COMET • Vol. 10, No. 12 – 9 May 2009


(1) Subject Matter Competence of Teachers of Mathematics

Source: California Commission on Teacher Credentialing (CCTC)
URL (Meeting Agenda):
URL (Agenda Item 3E):  

A webcast of the April 23-24 meeting of the California Commission on Teacher Credentialing (CCTC) was posted on the Commission’s Web site yesterday afternoon. The direct link to the April 23 webcast is  Three items on the Commission’s agenda (all covered on April 23) related to topics in mathematics education.

Item 3E “continues the discussion related to the teaching of mathematics in California. The focus of the item is the process for determining the subject matter competence of K-12 teachers of mathematics.” The item, which can be downloaded from the Web site above, was presented by Dr. Phyllis Jacobson, an administrator for CCTC’s Professional Services Division. Her presentation on the webcast commences at time marker 3:07.

“This agenda item focuses specifically on the mathematics content knowledge expected of beginning teachers, and looks at how this content knowledge is assessed through subject matter preparation programs and subject matter examinations. This item does not address teacher candidates’ level of pedagogical knowledge about how to teach mathematics content to K-12 students, nor does it focus on the pedagogical preparation received by teacher candidates within teacher preparation programs about how to teach mathematics content to K-12 students. The pedagogical preparation of teacher candidates to teach mathematics [(and how this pedagogical knowledge is assessed)] will be the topic for the next agenda item in this series of information items, to be presented at the June 2009 Commission meeting”…

“In order for the Commission to maintain viable, legally defensible examinations, the content of these examinations must be periodically reviewed as part of a validity study that ensures that the examination reflects the most current K-12 standards, frameworks, and other relevant documents. The next review of the CSET: Mathematics Examination [(and the CSET: Multiple Subject Examination)] is scheduled for 2012, to align with the revised state framework for mathematics which is due in 2011.”

Download this agenda item from for more information.


(2) Update on the Work of the Teaching Mathematics Advisory Panel

Source: California Commission on Teacher Credentialing (CCTC)
URL (Meeting Agenda):
URL (Agenda Item 3F):

Item 3F on the California Commission on Teacher Credentialing’s April 23 meeting agenda presents a progress report of the Teaching Mathematics Advisory Panel. On the webcast (, this item appears at time marker 3:16-3:25.

Executive Summary of the Item: “At its December 2008 meeting, the Commission directed that an advisory panel be convened to study the mathematics specialist authorization. The charge to the advisory panel was expanded at the January 2009 meeting. In addition to the information in this agenda item, an oral report on the work to date of the Teaching Mathematics Advisory Panel will be presented.”

Dr. Rebecca Parker, Consultant, and Teri Clark, Administrator, Professional Services Division, presented this information item. (See for a summary–the panel’s charge, expected timeline, etc.)

The presenters noted that the Panel met for the first time on March 30-31 and said that it is an “extremely diverse group.” It was half-jokingly stated that “it’s a little unclear what the charge is to the group since it’s been expanded each time there’s an agenda item [at a CCTC meeting].”

The speakers noted that “Dr. Stigler’s work parallels the work of the Panel” (see COMET Item 3 below). “Teachers, particularly Multiple Subject teachers, need to understand and have deep mathematics knowledge. How can we get Multiple Subject teachers to feel comfortable with having students struggle and explore concepts? A second issue that came up was that people are going to want a math specialist credential, but please, let’s not pull them out of classrooms.” There was discussion about school sites having math specialists sprinkled throughout the school.

Some on the Panel pointed to research in other states looking at other credential structures. If we had a sufficient number of math teachers, would we need math specialists?

It was noted that the current standards for a math specialist are extremely old and haven’t really been utilized. These standards require a full math credential. The Panel, however, “may not go this way.” They are looking at developing an elementary mathematics specialist requiring a considerable amount of pedagogical content knowledge preparation (e.g., common mathematical misconceptions students hold, etc.) — this means “not more advanced math, but more in-depth and more conceptual understanding. That is the direction that it looks like the panel may be going.”

Next Steps (from Agenda): It is anticipated that the work of the Teaching Mathematics Advisory Panel will occur over the next eight to ten months. The second meeting will take place on May 21-22, 2009 at the Commission offices. Staff will bring another update on the work of the panel to the August 2009 Commission meeting.


