
I. The Early TIMSS Findings
TIMSS is the most extensive and far-reaching cross-national comparative study ever attempted. It was conducted in 1995, with 42 countries participating in at least some part of the study. TIMSS tested three student populations: those who were mostly nine years old (grades three and four in the U.S.); those who were mostly 13 years old (grades seven and eight in the U.S.); and students in the last year of secondary school (12th grade in the U.S.). In addition to the student tests, the study included a great deal of other data collection, including extensive studies of curriculum. Findings from the curriculum study are the heart of this article; but first, let's review what's already been reported in the general press about TIMSS.
The Horse Race
The horse race--who comes in first, second, and third--is not particularly important in and of itself. In fact, the ranking of nations is simply the two-by-four by which to get people's attention. At the fourth-grade level, the U.S. did reasonably well on the TIMSS exam. Our students scored above the international average in both math and science. In science, in fact, we came very close to being number one in the world; our fourth-graders were second only to the South Koreans. In mathematics, on the other hand, our performance was only decent; it was above average, though not in the top tier of countries. (Detailed findings, including tables and graphs, can be found on our Web site, http://ustimss.msu.edu, or at the U.S. Department of Education's TIMSS Web site, http://nces.ed.gov/timss). By eighth grade, however, the U.S. dropped to the international average, slightly above average in science and slightly below average in mathematics. In other words, just four years along in our educational system, our scores fell to average or even below average. The decline continues so that by the end of secondary school our performance is near the bottom of the international distribution....
One of the most important findings from TIMSS is that the differences in achievement from country to country are related to what is taught in different countries. In other words, this is not primarily a matter of demographic variables or other variables that are not greatly affected by schooling. What we can see in TIMSS is that schooling makes a difference. Specifically, we can see that the curriculum itself--what is taught--makes a huge difference...
These findings emerged from a substantial line of research within TIMSS that examined what is taught in 37 countries. To get a rich picture of math and science instruction in each country, we looked at the "intended" content--that is, what officials intended for teachers to teach; and "enacted" content --that is, what teachers actually taught in their classrooms...
Based on these early analyses of TIMSS data, we can characterize the intended math and science content (as stated in sets of standards and textbooks) in the U.S., relative to others in the world, in four ways:
1. Our intended content is not focused. If you look at state standards, you'll find more topics at each grade level than in any other nation. If you look at U.S. textbooks, you'll find there is no textbook in the world that has as many topics as our mathematics textbooks, bar none. In fact, according to TIMSS data, eighth-grade mathematics textbooks in Japan have around 10 topics, but U.S. eighth-grade textbooks have over 30 topics. And finally, if you look in the classroom, you'll find that U.S. teachers cover more topics than teachers in any other country.
2. Our intended content is highly repetitive. We introduce topics early and then repeat them year after year. To make matters worse, very little depth is added each time the topic is addressed because each year we devote much of the time to reviewing the topic.
3. Our intended content is not very demanding by international standards. This is especially true in the middle-school years, when the relative performance of U.S. students declines. During these years, the rest of the world shifts its attention from the basics of arithmetic and elementary science to beginning concepts in algebra, geometry, chemistry, and physics.
4. Our intended content is incoherent. Math, for example, is really a handful of basic ideas; but in the United States, mathematics standards are long laundry lists of seemingly unrelated, separate topics. Our most recent analysis has more to say about this and we will return to it in the next section. As a result of these poorly designed standards and textbooks, the curriculum that is enacted in the U.S. (compared to the rest of the world) is highly repetitive, unfocused, unchallenging, and incoherent, especially during the middle-school years. There is an important implication here. Our teachers work in a context that demands that they teach a lot of things, but nothing in-depth. We truly have standards, and thus enacted curricula, that are a "mile wide and an inch deep."
One popular response to a study like TIMSS is to blame the teachers. But the teachers in our country are simply doing what we have asked them to do: "Teach everything you can. Don't worry about depth. Your goal is to teach 35 things briefly, not 10 things well."
II. The Coherent Curriculum
Discussion of the TIMSS achievement results has prompted policymakers in the U.S. and elsewhere to wonder just what it might mean to have a world-class mathematics or science curriculum. In response to this interest, we investigated the top achieving TIMSS countries' curricula in mathematics and science to distill what they considered essential content for virtually all students over the different grades of schooling. With this new analysis, we can go beyond the critique of our "mile-wide-inch-deep curricula" and look at the character and content of a world-class curriculum. Although we conducted this analysis for both math and science, in this article we will only address the math findings.
