Gunn High School algebra pilot shows mixed results

I do wish there would be more soul searching about whether we are trying to create a system of standardized measurement of people, or if we are trying to help young people learn math and become lifelong learners. There is an analog to the Heisenberg Uncertainty Principle in education: the more you try to measure the student for the benefit of the observer, the more you interfere with the student’s learning trajectory.

Why is this about grade improvement anyway? That’s only productive if the educational program is working well to begin with. Daphne Kohler at Stanford has shown you can eliminate the bell curve by teaching to mastery. Individualizing students’ math education is just not that difficult today.

There is a huge disconnect between math at elementary and middle school levels. The problems, in my experience, start with uneven and unfair practices in kindergarten and first grade. In an attempt to standardize things, some teachers actually discourage many kids’ natural affinity for math, but not all do. As time passes, the school program only amplifies early disadvantages and supports those with early advantages, including “redshirting” (the practice of holding kids back to start older and at a developmental advantage) which was pretty rampant among the now high-school crowd when they were younger.

A lot of these problems go away if you individualize/customize math education. Students have a chance to overcome past disadvantages, to learn at their own pace whether faster or slower, and to use scoring as a way to shore up knowledge rather than feeling constantly judged. The grade should be a destination, not a gauntlet.

There are many voices today, such as Neil de Grasse Tyson, who say that any grade less than an A represent the failure of teaching and school, not the student. Sal Khan uses a house-building analogy: why go to the trouble of identifying problems, only to move on according to a schedule to the next stage of building without fixing the problems? Customized/individualized learning solves those problems, and the tools have never been better to do this. Why are we sticking with old pedagogy?

Students focused on getting the grade don’t learn as much, don’t retain as much, don’t derive the same joy from learning (to become lifelong learners), and they develop highly negative learning habits such as being averse to making, identifying, and learning from mistakes.

Giving kids the chance to learn at their own pace, and to mastery, also improves the affinity for math. When students can learn in whatever way best allows them to succeed, the confidence helps them in future learning. Undoing the damage of the negative learning practices, even if students begin a customized program tomorrow, can take years, though.

I think this district suffers in a whole host of ways from being education control freaks. The last thing they can imagine doing is figuring out how to allow every child to be a master of their own learning and time, because it would mean affording families a level of respect and dignity that would require a whole different paradigm of existence.

I really, really resent reading that the kids are guinea pigs for another standardized approach, the way they were with Everyday Math. The school district should make an independent learning path available for anyone who chooses it. Let those who would endeavor to deserve it have a chance to focus on learning and be free of the relentless judging gauntlet. High school should be a chance to get a broad education and learn how to learn.

There aren’t many studies of homeschooler test scores, but the largest to date showed that there is no achievement or gender gap, even when the parents aren’t well educated themselves. The moral of the story is not that everyone should homeschool, but that schools should think about customizing education, too — which is now eminently possible because of technology.

What I get from this is that the probability of low income, minority and special ed students are not getting extra tutoring for financial or whatever reasons while the others are quite possibly getting extra tutoring from paid tutors or tutoring services.

Nothing too surprising here. There has always been a large number of Palo Alto students getting extra tutoring paid for by parents who want them to do better at math, whether it being after school or summer camp. The stigma of getting a poor math grade makes it automatic that a family with the means will pay to get the grade improved. A family that doesn’t have the means will let the poor grade continue as there is no real alternative to letting the school do the teaching.

Wake up.

One of the great flaws in our public education system is that it forces most students along a similar path of achievement despite differences in interest, intelligence and capabilities.

During college, I had a coworker who struggled with his grades. He was a first-generation Hispanic student who was fairly average in high school. In college, he decided to major in an engineering field. Yet, he couldn’t pass his math, science or engineering classes (all involving math).

We both had student jobs in the same department. One afternoon, we all took I.Q. tests from the school’s psychology department. Whereas most of us were varying degrees above average, this student scored in the mid-80s.

Several of us tried to talk him into changing his major (at least temporarily) until he could bring up his grades and achieve satisfactory academic progress. He refused. He wanted to “prove” to others that he could “do it.”

After failing to bring up his grades following a third academic progress waiver, he dropped out of school.

I asked some friends about him recently. He’s working in a trade and doing well (although he has quite a bit of student loan debt). I just wish that he would have considered alternatives to his major or career. He equated “success” only with a degree in a particular field — something that was largely outside of his intellectual capabilities.

Schools should not hold all students to the same types of career or educational road maps. My friend was capable of success — just not the type of success that the high school was focused upon.