(3) “Reflections on Mathematics Teaching and How to Improve It”—Presentation by Jim Stigler

Source: California Commission on Teacher Credentialing (CCTC)
URL (Meeting Agenda):
URL (Agenda Item):

Item I1 on the California Commission on Teacher Credentialing’s April 23 meeting agenda was presented by Dr. James W. Stigler, who provided a summary of the TIMMS Video Studies (see, including key findings and implications for teaching mathematics. On the webcast (, this item appears at time marker 1:47-2:25.

Dr. James Stigler is Professor of Psychology at UCLA , Director of the TIMSS Video Studies (1995 and 1999), and founder and CEO of LessonLab. He is co-author of two books: The Teaching Gap (with James Hiebert, 1999) and The Learning Gap (with Harold Stevenson, 1992). The report below includes information from slides that Dr. Stigler showed as well as a portion of his remarks. (The interested reader is encouraged to view the entire presentation on the webcast.)

[Jim Stigler] The most important things we have learned from this research and the implications that the research has for teaching (mathematics teaching in particular) are the following:

1. Teaching is a cultural activity. In Japan, the teachers all teach in much the same way. The same thing is true in the U.S. Most teachers don’t do what they were taught in their teacher education program but fall back on cultural routines that are learned implicitly. Most teaching is learned because you have experienced teaching for 13 years before you decide to be a teacher.
In Japan, teachers will give students problems to solve that they have never seen before. We actually don’t do that in our country. In Japan, they have a high tolerance for what I would say is “confusion” in the classroom. They’ll give a math problem and no one knows what to do. They sit there and they sweat and they look confused and they pull their hair out and they try to figure out what to do.  In the U.S., if you give a math problem and everyone looks confused, the teacher steps in right away to stop the confusion–clear it up, give a hint, tell them what to do—anything to stop the confusion.
Cultural activities are very hard to change. And one of the reasons for this is that there are all sorts of forces that work against changing cultural norms.  We have to recognize that fact as we try to figure out how to improve teaching.

2.  The second thing we’ve learned is that there are many ways to teach effectively… Teaching is contextual. There is no one best way.

3. Teaching quality needs to be defined not by what teachers DO but by the learning opportunities they create for students… One finding: we marked every time a math problem started and stopped. And then we categorized the problems into one of three types: (a) Stating Concepts (recall a fact), (b) Using Procedures (e.g., do a worksheet practicing a taught procedure), or (c) Making Connections (very rich problems that connect students with core mathematical concepts). Teachers in every TIMSS country used some of all of these types. However, when looking at the videos, a pattern emerged. In the higher performing TIMSS countries such as Japan or Hong Kong, “Making Connections” problems remained as “Making Connections” problems. However, when these types of problems were given in the U.S., the problems were translated into “Using Procedures” problems by every teacher, which was related to the observation above about a cultural proclivity toward alleviating student confusion in the classroom…

A review of research by Hiebert and Grouws identifies two features of classroom instruction that are associated with students’ understanding of mathematics:
– Connections: Making mathematical relationships—among concepts, procedures, ideas—explicit in the lesson
– Struggle: Students spend at least some time struggling with important mathematics.


1. We need to shift the emphasis from “teachers” to “teaching” (need to change cultural routines to make them better over time)
2. We need to redefine “quality teaching.” It’s not a set of skills and strategies (e.g., lecturing vs. using small groups) but making informed judgments in the classrooms–how what teachers do creates opportunities for students to achieve important learning goals (i.e., for math, explicit ideas and struggle).
a.  Clearly define learning goals and understandings needed to achieve them (subject matter knowledge essential)
b. Design lessons that use strategies shown effective for achieving the goals and judged appropriate for specific content.
c.  Study effectiveness based on students’ learning from instruction, and analyze teaching/learning as cause/effect (so teacher can learn from experience). Teachers need to analyze their students’ thinking and reasoning.
d. Provide teachers with opportunities to learn the knowledge, skills, and judgment they will need for continuous improvement: stable settings to work with colleagues to learn what works better and share what is learned with the profession.

[Stigler, in a response to a question from Commissioner David Pearson] The goals of mathematics learning in the United States are very procedural, and teachers don’t know how to talk about what it is that they want students to understand (apart from how to do procedures). It takes patience and fortitude to implement new teaching strategies, but it’s possible to create a new classroom culture… Too many people think that mathematics isn’t about thinking–it’s about remembering. Once you get to algebra, you have a lot of steps to remember. However, if you can reason about what the steps are, it gives you a lot more power. In science, there’s some real parallel findings. A lot of time is spent in lab activities, but not much time is being spent in the U.S. connecting the lab to science concepts.

