COMET • Vol. 14, No. 05 – 19 April 2013


Draft Mathematics Framework Released for Public Comment

Contact: Deborah Franklin, Curriculum Frameworks Unit, California Department of Education: 916-319-0442;

The draft Mathematics Framework for California Public Schools, Kindergarten through Grade Twelve was released yesterday for public comment. Superintendent of Public Instruction Tom Torlakson remarked, “This draft Math Framework is an important step on California’s path toward the Common Core State Standards (CCSS), which provide a practical way to prepare children for the challenges of a constantly changing world by learning step-by-step the practical skills they need for career and college. I’m looking forward to feedback from the public as we put these standards to work remodeling our education system.”

Framework chapters can be downloaded from, and the online survey can be accessed at The survey, which will be available online through 17 June 2013, does not require a response to every question or comments on every chapter. Comments that exceed the allotted length limit may be emailed to The public comments will be presented to the Instructional Quality Commission this summer for review and for possible inclusion into the final Mathematics Framework. The State Board of Education is expected to take action on the final Mathematics Framework later this year. 

An excerpt from page 4 of the Introduction to the draft Mathematics Framework follows below: 

“The development of these standards [was] informed by international benchmarking and began with research-based learning progressions detailing what is known about how students’ mathematical knowledge, skills, and understanding develop over time. The progression from kindergarten standards to standards for higher mathematics exemplifies the three principles of focus, coherence, and rigor that are the basis for the CCSSM.

“The standards stress not only procedural skills, but also conceptual understanding, to ensure that students are learning and absorbing the critical information they need in order to succeed at higher levels and can apply their learning in increasingly complex situations.

“The CCSSM include two types of standards: Eight Mathematical Practice Standards (the same at each grade level) and Mathematical Content Standards (different at each grade level). These standards address both ‘habits of mind’ that students should develop to foster mathematical understanding and expertise, and also skills and knowledge — what students need to know and be able to do. The standards also call for mathematical practices and mathematical content to be connected as students engage in mathematical tasks…”

Forum on Grade 8 Algebra and the Common Core State Standards 

Source: Silicon Valley Education Foundation (SVEF)

Last month, the Silicon Valley Community Foundation and Microsoft sponsored a forum discussion in Mountain View entitled, “Grade 8 Algebra and the New Common Core Standards: Getting the Facts Straight!” The forum sought to address pressing questions such as the following: 

– How does algebra at Grade 8 align with the new Common Core State Standards?
– How should districts handle math acceleration at the middle school level? 

Panelists included the following: 

– Manny Barbara, Vice President of Advocacy and Thought Leadership at the Silicon Valley Education Foundation
– Phil Daro, an expert on the development of the Common Core 
– Bill Honig, retired California Superintendent of Public Instruction and Chair of the Instructional Quality Commission 
– Jacki Horejs, Superintendent of Union School District 
– Mary Perry, Education Consultant and former Deputy Director of EdSource 
– Ze’ev Wurman, Silicon Valley executive and former participant on the State Academic Content Standards Commission 

An archived video of this panel discussion is available at

University of California Releases Formal Statement Supporting Both Integrated and Traditional High School Mathematics Pathways 

Source: Bill Jacob, Chair, Board of Admissions and Relations with Schools, UC Faculty Senate


The University of California (UC) and the California State University (CSU) systems both use “a-g” subject requirements (high school courses in defined categories) as a condition of admission. High school courses must be certified by UC and appear on the school’s a-g list in order for high school students to use the courses to satisfy a-g subject requirements when applying for admission to a UC or CSU campus (see

BOARS (Board of Admissions and Relations with Schools) is the committee of the UC Faculty Senate that sets admissions policy for UC and sets the criteria for a-g course approval, a power delegated to the Senate by the UC Regents. Today the Chair of BOARS, Bill Jacob, wrote that BOARS had reiterated its support for integrated sequences of mathematics courses and that courses (traditional or integrated) must be aligned with the CCSS for Mathematics–CCSSM (see )*. 

