COMET • Vol. 7, No. 02 – 17 January 2006


State Schools Chief Jack O’Connell Appoints  William Padia Deputy Superintendent for Assessment and Accountability

Source: California Department of Education

On Friday, January 13, Superintendent of Public Instruction Jack O’Connell announced that he has appointed William L. Padia as Deputy Superintendent for the Assessment and Accountability Branch of the California Department of Education (CDE).

“After a lengthy nationwide search for a deputy in charge of assessment and accountability, I found the best candidate right here in the department,” O’Connell said. “Bill Padia’s reputation and record of accomplishment are well established and he is respected by teachers, administrators, and policy makers throughout the state. He is well steeped in the issues facing the Assessment and Accountability Branch. I look forward to benefiting from Bill’s wisdom and experience in his new position.”

Padia has served as the director of CDE’s Policy and Evaluation Division since 1988. During that time, he led CDE’s efforts to develop and implement the Academic Performance Index, California’s accountability system, and the No Child Left Behind federal accountability system. He also implemented the requirements of the School Accountability Report Card, conducted policy studies and legislatively mandated evaluations, and administered state and national school recognition programs.

From 1979-1988 Padia served as CDE’s administrator in charge the Special Studies and Evaluation Reports Unit. He previously served as a consultant in CDE’s Office of Program Evaluation and Research.

Padia earned a bachelors degree, master’s degree and doctorate in educational research from the University of Colorado. In 2005, he was awarded the Lifetime Achievement Award by the California Educational Research Association.

He replaces Geno Flores, who left the Department of Education last fall to become Deputy Superintendent of the San Diego Unified School District.


(1) “Teaching to the Test” by Cathy Seeley

Source: National Council of Teachers of Mathematics (NCTM)

How can we balance teaching good mathematics and preparing for the state or provincial test? Are there effective test-preparation strategies that support student learning? Join NCTM President Cathy Seeley for an online chat about these and related questions on Thursday, February 2, at 1:00 p.m. PST or submit your comments beforehand at

[Background: President’s Message]  Our tests are driving our teaching. This is the message from coast to coast as pressure mounts to produce results and meet the Adequate Yearly Progress requirements of the No Child Left Behind (NCLB) Act. Is this good or bad, and can a good mathematics program survive in this kind of environment?

Accountability is important in mathematics teaching. As professional mathematics educators, we must be able to demonstrate that our students are learning mathematics. Furthermore, the reporting of group data required by NCLB sheds light on gaps and problems within the mathematics program, including whether any group of students is achieving or not. Nevertheless, the kinds of tests that many states require, and the ways that many schools prepare their students for these tests, have serious limitations.

On the positive side, if a test assesses important mathematics in ways that require students to demonstrate mathematical thinking and proficiency, the test might effectively support a comprehensive mathematics program. For example, the state tests used in Connecticut and Washington call for students to complete a variety of mathematical exercises, including open-ended problems designed to require more complex thinking than what is called for in many state assessments. Students in a well-balanced mathematics program anchored in understanding, proficiency, problem solving, and mathematical thinking are likely to do well on these tests with or without special preparation strategies.

However, many state tests fall short of this ideal. Some are based solely on content that can be tested economically in a multiple-choice format, which often encourages students to try out all possible answers to a problem rather than actually solving it. Furthermore, although some state curriculum standards may include complex and high-level mathematical ideas, testing students’ understanding of these ideas is not easy. This important content may get overlooked as teachers prepare students for items that are most likely to be included on the test. We must be cautious about the decisions that we make about students on the basis of such measures. No decision about a student’s future should be based on any single measure, particularly a large-scale measure with inherent issues of context, bias, and intended purpose.

In too many schools, teachers are expected to “set aside” their mathematics program and instead prepare students for the state test. This may mean weeks or even months of missed instructional time. If preparing for the test means practicing a few items to get used to the format, it might serve students well. Too often, however, test preparation also includes learning tricks and tips that may or may not prove helpful on the test. For example, some schools use materials built on “clue words” for solving story problems or teach other tricks about what to do if presented with particular types of problems. Students memorize such phrases and words as all together, more than, and total, associating each with a particular operation. This type of practice falls apart on two levels. First, it misleads students. For any clue word or trick, most of us could create a test item for which the trick does not work. Second, the time that students spend memorizing tricks or words without understanding the related mathematics is precious time they lose from instruction that could support their mathematics learning. Students are better served by learning the concepts behind the numbers and operations so well that they carry mental pictures of what addition, subtraction, multiplication, or division mean. Recognizing a mathematical operation in the context of a problem and knowing how to perform the operation are far better preparation strategies than memorizing tricks or a list of words.