Palo Alto is blessed to be a bastion of intelligence and academic success. However, this doesn’t mean that ALL of those students should be held to the same academic standards. Given the pool of students in this area, most wouldn’t have a problem with such classes. However, some might feel the pressure of taking classes that might just be outside of their range.

Schools should exist to not lump students all together. There should always be a standard for graduation. However, average and, yes, below average intellects shouldn’t be required to progress on that same academic or career road map.

Most Chinese students don’t seem to have a problem with math. It might be genetics or perhaps an environmental factor as their parents tend to stress excellence in the subject.

Proficiency in math and science often leads to better vocational opportunities.

Until others begin to put this simple 2+2 concept together, they will be relegated to second tier jobs and limited earning capacities.

It’s simple math + common sense.

To Green and Paly parent: What are you talking about re: repeating Algebra if you have less than a B? That is just plain not true.

@Why So Many Fail, what I don’t particularly like about your position is that the assumption is made that Chinese students have a natural affinity with mathematics. It is assumed that these students are innately gifted with a skill that is often taught and nurtured. No one comes out of the womb ready to solve, unsolve, debunk, argue graph theory and matrices.

In addition, it is unfair to single out one race that is known for “traditionally” succeeding in one area, further perpetuating the myth and associated ideas behind the Model Minority.

It is assumptions like this that create a snowball of unreal expectations, especially for our Asian youth who may self-harm or choose the other route…

In all, be careful of how you phrase your observations about the children in our community. They’re battling not only outside forces, but things inside them that may shout at them, “You can’t do this! You’ll never amount to anything your parents want you to be! You can forget about going to college – you’re useless!” Those are thoughts they may battle every day.

@Nayeli,
I do agree with you that education at this level should be broader and not so single track. I also wish there was better information and more respect for trades. (If you listen to Temple Grandin speak these days, that’s one of her big peeves, the lack of support for people who want to go into the trades, and consequently, a big lack of skilled tradespeople.). But I think that kind of broad approach has to start early. It’s a societal shift. My plumber makes a great living (more than we do), and is frankly a pretty smart guy. But at the end of the day, it’s a hard job that people don’t aspire to do from the getgo. (Which is too bad, because innovations in plumbing are a potential goldmine — and people with the experience and problems to solve in the field are the innovators.)

That said, it’s really important not to pigeonhole people. I went to one of the top and most selective universities in the country and one of the smartest people I knew (physicist, great student) told me he had never done well on an IQ test (he was below 100). He was told by his father his whole life that he was stupid and would never be able to do anything of worth. Talk about pulling up by one’s own boot straps. Yet he was one of those students who was able to help others even outside his field. Another one of the smartest and most grounded people I have ever known was there after quitting in the middle of his undergrad years and spending 10 years as a carpenter in construction. He came back to get his engineering degree because he was ready, but he wasn’t sorry for the years he spent in construction.

I also think that different people have different gifts (including for trades, which are an important part of our economy), and it’s just tragic that the person you mentioned didn’t have the opportunity of a broad education in order to find those gifts in a more positive way. But I think unfortunately our society is becoming more and more stratified by class again, and there is an aspect of people not wanting to be trapped in a certain class if they can avoid it, and the schools do not help.

I agree with you that everyone should not be tracked to go to college. In places like Switzerland, the training for things like trades is quite extensive, and consequently, their construction is way higher quality than ours. But they also have a much higher minimum salary.

The pilot of merging Algebra1A and Algebra1 has two very significant issues:

First, it was done before the recent change this year that would force all students that successfully completed 8th grade Algebra1 with a C+ to repeat the course in their 9th grade. This is happening next year and I expect it to significantly increase Algebra1 9th grade enrollment with many students that are much stronger. This will completely change the consistency of these classes.

Second, the only data that they seemed to have used are grades in the course. This is very highly biased data. First it can not be compared with middle school Algerba1 grades (where the student cohort is much stronger). Second it can change between years and teachers. What should be used to evaluate effectiveness are highly standardized and normed third party assessments. For example, MDTP or the NWEA MAP test. The district already uses these tools: MDTP to place students coming from outside the district and NWEA MAP as a pilot. But for some curious reason they chose instead to use this highly biased data for the Algebra1A/Algebra1 pilot. This is very poor scientific methodology.

More on the change of policy that defines “C = FAIL” for Algebra 8th students.

This is bordering being unlawful by SB359 (math placement act).

