Mathematics

• California Department of Education Mathematics Framework
• Common Core States Standards

Standard Pathway

Middle School

Grade 6	Grade 7	Grade 8
Foundational Math The content of this course is a combination of California’s Common Core State Standards from Grade 6, Grade 7, and Algebra. The areas of content focus are: number system, expressions and equations, ratios and proportions, two-dimensional geometry, and data analysis and statistics.	Concepts in Math The content of this course is a combination of California’s Common Core State Standards from Grade 6, Grade 7 and Math 8.The areas of content focus are: number system, expressions and equations, ratios and proportions, three-dimensional geometry, and probability and bivariate data.	Algebra 1 The content of this course encompasses the California’s Common Core State Standards for Algebra 1. The first part of the course is focused on linear functions. The second part of the course is focused on nonlinear functions.

• Middle school follows compacted program (4 years of math in 3 years)
• Algebra 1 leads to Geometry or Geometry H in 9th grade.

High School

Grade 9	Grade 10	Grade 11	Grade 12
Geometry H Geometry Algebra 1	Algebra 2/Trig H Algebra 2/Trig A Algebra 2 Geometry Statistics Applications	Analysis H Intro to Analysis & Calculus (IAC) Precalculus Algebra 2 AP Stats Intro to Data Science Statistics Applications Applied Math H	AP Calculus BC AP Calculus AB Calculus Precalculus AP Stats Intro to Data Science Statistics Applications Applied Math H

 

Acceleration Pathway

Middle School

Grade 6	Grade 7	Grade 8
Validation tests passed in May of 5th grade:
Concepts in Math	Algebra 1	Geometry H
Validation tests passed in May of 6th grade:
Foundational Math	Algebra 1	Geometry H
Validation tests passed in May of 7th grade:
Foundational Math	Concepts in Math	Geometry H

High School

Grade 9	Grade 10	Grade 11	Grade 12
Algebra 2/Trig H Algebra 2/Trig A	Analysis H Intro to Analysis & Calculus (IAC)	AP Calculus BC AP Calculus AB AP Stats Intro to Data Science Applied Math H	AP Stats Intro to Data Science Applied Math H Community college courses

Students who wish to accelerate beyond this already compacted program may take part in the Math Validation Process and, in effect, cover five years of math in three years. Students successful in the Math Validation Process may only accelerate one additional year in the PAUSD middle school pathway. Students may participate more than once if they do not pass the assessments in a previous validation process.

For Spring 2024, rising sixth, seventh, and eighth-grade students who wish to accelerate beyond the already compacted middle school math program may participate in the Math Validation Process.

The updated Math Validation Process will now consist of one paper-and-pencil assessment instead of the previous two-part test. This assessment will evaluate the readiness for the grade-level math course the student would like to challenge, in addition to the student's knowledge of the topics and skills covered in the course.

These assessments are aligned to the state-adopted mathematics content standards. They will consist of multiple-choice (MC) and free-response questions (FRQ). The updated assessments are being developed in partnership with WestEd, a national leader in research, development, and service, alongside PAUSD Math Instructional Leaders.

• Participating in the math validation process is optional. 

• The test will cover the PAUSD grade-specific standards and concepts for mastery.

Grade 6 Validation Process

Grade 5 students who attempt but do not pass the validation test will be enrolled in  Grade 6 Foundational Math as described in the sequence. Students who pass the test will be enrolled in 7th-grade Math Concepts.

Grade 7 Validation Process

Grade 6 students who attempt but do not pass the validation test will be enrolled in Grade 7 Math Concepts as described in the sequence. Concepts in Math is the appropriate math placement for most students for their 7th-grade year. Students who pass the test will be enrolled in 8th grade Algebra 1 (with 8th grade students).

Grade 8 Validation Process

Grade 7 students who attempt but do not pass the validation test will be enrolled in Algebra 1. Algebra 1 is the appropriate math placement for most students for their 8th-grade year. Students who pass the test will be enrolled in Geometry Honors.

Changing Math Placement

Students who feel they are not appropriately placed should meet with their teacher and counselor to determine if a schedule correction is needed (BP 6152.1). Within 10 school days of an initial placement decision or placement decision upon reevaluation, a student and their parent/guardian may appeal the decision to the Superintendent or designee.

Challenge by Examination

PAUSD Board Policy allows high school students to challenge courses by examination (BP 6155). This examination is aligned to state-adopted content standards in mathematics taught in the course being challenged. If a student successfully challenges a course, a grade based on their results and units will be added to their transcript with a note indicating that the requirement was met by examination.

Students wishing to take off-campus courses (non-PAUSD) must have prior approval. Please see the Gunn and Paly websites for more detailed information regarding off-campus courses.

Elementary School

Bridges in Mathematics, 2nd edition, published by the Math Learning Center

Middle School

• Foundational Math (select the green book).
• Concepts in Mathematics (select the red book).
• Algebra 1 (select the blue and gold book).

