COMET • Vol. 5, No. 26 – 22 October 2004


(1)  “Update on [CCTC] Teacher Examination Study”; Upcoming Stakeholders Meetings

Source: California Commission on Teacher Credentialing–CCTC (

Contact: Yvonne Novelli:

[August 2004 CCTC Meeting Agenda Item 4C]


At the June 5, 2003 meeting of the Commission on Teacher Credentialing, the Commission directed staff to research examination issues related to how the current California test specifications and test structures that measure basic skills, content knowledge, and pedagogy might be streamlined. Staff returned to the Commission with four broad policy issues for consideration at the June, 2004 meeting. The four exam issues presented for discussion at the meeting were:

— Basic skill exam requirements for teacher candidates,

— Overlapping content across current teacher licensure exams,

— Technology and the implementation of on-line, test center exams, and

— SB 2042 teaching performance assessment.

The Commission directed staff to develop an implementation plan detailing a public discussion process that would provide the opportunity for education stakeholders to discuss the four policy issues listed above.


California law requires that candidates preparing for a preliminary California teaching credential meet certain minimal requirements prior to attaining a credential. Over time, specific examinations have been added to these requirements for the purpose of ensuring accountability for basic skill competence, subject matter knowledge,  and pedagogy.

Education Code Section 44259(b)(5) requires the Commission to ensure that teacher preparation and examinations are fully aligned to the K-12 academic content standards for students. The Commission has been actively engaged in aligning program standards and subject matter examinations with the K-12 academic content standards since the passage of this requirement in 1998 (SB 2042). The Commission has also been engaged in the development and implementation of the California Teaching Performance Assessment (CA TPA), which enables programs to meet the requirement of Standard 19 and assess candidates on the teaching performance expectations (TPEs). However,  in a letter sent in early 2003 from the then- Secretary for Education, Kerry Mazzoni and Senator Dede Alpert, the authors of Senate Bill 2042, cautioned the Commission about the magnitude of the state budget crisis. The Commission was asked to work with representatives of the higher education institutions to determine whether the model teaching performance assessment could be redesigned to lower costs. Accordingly, this requirement is suspended until further Commission discussion and action

Proposed Implementation Plan for Public Discussion of Exam Issues

Commission staff proposes that at least four public meetings be held with educational stakeholders to discuss the four policy issues listed in the introduction of this item. Commission staff would invite stakeholders, develop an agenda, and facilitate the meetings. Each meeting will address one of the following policy questions.

= What is the appropriate way to assess basic skill competency?

= Is there overlapping content across the current teacher licensure exams?

= What are the implications of appropriate and secure on-line, test center exams?

= How should the SB 2042 teaching performance assessment requirement be maintained and implemented?

= Staff will synthesize the meeting discussions and provide exam update reports at appropriate Commission meetings. Staff proposes to bring an action item based on the public meetings to the Commission for its consideration at its April, 2005 meeting.



A series of four unique stakeholders meetings will be held by the Commission as part of the Examination Study, which is described in the August 2004 agenda item “Update on Teacher Examination Study” that can be found on the Commission’s web site at [excerpted in part above].  This study will be covering the assessment of basic skill competency, overlapping subject matter content, electronic testing, and the TPA maintenance and implementation.  We are inviting stakeholders from California colleges, universities, school districts, county offices of education, educational associations, and others interested to discuss possible changes to the examination structure.  Your suggestions will be submitted to a group of technical advisors from California colleges and universities who are knowledgeable about testing to discuss the possible implementation.  Attendees may participate in as many meetings as they choose.  All meetings will be held from 10 a.m. to 3 p.m. at the Commission on Teacher Credentialing office in Sacramento, California.

Dates and Topics:

November 16, 2004: Assess basic skill competency

January 25, 2005: Overlapping content

January 26, 2005: Electronic testing format

February 24, 2005: Teaching performance assessment

**If you are interested in attending any of these meetings, send you name, institution, position, email address, telephone number, and fax number to Yvonne Novelli at .  Further details will then be forwarded to you.

(2) Reminder: Mathematics Framework (August 2004 Draft) Field Review

Source: Joan Commons, Mathematics Project Specialist, San Diego County Office of Education

The California Association for Supervision and Curriculum Development sponsored videoconferences at ten County Offices of Education throughout the state to discuss the  August 2004 Draft Mathematics Framework document. During the videoconference held on October 19, Mary Sprague (California Department of Education) stated that only 30 responses to the document have been received via the online evaluation survey. Please visit to review the draft and submit any comments by the November 9 deadline.