In response to a question about diversity: In a culturally diverse state like California, I think you need different strategies, but every country has diversity… In Japan, a lot of time is spent explicitly teaching students how to be students in their classrooms—how to play their role in the classroom. It isn’t assumed that they already know this.

In response to a question about teacher preparation: The main difference [among TIMSS countries] in teacher learning opportunities is not what they get in their teacher education, but what they get after their teacher education. Do they have a serious apprenticeship period? In Japan they will tell you that it takes 10 years to learn how to be a competent teacher, and they think very long-term about how they are going to be able to provide experiences for teachers… A lot of these [other] countries provide a lot more time on the job to work on learning opportunities for teachers. I think we provide the least amount of time of any country that I know about…


(4) State Schools Chief Jack O’Connell Announces Release of $2.56 Billion in Economic Recovery Funds for Education

Source: California Department of Education

In a presentation today at the California Academy for Liberal Studies (CALS) Charter Middle School in Los Angeles, State Superintendent of Public Instruction Jack O’Connell announced the release of the preliminary allocations of the $2.56 billion in State Fiscal Stabilization Funds (SFSF) that are available for public education through the American Recovery and Reinvestment Act (ARRA).

The allocation is based on an amount equal to cuts made to each local educational agency’s revenue limit funding in the February 2009 California State Budget. In about a month, additional SFSF funding allocations will be calculated to restore cuts made to categorical program funding from that same budget.

O’Connell directed California Department of Education staff to create a special on-line searchable data base that the public can use to easily look up the SFSF grant amount for any district, county office of education or direct funded charter school. This information can be accessed at

“These funds will have an immediate and noticeable impact on California’s K-12 and higher education systems by helping schools keep teachers and other important staff employed, by continuing our efforts to improve student achievement, and furthering our work to close the achievement gap,” O’Connell said. “While this is a brief respite for the education community, we should all recognize there are more tough times ahead, but I am truly heartened by the cooperation that we have received from President Obama and his Administration, specifically U.S. Secretary of Education Arne Duncan.”



Strengthening America’s Competitiveness through Common Academic Standards

Source: Education and Labor Committee, U.S. House of Representatives

On April 29, the Chairman of the U.S. House of Representatives Education and Labor Committee, Congressman George Miller, convened a hearing on “Strengthening America’s Competitiveness through Common Academic Standards.” An archived webcast of this hearing is available at The development of common core state academic standards is a topic that has gained traction and momentum; thus, considerable space is given below to this hearing.

A portion of Chairman Miller’s prepared remarks appears immediately below (also see for the video, and for the full text, see

Today our Committee will examine the great momentum that is building for improving our schools and our competitiveness though internationally-benchmarked common academic standards.

Our nation faces unprecedented challenges that threaten our competitiveness. We face an achievement gap within our schools but we also face an achievement gap between the U.S. and other countries whose educational outcomes are surging while ours are stagnating.

President Obama and Secretary Duncan recognize that our economy’s fate is directly linked to addressing both achievement gaps. They know we won’t be able to build the world-class education system our economy needs and our children deserve unless all students are taught to rigorous standards that prepare them for college and good jobs…

I’m pleased to finally see major momentum behind the effort for common state standards. There is a shared recognition that the patchwork of standards in place today is holding us back not lifting us up. And it’s students, and ultimately our economy, that will pay the price. So far, a core of forward-thinking states has been leading the way toward stronger, common standards.

I want to commend the Alliance for Excellent Education, the National Governor’s Association, the Council of Chief State School Officers and all of their partners in this effort for their leadership. They deserve great credit for how they’ve already helped move the needle.

Let me be clear: I want this committee, and the Congress, to do whatever we can to support this state-led, bipartisan effort. That’s why we’re here today–to learn more about this work and to hear from you all about how the federal government can best support it.

We forged a good start by making historic investments in education in the American Recovery and Reinvestment Act (ARRA).

We created an unprecedented, $5 billion Race to the Top fund that will allow Secretary Duncan to encourage states to innovate. This includes improving standards and assessments so they are aligned with career and college-readiness.

This fund will lay the foundation for the significant changes we’ll need to make to truly improve our schools, make sure students graduate with the skills they need, and cultivate a workforce that can compete globally.

For years we’ve talked about how to close the achievement gap among students domestically. But that isn’t enough. We’ve got to focus on closing the international achievement gap too.

The goal of the No Child Left Behind Act is to make sure every child receives an excellent public education based on high standards. While some states have done a good job insisting on higher standards, others have set the bar far too low. The quality of a child’s education shouldn’t be left to the luck of the draw.