One other method of teaching to the test is periodic benchmark testing. Some school systems expect students to take tests throughout the year that are similar in format and content to the state accountability test. This can be an appropriate application of datadriven decision making. However, to be effective, any such strategy should be weighed according to cost and benefit. How much information is gained in a usable and timely manner for guiding and improving students’ learning on a day-to-day basis? And what are the costs in instructional time and teacher time for planning, administering, interpreting and reporting results, and incorporating those results into the teaching process? These questions are essential to consider in any decision about testing and preparing for tests.

The best preparation for any test is teaching a good mathematics program well to every student. Even if the accountability test is a less-than-ideal measure, a strong mathematical foundation can prepare students to perform well. The reverse is not true, however. If we focus on test preparation at the expense of longterm learning, we may see short-term gains, but students are unlikely to be able to build on their learning from year to year. And some schools that devote excessive time to test preparation at the elementary grades may actually find, a few years later, that their middle school test scores have fallen. The bottom line is that professional mathematics educators need to be skeptical consumers of test-preparation programs and materials and knowledgeable judges of quality assessment practices that support students’ learning. Most of all, professional mathematics educators need to be outspoken advocates for students, raising our voices when testing practices may not serve the best interests of students.


Related Link — NCTM’s position statement (January 2006) about high stakes testing:

(2) “Adding Up Math Problem” by Heather Bremner

Source: Gilroy Dispatch – 16 January 2006

It’s a simple concept: Learn the basics and use them as the building blocks as you excel.

But those seemingly obvious steps are exactly what elementary and middle school educators are neglecting when they teach mathematics and that oversight has caused a frightening trend in American society: math illiteracy.

“The problem is children don’t learn in elementary school,” said Hung-Hsi Wu, a University of California, Berkeley, math professor. “Many haven’t learned times tables. Imagine trying to write an essay without knowing your ABCs. How do you teach someone English if he refuses to memorize the alphabet?”

That was one of the issues Wu discussed with the 55 or so teachers, administrators and board members who attended last Saturday’s math summit at the Gilroy [California] Unified School District. The summit is just the beginning of the district’s efforts to reverse a stubborn trend–that student performance in math continues to drop after the fourth grade.

Wu, who conducts summer math institutes, and R. James Milgram, a Stanford University math professor, spent the day discussing ways to improve the way teachers teach math in the elementary and middle school so students master basic skills before entering high school…

At the onset of the seminar, Superintendent Edwin Diaz gave a general introduction and showed the group student performance on the California Standards Test in math. Gilroy students are improving steadily but there is a drastic drop when students make the transition from third to fourth grade that continues to fall all the way through high school. And once students enter high school the decrease is significant.

GUSD Assistant Superintendent Jacki Horejs, who helped organize the seminar, pointed out that although there is steady growth from year to year, the issue is that CST scores continue to decrease significantly in the upper grades.

“The same trend exists in the state (and nation),” she said. “This is a national trend.”

In the afternoon, participants broke off into groups and each discussed a specific area of math instruction.

One group addressed the issue of time, particularly looking at the 45-minute periods for middle school students and Gilroy High School’s block schedule. The middle school periods are too short for students to develop a real foundation and because of the block schedule at GHS, students have math every other day, Horejs said.

Participants discussed offering incentives, signing bonuses and extra stipends to attract qualified math professionals to the teaching field. They also talked about staging Saturday and summer academies. Wu said he will hold at least three weekend sessions in Gilroy, Horejs said.

Milgram, who serves as an advisor to NASA and the U.S. Department of Education, said the concern is not that scores are low in math but that so few students are reaching advanced or proficient levels.

“What is desired by everybody is that at least 50 percent of the students should score in those categories,” he said.

Both Milgram and Wu said although scores are the lowest in the upper grades, high school is not the problem. Students aren’t learning the basics because teachers aren’t adding key ingredients to math instruction in elementary and middle school.

Those three basic components – unambiguous statements, no hidden assumptions and defining basic terms – are the building blocks of math. And teachers aren’t defining simple skills such as multiplication, division and fractions.

“And without those definitions nothing makes sense,” Milgram said.

Jenny Belcher, a South Valley Middle School math teacher and one of the educators who attended Saturday’s summit, said she’s really happy that the district has identified the problem and is doing something to remedy it.

Belcher, who has taught for 20 years and was Gilroy Economic Foundation teacher of the year in 2003 and GUSD teacher of the year for Santa Clara County in 2003, echoed Milgram and Wu’s comments that students aren’t learning the basics.

“The further it goes the worse it gets,” she said.