(1) “Research Matters / Teach Mathematics Right the First Time” by Steve Leinwand and Steve Fleischman

Source: Educational Leadership – September 2004 (pp. 88-89)


[Preface] In this new column for Educational Leadership, experienced researchers at the American Institutes for Research [AIR] will discuss research-based practices, providing educators on the front lines of school improvement efforts with the information they need to make the best instructional decisions. Steve Fleischman, a principal research scientist at AIR, will be series editor, identifying the effective practices featured here each month. Send questions or topic suggestions to Steve at We also welcome your comments at

Steve Leinwand, the author of [the below article], is a Principal Research Scientist at the American Institutes for Research (AIR), specializing in mathematics instruction and assessment. He is the author of Sensible Mathematics: A Guide for School Leaders (Heinemann, 2000).


[Article]  In mathematics instruction, a chasm exists between research and practice. For evidence of this gap, look no further than the mismatch between what research says about developing students’ conceptual mathematics understanding and what we actually do. An example is the way we teach math content in elementary and middle schools. A growing body of promising research shows that if initial instruction focuses exclusively on procedural skills, then students may have difficulty developing an understanding of math concepts.

Listen to 7th graders define perimeter as “adding up all the numbers,” and watch as their teacher struggles, often unsuccessfully, to move these students toward more appropriate understandings: that perimeter is actually the distance around an object,relates to the words border and surrounding, and is a special case of measuring length. Unfortunately, many people will blame this situation on the “mathematical weaknesses” of the students, or even of the teacher, rather than on instructional sequencing that flies in the face of research.

What We Know

Richard Skemp (1987) coined the terms instrumental practices and relational practices to differentiate two approaches to teaching and learning. Instrumental practices involve memorizing and routinely applying procedures and formulas. These practices focus on what to do and how to get answers. In contrast, relational practices emphasize the why of learning. These practices involve explaining, reasoning, and relying on multiple representations–that is, on teaching for meaning and helping students develop their own understanding of content.

Since the 1980s, several studies have examined the role and impact of instrumental and relational practices on student achievement outcomes. Although the research base is somewhat limited and should be replicated to validate the findings, results consistently point to the importance of using relational practices for teaching mathematics. In the existing research, students who learn rules before they learn concepts tend to score significantly lower than do students who learn concepts first.

For example, Kieran (1984) looked at two groups of students learning to solve simple equations, such as 6 + x = 18. One group was taught procedures (subtract 6 from both sides); the other was not. Both groups then received instruction about the meaning of variables and equations. Next, they used trial and error to balance an equation. On post-tests, the students who received only meaningful, or relational, instruction performed better in applying the procedure and solving the equations. In contrast, the students who first received procedural instruction on how to solve an equation tended to resist new ideas and appeared to apply procedures without understanding.

Wearne and Hiebert (1988) investigated the effectiveness of different approaches for teaching decimal concepts. They suggested that “students who have already routinized rules without establishing connections between symbols [and what they mean] will be less likely to engage in the [conceptual] processes than students who are encountering decimals for the first time.” (p. 374)

Perhaps most convincing is the work of Pesek and Kirshner (2000). They studied students who were learning about area and perimeter and concluded that “initial rote learning of a concept can create interference to later meaningful learning” (p. 537). Students who were exposed to instrumental instruction before they received relational instruction “achieved no more, and most probably less, conceptual understanding than students exposed only to the relational unit.” Even more telling was the way students in the two study groups approached solving problems. Students who learned area and perimeter as a set of how-to rules referred to formulas, operations, and fixed procedures to solve problems. In contrast, students whose initial experiences were relational used conceptual and flexible methods to develop solutions.

This research strongly reinforces our understanding that the form of instruction humorously but accurately characterized as yours is not to reason why, just invert and multiply may not enhance the performance of many students. Alternatively, instruction that places a premium from the start on meaning and conceptual understanding may improve classroom productivity.

What You Can Do

Mathematics teachers can take simple and immediate steps to put the gist of this research into practice.

*  Promote students’ discussion of making meaning by posing open-ended questions: Why do you think that? Can you explain your reasoning? How do you know that?

*  Make explicit connections and incorporate pictures, concrete materials, and role playing as part of instruction so that students have multiple representations of concepts and alternative paths to developing understanding.

*  Avoid instruction focused on teaching a single correct approach to arrive at a single correct answer.

Educators Take Note

In his review of the scientific research on mathematics instruction, Grover Whitehurst, the director of the U.S. Department of Education’s Institute of Educational Sciences, rightly points out that educators should be wary about basing instructional practices on potentially unsubstantiated translations of study findings (2003). Whitehurst adds, however, that “literature demonstrates the limits of generalization of math skills that can occur when instruction focuses exclusively on learning facts and procedures.”

This month’s column offers some research-based guidelines for mathematics instruction in the hope that they will support improved student achievement. The research message is strong: Teach for meaning initially, or risk never getting students beyond a superficial understanding that leaves them unprepared to apply their learning.

[The complete article includes a reference list.]

