The purpose of Senate Bill 359 is to serve pupils entering grade 9 and students who are transitioning between elementary and middle school. SB 359 requires that before the beginning of the 2016–17 school year, to post the fair, objective, and transparent mathematics placement policy on its Internet Web site.

In the California Mathematics Placement Act of 2015, the State of California documents:

“Pupil achievement in mathematics is important to prepare pupils for college and their future careers, especially those careers in the fields of science, technology, engineering, and mathematics (STEM). Placement in appropriate mathematics courses is critically important for a pupil during the middle and high school years. A pupil’s 9th grade math course placement is a crucial crossroads for future educational success. Misplacement in the sequence of mathematics courses creates a number of barriers and results in pupils being less competitive for college admissions, including admissions at the California State University and University of California.

“New research shows that it is less common for pupils of color, even high-achieving pupils of color, to reach calculus by grade 12 compared to their white and Asian peers. All pupils, regardless of race, ethnicity, gender, or socioeconomic background, deserve an equal chance to advance in mathematics. With the shift towards implementation of the Common Core State Standards for Mathematics, it is particularly important for all pupils to have access to high-quality mathematics programs that meet the goals and expectations of these standards. It is crucial for teachers and guidance personnel to advise pupils and parents on the importance of accurate mathematics course placement and its impact on future college eligibility so pupils may take each course in the mathematics course sequence.”

Although only the information about placement of students from grades 8 to 9 and grades 5 to 6 are required by SB 359, in PAUSD, laning begins in 7th grade. **Because PAUSD utilizes lanes instead of tracks, below you find a systems view of math paths through PAUSD from grade 6 through 12 in order to understand the choices and opportunities among the course offerings.** The documents that you can access below illuminate placement from grades 5 through 12, especially detailing placement considerations throughout the middle school years.

Secondary Math Placement SB 359 – Downloadable Version

Matemáticas - colocación secundaria

Math Flow Chart for 2017/18 showing the flexibility of the paths

The PAUSD provides an exceptional math program that supports students developmentally. Our sixth grade math teachers embrace the philosophy of cultivating successful middle school students from elementary students. In order to support the students’ transition from Grade 5 Elementary School to Grade 6 Middle School, ** all **students matriculate from Math 5 to Math 6. (For students receiving special education services, the mathematics placement will be determined by the student’s IEP team.)

In sixth grade our students typically have two teachers for the four core subjects as they learn higher order study skills, self-advocacy, and build friendships that are necessary to navigate their secondary schools. As students learn to manage the myriad of middle school challenges, the flexible clustering available because of the heterogeneous grouping in the core classes allows students and teachers to suspend any hasty evaluations as they support the students’ sense of growth and possibilities.

In Math 6 students study the Sixth-grade California Common Core State Standards. Students work both independently and in cooperative groups with instruction that is differentiated to appropriately challenge all students. Sixth grade teachers are completely prepared to support students who require extension, support, and enrichment opportunities.

### 6^{th} Grade Math Differentiation

- For Math Support or Additional Help
- Math workshop course (where available) or other structured support
- Working with the Teacher outside of class time.

- For Extra Challenge and Deeper Math Experiences
- Math Extensions/Einsteins and investigations of classroom problems
- Math Extensions/Einstein Problems are
- Weekly or monthly packets that contain numerous math problems intended to provide individuals additional challenge and differentiation.
- Each set of Math Extensions/Einsteins contains problems at varying levels to help students think deeply about math in the real world and to engage their problem solving skills.

- Join Math Club
- Math Club activities include studying non-standard mathematical topics, engagement in math contests, and explorations of a variety of mathematical ideas.

- Working with the Teacher outside of class time.

- All sixth grade students begin in 6
^{th}grade math. Sixth grade math teachers use a variety of methods to evaluate each student at the*beginning of the year*. Occasionally a teacher recognizes that an individual is working well beyond the sixth grade level.- Sixth-grade math teachers are equipped to differentiate for students who are advanced a year above sixth-grade level in math which allows the student to remain with the student’s class during the transition year.
- When the sixth-grade math teacher identifies a student who is potentially ready for Algebra (typically an eighth- or ninth-grade course), the teacher notifies the parents and offers the student an opportunity to take the
*Math 7A Mastery**Test*. Should the student pass the test, a parent-conference is called. Although the student’s mathematical readiness for Algebra 8 is indicated, the student’s social needs and the level of the student’s interest and joy in math are considered. Subsequent logistical challenges for the next few years are considered. If chosen, placement in Algebra 8 is completed as soon as possible.