Belcher also said because the majority of elementary school teachers’ strengths lie in the liberal arts and aren’t trained in mathematics, students don’t receive a firm math foundation before middle or high school…

(3) “Big Cities Credit Conceptual Math for Higher Scores” by Sean Cavanagh

Source: Education Week – 11 January 2006

The two city districts that made the greatest strides in math on the latest national assessment relied on similar strategies: building students’ conceptual math skills and investing in professional development in that subject for elementary and middle school teachers.

While administrators in Boston and San Diego say that many factors were at work in their gains on the recent National Assessment of Educational Progress, they believe their approach is giving students greater ability to solve a broad variety of math problems and preparing them for more complex mathematics later in school.

“It’s not enough to memorize algorithms,” said J. Chris Coxon, the deputy superintendent for teaching and learning in the 57,000-student Boston district. “If [schools] are going to be successful in teaching math, they have to be open to students’ using different ways of solving math problems.”

Conceptual math generally seeks to cultivate students’ overall understanding of different math concepts, and lessen their reliance on memorizing set formulas and procedures. San Diego and Boston officials, as well as many math and curriculum experts, believe that approach is helping students learn to solve problems in a variety of ways, as well as preparing them for higher-level math.

Both districts’ math efforts have received grant money in recent years through the National Science Foundation. The independent federal agency has been a strong supporter of conceptual math.

NAEP provided results last month as part of what is known as the Trial Urban District Assessment. The test showed average math scores for 11 urban districts rising at both the 4th and 8th grade levels. Such gains were not echoed in reading, where performance remained mostly stagnant.

Overall, urban schools remained well below national averages in both subjects, with greater percentages of students showing only “below basic” skills. Boston and San Diego, by contrast, each had combined improvements at the 4th and 8th grade levels in math that exceeded those nationwide gains.

Still, some math researchers are reluctant to attribute the districts’ improvements in scores to a commitment to conceptual math, or any single educational strategy.

“It’s not wise to read too much into one wiggle in NAEP data,” said Tom Loveless, a senior fellow at the Washington-based Brookings Institution, who has studied state and local math scores in depth.

Many Approaches

Researchers and school officials have debated for years the most effective way to teach math. The so-called “math wars,” which gained intensity in the late 1990s, featured supporters of a more conceptual approach to teaching math arguing from one perspective. Backers of conceptual math see evidence of its effectiveness in foreign nations, particularly in Asia, whose students routinely outperform their U.S. peers on tests of math skill.

Critics of that approach, however, said American students’ shortcomings were most likely the result of a lack of fundamental math skills.

In recent years, both camps have emphasized that a balance between conceptual math and basic skills is needed.

San Diego and Boston officials say they had no interest in revisiting those math conflicts.

Kris Acquarelli, the mathematics director for the 137,000-student Southern California district, said the school system has made changes in its approach to math over the past five or six years, some of them with the help of philanthropic and corporate backers, such as the San Diego-based technology giant Qualcomm Inc.

A central focus of San Diego’s plan has been to make math more digestible for teachers and students alike. While the district uses state-approved math textbooks at all grade levels, many elementary teachers–particularly inexperienced ones–have difficulty choosing lessons and determining which areas of math should receive the most emphasis.

To help them, San Diego officials produced a number of additional materials, including “curriculum maps,” which point to important concepts in textbook chapters; pacing guides, which help teachers balance the amount of time spent on various topics; and modules, which give teachers ideas for individual lessons.

“They help teachers navigate the curriculum,” Ms. Acquarelli said of those tools.

An overriding goal is to broaden students’ overall problem-solving skills, rather than just encouraging them to memorize formulas. “We want to make sure they learn the meaning behind the mathematics,” she said, “rather than just rules and procedures.”

San Diego is also aggressively promoting professional development, according to Ms. Acquarelli. The district arranges workshops throughout the year for K-12 teachers, some mandatory, some optional. It also has placed math resource teachers, instructors who are especially strong in the subject, in its lowest-performing elementary schools.

More Math for Teachers

The National Council of Teachers of Mathematics, in Reston, Va., has encouraged states and teacher-training programs to require more math of aspirants. Teachers need to have taken enough math courses to understand how basic concepts lead to more complex topics, NCTM President Cathy L. Seeley said.

“You need to know more than just elementary math to teach elementary math,” said Ms. Seeley, a research fellow at the University of Texas at Austin.

Michelle Collins, a 4th grade teacher at Ibarra Elementary School in San Diego, considers herself fortunate. Her master’s-degree training included an emphasis in math. But when she joined the district five years ago, many elementary instructors struggled to find the best way to use textbooks or interpret the goals outlined in California’s state standards, she recalled. The pacing guides and workshops have helped, she said.