Second, parents please note that your students are being tripped here. Your students that might “fail” would otherwise (same demographic) do very well did they have a balanced pathway (similar to Saratoga or Sunnyvale). Our pathway is highly imbalanced: ineffective slow 6th grade and a large amount of new material introduced in the last second semester of Algebra8, where it is the FIRST time kids factor binomials and solve and analyze quadratics). MANY students start struggling for the first time in second semester of Algebra8. Also our Algebra8 class sizes are very large compared with other core classes. Students that can not afford tutors (or their parents are misled to believe that they should not support them) can very easily fail (get a C) even if they are highly capable to finish middle school ready for high school Geometry.

Instead of exercising social engineering with our kids, I suggests that the educators consider what skills are needed for jobs of future. To create, shape and organize jobs of future, we need a few highly skilled talented professionals. The solution to the tough problems of future can only be found by a few really top notch scientists, and not by an army of average graduates. The educators must not block those good talents.

Of course, the rest of us will have important roles in many needed supporting functions too where pooled team talents are needed. So, the best way to help all students, particularly the struggling students, is to help them function effectively in team projects where they can leverage from the diverse talent and skills of team members to advance the team goals, and therefore to advance individual goals.

@Green and Paly parent: Isn’t a C+ grade an indicator that there are serious gaps in the child’s understanding of very rudimentary (and simple) topics in basic algebra? I would think that even a B+ or lower would indicate some trouble ahead in later courses. It would be in the child’s interest to repeat the subject to get a real understanding of it rather than push the child ahead with a shallow facility in basic mathematics.

@kids: My kids taking Algebra 8 now. The kids are given second chances in all the tests and the homework assignments. There is no way a “10 minute plan” will fix a kid who is getting B’s or less. There are fundamental gaps in their understanding of the material. It’s possible they are unmotivated and don’t want to put in the effort. Maybe repeating a year is not the answer, but neither is a “10 minute plan”.

@member some add-on to my response to your comment on what the course grade really means:

The way our honors math classes are structured, and the second semester of 8th grade Algebra mimics that, is that many new concepts are introduced for the first time shortly before a test that also requires applying them in more involved ways. For few kids this is fine. But many students only internalize these concepts AFTER the test, simply because some more time is needed for them to “sink in”. So they are proficeint in the material, even though the course grades do not reflect that. The messages from that are that:

(i) This is one of the severe limitations of using a course grade alone for the purpose of placement. We should be using standards-based normed preferebaly untimed assessment tools (such as NWEA MAP) on a periodic basis for the purposes of better understanding each student learning patterns and more accurate placement. Holding a student back a year because of a C+ without looking more closely on their needs can be a grave derailing mistake.

(ii) Because of how our advanced courses are designed, students that already visited the material have a huge advantage. Spiraling and revisiting math concepts is *critical* in allowing concepts to “sink in.” This is why external support is such a huge plus for students at PAUSD and the students that do not have access to it are highly disadvantaged.

Member

10 minutes to look at a test and know what was not taught well in a precise way. If you go on the AOPS website and search pre algebra videos , they are great and actually very fun to watch and work along with and are really algebra. Best explanations of algebra. It is only going to get worse . Take lowest lane alg 2 then take all math anywhere else. Russian school of math is expensive but totally worth knowing your kid will know math and be able to pass sat and college entrance exams. Paly math is lecture and then a test that may or may not have been covered. they should be teaching alg in 6grade with geometry to present ideas instead of hanging out with fractions and long division again and again. The elementary program is very weak. To apply to sci majors Calc is the lowest level by sr year and that is actually low now at larger colleges. Try not to get lost in the time sucking mean math web. Join SJSU math circle. Fun and welcoming!

@Greene and Paly parent:

I might agree with your points in theory, but in practice I have trouble accepting them. I have not seen an accelerated pace in the second semester. I asked my child and he said he did not notice a difference between first and second semester thus far. Also the problem sets for the homework are extremely pedestrian (online Big Ideas), and if they are reflective of the tests, then getting a B is a very low bar. As I have mentioned if silly mistakes are made on the tests, the students are given a chance to correct them (for full credit), so again getting a B should be really easy if you have understood the concepts. Yes there could be students who have command of the material, but do not show it on the tests, but these would be rare in my opinion.

@Criteria for Geometry

What I am advocating for is an improved middle school math program that better serves all our children, across the abilities/interest/financial spectrum.

