COMET  Vol. 12, No. 7 - 10 April 2011

In This Issue...


CCTC Recommends Reduction in Units Required for Foundational-Level Mathematics Subject Matter Programs

Source: California Commission on Teacher Credentialing (CCTC)

The California Commission on Teacher Credentialing (CCTC) has posted the April 14-15 meeting agenda at  An action item (3C) is included in which CCTC staff recommends reducing the number of math/affiliated semester units required for Foundational-Level Mathematics subject matter programs from 45 to 32 (at least 20 units in math and at least 12 in mathematics-based or affiliated courses). For details, see 

This topic generated quite a bit of discussion during last month's Commission meeting. Visit for a recap.

Excerpt from Agenda Item 2C:
     "If the Commission adopts the revised Preconditions, ...program sponsors would be allowed to apply for approval of Foundational-Level Mathematics [(FLM)] subject-matter programs. Programs that are currently approved to offer the full mathematics subject-matter programs would be allowed to recommend candidates for the FLM credential immediately through written statement to the Commission that the program intends to use its approved general mathematics coursework as an approved FLM subject-matter program."


U.S. Students and Science: AAAS Testing Gives New Insight on What Students Know and Their Misconceptions

Source: American Association for the Advancement of Science - 7 April 2011
URL (Press release):


The American Association for the Advancement of Science (AAAS) has launched an innovative website to help educators assess more precisely what students know about key ideas in science and -- just as importantly -- the incorrect ideas they have. It offers a detailed picture of how middle and high school students across the United States are currently doing in science and features information on what they know and on hundreds of misconceptions they have about everything from the size of atoms to whether all organisms have DNA.

Knowing these misconceptions and how pervasive they are--which is not typically part of the analysis of test results from state testing or from leading national and international testing organizations--can help teachers improve instruction and design their own test questions to better assess whether students truly understand the science concepts they are being taught.

The newly developed test questions also counter the widely held view that multiple choice questions are useful only for testing recall of memorized definitions and trivial facts, says George DeBoer, deputy director of Project 2061, the AAAS program that developed the new assessment website.

"As a result of our efforts, many of the test questions included in the new website measure not only knowledge of factual information, but they also probe a student's ability to explain real-world phenomena, reason logically through problem situations, or identify the reason why a claim is true," DeBoer said...

The new AAAS website ( presents detailed information on how a national sample of students answered each question, along with an analysis of both their correct and incorrect responses. In contrast, national and international assessment programs such as the National Assessment of Educational Progress (NAEP), Trends in International Mathematics and Science Study (TIMSS), and Program in International Student Assessment (PISA) report on the percent of students in participating states or countries who answer items correctly but do not report on the incorrect ideas students have, DeBoer said. Project 2061, founded in 1985 by AAAS to improve science education, developed the assessment items and collected data on them under a grant from the National Science Foundation.

The website includes data on student performance by gender, grade level, and whether or not English is the student's primary language. Each question typically was answered by at least 2000 students in field tests involving school districts across the nation. In 2010, for example, more than 90,000 students in 814 schools participated in the field tests. Project 2061 researchers also conducted on-site interviews with students to gauge the effectiveness of the questions...

With increasing calls for national science standards and a common core curriculum for middle-school and high-school students, it is more important than ever to get assessment right, DeBoer said. "Good assessments can be used to actually improve students' learning and not just to hold teachers and schools accountable," he added. "Assessments that are designed to diagnose students' misconceptions can be powerful educational tools."

For the key idea that "all matter is made up of atoms," the AAAS website notes that 27% of the middle school students and 20% of the high school students who were tested incorrectly believed that "cells are not made up of atoms." On the key idea that "genetic information is encoded in DNA molecules," 40% of middle school students and 30% of high school students had the misconception that only animals have DNA while plants and mushrooms do not.

Having information about such misconceptions is just as important as knowing how many students answered a question correctly, DeBoer said. It can reveal gaps that prevent a coherent understanding of the topic.

The AAAS website is organized to quickly give users a picture of what students know and the misconceptions they have. The test questions for a specific science concept are listed together, arranged from the highest to lowest percent correct. The misconceptions also are listed in order, with the misconceptions selected most frequently at the top of the list...

The emphasis on student misconceptions is particularly helpful, said Deagan Andrews, a curriculum and assessment specialist in the Greeley, Colorado, school district. Referring to some of the major standardized test programs, he said: "No one releases any information about misconceptions. They are interested in whether students got it right or wrong." He said the emphasis on misconceptions "is a critical piece that has been missing," offering teachers an opportunity to "think about their instruction and what they may be doing that may be perpetuating misconceptions"...


