Middle School Math and improvements 

Overview of the PAUSD middle school math program

Middle school is a transition between elementary and high school. It is also a critical time to support math growth. A point that is often overlooked is that in middle school, grades have little long term significance. This ideally frees students to push their limits and develop both skills and appreciation of math before hitting high school where the focus of many PAUSD students often shifts to optimizing grades to prepare the college application portfolio. The instruction method in middle school (starting 6th grade) is the same as in high school. In elementary schools, a wide range of aptitude and levels is accommodated by teacher discretion: Allowing students that master the curriculum to do alternative work that is external or teacher provided. In contrast, in secondary schools students are all required to study the same math content.  Even in the transition year of 6th grade, there is no differentiated instruction and the only differentiation provided for class work is very limited in-lesson differentiation. 

The PAUSD middle school math courses include the common core aligned math 6/7/8 (for 6th, 7th, and 8th grade) that follow the minimum required curriculum.  For 7th and 8th grade there is an organic "higher" lane of "math 7A" that leads to "Algebra 8."   The Algebra 8 course covers the common core "Algebra 1" standards and is a critical step stone  for college and in particular to a STEM career.  The majority of PAUSD students (65%) are enrolled in 7A/Algebra for 7th and 8th grade.  PAUSD also offers an in-house Geometry H course at each of the middle schools, but it is not part of an organic pathway and has only about 6% enrollment.   

The district documents and presentations refer to 7A/Algebra as an "accelerated" pathway and seems to discourage students from taking it.  We find the use of the term "acceleration" here to be misleading and encourage families to view this as the "standard" pathway, noting that 8th grade Algebra was the  CA state standard before Common Core and it is considered essential for college bound students.  The term "acceleration"  is usually associated with a pathway that includes 6th grade "pre-algebra",  7th grade "Algebra 1"  and 8th grade "Geometry."   In fact, the latter is the an optional organic pathway at many public school districts with similar demographics (typically with over 40% enrollment).  It provides students with  very strong foundations for success in high school and beyond.

Below we include concrete advice for 6th grade families,  point out concern with the middle school program,  and propose short and long term improvements. 

Advice to parents of 6th grade students: 

• We recommend that you provide after school math support/enrichment to your student so that they continue to grow and have the challenge necessary for growth.  The 6th grade classes have students with a very wide range of levels (more than 2.5  grade levels spread),  very rigid instruction method with no suitable differentiation,  and teachers that by and large are not math specialists.  If your student is struggling,  it is critical to catch this early and support them after school so that they gain proficiency of the basic curriculum and build confidence in their own ability.   If your student is bored,  it is important that they continue to learn, in particular gain proficiency of pre-algebra  (math 7A) topics.   This will open doors for them to other STEM activities (coding, science) and pave a path to success in faster-paced future math courses.

• At the end of 6th grade the school provides a "rubric" based recommendation for 7th grade placement (math 7 or math 7A).    We strongly  recommend that even if the rubric indicates "math 7" (3/6 points or less), families consider enrolling their students  in 7A  and read the rubric as a sign that (for some reason) the school instruction was not as effective for their student and provide them with support (20 minutes a day of quality time can go a long way).    The 7th grade math teachers are specialists and likely to be more effective but also the 7A classes are faster paced.  Some after school (or summer) intervention might be critical to restore confidence and build foundations.   Placing a student prematurely in math 7 can have long term negative consequences and in particular will make it much harder later to get to Algebra 8.  You do not need to worry at all about grades in middle school.  There are no consequences for lower grades.  The important thing is to support learning, self confidence, and growth.  Data shows that many more PAUSD students take the "grade level" math 7 than neighboring districts. 

• If your student is above grade level then it is better to understand the options in advance and be prepared to support them.    They can expect an unproductive math time at school during 6th grade year and will need to navigate a very harsh obstacle course to avoid an unproductive 7th grade year.   See Information and advice for families of incoming 6th graders that are above-grade-level.

Points of concern with the  PAUSD middle school math program

• Data analysis shows that many PAUSD middle school students (30%+)  take their primary math education privately after school, well above their school placement.  Many others that choose not to supplement "above grade" (30%+) graduate middle school less proficeint in a statistically significant way than a similar demographic at Los Altos (LASD) and Menlo Park (MPCSD).   The cohort that does not have the means to supplement also seems to be worse off at PAUSD despite a much higher spending per student.  