I work in the tech industry, I see what the needs are. Math growth and building positive attitude to math during the middle school years is developmentally critical: A weak middle school preparation means that students can get much less out of high school, where unfortunately students optimize portfolio/graders instead of learning. Moreover, because the way our brains develop, and the way math is (think language or physical development) you can not really catch up as effectively as an adult on what is deprived in the formative years. I find your assertion that “you anyhow repeat the course in college” to be very inaccurate. In my experience, if the first time you see calculus is in your college years you are at a significant disadvantage for a tech job. In particular, your chances of working on the same floor as I do now are slim.

When advocating for improving our program, I am comparing us to nearby and less-funded public school districts (Saratoga and Los Altos for example). Because of the particular way our program is structured, students witout expensive after school support or with no desire for significant after school academics can easily be derailed from where they would be at our sister districts. Moreover, our 3-year program needlessly has multiple failure points for students to get demoralized and derailed: develop negative attitudes towards math and their own adequacy.

Below I will now elaborate, by cohort, on what we do and how we can do better.

First, our “average” math students (roughly, 35% to 75% percentiles). These students are in the top 20% in CA. The goal post for them is to emerge from middle school with strong Algebra1 foundations and perhaps aim tp AP AB calculus in high school. These students follow our “primary” pathway of math6, math 7A, and Algebra8. Here are the failure points:
(i) This pathway is highly imblaanced in terms of curriculum: Very slow 6th grade, somewhat higher pacing in 7A, leading to the highest pace is in the second semester of 8th grade Algebra where a lot of new material is introduced for the first time. The pace in the second semester is similar to the high school “H” lane, which derails the students that otherwise would go to the “A” line.
(ii) Our ineffective 6th grade. Our 6th grade math teahers are not math specialist (they do not have the qualification to teach prealgebra). Few are ineffective even for teaching “math 6″. Student that happened to get a less effective teacher are automatically derailed from doing well in 7A (unless they get a tutor).
(iii) Because we are missing a “high” lane, the top 35% of students and the next 40% are essentially grouped together in Agebra8. Sitting with students that are already proficient in a new curriculum you are trying to learn is a highly demoralizing experience for the second cohort. The students that actually belong in 8th grade algebra pathway feel they are out of place. “Eye rolls” make it hard to ask questions. Sometimes teachers respond more to top students.
(iv) Our Algebra8 and 7A classes are on average larger (28-30) students than other core classes. This is because the district choses to keep math7/8 courses small.
(v) New this year: The district raised the bar for GeoA to match that of GeoH (!) a “B” is required to pass Algebra8. I expect very many students to be derailed by this.

How we can serve these students better:
Other districts (look at Sunnyvale and Saratoga) have a balanced pathway with specialist teachers starting 6th grade. So students learn CCSS M6 and most of CCSS M7 in 6th grade. Then learn CCSS M7/M8 in 7th grade. This allows them to focuse on Algebra1 curriculum in 8th, with much spiraling and lower pace (at Palo Alto, our Algebra8 course is Algebra1+most of CCSS M8). These balanced pathway provide all students an apportunity to build stronger Algebra foundations even without expensive tutors. BTW, the “C+=Fail’ rule (must repeat Algebra) is a new Palo Alto only rule. Other districts consider C+ to be a passing grade.

Second: Our “top” 35% of math students. Don Austin shared data in October that shows that (on average) 35% of our 6th graders START 6th being proficient (exceed state standard (!)) of the *grade 7* CCSS M7 standards (!!). These students have little to nothing to gain from their school time math course (“math 6″). Moreover, courses are rigid with no appropriate differentiaiton (the very limited in-lesson differentiateion is not designed to support already-proficient students). Being sidelined by teachers that are focused on the needs of other students, being in a rigid inappropriate course, and being offered no path for productive use of time, induces social and behavioral problems on many of these students. Academially, their only path for growth is by taking a structure after-school course (at loss of after school time).

What other districts do: At Los Altos and Saratoga 35%-40% of 6th graders are placed in math courses that cover our “7A”. These courses are taught by specialist teachers that are qualified to teach this curriculum.

What Palo Alto can do to serve these students is to open 7A placement to qualified 6th graders. There is a convoluted “justification” to this restriction in placement docs. The real issue is that most of our current 6th grade math teachers are not qualified to teach 7th grade math and providing the “right” program for 75% of our students would require specialist teachers.

Last but not least: “Bottom” 25% (many low SES). What usually works there is informed intervention in small homogenuous groups by specialists teachers, during school time. We are doing worse than other districts also for these students.