One of the most important things we can do to fulfill the law’s promise is to develop internationally-benchmarked standards that will prepare all students for the rigors of a college or a career.

There is already a great deal of consensus among high performing nations about what our students need to know to succeed. In the highest performing countries, standards cover a smaller number of topics in much greater depth. In the U.S., state standards typically cover a larger number of topics in each grade level. Schools end up with a curriculum that, as they say, is “a mile wide and inch deep.” This means teachers can’t teach it, students can’t learn it, and parents can’t reinforce it.

As NAEP shows us year after year, the unintended consequences of a system that varies vastly from state to state is rather than striving for excellence, states are camouflaging poor performance. The result is a generation of students without the complex skills and knowledge needed to succeed in the jobs of the future.

This is why we’ve brought you all here today. We’ll hear from witnesses about the state-led effort underway to develop a common core of fewer, clearer and higher standards. This hearing will focus on what we need to do to raise our standards so that students in every state, from Mississippi to California to Tennessee, have access to a world-class education system that launches the next great era of American competitiveness.


The following witnesses appeared and provided testimony. Each of their presentations is available as a separate YouTube video available at  Each statement (PDF) is worth perusing.

(a) The Honorable James B. Hunt, Jr (Former Governor of North Carolina and Foundation Chair, James B. Hunt, Jr. Institute for Educational Leadership and Policy):


Content standards must form a clear, coherent message about teaching and learning in each subject area, and we must ensure that world-class content standards form the basis of every child’s education.

In 2007, the Hunt Institute began partnering with the Alliance for Excellent Education and the Council of Chief State School Officers (CCSSO) to explore the potential for a common set of content standards. Findings from the Hunt Institute’s project with the National Research Council (NRC) and discussions during our 2007 and 2008 Governors Education Symposia informed this effort.

The partner organizations agreed that a common set of state standards should be fewer, clearer, and higher than our current state standards. They must be internationally benchmarked and based on evidence about the essential knowledge and skills that students need to be prepared for college and work.

I believe that this can be accomplished through a state-led effort that is voluntary but that is externally validated to ensure that we have the very best standards. I would encourage all states to participate in such an effort. But, I would also caution states to resist the urge to expand–or otherwise dilute–them. Evidence from the NRC studies clearly indicates what happens when states are too inclusive…

EdWeek reported last month that experts are siding with depth of knowledge versus breadth of knowledge–especially when it comes to the sciences.

The Carnegie-IAS Commission on Mathematics and Science Education, on which I serve, is focusing on new standards and assessments in math and science that are fewer, clearer, and more rigorous. We want to achieve higher levels of math and science learning for all American students and redesign schools and systems to deliver math and science learning more effectively. Essentially, we are using math and science as a lens to look at systemic reform.

The Commission will detail how weaving together strategies that are often treated as separate—developing fewer, more rigorous, common standards that are aligned to high-quality assessments; building teacher effectiveness; encouraging innovations at all levels throughout the education system; redesigning how curriculum is delivered—can create a unified plan for raising math and science achievement for all American students.

Assessment plays a critical role in determining what gets taught. Understanding this, the Hunt Institute is excited to once again engage the NRC in an effort to consider the status of our current tests and envision a new generation of assessments. If we could develop assessment systems that better evaluate the individual progress of students, we’d open the door for new measures of accountability under the Elementary and Secondary Education Act (ESEA) reauthorization…

(b)  Ken James (Commissioner of Education, Arkansas Department of Education; President, CCSSO):

Excerpt:  Two weeks ago, CCSSO and the NGA hosted a meeting for state chiefs and governors’ education advisors whose states might be interested in formally joining a coalition to commit to engaging in a process that would ultimately deliver the first sets of common standards in the areas of mathematics and English language arts. That meeting occurred on April 17 in Chicago; and I am pleased to report that 40 of my colleagues along with representatives from their governors’ offices attended. In addition, we were joined by representatives from Achieve, the College Board, ACT, and the National Governors Association. That makes 41 states and many key stakeholders expressing a strong interest in pursuing this goal of state-led common standards. Realizing that not all states will be able to immediately commit to this important effort, I was still extremely encouraged by the breadth of interest across the country. And I do believe that we will have a strong showing of states ready to continue the next stage of the standards development process during the coming weeks and months.

[Note: Visit to follow the progress of the Common Core State Standards Initiative.]