Jacob also noted that high schools will need to complete the Mathematics Subject template available online at courses are updated to align with the CCSS-Mathematics. He stressed that applications for area ‘c’ approval must address all of the Standards for Mathematical Practice and show that the Practices are addressed in a balanced way in the courses as a condition for approval by UC. 

* Excerpt from the Statement on High School Mathematics Curriculum Development under the Common Core State Standards: 

“The Board of Admissions and Relations with Schools (BOARS) recognizes the significant changes that high schools across the state must make in their mathematical curricula as they implement the Common Core State Standards for Mathematics (CCSSM), and seeks to support schools in this important effort. Developing a coherent mathematics curriculum that is fully consistent with the CCSSM will involve much more than simply reordering topics to be covered. As courses and curricula are developed, schools will be guided by the Model Course Pathways in Mathematics that were published as an appendix to the CCSSM, and by state frameworks that are being developed currently. 

“Four Model Course Pathways are offered in the appendix to the CCSSM, two that involve the traditional Algebra 1, Geometry, Algebra 2 sequence most often found in US schools, and two that involve an integrated sequence of three courses, each of which includes elements of algebra, geometry, probability, and statistics. Such an integrated sequence is more common in the rest of the world. 

“Consistent with past policy and practice for course approval, BOARS reiterates its full support for either the integrated pathways or the traditional pathways, as stated in the A-G Guide’s section on Mathematics (“c”). It is BOARS’ expectation that courses developed in accordance with either sequence will receive subject area “c” approval provided that they satisfy the course requirements for area “c” presented in the A-G Guide and that they support students in achieving the Standards of Mathematical Practice given in the CCSSM: 

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively. 
3. Construct viable arguments and critique the reasoning of others. 
4. Model with mathematics. 
5. Use appropriate tools strategically. 
6. Attend to precision. 
7. Look for and make use of structure. 
8. Look for and express regularity in repeated reasoning. 

“BOARS looks forward to the full implementation of curricula based on the Common Core State Standards in both Mathematics and English Language Arts in California’s schools.”

Next Generation Science Standards (NGSS) Released; Three Public Meetings on the NGSS with be Held in California Over the Next Two Weeks 

Sources: Achieve, Inc., California Department of Education, National Science Teachers Association

On April 9, Achieve, Inc. (nonprofit organization based in Washington, DC) released the final draft of the Next Generation Science Standards (NGSS). The NGSS were developed through a collaborative, state-level process. California joined twenty-five other lead states and their broad-based teams in working together for two years with a 41-member writing team ( and partners ( to develop the standards. The NGSS identify science and engineering practices and subject matter content that all K-12 students should master in order to be fully prepared for college, careers, and citizenship. The NGSS were built upon a vision for science education established by A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas, produced by the National Research Council (NRC) in 2011. 

“We applaud the completion of the Standards,” said Helen Quinn, Chair of the NRC committee that produced the Framework report and Professor Emerita of Physics at Stanford University. “They represent a key step in bringing the science education vision put forward by our Framework closer to realization in classrooms across the country.”

David Evans, Executive Director of the National Science Teachers Association, was quoted in U.S. News & World Report ( “The way I imagine that it might play out is that there will be more hands-on time for students. There will be deeper investigations into the smaller number of ideas, and perhaps even a better opportunity for students to formulate some of the experiments themselves.” 

Bruce Alberts, who is Editor-in-Chief of Science and served two six-year terms as President of the National Academy of Sciences, stated, “As emphasized in the Framework, an active learning of scientific practices is critical, and takes time. A focus on these practices, rather than on content alone, leads to a deep, sustained learning of the skills needed to be a successful adult, regardless of career choice,” said “We must teach our science students to do something in science class, not to memorize facts.” 