### Background information

The transition from elementary school to middle school is more than a transition in grade levels or school buildings. The students’ transition is social, emotional, physical and academic. Children become adolescents. Schoolwork becomes more codified, more complex, more integrated, and more challenging. Middle school students find themselves taking risks, making errors, trying new ideas, awakening to themselves, building and knocking down their self-confidence, making friends, and feeling lonely; they are *becoming*. The transition takes time. The PAUSD secondary math program allows for a difference in growth rates and has crafted courses that meet the California Common Core State Standards in Mathematics (CCSS-M) for every student throughout the secondary schools. The CCSS-M standards are comprised of two types of standards: eight Mathematical Practice Standards and Math Content Standards (building mathematical understanding, skills, knowledge, and expertise throughout the years from K-12).

The PAUSD mathematics program offers two seventh-grade courses to provide the appropriate balance of the level of challenge and success to seventh-grade students: Math 7 and Math 7A. Math 7 meets all of the standards of the CCSS-M for Math 7. Math 7A is an accelerated course. Math 7A is a combined course of all of the CCSS-M Math 7 and more than half of the CCSS-M Math 8 standards. Math 7A compresses more than 1 ½ years of CCSS-M mathematics into its year of study. (The Math 7 course is followed by Math 8. The Math 7A course is followed by Algebra 8, which is a combination of the remaining topics of CCSS-M Math 8 and the topics of Algebra 1 at an advanced depth.)

Secondary math teachers give input or recommendations to help parents and students choose the appropriate course by organizing a variety of observable factors and linking the factors to subsequent success in course placement. The factors include achievement on classroom tests, homework completion, interest in mathematics as evidenced by their participation in classroom extensions, successful application of mathematical concepts, and achievement on the comprehensive end of year exam. The organization is a criteria table found on the next page.

For students receiving special education services, the mathematics placement will be determined by the student’s IEP team.

### The Organization of this Document

The sixth-grade math teachers will provide personal input to students and parents utilizing on of the two criteria tables on the next page. (Please note that students whose teachers use *evidenced-based grading* will earn rubric scores and all other students will earn percentages.) The top call-out to the right of each table explains the general indications for the recommendation to either seventh-grade math course placement. The call-out also provides information regarding students who are advanced in their mastery of middle school math curriculum.

Regardless of the recommendation, teachers, counselors and mathematicians recognize the conundrum of the *case of the individual* versus the* flow of the trends*. Therefore parents and students are urged to choose the most appropriate math course that will give the student the suitable amount of challenge and success within it.

Criteria Table 1: an “X” in the column for each criteria indicates the appropriate placement for the student

^{1 }Students may enroll in any *lane* of the course. The teacher’s input for enrollment is based on the historical progress of students through the middle school math courses. (That is, if the student is recommended for any Math 7 course, students may request placement in either Math 7 or Math 7A.) Students having difficulty in their class despite putting in their best effort can request a lane change. Such changes are contingent on class size and must be approved by the IS. Changes can only be made before the end of the first quarter or at the semester break. Students who change lanes during first semester carry over their grade at the time to the new lane.

^{2}The Math 7A is an accelerated course combined of all of the CCSS-M Math 7 and more than half of the CCSS-M Math 8 standards. The Math 7A course is followed by Algebra 8, which is a combination of the remaining topics of CCSS-M Math 8 and the topics of Algebra 1 at an advanced depth.

^{3}The grade-level course, Math 7, meets the standards of the CCSS-M Math 7. The Math 7 course is followed by Math 8, or, with summer work, Algebra 8.

^{5 }Students may enroll in any *lane* of the course. The teacher’s input for enrollment is based on the historical progress of students through the middle school math courses. (That is, if the student is recommended for any Math 7 course, the student may request placement in either Math 7 or Math 7A.) Students having difficulty in their class despite putting in their best effort can request a lane change. Such changes are contingent on class size and must be approved by the IS. Changes can only be made before the end of the first quarter or at the semester break. Students who change lanes during first semester carry over their grade at the time to the new lane.

^{6}The Math 7A is an accelerated course combined of all of the CCSS-M Math 7 and more than half of the CCSS-M Math 8 standards. The Math 7A course is followed by Algebra 8, which is a combination of the remaining topics of CCSS-M Math 8 and the topics of Algebra 1 at an advanced depth.

^{7}The grade-level course, Math 7, meets the standards of the CCSS-M Math 7. The Math 7 course is followed by Math 8, or, with summer work, Algebra 8.