(c) Greg Jones (Chair, California Business for Excellence in Education—CBEE; Chair, California Business Roundtable; Retired CEO and President for State Farm General Insurance; Member, California State Board of Education):


As many of you know, if California was a country, its economic engine would be the fifth largest in the world. According to Achieve and other respected organizations, California has high quality and rigorous standards. Yet, we continually face legal and legislative challenges to lower our content standards and make our state tests easier. Watering down our standards and lowering our expectations might result in a higher number of meaningless high school diplomas, but how would that help the students who will have to compete with in-state, out-of-state, and international peers? There are three important lessons from California’s experience:
– First, it’s not enough to have excellent standards. Aligned tests, meaningful accountability and high-quality instruction are also critical.
– Second, holding all students to the same expectations and reporting results publicly reveal disturbing achievement gaps based on race and economic levels.
– And third, we have data that demonstrates irrefutably that these achievement gaps can be closed without lowering standards or expectations to meet them…

Ed Rust, the CEO of State Farm, is on the Achieve Board, and the Governors and CEOs on that Board have concluded from past history that a top-down, federal approach will not produce a quality product or a politically acceptable result. There’s already a bottom-up process underway led by the states to develop common state academic standards, and Secretary of Education Duncan is seriously considering using the Race to the Top Fund to provide incentives for states to collaborate on the development of common standards and tests.

Common state academic standards will strengthen U.S. competitiveness and individual success:
— if states commit to rigor and quality;
— if federal funds only support states committed to rigor and quality;
— if teaching and instruction are aligned to high quality common standards and tests; and
— if students receive the instruction and inspiration they need to graduate from high school prepared to succeed in college and work.

If standards are watered down, or individual states refuse to join the common state standards effort, we will not succeed in creating the globally competitive workforce of tomorrow.

(d) Dave Levin (Co-Founder, KIPP: Knowledge Is Power Program, New York, NY):

(e) Randi Weingarten (President, American Federation of Teachers):

Excerpt: High standards improve teaching and learning. If we really believe that all children can and should reach high levels of achievement, it only makes sense to define those benchmarks. The time has come for a serious consideration of common state academic standards, and for the development of a richer and fairer accountability system to measure our progress in reaching them.  The AFT is ready to assist in any way we can to help move in this direction.

Additional Item Submitted for the Record:
The Honorable Sonny Perdue, Governor of Georgia, on behalf of The National Governors Association:

Governors know that ensuring state education systems are internationally competitive requires a joint effort, which is why we partnered with organizations representing our nation’s education chiefs and business leaders to develop a set of state actions. These recommendations are included in Benchmarking for Success: Ensuring U.S. Students Receive a World-Class
Education, a report issued by the National Governors Association, the Council of Chief State School Officers, and Achieve, Inc (see To develop these recommendations, our organizations convened a top-notch advisory group that I co-chaired along with former Arizona Governor Janet Napolitano and Intel Chairman Craig Barrett. Members of the group included leading educators, researchers, business executives, and current and former state and federal officials.

The advisory group insisted that the effort be led by states, that the recommended actions be bold, and that the report be based on the most current research and practices. The group unanimously agreed to five action steps that states can take:
– Upgrade state standards by adopting a common core of internationally benchmarked standards in math and language arts for grades K-12 to ensure that students are equipped with the necessary knowledge and skills to be globally competitive;
– Leverage states’ collective influence to ensure that textbooks, digital media, curricula, and assessments are aligned to internationally benchmarked standards and draw on lessons from high-performing nations and states;
– Revise state policies for recruiting, preparing, developing, and supporting teachers and school leaders to reflect the human capital practices of top-performing nations and states around the world;
– Hold schools and systems accountable through monitoring, interventions, and support to ensure consistently high performance, drawing upon international best practices; and
– Measure state-level education performance globally by examining student achievement and attainment in an international context to ensure that, over time, students are receiving the education they need to compete in the 21st century economy.

Benchmarking is not just about measuring and comparing outcomes. It is also–and most critically–about improving policy, and because of that, states must take the lead. States have primary authority over policy areas that other nations are most eager to benchmark and improve: standards, assessment, curriculum, and the education workforce.

Recent State Action

Governors and chief state school officers are actively forging a partnership among states to develop a set of common core standards that will be aligned with college and work expectations, include rigorous content and skills, and be benchmarked internationally. Working under the auspices of NGA and CCSSO, states will develop K-12 standards in English language arts and mathematics that are based on best research and evidence, and will develop common assessments aligned to these standards.


Governors and state education leaders are moving quickly to take action. We look forward to engaging the support of Congress and the Administration. Especially in light of the current economic downturn, more than ever we must ensure that American students are well prepared to compete for jobs in the global economy. The future of our nation depends on it.