California State Superintendent of Public Instruction Tom Torlakson stated, “In the next decade, the number of jobs requiring highly technical skills is expected to outpace other occupations. These Next Generation Science Standards will help students achieve real-world practical skills so they can help maintain California’s economic and technological leadership in the world.” 

Three public meetings will be held throughout California over the next two weeks to accept public comment on the NGSS (see below). These comments, together with feedback from a panel of science experts, will be considered by the State Board of Education. Then in the fall, the State Board is expected to consider state adoption of the NGSS. 

The public may also submit comments by Webinar at the second public meeting listed below; by email to; by mail to 1430 N Street, Room 4309, Sacramento, CA, 95814-5901; or by fax to 916-323-2833. 

Public Meetings: 

  • Date: Monday, 29 April 2013; 3-5 p.m.
    Location: Sacramento County Office of Education, 10474 Mather Boulevard, Mather, CA 95655
    Contact: Phil Romig, Curriculum Specialist, K-12 Curriculum and Intervention/Science
  • Date: Tuesday, 30 April 2013; 3-5 p.m.
    Location: Santa Clara County Office of Education, 1290 Ridder Park Drive, San Jose, CA 95131-2304
    Contact: Sandi Yellenberg, Coordinator, Science ­– 408-453-6692
  • Date: Tuesday, 2 May 2013; 3-5 p.m.
    Location: Riverside County Office of Education, 3939 Thirteenth Street, Riverside, CA 92501
    Contact: Yamileth Shimojyo, Coordinator, Instructional Services — 951-600-5658

Related Items: 

Webinar: “Introducing the Next Generation Science Standards”

Source: National Science Teachers Association (NSTA)

NSTA has a Web site dedicated to the NGSS at NSTA has also produced a number of useful Web seminars about the NGSS. The latest, “Introducing the Next Generation Science Standards,” was held this past Tuesday (4/16/2013) and is currently archived at the Web site above. 

California and the Next Generation Science Standards

Visit www.nextgenscienceorg/California and to learn more about California’s involvement in the development of the NGSS and for updates. 


Seven California State University Campuses Receive Grant Support to Develop Programs Aligned with the NGSS to Prepare Future K-6 Teachers 

Source: California State University (CSU) Chancellor’s Office

Seven California State University (CSU) campuses recently received funding to support the development of models of undergraduate course reforms for preparing future elementary teachers in science that conform to the Next Generation Science Standards and A Framework for K-12 Science Education. The models will be shared with faculty across the CSU system next year. The goals of these programs are to enhance the science confidence, competence, knowledge, and excitement of future elementary teachers. Brief summaries of the projects appear below. For more information, copies of the proposals, and project contacts, please visit the Web site above. 

Cal Poly San Luis Obispo: The project will create engineering modules and related NGSS course reforms that can be utilized in preparing pre-service candidates and, in turn, their future students. The modules will be included within six courses covering the lower division General Education sequence and two upper division capstone courses… 

CSU Bakersfield: This project will revise the upper division capstone science course and the science methods and assessment course and add an after-school practicum for future elementary teachers. The course revisions will focus on inquiry-based scientific and engineering practices in connecting the two courses, which will each also address science and literacy… 

CSU Chico: This project will revise labs in three science courses for future K-6 teachers: Concepts in Physical Science, Concepts in Life Science, and Concepts in Earth and Space Science. The goal of the revision is to better address crosscutting concepts in the K-12 Science Education Framework and present future K-8 teachers with a deeper understanding of energy, while also building capacity among faculty… 

CSU Fresno: This project will develop a new 12-semester-unit STEM Concentration in Liberal Studies. A cross-disciplinary team will collaborate to revise three existing upper-division science courses, develop a new Engineering Literacy course, and provide professional development workshops for course instructors… 

CSU Fullerton: This project will introduce a collaboration with the innovative Introduction to Engineering course for non majors offered in the College of Engineering and Computer Science and three inquiry oriented courses for future K-6 teachers: Biology, Earth/Astronomical Science, and Physical Science for Future Elementary Teachers. The courses are taught in a laboratory setting and focus on structured and collaborative group work rather than lecture… 

