Common Core Math – Recommended Courses and Pathways

The California Department of Education adopted the Common Core State Standards (CCSS) on August 2, 2010, with full implementation planned for the 2014-15 school year. The Common Core State Standards for Mathematics replaced the California State Standards for Mathematics (1997).

The CCSS require a specific sequencing of mathematics concepts, and demonstrated proficiency in applying those concepts to solve problems, to build a foundation for the mastery of algebra. This approach is based on what is considered both cognitively and developmentally appropriate, to promote better comprehension and retention of math concepts.

This approach is also based on the content and practice standards used to teach math in other developed countries where students typically outperform their United States’ counterparts.

Adopting the new standards, the State Board of Education determined that the CCSS are more rigorous than the 1997 standards, and provide a stronger foundation for more advanced math and for application of math concepts in the sciences. Last year, the PUSD Board of Education adopted a structured transition from the existing Piedmont Middle School math course progression (based on the 1997 Standards) to the new Common Core math classes.


Math Task Force

In order to develop Common Core pathways that address PUSD’s various learners, the district formed the PUSD Math Task Force and charged it with researching, reviewing, and recommending PUSD Math Pathways to the Superintendent and the Board of Education for consideration and implementation in 2015-16. Furthermore, the Board of Education provided a framework for developing math pathways that included compression opportunities at PMS and PHS/MHS and a pathway to AP Calculus AB and AP Calculus BC.

The Math Task Force investigated and discussed practical experience and insight gained by the PUSD math faculty during the first semester of this school year; input from math experts at Alameda County Office of Education; and input from members of the Silicon Valley Math Initiative (SVMI).

The Math Task Force is comprised of teachers, parents, students, and administrators.

Parents: Julie Caskey, Larry Hawkins, Brad Kraetzer, Carol Menz, Stacy Merickel, Cory Smegal, Sameer Srivastava, Kelly Wiesbrock

Teachers: Sarah Kingston, Tammy Medress, Doyle O’Regan, Stephanie Roth, Auban Willats.

Students: Remy Afong, Polina Dorfman Su, Tobias Fischer, Madeline Malan, Isabella Schwartz, Lauren Young

Administrators: Randall Booker, Carol Cramer, Brent Daniels, Ryan Fletcher, Ting Hsu Engelman, Julie Moll, Ginna Myers, Cheryl Wozniak

Board Observers: Sarah Pearson, Andrea Swenson


Integrated Math

The Math Task Force investigated whether to recommend either “traditional” or “integrated” courses for the courses that follow CC-8 Math at Piedmont Middle School.  Under the traditional approach, students would take sequential courses in Algebra, Geometry, Algebra II, and Math Analysis.

imUnder the integrated (or “international”) approach, the content of these courses would be mixed over a period of years.  The District currently offers traditional courses, although the courses will change significantly under Common Core regardless of the choice between the traditional and integrated approach.  CC-8 Math is an integrated course, with elements of Algebra and Functions, Geometry, and Statistics.

The Math Task Force developed criteria for evaluating and recommending either the Common Core traditional or integrated course approach to the Board.  For example, the MTF considered whether one approach or the other better supports: the three shifts in math instruction (focus, coherence, rigor); the cognitive development of students; mastery of both the content and practice standards; opportunities for differentiation; and practical considerations about how to achieve coherent compression (speeding up) and expansion (slowing down) of the curriculum for students who do not follow the grade-level progression.

The MTF also discussed possible pathways for compression and identified preliminary considerations including the following:

  • there may need to be transitional pathways in addition to “final” pathways;
  • the pathways should provide flexibility to compress and expand at various points, including the opportunity to take summer classes; and
  • questions must be addressed about how to assess a student’s readiness for compression.

The Math Task Force came to consensus and recommends the Common Core Integrated approach for secondary math courses in PUSD. The following rationale supports this recommendation:

  • Students are exposed to the Integrated approach K-8 and then again in advanced mathematics courses.
  • The majority of other countries, including the countries with the highest-performing math students, follow the integrated model.
  • Research suggests that an integrated math curriculum has the potential to facilitate students’ mathematical thinking more effectively than a traditional math curriculum especially in certain areas, such as conceptual understanding.
    • There are few research studies investigating the relative effectiveness of these approaches.  The District commissioned Cheryl Holzmeyer, Ph.D. to prepare an analysis of the research and available data comparing the traditional and international models.  Please visit the following link for the complete report, which was issued in December 2014:
    • The integrated approach allows for introducing the increasingly complex concepts in Algebra and Geometry over a period of several years, as students are more developmentally ready.
    • The integrated approach lends itself to better course compression options (acceleration for advanced learners) more so than some traditional courses.