Also, in Palo Alto, our low SES students have an effectively hard “ceiling” of math8 at 8th grade. One stats that stands out compared to other districts is the much lower fraction of “exceeding standard” SES students.

@Criteria for Geometry

I really appreciate this discussion. Some comments on your proposal:

— Our Algebra8 course must include the full CCSS Algebra1 content for compliance and math 6/7/8 must be covered in middle school. I don’t think we can cut off content. The only option really is to balance the pathway byo (similarly to Saratoga) pushing content down to 6th grade so that our 8th graders can focus on Algebra1 for the entire year.

— About your reference to PAUSD putting a “high bar” on so called “above grade” placement (Algebra in 7th grade). I am guessing your kids have not been subjected to that process. Mine were. I can elaborate if you wish, but the high level is that the process that is applied to kids is unprofessional, defies scientific and education norms, and harmful. Also, simply looking at numbers, does it make sense to you that carefully calibrated normed assessmenets at Los Altos, Saratoga, and Cupertino end up in 35%-45% of their students doing Algebra1 in 7th grade whereas we are at 5%?

— You are making some nebulous distinction between “truly talented” and “tutored” kids while expressing frustration towards the kids that you call “tutored”. I think you are not being fair. We have a program that holds 30% of our kids back a year from where they would be in Los Altos, Saratoga, or Cupertino. Are you surprised that many kids are compensating after school?

— I think it is important to understand that the dis-serrvice of one group, no matter which way, and ending up with courses where many students do not belong, harms all students, including those that do belong.

Our neighboring districts engage in continuous revision and improvement of their middle school math programs. They share experiences and analyze data and feedback from their stake holders. They showed us that it is possible to server well all students. That when underserving one segment we actually negatively impact other segments — the math program is not a zero sum game. Our neighbors offer a broader program that support more students and everyone benefits. Data shows that they are obtaining much better results than us for comparable segments. Their students are more advanced. Their top students excel in math competitions and many more of their low SES students exceed standards. We are a much richer district, with a much larger budget per student, and manage to blow it off by a program that unnecessarily derails and demoralizes many.

Up to a decade ago, PAUSD used to be the district that our neighbors look up to and learn for. But now we are no longer on that map. We can see that the latest revision at CUSD was based on reviews of programs from around the county:

https://www.cusdk8.org/cms/lib/CA02218495/Centricity/Domain/82/CUSD%20Math%20Advisory%20Council%2011%2015%2018.pdf

They looked at Saratoga, Los Altos, Sunnyvale, and Hillview. Palo Alto was not even looked at…

This is not surprising for those that experience our program from within. Our program was in stagnation/deterioration for decades, oblivious to the needs of our changing demographics and the 21st century. Many families (including board members!) choose to bypass our middle schools. This open secret harms our children but may soon start impacting our property values

The failed and misconceived experiment of the 9th grade Algebra course only serves to demonstrate the severe issues with our processes. That experiment went against expert recommendations (the Hanover report). It demonstrates a failure not only in its results but also of methodology. Of significant concern is our education board decision (in departure from our neighbors) of not only not providing oversight on our math program, but also requesting to not be informed (!).

I have something to say on the “going deeper” phrase. Please do not trust the district’s (mis)representation of their program and their (ill informed and often derailing) recommendations for your kids.

The district math placement documents contain many misrepresentations, biased ill advice, and misleading claims about the program. The instructional ISs and teachers are trained to repeat these lines. When you ask for substative data, further explanation, or sense, it is not provided because it does not exist.

They use intimidation, stonewalling, and misrepresentation, year after year, on children and parents, until the concerns that are not addressed are no longer relevant. Then they repeat.

The “going deeper into the curriculum” is just one of their vacious favourite phrases. This propaganda is used to provide a “justification” for their inadequate program and widespread egregious misplacements of hundreds of students, in particular in 6h grade. The education world agrees that a year with no growth and math development, during middle school, can have long term negative impact. So they must have an answer for the very many 6th graders that are essentially proficient in CCSS M6 year start, but placed in “math 6″, where all instruction time is used on the CCSS M6 curriculum and instructin is rigid (no alternative work outside the curriculum is permitted). The story is that these students are provided an opportunity to “go deeper” and they can grow this way. Another is that “it is important to be solid” (but they do not have a methodology to determine level and solidness….).