CSU Sacramento: The project will revise the four science courses taken by future elementary teachers (biology, chemistry, geology, and physics), addressing both the NGSS and the CCSS-M. The revisions to each course will focus on incorporating engineering practices, crosscutting concepts, and core disciplinary ideas from the NGSS… 

San Diego State University: This project will modify the existing science content courses taken by future elementary teachers, including the nationally recognized Physics and Everyday Thinking, to align with the Framework and the NGSS. In addition, the project will develop kit-based activities and accompanying reflection activities that candidates will do at home and can use with their own students… 

Chamber of Commerce Develops Information Flyer to Inform Business Community about the Smarter Balanced Assessment System 

Source: California Department of Education

The American Chamber of Commerce Executives, in collaboration with the Smarter Balanced Assessment Consortium, developed an informational flyer to inform the business community about the Smarter Balanced assessment system. This flyer is available at

Related Topic: 

Smarter Balanced Assessment Consortium FAQs 

Source: California Department of Education 

Frequently asked questions (FAQs) about the Smarter Balanced Assessment Consortium (SBAC) student assessments can be found at


Smarter Balanced Practice Tests 

Source: The California Department of Education (CDE) Smarter Balanced Update – 15 April 2013

On 29 May 2013, Smarter Balanced will release a set of computer-based Practice Tests for grades 3 through 8 and grade 11. For each grade, a Practice Test will be available in both English language arts (ELA) and mathematics. The Practice Tests will include an array of item types, including selected response, constructed response, and performance tasks, and will be built using test blueprints similar to those for the operational tests. In addition, the Practice Tests will support several accessibility accommodations. The Practice Tests will be publicly available on the Smarter Balanced Web site and will be accessible until the implementation of the operational Smarter Balanced assessments in the 2014-15 school year. 

Additional information about Smarter Balanced is available on the CDE Smarter Balanced Web page at and on the Smarter Balanced Assessment Consortium’s Web site:

Ignite! Sessions at the 2012 CMC-North Conference 

Source: Key Curriculum

Key Curriculum continues its tradition of sponsoring and videotaping Ignite! sessions at mathematics education conferences. Andres Marti writes, “This will be my fourth year taping and editing videos of the Ignite talks at the national math conferences [this week], and I still find these talks to be the most compelling and entertaining events at these conferences. For those of you unfamiliar with the Ignite format, the speaker gives a 5-minute talk while a 20-slide PowerPoint presentation automatically advances to the next slide every 15 seconds. Our most recent Ignite event was the CMC-North conference in Asilomar in December. I finally finished editing all nine speakers… The complete playlist is available on our YouTube page” (see above for the URL). 

Following are the titles and speakers of the Ignite! Presentations at CMC-North:

“A Humble Proof (if there’s room in the margins)” by Avery Pickford
“Up to the Challenge: Embracing the Common Core State Standards” by Jennifer North Morris 
“On the Importance of Language and Mathematics” by Harold Asturias
“Data Games” by Bill Finzer
“Unsilence Students’ Voices” by Suzanne Alejandre
“Why Teach Math and Language History?” by Lew Douglas 
“Do We Really Want Them to Reason?” by Ruth Parker
“9 Surprises” by Scott Farrand 
“The Plight of Math Teachers: Dreams and Concerns” by Mike Shaughnessy


“A U.S. Makeover for STEM Education: What It Means for NSF and the Education Department” by Jeffrey Mervis

Source: 18 April 2013

A proposed reshuffling of federal STEM (science, technology, engineering, and mathematics) education programs in the United States would move the Department of Education (ED) and the National Science Foundation (NSF) to the head of the class. Their new status would be a major change for the federal government, which now spends nearly $3 billion on 226 STEM education programs run by a dozen agencies.