After identifying the top achieving (or A+) countries and devising a methodology to determine the topics that were common to their curricula, we developed a composite set of topics consisting of the topics that at least two-thirds of the A+ countries included in their curricula...Next, composites for U.S. mathematics standards from 21 states and 50 districts were also developed and compared to the A+ composite...
To date, most discussions and evaluations of the quality of American standards have revolved around such characteristics as clarity, specificity, and, often, a particular ideology. For example, in mathematics these distinctions have been revealed in what is called the "math wars," a debate over what constitutes basic mathematics for the school curriculum.
With our look at the A+ composite, our definition of quality moves beyond these issues to what we believe is a deeper, more fundamental characteristic. We feel that one of the most important characteristics defining quality in content standards is what we term coherence.
We define content standards and curricula to be coherent if they are articulated over time as a sequence of topics and performances that are logical and reflect, where appropriate, the sequential or hierarchical nature of the disciplinary content from which the subject matter derives. That is, what and how students are taught should reflect not only the topics that fall within a certain academic discipline, but also the key ideas that determine how knowledge is organized and generated within that discipline.
This implies that "to be coherent," a set of content standards must evolve from particulars (e.g., the meaning and operations of whole numbers, including simple math facts and routine computational procedures associated with whole numbers and fractions) to deeper structures inherent in the discipline. This deeper structure then serves as a means for connecting the particulars (such as an understanding of the rational number system and its properties). The evolution from particulars to deeper structures should occur over the school year within a particular grade level and as the student progresses across grades.
Based on this definition of coherence, the A+ composite is very strong and seems likely to build students' understanding of the big ideas and the particulars of mathematics and to assure that all students are exposed to substantial math content.
In sum,...some topics were designed to provide a base for mathematics understanding and, correspondingly, were covered in the early grades. Increasingly over the grades, the curricula of the top achieving countries becomes more sophisticated and rigorous in terms of the mathematics topics covered. As a result, it reflects a logic that we would argue is inherent in the nature of mathematics itself... the U.S. state and district standards do not reflect a comparable logical structure...
This common, coherent curriculum makes possible a cascade of benefits for students' education. The possible net effects of these benefits are: 1) to positively influence overall student achievement (as reported in the opening section of this article); 2) to greatly reduce the differential achievement effects that are produced (in the U.S.) by standards and curricula of different quality; and, as a result, 3) to substantially weaken the relationship between student achievement and socioeconomic status (a link which is quite strong in the U.S.)...
Lower Achievement and Less Equity
...We saw at the beginning of this article that the average achievement in the U.S. is low in comparison to many other countries. Moreover, the gap in students' achievement between our most- and least-advantaged schools is much greater than the comparable gap in most TIMSS countries.
In fact, a recent study conducted by researchers at Boston College demonstrated that in the U.S. about 40 percent of the variation among schools in students' test scores is explained by socioeconomic factors. In comparison, across all of the TIMSS countries, socioeconomic factors explain less than 20 percent of this type of variation.
We believe that America's poor average achievement, as well as our strong link between achievement and SES, can be traced in part to our lack of a common, coherent curriculum. The A+ countries have a common curriculum for virtually all students through the eighth grade. In those countries, all schools have roughly comparable access to the full array of materials, professional development, and assessments that can help teachers lead students to high achievement. Further, students' opportunities to learn are enhanced by the benefits that accompany a common curriculum: teachers can work together with a shared language and shared goals; new teachers can receive clear guidance on what to teach; professional development may be anchored in the curriculum that teachers teach; textbooks may be more focused and go into greater depth with a smaller set of topics; and transient students (and teachers) may more easily adapt to new schools. All of this contributes to greater consistency and quality across schools...
Articles interspersed among the pages of the article above include the following:
(1) "The Benefit to Equity" by E.D. Hirsch, Jr.
(2) " The Benefit to Subject-Matter Knowledge" by William Schmidt --
"Professional development in high-performing countries is generally geared to the grade in which teachers teach. The subject matter content and how to teach it are often the focus. It is about the content that they are teaching their students in the classroom, not about abstract mathematical or other content. In turn, it's not necessary to teach all teachers in a particular field, like mathematics, advanced topics--not all math teachers need to take and know calculus. What fourth-grade teachers need, for example, is an advanced treatment of elementary mathematics..."
(3) "The Benefit to Professional Development" by American Educator Editors
(4) "The Case of California" by David Cohen and Heather Hill
(5) "Content Matters Most" by Mary Kennedy
COMET is sponsored in part by a grant from the California Mathematics Project.
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