For more detailed information on Integrated and Traditional Math, please visit the following link for the PUSD Integrated and Traditional Math FAQ:


Course Pathways

The Math Task Force recommends the math courses and math pathways described below. These recommendations include:

  • pathways to Calculus AB and BC for qualified students;
  • multiple “compression” options for students who are ready for more challenge;
  • opportunities to take summer school classes/self-study materials that provide additional entry points to the compression tracks; and
  • support classes for learners who need additional time to master concepts.

The recommended courses and pathways were originally formulated by the PMS, PHS, and MHS math educators and represent what the teachers consider to be the most practical, feasible, coherent way to “compress” and “expand” the math units.  The Math Task Force vetted these pathways and recommend these to the Board of Education for adoption. These recommendations provide more opportunity for students seeking to accelerate than are currently in place.

  • In developing this recommendation, the Math Task Force met on 8 separate occasions to research, review, and discuss the varying interests and opportunities for students. We enlisted the support of David Foster, Silicon Valley Math Initiative’s (SVMI) Executive Director and math experts from the Alameda County Office of Education. We performed site visits at schools in the Bay Area and contracted an independent research report by Cheryl Holzmeyer, Ph.D., a Public Knowledge Project Research Associate at the Graduate School of Education, Stanford University. This report, entitled Common Core Mathematics: Middle & High School Pathways to College, Careers, and Citizenship can be reviewed by visiting the following link:


Parent Engagement

Recognizing that the parent community is tremendously invested in the implementation of Common Core Mathematics across the district, we developed a series of opportunities for the community to learn about and provide input on the recommended courses and course pathways.

In 2013-14, the district hosted the following engagement opportunities:

  • 6 Parent Club Meetings
  • 4 Parent Education Nights
  • 4 Board of Education Meetings
  • 3 Curriculum Forum Meetings
  • 8 Site Council Meetings

In 2014-15, the district hosted additional engagement opportunities:

  • 5 Parent Club Meetings
  • 3 Parent Education Nights
  • 2 Site Council Meetings
  • 2 School Board Meetings
  • 1 PMS Family Math Night
  • 1 Speaker Series Event

For more detailed information on the proposed math courses and math pathways, please visit the following link for the PUSD Math Task Force Recommended Math Course Pathways FAQ:

Overview of Recommended Pathways

Current 5th Grade Students

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Current 6th Grade Students

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Current 7th Grade Students

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Current 7th Grade Students in CC-8

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Current 8th Grade Students

Screen Shot 2015-02-25 at 3.23.52 PM





arrowIn addition to the compression options indicated by the black arrows in the diagrams above, students who want more opportunity to accelerate have the option to accelerate from IM-1 to the compressed IM-2B/IM-3 course. This added option is indicated by the dashed-orange arrows in the diagrams above. To take advantage of this extra option, the student can take Integrated Math 2-A (IM-2A) either as a summer course (a semester’s worth of material covered over a 6-week summer program hosted by PUSD) or as a self-study program. In either case, the student will be required to demonstrate mastery of the IM-2A material by means of an assessment before enrolling in IM-2B/IM-3.


During this transition to the Common Core Standards, PUSD recognizes the need to provide additional professional development for teachers, as well as additional support for students. Our partnership with the Silicon Valley Math Initiative provides the district with an opportunity to collaborate with comparable school districts and receive support and professional development in the areas of differentiation, curriculum development, and assessment.


As we continue Common Core Math instruction, we will need to assess student performance. Working closely with the PMS/PHS/MHS Math Departments, we will review student performance data to inform instruction and future revisions to the curriculum and course pathways.


  1 comment for “Common Core Math – Recommended Courses and Pathways

  1. Cynthia Perez
    March 2, 2015 at 4:36 pm

    I agree with the recommended pathways BECAUASE it does provide more opportunities for compression and ultimately AP Calculus BC for current 8th graders.

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