Math curriculum changes essential to student learning, equality
Graphic by Audrey Tseng
This opinion piece on our middle school mathematics program is written by two PAUSD parents, Edith Cohen and Allyson Rosen.
Superintendent Dr. Don Austin recently initiated a revisit of our middle school mathematics program amid concerns with our program’s effectiveness in supporting the diverse needs of Palo Alto students. We welcome this initiative. Palo Alto Unified School District (PAUSD) students in the same grade have an extreme range of levels and abilities but face a rigid and limited program that has been essentially unchanged for decades (“cast in stone” in Dr. Austin’s words). Our socioeconomically disadvantaged (SED) students experience very limited growth whereas over one third of our students are systematically misplaced to repeat material in which they are already proficient. Course placement alone has been highly contentious. Many misplaced students sustain growth by studying outside of school what peers at neighboring districts learn in school. Even students who are correctly placed have their learning and mindset negatively impacted by the misplacement of so many. Overall, PAUSD students entering high school are on average half a year of accelerated curriculum behind peers at neighboring districts and thus at a disadvantage. In sum, the current system is unsuitable for an overwhelming number of our students.
We find these outcomes concerning. Sustained growth in math for all our students, at an appropriate level and pacing, is developmentally important. Research suggests that math learning during childhood and adolescence engages the brain differently than in adults and therefore stymied growth early on may not be effectively compensated for in later years. Studies establish that the opportunity to advance when ready carries significant short and long term benefits. Finally, the middle school years, when grades carry little consequences and overall workload is small, are a rare opportunity to build foundations, take on challenges that may push one’s limits, and focus on learning (rather than on building a portfolio). Our high schools are fast-paced and many of our students struggle to find the time to balance extracurricular activities with challenging academics. Students who start high school more prepared, proficient and confident are better positioned to set and achieve appropriate goals while experiencing less stress.
These disappointing results come despite our built-in advantages of higher funding, more educated families and many excellent teachers, and we believe they can be vastly improved by redesigned pathways and placement. Indeed, during the last decade, neighboring districts (including Menlo Park City, Los Altos, Mountain View Whisman, Cupertino and Saratoga) implemented pathways to both eighth grade geometry and algebra with pacing that is balanced through the three middle school years. These pathways serve the vast majority of students. The particulars vary, but all these other districts provide opportunities to cover more content during sixth grade and use modern assessment tools to inform planning, placement and intervention.
Learning algebra by eighth grade is broadly considered a critical stepping stone for a STEM career. The PAUSD algebra pathway is imbalanced, with an unchallenging sixth grade and a fast-paced, intense eighth grade, when many families hire tutors to keep up. Families choose between an algebra pathway and a “grade level” pathway at the end of sixth grade based on an internal rubric whose effectiveness as a predictor of success has never been established publicly and which often seems to discourage and mislead potentially algebra-ready students. A balanced and better supported algebra pathway (such as in Saratoga, Menlo Park City and Mountain View) would benefit all our students and particularly our less-resourced students that in the current program get disproportionately discouraged and derailed.
Middle school geometry at PAUSD can only be reached by what is colloquially known as “skipping,” which requires external learning of a year of accelerated content and navigating unusual and biased placement requirements. Skipping carries significant academic and social benefits: the 6% of our students that navigate the process are challenged, inspire each other, enter high school more confident and proficient, can take AP calculus by junior year and are better equipped to pursue extracurricular STEM passions while in high school. But the high stakes process to gain “admission” induces anxiety (often artificially created by ill-designed procedures) and excludes many students who could excel in middle school geometry. Students are excluded by not being in the know about a poorly publicized process, by not having resources or after school time, by getting disqualified by missing a single rubric point on class-based metrics and (in recent years) by not successfully completing a small set of competition-style math problems required even to take the placement test. If allowed to take the placement test, students need to score 85% on a one-shot, time-pressured test that is provided with no adequate review material, examples, or even syllabus and that is intentionally designed not to be passable by the vast majority of students that successfully completed the corresponding PAUSD course. Finally, the middle school Geometry Honors courses are deeper and broader than our respective high school courses and at the same time are graded more harshly with students required to maintain an average of 80% or 90% (varies between schools) or else drop back as much as a full year. Our middle school geometry courses have wider gender gaps than neighboring districts, which we attribute to the unnecessary requirement of external learning and the emphasis on competition math skills: these PAUSD courses are only 22% female versus nearly gender balanced courses at other districts. The gap carries on, with PAUSD BC calculus takers being only 38% female, even below the national average of 41%. Moreover, only 24% of our BC Calculus takers do so before senior year versus 35% nationally. We advocate that PAUSD implement a balanced inclusive geometry pathway (such as the one found in Saratoga, Menlo Park City, Mountain View, Cupertino and Los Altos). Similar districts have over 40% of their middle schoolers in geometry and we can expect the same once our pathway is improved. “Skipping” and external learning of content should be necessary only for the much smaller fraction of our students that need pacing beyond the geometry pathway.
Gunn students, particularly those who experienced the entire PAUSD program, can provide important insights and should make their voices heard. Mathematics development at a suitable level and pacing is critically important for all students and even more so for those whose interest is in STEM. A revision of our pathways and placement can help us convert PAUSD’s inherent advantages to better experiences and outcomes for our students. As our district is considering revisions, we urge the district to avoid undue reliance on existing practices, inertia or personal biases. We ask for transparency and involvement of all stakeholders, and for decisions that are based on critical assessments of research, analysis of data including standardized nationally normed assessment tools and the vast experience of similar districts.
–Cohen, a computer scientist and Rosen, a clinical neuropsychologist, are guest columnists. Their children attend PAUSD middle and high schools.
Your donation will support the student journalists of Henry M. Gunn High School. Your contribution will allow us to purchase equipment and cover our annual website hosting costs.