"Math-Gender Stereotypes in Elementary School Children" by Dario Cvencek, Andrew N. Meltzoff, and Anthony G. Greenwald

Source: Child Development - March/April 2011

Abstract: A total of 247 American children between 6 and 10 years of age (126 girls and 121 boys) completed Implicit Association Tests and explicit self-report measures assessing the association of (a) me with male (gender identity), (b) male with math (math–gender stereotype), and (c) me with math (math self-concept).

Two findings emerged. First, as early as second grade, the children demonstrated the American cultural stereotype that math is for boys on both implicit and explicit measures. Second, elementary school boys identified with math more strongly than did girls on both implicit and self-report measures. The findings suggest that the math-gender stereotype is acquired early and influences emerging math self-concepts prior to ages at which there are actual differences in math achievement. [The full article can be downloaded from the Web site above.]

Related Articles

Gender Stereotypes About Math Develop as Early as Second Grade

Source: Science Daily - 14 March 2011

Children express the stereotype that mathematics is for boys, not for girls, as early as second grade, according to a new study by University of Washington researchers. And the children applied the stereotype to themselves: boys identified themselves with math, whereas girls did not.
The "math is for boys" stereotype has been used as part of the explanation for why so few women pursue science, mathematics and engineering careers. The cultural stereotype may nudge girls to think that "math is not for me," which can affect what activities they engage in and their career aspirations.

The new study, published in the March/April issue of Child Development, suggests that for girls, lack of interest in mathematics may come from culturally-communicated messages about math being more appropriate for boys than for girls, the researchers said.

But the stereotype that girls don't do math was odd to lead author Dario Cvencek, who was born and raised in the former Yugoslavia. "We didn't have that stereotype where I grew up," said Cvencek, a postdoctoral fellow at the UW Institute for Learning & Brain Sciences. "People there thought that math went with girls just as much as it did with boys."

Cvencek and his co-authors wanted to examine whether American children have adopted the cultural stereotype that math is for boys during elementary-school years, and if so, whether they apply that stereotype to themselves...[access the full article for more details]

"Our results show that cultural stereotypes about math are absorbed strikingly early in development, prior to ages at which there are gender differences in math achievement," said co-author Andrew Meltzoff, a UW psychology professor and co-director of the UW Institute for Learning & Brain Sciences...

Parental and educational practices aimed at enhancing girls' self-concepts for math might be beneficial as early as elementary school, when the youngsters are already beginning to develop ideas about who does math, the researchers said.

"Children have their antennae up and are assimilating the stereotypes exhibited by parents, educators, peers, games and the media," Meltzoff said. "Perhaps if we can depict math as being equally for boys and girls, we can help broaden the interests and aspirations of all our children."


Free Webinar This Thursday: "Getting them There: Recruitment and Retention of Girls in STEM"

Source: Siemens STEM Academy

Through this free webinar, educators will learn some of the hidden signals today's society sends girls in science, math, and technology in addition to discovering the ways many educators unintentionally discourage girls from careers in STEM. Elaine Plybon will help attendees understand stereotype threat and how it can be overcome. Additionally, she will examine data from successful recruitment efforts in high schools, as well as measurable outcomes in one Texas school district after a widespread awareness effort. Participants will learn how to develop action plans for a campus to increase recruitment, retention, and achievement for girls in STEM fields.

Date: Thursday, 14 April 2011
Time: 4:00 p.m. PT
Prewebinar Resources (upper right-hand side of page):
To Register:


Presentation Files Available from "Gearing Up for the Common Core State Standards in Mathematics" Workshop

Source: Institute for Mathematics and Education - University of Arizona

The Institute for Mathematics and Education at the University of Arizona coordinated a workshop on 1-3 April 2011 to identify and discuss which areas of the Common Core State Standards (CCSS) for Mathematics should be the initial target for professional development (PD) as states gear up to implement the Standards. Subsequent collaborative efforts will consider how professional development should be implemented; the focus of last week's workshop was on content. The workshop was cosponsored by the Institute for Research on Mathematics and Science Education at Michigan State University and by the Center for Science, Mathematics, & Computer Education at the University of Nebraska.

Before the workshop, participants were sent tasks and problems that have been written to illustrate the Common Core's goal of raising standards through (a) focus on a few critical areas, (b) mathematical coherence across grade levels, and (c) an emphasis on conceptual understanding. Participants used these tasks as a tool for engaging in conversations about content areas where the Standards require a step up in professional development, and areas that should be de-emphasized.

At the workshop, participants presented their findings and discussed the appropriate initial focus of PD materials supporting the Standards at the elementary, middle, and high school grade levels. They identified existing materials that address some of the areas and also areas where additional materials are needed.