• The school and district administration are process oriented but are not geared to investigate and address issues with the process (even those that are glaring and affect large groups of children), issues that arise for students due to issues with the process, or more generally offer options or flexibility to better support individual students that don't squarely fit in the box. Specific 2017-2018 examples and the responses of the administration are detailed in the experience document. As a results, students remain in unfavorable situations for extended time with no discussion or a way out.

• The district has a practice of withholding potentially helpful data on student level and growth from parents, even when explicitly requested.  Results of middle school placement tests (beyond pass/no pass) are not shared. The district does administer the NWEA MAP adaptive assessments to all students (at least through grades 5-7).  These adaptive untimed standards-aligned tests are normed and calibrated over millions of students and can identify student level (even well below or well above standards), areas for growth, and growth between assessments.  Such information when provided in a timely manner can help families support students better when there is a mistmath in teaching-learning styles or between student level and school placement.   Currently, only uncalibrated grades and the mandatory CAASPP results are shared with parents. But these results are shared too late (August following the end of the school year) to be actionable and are too limited (not adaptive, so accurate only for students within the grade level range).  

• Many PAUSD teachers are amazing, but some are not and there can also be a mismatch between learning and teaching styles. There is no feedback collection process from families on teacher performance that can help teachers improve in the longer term. There is no sharing with parents of teacher effectiveness data that can assist parents in determining need for after school support. Mismatch between styles are almost never resolved. Because of the nature of math learning, students are particularly susceptible to long term consequences (weaker foundations, lost confidence, or negative shift in attitude towards math).

• The 6th grade math program offers a single course "math 6" that is aligned with the minimum required by the state (CCSS M6). The course offers no differentiation suitable for students already proficient in the curriculum. Moreover, there is no path for these students for productive use of time such as being allowed to work independently on suitable curriculum after testing out or by teacher discretion. A large number of students are denied of the challenge necessary for adequate growth.

• PAUSD has many high-aptitude students (60% of students at our district exceed the state standards versus 20% in CA over all). Many of these students pursue math programs where they graduate high school well above the bare minimum requirements (bare minimum is Algebra2 whereas nearly 50% of PAUSD students take AP calculus). The slow paced year in 6th grade inevitably forces an imbalanced path forward: The majority of PAUSD 8th graders take 8th grade Algebra, which is necessary step stone to high school calculus. To compensate for the slow pace in 6th grade, the PAUSD 8th grade class is packed with half of CCSS M8 as well as CCSS HS Algebra 1. This imbalanced pathway makes it harder for some students to succeed in Algebra: A common pattern is of students having a very easy 6th grade year but get outpaced in 8th grade which results in lower confidence, choosing a lower lane, and being less prepared in high school, all this at the point where grades start to matter. Moreover, many families hire tutors at this point which leaves behind those that can not afford the outside help. An option to a more productive 6th grade class that covers some or all of CCSS M7 will allow more PAUSD students to succeed in 8th grade Algebra, which can then focus on CCSS Algebra 1, and emerge from middle school better prepared. Such pathways are offered in school districts with similar socioeconomics (see slides for details). Also see study by Ze'ev Wurman of the Hoover Institution on how the common core pacing decreases success of students in 8th grade Algebra 1, and disproportionally that of economically disadvantaged students. The study findings strongly suggest that all students should be offered and encouraged to take a faster paced 6th grade math class.

• Because of the disparity between the middle school PAUSD math program and that of other public school districts of similar socioeconomics (Los Altos, Menlo Park, Cupertino, Sunnyvale, Suburban East Coast/Mid West) and also that of private schools, PAUSD students that transfer after 6th grade to a school outside PAUSD and did not have private after school classes will be at a disadvantage and place into a lower lane than students with similar aptitude. 