At least the teachers, when asked, must cover this. So “deeper” at pausd was work provided to kids to do independently without any meaningful feedback, discussion, instruction, or supervison in their own time. For example, the Einstein packets until last year and some SCCOE material this year (that they had the “hutspa” to announce in October as inovation…). They also not misrepresent the
very limited “in-lesson” variety of problems (sometimes know us the “either” and the “or” HW choices to those subjected to it). This variety is built into the “big ideas” curriculum. But even the “Big Ideas” (the text books) publishers and authors do not agree that this is adequate to support students that are already proficient(!)

Be careful interpreting the propaganda. Be very careful taking their recommendations. I know that it is hard for parents to override such forcefully expressed misguidance from “professionals”. But please seek external input if in doubt. I saw so many kids get derailed with the 7/7A recommendations. I saw kids that overrod it and went to 7A and are doing very well (the 7A teachers are specialists and are generally better).

Lets look now at the 2018 data of another neighbor: Los Altos. How are their white students are doing in middle school math compared to ours?

Los Altos offers a middle school math program that supercedes ours in that they also offer a higher lane starting 6th grade that leads to 7th grade Algebra and 8th grade Geometry. From reports, I gather that the high lane (Geometry in 8th) is predominantly Asian. The middle lane (Algebra in 8th) is predominantly white.
https://www.blachschool.org/georginais/7708-Untitled.html

Lets think of the experience of the (mostly white) cohort that a combination of motivation/family/natural-learning-pace would take to Algebra in 8th grade. The PRO at Los Altos is that they can focus on learning without the potentially intimidating presence of 50% of alread-proficient students in their class. The CON at Los Altos is that in the back of their mind they know there is a high lane and that they are not in the high lane.

So where is the Los Altos white segment in terms of proficiency of standards compares to Palo Alto?

We can first look at 6th graders. Los Altos has a (laned) 6th grade in elementary school. So we need to look at each of the many elementary schools. Recall that at our Greene, 53% of white students exceed standards. Here is what is happening in Los Altos (the numbers speak for themselves):

Santa Rita: 64% of 6th graders exceed standard (45 students)
https://caaspp.cde.ca.gov/sb2018/ViewReport?ps=true&lstTestYear=2018&lstTestType=B&lstGroup=5&lstCounty=43&lstDistrict=69518-000&lstSchool=6047492

Almond: 71% (out of 29)

Covington 73% (out of 33)

Gardner Bullis 71% (out of 24)

Loyola 51% (out of 37)

Oak Avenue 64% (out of 29)

Springer 68% (out of 44)

What is happening for white Los Altos 8th graders?

The 8th grade is important – right before high school. Recall that at Greene we have 59% of our white 8th graders exceeding standard. (Recall that the number was 70% at Hillview, Menlo Park).

Los Altos has two middle schools. At both, 70% of white students exceed standards (!) Again, a statistically very significant advantage over PAUSD white students. The white students out of Los Altos middle schools are more solid and more prepared for high school that out of our PAUSD middle schools. So this is another strong case for laning.

Egan Middle 8th graders 70% (139 white students) exceed standards
https://caaspp.cde.ca.gov/sb2018/ViewReport?ps=true&lstTestYear=2018&lstTestType=B&lstGroup=5&lstCounty=43&lstDistrict=69518-000&lstSchool=6047385

Blach Middle 8th graders 71% (128 white students) exceed standards
https://caaspp.cde.ca.gov/sb2018/ViewReport?ps=true&lstTestYear=2018&lstTestType=B&lstGroup=5&lstCounty=43&lstDistrict=69518-000&lstSchool=6047435

Again, we should not be thinking “my kid OR yours” we should go for a program that serves “my kid AND yours”.

@Criteria-for-Geometry what do you say?

@Manny: You should keep in mind that we are on the cusp of a revolution in technology. Many jobs of today will simply not exist in the not too distant future. With the advances we see today in AI you can expect they will be done by semi-intelligent robots. Wouldn’t it be much better to have a robot do high rise welding? It would be safer, cheaper, and able to work night and day at breakneck speed. You should want to learn everything you can now while you have the chance to do so with little other obligations to insulate yourself from an uncertain future. BTW, don’t feel bad, even primary care doctors will be replaced by AI.

I completely agree with @kids that Art of Problem Solving (AoPS)
https://artofproblemsolving.com
has an amazing curriculum. To me, it is the bible of k12++ math. It is pure joy to go through. The Big Idea curriculum, in contrast, make me quizzy — I can open the book anywhere and within few minutes of browsing see a significant error or an ill-formed example/question. But all that said, the AoPS curriculum (prealgebra and on) is not for everyone. There is not enough drilling and very quickly it goes to problems that need more complex application of concepts. Many kids need more drilling and even some kids that enjoy AoPS would benefit from first covering the curriculum in a more basic way such as Khan academy or aleks.com (but the AoPS elementary program “beast academy” has a very broad appeal).