(2) “Third Year of NSF’s Math and Science Partnerships to Focus on Teachers”

Source: National Science Foundation – 19 October 2004

Program Contact: Diane Spresser, National Science Foundation, (703) 292-5118,

Many teachers in K-12 will be able to experience a more intense learning and leadership environment as the National Science Foundation (NSF) embarks on a major effort to improve the mathematics and science education of the nation’s youth.

NSF has announced that seven new Institute Partnerships: Teacher Institutes for the 21st Century will be formed as a result of five-year grants made to universities in the third year of competition for NSF’s Math and Science Partnership (MSP) program. The new institutes represent an investment of more than $31 million over five years for NSF’s newest MSP program component.

The awards for teacher institutes will be directed to disciplinary faculty of higher learning institutions to work with experienced teachers of mathematics and the sciences. This relationship is expected to deepen teachers’ knowledge of content and instructional skills so they may become school-based intellectual leaders in their fields. A prototype institute is already underway at the Institute for Advanced Study at Park City, Utah.

New institute awards have been made to the University of Nebraska, Oregon State University, Tufts University and the University of Pennsylvania–each receiving $5 million over five years. Math and science teachers will study during summers or during the academic year at the new institutes being formed at these campuses. U-Penn (grades 5-12) and Tufts (grades K-8) institutes will specialize in science. At U-Nebraska (grades 5-8) and Oregon State University (grades K-12) institutes will be for math teachers.

Three more institute awards have been made to Rice University (Houston), Virginia Commonwealth University (Richmond) and Florida Atlantic University (Boca Raton), and will focus on mathematics teaching. The Rice institute ($3.8 million) will focus on grades 9-12, Florida Atlantic will specialize at grades 5-8. And VCU will develop math specialists at K-5 levels.

“The new institute partnerships address a national need for a new generation of experienced teacher-leaders at a time when many teachers of similar stature are retiring” says Joyce Evans, MSP program director. “These multi-year programs will provide courses and experiences that enable teachers to deepen and update their content knowledge, become more effective in the classroom, contribute to the development of more challenging or advanced courses, and become leaders and catalysts for reforming the mathematics and science programs in their schools.”

Institute participants, Evans explains further, should be able to assume increased responsibilities in their schools after successfully completing an institute program. To make that a reality, schools and districts are expected to provide the time, administrative support, resources and the recognition and rewards commensurate with this increased responsibility.

Meanwhile, NSF also announced five large Targeted Partnerships with grants amounting to a combined $60 million over five years, aimed at improving math and science performance in nationwide classrooms. Some 224,000 students will be reached through these partnerships that will unite 13 institutions of higher education with 21 local school districts to improve student achievement in specific disciplines or grade ranges.

Arizona State University and City College of New York (CUNY) are each expected to receive $12.5 million over the next five years to target science and mathematics learning at grades 9-12 by testing a model of graduate courses to deepen teachers’ understanding of fundamental concepts in mathematics and science. The project will also support teachers in several Arizona school districts (Chandler, Mesa, Tempe and Tolleson) through learning communities with higher education faculty. The CUNY project will create hub high schools as “clinics” for teacher training and education excellence that will address shortages and retention rates among teachers in New York City schools, and create school cultures that emphasize research-driven classroom practices. The project also seeks to improve student performance beyond 8th grade.

Meanwhile, the University of Massachusetts, Boston, is receiving $12.5 million over five years to improve student achievement in science at grades 6-12 in Boston’s public schools by enhancing teacher content knowledge and instructional skill. The partnership includes Northeastern University, Harvard University and the College Board.

The other new targeted partnerships will focus on grades 6-8. The University of Colorado, Denver, along with several nearby college and university partners will lead a $12.5 million project to improve student achievement through a combination of high quality coursework in math and science and a push to reduce the achievement gap between minority and non-minority middle school students ö a program project leaders call “15 months to HQ (high quality).” One facet of this project includes an on-line delivery of teacher coursework that will engage teachers in the more rural regions of Colorado. Another $10 million grant to Birmingham Southern College in Alabama aims to improve middle school mathematics for students while boosting the professional development of high school math teachers. The college is working with the University of Alabama, Birmingham and the eight Greater Birmingham Alabama school districts, and will incorporate engineering modules into classrooms to help answer the age-old question, “Why do I need to know this?” Research from this project will also focus on engaging parents to be better informed about, and advocates for, high quality mathematics in schools.

NSF’s newly announced MSP awards bring to 48 the total number of comprehensive, targeted and teacher institute projects underway across the country.

NSF also announced other MSP awards for capacity building–including research, evaluation and technical assistance. The largest, $4.6 million to Horizon Research, Inc., will involve comprehensive “knowledge management and dissemination” for the overall MSP program. Northwestern University has received $2.3 million for a program to study, define and understand teacher leaders and the roles they play. Westat, Inc. received $900,000 to study over time the effects of university disciplinary faculty engagement with the MSP process. This is considered an important facet of MSP and the newly forged relationships that are occurring between disciplinary faculty with K-12 teachers.