### Background information

PAUSD strives to offer math courses that give students the appropriate amount of challenge and success. In the middle schools, PAUSD supports well-paced responsive or adaptable student placement. Seventh grade students are enrolled in one of two courses: Math 7 and Math 7A. Math 7 satisfies the Common Core State Standards (CCSS-M 7) while Math 7A is an accelerated course that includes both the CCSS-M 7 standards and more than half of the CCSS-M 8 standards. Successful placement of rising eighth-grade students is dependent on the student’s experience in Math 7 or Math 7A. Usually in eighth grade, two courses are available to students: Math 8 and Algebra 8. Math 8 satisfies the CCSS-M 8 standards. Algebra 8 is an accelerated course that includes less than 50% of the CCSS-M 8 standards, and all of the CCSS-Algebra standards at an advanced level (some topics are extended to Algebra 2 levels).

The seventh-grade student’s consistent classroom test scores are a reliable indicator of the student’s mastery of the Math 7 content. The overall math grade may reflect behavior such as study skills, homework completion or remittance, or classroom participation. Thus the overall math grade tends to be less of an appropriate predictor of academic success. For appropriate placement recommendation, use the student’s first experience of classroom tests.

As middle students grow and develop, they foster varied appreciation for one academic subject over another. Therefore, flexibility is appropriate as a student moves from grade 7 to grade 8. To move to Algebra 8 from Math 7 requires summer work in the Math 8 topics not covered in Math 7. Students who are likely to be successful in the move to the accelerated work have earned high marks in their Math 7 classroom exams.

### The Organization of this Document

The flow chart indicates both the more usual move from one course to another at the same level of pacing and challenge, as well as the moves to support a student’s independent and successful math achievement. To move from the grade-level work to the accelerated work requires a four-week summer course, and the expectation that the compressed time for the work increased the pace of the work. The summer course provides the student with the opportunity to master the CCSS-M 8 topics not included in Math 7, but integrated in Math 7A.

If a student is having difficulty in the seventh-grade accelerated course, Math 7A, it is appropriate to move over to the grade-level course to produce student confidence, as well as joy and interest, back into the student’s relationship with mathematics.

For students receiving special education services, the mathematics placement will be determined by the student’s IEP team.

Regardless of the recommendation, teachers, counselors and mathematicians recognize the conundrum of the *case of the individual* versus the* flow of the trends*. Therefore, throughout secondary mathematics, parents and students are urged to choose the most appropriate math course annually to give the student the suitable amount of challenge and success within it.

^{1} Students may enroll in any course within the *lane* of the course. (That is, if the student is recommended for Math 8, the student may request placement in either Math 8 or Algebra 8.) Students having difficulty in the class despite putting in the student’s best effort can request a lane change. Such changes are contingent on class size and must be approved by the IS. Changes can only be made before the end of the first quarter or at the semester break. Students who change lanes during first semester carry over their grade at the time to the new lane.

^{2} Students who consistently earn a B- or less on tests in Math 7A need support. They have a choice of either moving to course in which the level of challenge and success is more appropriate, Math 8, or to build skills, concepts and personal confidence in some of the accelerated topics over the summer in the *Bridge to Algebra 8* course, and continue on to Algebra 8.

^{3}The curriculum of the 4-week summer school course, *Bridge to Algebra 8*, is the topics from CCSS-M 8 that were included in Math 7A, but not Math 7.

^{4}The ** Algebra 8 Mastery Test** is offered in

**August**. A student may only attempt the

*Algebra 8 Mastery Test*one time. Non-PAUSD students who perform well on the

*8*and who demonstrate some Algebra knowledge to an 8th grade math teacher (a few informal questions that require work demonstrated) may attempt the

^{th}grade Placement Test*Algebra 8 Mastery Test*. Students transferring in from non-PAUSD schools must pass the test in order to be placed ahead of grade level.

### Background information

Successful high school math course placement of rising ninth-grade students is dependent on a variety of factors. The eighth-grade student’s *overall* math grade often includes items that are not connected to successfully meeting the curriculum standards. The overall math grade may reflect behavior such as study skills, homework completion or remittance, or classroom participation. Thus the overall math grade is less of an appropriate predictor of academic success. Many of the factors are subjective and personal, such as the student’s interest in math, the student’s prior experiences in math, the student’s self-view, or the student’s mindset with respect to the variety of upcoming academic challenges. **Generally,** **the best predictor of academic success in a ninth-grade math placement is the eighth-grade student’s classroom test scores which indicate the student’s mastery of the content. **

- The classroom tests and their rubrics are collaboratively developed by the teachers of the course at each school. Unusual student answers are often jointly evaluated by the teaching team.
- The classroom tests are designed to correlate directly to the standards taught in the unit.
- Classroom tests are completed individually and illuminate the depth of the student’s grasp of the standards taught and the student’s command of the eight mathematical practices.
- Classroom tests do not reflect any aspect of student social behavior.
- Classroom tests do not directly measure homework or study habits.
- Classroom tests are a strong indicator of student progress in the acquisition and utilization of the mathematics and practices of the course.