High School

• Algebra 1 (Prentice Hall); Charles, Hall, Kennedy, et al (Pearson Ed)
• Algebra 1 Common Core; Randall Charles, et. al.; Pearson
• Algebra 2 (Prentice Hall); Charles, Hall, Kennedy, et al (Pearson Ed)
• Algebra and Trigonometry Graphs & Models, Third Edition; Bittinger, Beecher, Ellenbogen and Penna (Pearson Ed)
• Algebra and Trigonometry: Graphs & Models 4th ed
• Calculus, Concepts and Applications Second Edition; Paul A Foerster (Key Curriculum Press)
• Calculus, Early Transcendentals, 8th Edition
• The Practice of Statistics by Starnes et al; published by BFW; 5th ed
• Geometry (Prentice Hall) Foundation Series; Charles, Hall, Kennedy, et al (Pearson Ed)
• Geometry Common Core by Charles, Hall, Kennedy, Bass, Johnson, Murphy, and Wiggins
• Geometry by Jurgenson Brown Jurgenson Published by Houghton Mifflin
• Precalculus Graphical, Numerical, Algebraic Seventh Ed; Demana, Waits, Foley, & Kennedy (Addison Wesley)
• Precalculus, A Graphing Approach; Holt, Rinehart, and Winston (Harcourt Classroom Edu Co) *reference*

Elementary School

• Bridges Family Support Resources.
• Bridges in Mathematics is a research based program.
• What you need to know about Bridges.
• Parent Handout - English | Spanish.

Middle School

• Foundational Math (select the green book).
• Concepts in Mathematics (select the red book).
• Algebra 1 (select the blue and gold book).

In accordance with Senate Bill 359, annually, the Board and the Superintendent or designee shall review student data related to placement and advancement in the mathematics courses offered at District high schools to ensure that ninth-grade students who are qualified to progress in mathematics courses based on their performance on objective academic measures are not held back in a disproportionate manner on the basis of their race, ethnicity, gender, or socioeconomic background.

This report provides the Board with information about 2023-24 current ninth-grade enrollment, class size, and associated trends in mathematics courses. This report is based on data from two weeks after the end of the first quarter. In the future, the math placement data will be collected two weeks after the end of the first quarter and will be presented to the Board thereafter.

• Is my child required to take the math validation test?
  No, this test is optional.
   

• What are the dates for the validation test?
  May 2024 test dates are being finalized.
   

• Where will the validation test be held?
  Validation tests will be administered (after school hours) at your neighborhood middle school.
   

• How long does the test take?
  Test time will be approximately 1.5 – 2 hours.
   

• Are there study materials for the test?
  No. Only the information on the standards of the course being challenged will be available.
   

• Is there just one test, or is there a separate test for each challenged course?
  There will be only one test for each challenged course. (i.e., one for each of grade levels 6, 7, and 8).
   

• Who is scoring the paper-and-pencil test?
  PAUSD middle school math teachers will score the test.
   

• Will my child’s results be shared with me after they are scored?
  Yes.
   

• What happens if my child doesn’t pass the validation test?
  Students who do not pass the validation test will be placed in a math course based on their current grade-level sequence.
   

• Are retakes allowed?
  No. Retakes will not be allowed.
   

• May I accompany my child during the test?
  No. Students will be tested in a secured location with other students.
   

• May a parent review the test if they believe there was an error in scoring?
  No, as these are secured tests.

This FAQ applies to both Multivariable Calculus and Linear Algebra courses.
Students who have taken Multivariable Calculus may choose to move on to Linear Algebra.

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What type of course is Multivariable Calculus (MVC) in PAUSD?

MVC is categorized under the concurrent (not dual) enrollment category. Foothill College has been offering MVC as an online course outside of the regular bell schedule since the 2019-20 school year. The Foothill instructor does not hold a high school teaching credential. Scroll down for definitions of Concurrent and Dual Enrollment.

How many sections of the course have traditionally been taught?

One (1) section for approximately 30 students from both high schools in PAUSD.

What is the history of advanced math courses from community college at PAUSD high schools?

2012-2015
A PAUSD teacher, who was also employed by Cañada College as an instructor, taught the classes through Cañada College. The course was offered outside of school hours. Students from both Paly and Gunn could participate and had to travel to the high school campus where the course was offered, if it was not at their campus of enrollment.

2016-2018
The advanced math courses were taught by other Cañada College instructors; offered mid-way through 7th period plus after school hours, to accommodate the course being a college course and students traveling to either Gunn or Palo Alto High School.

2019-2023
Beginning in 2020, the course moved to an online platform taught by a Foothill College instructor outside of school hours.

The California Department of Education (CDE) updated the dual enrollment parameters in the 2020-21 school year, categorizing these courses as concurrent enrollment.

What is concurrent enrollment?

Concurrent enrollment refers to students taking community college courses that have not undergone curricular alignment or articulation with high school courses. Students in concurrent enrollment courses may transfer credit based on the credit acceptance policy, and these courses are generally scheduled outside of regular bell schedules. The instructors teaching concurrent enrollment courses at the college level do not need high school teaching credentials.