I strongly recommend supporting your kid’s growth in math outside of PAUSD regardless of their level and ability. Even 15-20 minutes a day can go a very long way, starting elementary school. And if the kid needs more challenge then AoPS is amazing.

AoPS academy (AoPS just now opened a new academy (live classes) in Fremont):
https://fremont.aopsacademy.org
AoPS online (prealgebra to calculus and more, online and books. Also Python):
https://artofproblemsolving.com/school
Beast Academy (elementary school curriculum, online and books):
https://beastacademy.com

While we all wait for a broader program, think about supporting your kids outside of school.

A comment made by @kids early on was with regard to how our middle school math program discourages girls even more than boys. PAUSD does not share data on gender and ethnic consistency in its different courses/grades, so my comments are based on observations and student-reports on enrollments balance over years.

One data point is our most challenging courses: Our middle school Geometry courses have much fewer girls than boys. Interestingly, middle school Geometry courses in neighboring districts seem balanced — Reports from Los Altos say that their middle school Geometry courses (and 7th grade Algebra) have MOSTLY girls.

Eventually, our gender imbalance seems to carry over to our BC calculus courses.

How are we discouraging girls?

One significant difference between us and Los Altos is our pathway. The only way in Palo Alto to middle school GeoH is basically by an after school program that is 1-2 years of curriculum above grade and must be concurrent to misplacement at school. Then going through an insane and discouraging filtering process (“placement”) that throws out most qualified kids. Even our pathway to (passing) Algebra8 in 8th grade discourages many. This is also because so many “already proficient” students are misplaced in the same courses and students that do belong feel like they do not belong. Moreover, the program accelerates so those without solid after school preparation ar disdvantaged (see early comments on this thread).

Here are two explanations to why our program discourages girls more than programs at neighboring districts. I wish we could look into this thouroughly and be able to do surveys and data analysis. But our district is very resistant to collecting and sharing aggregate data.

Girls, that tend to be broader and more social than boys are less likely to push their primary math education to an after school program even when the school program is not effective. Los Altos and Hillview (Menlo Park), with their broader and more effective 6-8 program, allows students to succeed based on the program at school.

Girls might also be more susceptible to discouragement, of which we have plenty (at least at Greene). One of my challenges as a middle school parent at Greene was to “reverse” the harmful impact of this discouragement on my children and retain their growth mindset. Kids are discouraged by being misplaced (and told they are not). They are discouraged by being sidelided by a teacher (that has to focus on other kids), by having a large group of already-proficient kids in their class, and by being told that our courses are “hard” when they are suitable.

I would encourage families with female students to be sensitive to all this and encourage their students to aim high. This of course is much easier said than done.

@Paly Math
My data points are from the middle school Geometry H in some years that I talked to a student in the class. There are girls and they do very well in middle school GeoH, but it seems to be 30%-40% whereas elsewhere (Los Altos) people report it is 50%+ in middle school Geometry.

The imbalance might carry over also to AnalysisH/BC calc because about 1/3 of that course are kids that did middle school Geometry.

Yes, the high school Geometry and Algebra2 courses are balanced.

@criteria-for-geometry

I believe the CAASPP data (see the more elaborate Hillview post and the Los Altos posts that includes segment sizes) is highly indicative. I would love to get your thoughts.

Let me summarize the data/analysis:

The data from Greene (PAUSD), Menlo Park (Hillview), and Los Altos clearly shows in a statistically significant way that our Greene white students in the end of 6th grade and also just before high school (8th grade) are less solid and less proficient in math standards than their white peers at Hillview and Los Altos. This is from the most recent 2018 CAASPP data. These results are meaningful because our population is more educated and we spend much more per student, so with all else equal, our students should do better.

As for other segments (Asian and (SED) Latino students), our program is less suitable to start with. The breakdown I am using for white/Asian/Latino students is dictated by the published aggregate data (gross level (1-4) breakdown and average scores by segment). Comparison between districts broken down by segment is informative because these segments have very different patterns: On average, Asian students score significantly higher than white students which score significantly higher than Latinos. By comparing by segment we factor out effect of different segment sizes at different districts.