### The Organization of this Document

In middle school eighth-grade, most students are enrolled in one of two courses: Math 8 or Algebra 8. In rare circumstances, student are enrolled in Geometry H, a high school honors course offered at the middle school sites. Recommended placement in their ninth-grade math course can be determined by traversing the flow chart headed by the particular eighth-grade course title. Some differences in course offerings exist between Henry M. Gunn High School and Palo Alto High School and placement will vary slightly. The differences are noted within each flow chart.

For students receiving special education services, the mathematics placement will be determined by the student’s IEP team.

Regardless of the recommendation, teachers, counselors and mathematicians recognize the conundrum of the *case of the individual* versus the* flow of the trends*. Therefore, entering and throughout high school, parents and students are urged to choose the most appropriate math course annually to give the student the suitable amount of challenge and success within it.

### Ninth-Grade Placement Recommendations^{1} for Students enrolled in **Math 8**

^{1} Students may enroll in any course within the *lane* of the course. (That is, if the student is recommended for any Algebra 1 course, the student may request placement in any level of Algebra 1 (Alg 1.1, Alg 1, or Alg 1A). Students having difficulty in their class despite putting in their best effort can request a lane change. Such changes are contingent on class size and must be approved by the IS. Changes can only be made before the end of the first quarter or at the semester break. Students who change lanes during first semester carry over their grade at the time to the new lane.

^{2 }Recommendations are reviewed at the Middle Schools at the end of the school year in May/June.

^{3 }Discussions include consideration of parental insights, case-manager’s (if applicable) insights, student interest, homework completion, challenge problem completion, and choice of test level (in Math 8, two levels of tests are often available in the second semester).

### Ninth-Grade Placement Recommendations4 for Students enrolled in Alg 8

^{4} Students may enroll in any *lane* of the course. (That is, if students are recommended for any level of Geometry, students may request placement in any Geometry course (excluding grade-level Geometry, a tenth-grade course). If the student is recommended for any Algebra 1 course, the student may request placement in any level of Algebra 1 (Alg 1.1, Alg 1, or Alg 1A). Students having difficulty in their class despite putting in their best effort can request a lane change. Such changes are contingent on class size and must be approved by the IS. Changes can only be made before the end of the first quarter or at the semester break. Students who change lanes during first semester carry over their grade at the time to the new lane.

### Ninth-Grade Placement Recommendations5 for Eighth-Grade Students enrolled in Geo H

^{5} Students a year (or more) ahead in the honors lane of mathematics are expected to earn As in the courses in order to *remain competitive in the application process* for university work. Students having difficulty in their class despite putting in their best effort can request a lane change. Such changes are contingent on class size and must be approved by the IS. Changes can only be made before the end of the first quarter or at the semester break. Students who change lanes during first semester carry over their grade at the time to the new lane.

Mathematics electives include AP Statistics, Statistics Applications (AAR), and Advanced Problem Solving (levels 1 – 4). Elective courses that can be taken for either Mathematics or Career/Technology Education credit include the Computer Science courses Intro to Java, Programming Concepts, Advanced Java, Programming Using Java, AP CS A, and Gunn BEAM (business math applications course).

### Considerations

It is important that a student chooses or is placed appropriately for both challenge and success in math courses throughout secondary education. Building success is a journey, *not* a race. Student success is not only the mastery of content and skills, but includes enthusiasm for math along with a healthy, balanced, and happy life.

The UC Requirements for Admission (and PAUSD Graduation Requirements) in mathematics is the successful completion of an Algebra 2 Course. There is interest in the PAUSD community for our students to reach a calculus course by their senior year of high school. Because students mature academically at different rates, there are a variety of paths for students to reach the calculus goal while maintaining a solid level of success and joy in their math courses. If you are interested in such a goal, some possible paths to calculus are given in the following table (these are *samples* of the variety of pathways).

### Sample Pathways to AP Calculus AB

PAUSD has a variety of levels of math courses (all meeting State standards) with the intention that students will find the appropriate level of challenge which they can successfully *meet on their own*. There is no reason to hurry the process of working toward 12th-grade calculus if your student is unhappy or turned off in their math course. There is no reason to race toward calculus if your student requires constant tutoring in order to learn the skills of the course, sometimes without understanding the concepts. There are plenty of opportunities to create a path that leads to calculus either in high school or within the first year of university work. Be sure to find out what is in your child’s heart as you and your child determine in which math course to register.