• The PAUSD above-grade-level placement process is broken in that it curbs above-grade-level placement rather than what parents would expect, which is allowing students to place in the most suitable math course. For a start, 6th graders may only place into "math 6" or into "algebra 8" (8th grade) which already means that many students that have full mastery of CCSS M6 are placed in math 6, a class that offers them no path for growth. On top of that, the placement process is not designed nor does it achieve a diagnostics of the most appropriate class. In uses uncalibrated one-shot tests that were developed in house and on strict eligibility requirements for even testing that depend on factors other than math proficiency. Therefore, only few of the students that are ready to succeed in a target course will have the option of taking it and many end up misplaced in a course that is a year or more of curriculum below their level. The broken placement process affects students not only by an end result of irrevocable year long misplacement but also by inducing anxiety and stress that are well beyond the norm for the age group. Moreover, a large number of misplaced students (about 35% of all 6th grade students) end up taking a full above-grade math courses in their after school time which allows them to continue growing in math but also cuts into their important time to unwind and pursue enrichments. A rationale for elements of the broken process (placing students ready for 7th grade math in math 6) is provided at the district document that states that above grade placement is stressful and interferes with social development. However, any requests for evidence supporting these claims were denied.  In fact,  there is strong evidence for long term detrimental effects of misplacement (for example, here), and analysis based on 2018 CAASPP results  shows that our students are at a disadvantage going into high school.   Moreover,  the ground-level reality at PAUSD is that many families respond to misplacement by taking their students primary math education to after school private programs -- this only adds to the load on student time and also leaves behind students with fewer resources.  This combined with large-scale misplacement of the already-proficient students makes our courses ineffective and demoralizing  for other students that are suitable placed and  are there to learn.

• The organic math learning pathways at PAUSD are more limited than what is available in school districts with similar demographics across the country. The highest organic pathway at PAUSD only leads to HS Algebra 1 in 8th grade and to AP BC calculus in 12th grade. PAUSD students for which a faster pace is more suitable must rely on private after school classes and "skipping" through the (broken) placement process. School districts with similar demographics (see slides) offer such students a more equitable and satisfying organic pathway that lead to 8th grade CCSS HS Geometry. This provides students with strong preparation for the fast pace of high school when grades start to matter. Moreover, students completing Geo at 8th grade have an option to take BC calculus before 12th grade, which allows them to take above-AP math courses in high school such as multi-variable calculus and linear algebra and emerge with really strong foundations for advanced studies.  These courses are offered locally at most neighboring  high schools  in collaboration with community colleges (Foothills).  While these above-AP courses are offered at Paly and Gunn (alternating location every year), the only path to actually get to these classes relies on private after-school preparation. At Los Altos, Saratoga, and Cupertino, more than 40% of students are enrolled in an accelerated organic pathway leading to 8th grade Geometry. In typical NJ suburban schools it is 20%. At PAUSD only about 6% of students take Geometry at 8th grade and this through the mentioned inequitable path.

Proposals for improving the program

• Communication and putting children at the center: Allow for discussion of solution for students that for a wide variety of reasons are not served well by the math course in which they are placed at school. This includes students that do not fit in the box (eg, mismatch between math aptitude and study or social skills or with learning differences) or have learning styles that do not match with teaching style. Discussion should happen at the circle closest to the student with student, parents, and counselor. Open up options such as independent study through external accredited programs or guided independent work at library. Help students feel supported and allow for intervention before students incur long term undesirable consequences. 

• Implement an adequate placement process of students into the math courses that are offered at the school. Courses are designed to best support the middle range of their students, so students that will be solid top 50% in a class certainly belong there and not in courses that are a year of curriculum below. We encourage the district to adopt solutions from other school districts using widely used 3rd party reliable measuring solutions to objectively measure the students level and progress through time and provide feedback on areas of growth and strength. 

• Implement differentiated instruction in  the 6th grade math course (via cross-TEAM groupings) so that it can support and allow for adequate growth to the full range of 6th graders placed in it.  In particular:  (i)  provide a path for students that master the 6th grade curriculum or particular topics which allows them during class time to learn and establish mastery of part or all of the 7A curriculum (alleviate the need for harsh one-shot placement year end and reduce need for private after school programs).  Data indicates that this is suitable for 30%-40% of our 6th graders (ii) Provide small-group intervention support for 6th graders for which the instruction is not as effective. 

• Work towards longer-term improvements of middle school math pathways. Resources are limited, but transparency and a data driven approach can  determine what pathways will better serve more students so that more students emerge from middle school with stronger math foundations. Use widely used 3rd party measures of our math education and share results. Lessons from other districts suggest that (i) a large cohort that includes less privileged kids may benefit from a more balanced pathway starting 6th grade to 8th grade Algebra1 (ii) High achieving kids (top 30%) will benefit from a balanced accelerated compacted pathway to Geometry in 8th grade (iii)  Study benefit of small-group per-unit intervention support 

• Document with some proposed improvements that was shared with district staff in May 2018