“We talk openly about our comfort level in math,” Ms. Collins said.

How Much Progress?

Boston administrators have heard elementary teachers voice doubts about their math-teaching abilities, compared with their comfort with literacy lessons, Mr. Coxon said. The district has established math-leadership teams and math coaches at its schools, to try to provide “constant support” in the subject, he said. It has also arranged professional-development sessions focused on math at night and on weekends.

“Teacher training is pretty much the cornerstone of whether we’ll be successful,” Mr. Coxon said.

Especially, he said, because Boston is teaching math much differently than it had a number of years ago. The district has phased in the use of two sets of curriculum programs that emphasize conceptual math. In elementary schools, it uses Investigations in Number, Data, and Space, crafted by the Cambridge, Mass.-based TERC, formerly the Technical Education Research Center, a nonprofit that specializes in math, science, and technology education. In its middle schools, the district uses Connected Math. Both programs were developed with NSF funding.

Other urban districts face challenges in trying to ensure that math is taught consistently. Chicago officials recently counted 86 different texts and editions of math textbooks in use in their K-8 schools, said Martin Gartzman, the chief math and science officer for the 427,000-student district.

Three years ago, the district launched a math and science initiative, aimed in part at fostering a more coherent curriculum. The district is now encouraging schools to adopt conceptually driven math curricula in the K-8 grades. Chicago’s scores on the urban NAEP improved, but not by a statistically significant margin.

“We’ve got a long way to go,” said Mr. Gartzman.

Those who are wary of the conceptual approach to math instruction say other factors may be behind the districts’ improved NAEP scores. Martha Schwartz, a co-founder of Mathematically Correct, which advocates the strong teaching of basic math skills, attributes San Diego’s progress in part to a greater emphasis on basic content in California’s math standards in the late 1990s.

“We have strong standards that people have pushed for,” said Ms. Schwartz, who lives in the Los Angeles area.

Mr. Loveless noted that San Diego is just one of many California districts that made headway on state math assessments in the past five years.

While she is encouraged by San Diego’s NAEP scores, Ms. Acquarelli does not believe that an allegiance to conceptual math, or any single strategy, is enough to help a district.

“The language gets in our way,” she said, referring to debates about math instruction. “We have similar goals. …Are we where we want to be? Absolutely not. We want to continue to make steady progress.”

(4) U.S. Department of Education’s Teacher-To-Teacher Initiative Supports Record Number of Educators, Seeks Nominations for Stars of Teaching

Source: U.S. Department of Education – 11 January 2006

The U.S. Department of Education supported a record number of educators last year through its Teacher-to-Teacher Initiative, a comprehensive program that offers professional development, research-based classroom strategies, and other support for teachers.

Tens of thousands of educators have participated in this Initiative, which includes summer workshops and roundtables, e-Learning courses, “Ask the Secretary” sessions with U.S. Education Secretary Margaret Spellings, e-mail updates, the new Teacher Training Corps, and the American Stars of Teaching project.

“Teachers are responding enthusiastically, and the Department is working hard to meet educators’ demands for high-quality training and assistance,” said Secretary Spellings. “The new Teacher Training Corps is now out in the field working with educators and school districts from California to New Jersey. We are offering targeted workshops in math, science, reading and a range of other subjects,” she said.

Seventy teachers and district officials, selected from more than 1,600 applicants, comprise the Teacher Training Corps. These individuals are practitioners who have developed presentations based on sound research and who can demonstrate results in raising student achievement. The goal of the corps is to increase teachers’ subject knowledge and improve instruction skills. Teams are already working with districts and states to support professional development efforts for teachers.

In addition, the Department is seeking nominations of outstanding teachers deserving recognition as an American Star of Teaching for raising academic achievement. “Teachers are doing great things in classrooms every day,” Spellings said. “The American Stars project is a way to recognize good teachers, highlight what works and share those strategies throughout the education community.”

Teachers across all grade levels and disciplines will be honored this fall as the 2006 American Stars of Teaching. One teacher will be recognized in every state and the District of Columbia. Parents, students, colleagues, school administrators or others can nominate a teacher who they believe has the qualities to be an American Star of Teaching.

U.S. Department of Education officials will again be visiting the schools of American Star teachers to congratulate them on their success. Last year, the Department received more than 2,000 nominations. To see the winners for the past two years for each state, visit  An online nomination form is available at The deadline for nominations is April 15.

Since 2001, President Bush and Congress have provided $22 billion in federal funding to support the teaching profession. Congress recently appropriated $99 million for President Bush’s Teacher Incentive Fund to reward K-12 educators who make outstanding progress in raising student achievement or narrowing the achievement gap.