The organizing committee for the workshop consisted of Bill McCallum (Chair), Deborah Hughes-Hallett, Jim Lewis, Rebecca McGraw, Cody Patterson, and William Schmidt.

The agenda is available at  Bill McCallum's opening presentation is available at

Workshop files from each breakout group are available for download from

Related Articles

"Mathematicians in Mathematics Education"


The Institute for Mathematics and Education at the University of Arizona will host the "Mathematicians in Mathematics Education" workshop on 23-25 April 2011

This workshop will orient mathematicians on key issues: the core mathematics of K–12, the mathematical knowledge of teachers, the nature of the educational system, the variety of curricula, and mathematics education research. A particular focus of this year's workshop will be orienting mathematicians to undertake productive work supporting assessment, professional development, and curriculum work around the Common Core Math Standards. The workshop is aimed at the general audience of university mathematicians who wish to become involved in helping solve the problems in mathematics education.

Like the April 1-3 workshop, the organizing committee is chaired by Bill McCallum. Other members of the organizing committee are Hyman Bass, Roger Howe, and Deborah Loewenberg Ball.

To register for this workshop, visit


Tools for the Common Core Standards

Source: Institute for Mathematics and Education - University of Arizona

University of Arizona professor Bill McCallum has created a Web site containing "news about tools that are being developed to support implementation of the Common Core State Standards." Visit to peruse this useful site. (A hyperlinked version of the CCSS, for example, is available at

McCallum's most recent post (April 6) presents "the first public draft of the progressions project [(please visit], on Number and Operations in Base Ten." He states, "We welcome any comments or suggested changes, which will be considered for the final draft. Please post comments to this thread. We will be releasing other draft progressions for elementary and middle school over the coming weeks."

The direct link for this latest report is   COMET readers are encouraged to review this document, a well as peruse the description of the progressions project that McCallum chairs. Also see the article below.

Related Articles

Common Core State Standards Resources

Source: California Department of Education


A Look at Learning Trajectories in Mathematics

Source: Teachers College Press - 11 March 2011

Released by the Center on Continuous Instructional Improvement (CCII), a Teachers College-based arm of the Consortium for Policy Research in Education (CPRE), the report, "Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction," details current work and thinking in one of the most promising areas for improving K-12 mathematics education.

"Learning Trajectories in Mathematics" can be viewed and downloaded at

Teaching and learning trajectories--sometimes called learning progressions--are sequences of learning experiences hypothesized and designed to build a deep and increasingly sophisticated understanding of core concepts and practices within various disciplines. The trajectories are based on empirical evidence of how students’ understanding actually develops in response to instruction and where it might break down.

The new report "aims to provide a useful introduction to current work and thinking about learning trajectories for mathematics education; why we should care about these questions; and how to think about what is being attempted," write the authors, Phil Daro, Frederic A. Mosher and Tom Corcoran...

While it is clear from current evidence that no single mathematics trajectory is appropriate for all students, "trajectories are useful as modal descriptions of the development of student thinking over shorter ranges of specific mathematical topics and instruction, and within particular cultural and curricular contexts." Trajectories can also provide "a basis for informing teachers about the (sometimes wide) range of student understanding they are likely to encounter, and the kinds of pedagogical responses that are likely to help students move along.

The 79-page report includes sections on what learning trajectories are, trajectories and assessment, adapting trajectories to real-world practice, and the relationship between trajectories and the Common Core State Standards. The report also includes samples of learning trajectories and of a "multiplicative reasoning framework" developed by educators in Vermont. The authors make a number of recommendations, including that mathematics educators and funding agencies should recognize the importance of research on learning trajectories; that work should be done to consolidate existing learning trajectories; that studies should be undertaken of the development of students from different cultural backgrounds and with differing initial skill levels; and that investments should be made in development of assessment tools based on learning trajectories for use by teachers and schools.

Phil Daro is a member of the lead writing team for the K-12 Common Core State Standards, senior fellow for Mathematics of America’s Choice, and director of the San Francisco Strategic Education Partnership maintained by UC Berkeley, Stanford and the San Francisco Unified School District. Frederic Mosher, a cognitive/social psychologist, is senior research consultant to CPRE. Tom Corcoran is co-director of CPRE at TC and principal investigator of CCII.

Established in 1985, CPRE unites research from seven of the nation’s leading research institutions in efforts to improve elementary and secondary education through practical research on policy, finance, school reform and school governance. The Consortium’s member institutions are Teachers College-Columbia University, the University of Pennsylvania, Harvard University, Stanford University, the University of Michigan, the University of Wisconsin-Madison, and Northwestern University.

CCII, launched by CPRE in 2006, engages in research and development on tools, processes and policies intended to promote the continuous improvement of instructional practice.


COMET is sponsored in part by a grant from the California Mathematics Project.

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