What is dual enrollment?

Dual enrollment is a type of concurrent enrollment guided by the College and Career Access Pathways Act-CCAP (AB 288).

Dual enrollment students take courses, during the regular bell schedule, from PAUSD teachers who hold a high school teaching credential. The California Community College system requires that these instructors meet the minimum qualifications to issue college credit. These courses have gone through a curricular alignment process with Foothill-De Anza Community College District. In addition, PAUSD staff are authorized by the Foothill-De Anza Community College District to teach specific dual enrollment courses through College and Career Access Pathways (CCAP).

Whom may I contact for questions regarding dual enrollment guidelines?

For questions or additional information: Click Here.

What is the difference between College and Career Access Pathways (CCAP) courses and non-CCAP courses?

Dual enrollment courses refer to high school courses that have gone through curricular alignment with a community college. Dual enrollment students are enrolled in two institutions concurrently, therefore earning high school credits and college credits simultaneously. There are two categories: College and Career Access Pathways (CCAP) and non-CCAP.

1. CCAP authorizes California Community College districts to enter into formal partnership agreements with local school districts to expand access to concurrent enrollment opportunities for high school students (AB 288) opportunities for students who may not already be college bound or who are underrepresented in higher education. These courses are taught during the school day by Palo Alto Unified School District (PAUSD) teachers, who are authorized by the Foothill-De Anza Community College District to teach specific dual enrollment courses. Grading for CCAP dual enrollment courses is as follows:
   1. Students in dual enrollment courses receive regular credit per course. For example, if a high school level course earns five credits, the dual enrollment version of that course also earns five credits.
   2. Grades, upon completion of the course, will be weighted similarly to Advanced Placement (AP) or Honors (H) classes in weighted Grade Point Average (GPA) calculations, as they are rigorous courses that have gone through an alignment process with the community college.
2. All other community college courses are non-CCAP courses. Non-CCAP courses are taught by community college instructors during after-school hours.
   1. Prior approval is needed to enroll, and the official community college transcript is provided to the high school so that the course may be added to the high school transcript.
   2. Non-CCAP courses receive double credit; e.g., a five-unit class receives 10 units of credit.
   3. Courses taken off-campus with prior approval will be listed as Credit or No Credit on the PAUSD transcript and will not be included in the GPA.
   4. Students are expected to include their official community college transcript/s as part of their college applications, in addition to the PAUSD transcript. (PAUSD Administrative Regulation AR 6146.11 - Alternative Credits Toward Graduation)

What resources are available for students taking Multivariable Calculus?

Students should contact their counselors with specific questions regarding transcript and graduation requirements, or visit the high school's Off-Campus Courses Frequently Asked Questions (FAQ) page (Palo Alto High or Gunn High).

Is there a cost for classes?

Foothill and De Anza Colleges offer multiple sections of MVC at no cost. High school students are eligible to enroll in any community college in the state without charge as long as they are enrolled in courses that earn them less than the number of units determined by the college. Please refer to the Foothill and De Anza websites for specific information.

How are these math courses identified at Foothill and De Anza colleges?

Foothill course codes are:

• Multivariable Calculus: MATH 1C and 1D
• Linear Algebra: MATH 2B

Can students take Multivariable Calculus at a college or university other than Foothill or De Anza?

Yes, students can take courses from colleges other than Foothill or De Anza and may transfer credit based on the credit acceptance policy, which includes pre-approval. There may be a cost at other colleges.

What is the teaching credential requirement for dual enrollment?

With a recent update from CDE, community college instructors need a high school teaching credential to issue high school credit in dual enrollment (More information at this link for the CDE's Frequently Asked Questions page - question 1). In order to teach a dual enrollment course, PAUSD teachers need to be authorized by the community college to issue college credit.

What is the difference between Single Credit (Concurrent) versus Dual Credit (Dual Enrollment) course?

What are the requirements to teach at a public high school in California?

Teachers must meet the proper credentialing requirements of the state of California. Information can be found at: www.ctc.ca.gov

How can a student sign up for the advanced math course at Foothill?

Foothill offers advanced math courses in various modalities, including asynchronous sections for students with specific schedule needs. In partnership with PAUSD, Foothill screens students to ensure that they meet the prerequisites for the course and makes an effort to accommodate students who wish to be in the same section as their peers. Please contact Foothill Coordinator, Alejandro Favela, for questions regarding the prerequisite screening or enrollment process.

Math continues to be a topic of interest with a high volume of engagement. In addition to the ongoing math department and steering programming discussions, below is a summary of the volume of feedback in the last six months (since Spring of 2023).

• Counselor meetings (34 staff members)
• Math department meetings (28 staff members)
• Math steering meetings (7 staff members)
• 2210 High School Math survey responses
• Two student feedback sessions led by Principals 
• 157 Public comments
   

• Court Upholds District Math Policy
• Order After Hearing On Petition for Writ of Mandate