Many of those programs were created to address a specific problem or at the behest of Congress to serve a specific constituency. However, the resulting fragmentation has hampered efforts to coordinate and assess the impact of the government’s investment. The proposed realignment, part of the President’s 2014 budget request to Congress, would slice the overall number of programs in half by slashing the education activities of mission agencies such as NASA, the National Oceanic and Atmospheric Administration, and the National Institutes of Health.

The reorganization unveiled last week surprised science educators, legislators, and even other federal officials. While the upcoming debate in Congress is likely to focus on whether some of the programs targeted for elimination should be preserved, the broader issue is the wisdom of creating two executive branch heavyweights in STEM education. Under the proposal, ED would oversee federally funded activities to improve elementary and secondary school (K-12) science education, while NSF would lead the way in undergraduate and graduate STEM education. (The Smithsonian Institution was given the green light, and $25 million, to expand its activities in informal, or nonclassroom, science education.) The realignment is designed to tap into ED’s extensive ties to, and experience working with, local schools as well as NSF’s expertise in funding high-quality STEM education activities.

The administration has targeted 78 programs for elimination, and an additional 49 would be consolidated. But it has also proposed 13 new programs, and its 2014 budget request of $3.1 billion for all STEM education activities would be 7% higher than what was spent in 2012.

Yesterday, presidential science adviser John Holdren told the House of Representatives science committee that the reorganization would also “leave intact” programs aimed at attracting underrepresented groups into STEM fields. “There has been a very serious effect to preserve the programs that most leverage the unique assets of the mission agencies, including programs that reach women and other underrepresented groups in STEM,” Holdren explained during a hearing on the administration’s overall 2014 request for research.

To learn more about the proposed reorganization, ScienceInsider spoke last week with top officials at each agency. Joan Ferrini-Mundy is head of NSF’s education directorate, and James Lightbourne oversees graduate education within the directorate. ScienceInsider also exchanged e-mails with Camsie McAdams, ED’s senior adviser on STEM education. [Visit to read edited transcripts of these interviews.]

Teachers’ Gestures Boost Math Learning

Source: Michigan State University; Contact: Kimberly Finn:
URL (Abstract):

Students perform better when their instructors use hand gestures — a simple teaching tool that could yield benefits in higher-level math such as algebra.

A study published in Child Development provides some of the strongest evidence yet that gesturing may have a unique effect on learning. Teachers in the United States tend to use gestures less than teachers in other countries.

“Gesturing can be a very beneficial tool that is completely free and easily employed in classrooms,” said Kimberly Fenn, study co-author and assistant professor of psychology at Michigan State University (MSU). “And I think it can have long-lasting effects.”

Fenn and Ryan Duffy of MSU and Susan Cook of the University of Iowa conducted an experiment with 184 second-, third- and fourth-graders in Michigan elementary classrooms.

Half of the students were shown videos of an instructor teaching math problems using only speech. The others were shown videos of the instructor teaching the same problems using both speech and gestures.

The problem involved mathematical equivalence (i.e., 4+5+7=__+7), which is known to be critical to later algebraic learning. In the speech-only videos, the instructor simply explains the problem. In the other videos, the instructor uses two hand gestures while speaking, using different hands to refer to the two sides of the equation.

Students who learned from the gesture videos performed better on a test given immediately afterward than those who learned from the speech-only video.

Another test was given 24 hours later, and the gesture students showed improvement in their performance while the speech-only students did not. The gesture group also showed stronger transfer to different problem types.

While previous research has shown the benefits of gestures in a one-on-one tutoring-style environment, the new study is the first to test the role of gestures in equivalence learning in a regular classroom.

The study also is the first to show that gestures can help students transfer learning to new contexts — such as transferring the knowledge learned in an addition-based equation to a multiplication-based equation.

Fenn noted that U.S. students lag behind those in many other Western countries in math and have a particularly hard time mastering equivalence problems in early grades.

“So if we can help them grasp this foundational knowledge earlier,” she said, “it will help them as they learn algebra and higher levels of mathematics.”