Now some analysis. PAUSD, LASD, and Menlo Park, all use the “Big Ideas” middle school math curriculum. The difference is in the program/pathways/placement: Our program is much narrower than Hillview or Los Altos. In particular, Hillview and Los Altos offer school-time intervention support for struggling students and compacted accelerated pathways that allow motivated/stronger students to be a year or more above their PAUSD peers.

Our narrower program underserves most of our Asian students. The Asian students average CAASPP scores already exceed the standards of the *next* grade level (5th grade average score already exceeds 7th grade standards). At Hillview or Los Alto most of these students would be placed in a compacted accelerated pathway to Algebra in 7th grade. Our program also underserved students, in particular SED students, that need more intervention. What is surprising here, given theses limitations of the program, is that we also do worse for our white segment, for which, on the surface, we do have pathways consistent with what most white students do in Los Altos or Hillview.

These are the issues that I suspect make our program less effective.

— The primary pathway taken by white students is to Algebra in 8th grade. This pathway is not balanced (slow 6th grade and very high pace in the second semester of Algebra in which “B” is required to pass). Hillview offers a balanced pathway where more is done earlier on. Our Algebra courses compact Algebra with half of “CCSS M8″. At Hillview, 8th graders can focus on “Algebra1″.

— Our classes include a large fraction of students that are well-above the curriculum (in math6/7A/algebra8) or well-below (in math6). But the instruction style is rigid and not suitable to support all of them. Teaching is much more of a challenge. This seems to demoralize and make the courses less effective also for the students for which the curriculum and pacing are right. The broader programs at Hillview and Los Altos result in more homogenous, and data indicates also more effective, classes.

— This is based on my observations only (no data) – but due to various reasons (that include few less effective 6th grade teachers and inaccurate recommendations) many white students that are at “Exceeding standard” level seem to needlessly follow recommendations to “lane down” (go to math7/math8).

— I suspect that the new placement rule (this year “B” is required to pass 8th grade Algebra) will further derail our white students, already less solid than peers in Los Altos and Hillview. Many more will be forced to repeat Algebra in 9th grade. This in turn, will percolate down, disadvantage the students that did not yet study algebra (completed math8) that will be placed in the same courses now with mostly proficient students.

My conclusion is that a broader and well designed program, similar to our neighbors, would better support all our students. We all focus on the needs of our own children, but the data shows that a program that underserves one segments results in worse performance also for the students that are supposedly supported.

@Greene and Paly parent, fwiw your description of some of the issues resonates here. Anecdotally, our (underrepresented minority) child took the 6-7A-Algebra 8 path in PAUSD, and did fine grade-wise but regularly reported back on feeling stupid and clearly understanding that other kids were “the smart ones.” Complained about hating math. Same child is now in private high school for a variety of reasons, and seems to have a much healthier perspective on math classes: doing well, still not the favorite class, but not a regular source of feeling stupid or out of place.

@Parent
I really appreciate you sharing! I heared similar stories from multiple people. Really happy your child is doing well now! BTW, an out-of-scale brilliant white boy at Greene told me few month ago that he feels “stupid”. It seems that our students do not even need to be historically under represented to view themselves as inadequate and get demoralized. I wish we can change this so all our students are encouraged and supported and motivated.

@criteria for geometry

First, the comparison data can not be easily dismissed. It is key to helping us understand where we are at and how to improve. I can see your point that “growth” with respect to year-start baseline is more meaningful data rather than the same-grade cross districts data that is avaialble and I was using. You are correct that in some perceived situations it is only meaningful to look at “growth” — for example — if each district each year was getting out of nowhere groups of students with different baselines. But this is not the case. The districts offer k-12 programs (or k-8) and feed from their own students. And if anything, we have an advantaged starting point in terms of education and funds. It also seems that our 3rd and 4th grade performance at Palo Alto is similar to the compared districts and we mostly lose ground later on. So here is a uniform starting point.

The comparison data, that should not be dismissed, does show that we are doing more poorly than neighbors that offer broader programs. These neighbors also operate on lower budgets.

Some additional comments on your post:

— I agree that there is also an issue with students losing ground in 5th grade, not only in 6th. Some districts are also broadening their 5th grade programs. We may want to look at this.

— You seem to assume that our placement works and that courses only include kids that are a “fraction” of a grade ahead. You are right that it is not clear what can be done with kids that are say half a grade ahead. These kids may need higher pacing, and perhaps the best solution is to allow them to independently progress and get appropraite placement the following year.

A point that you seem to be utterly missing — and I don’t blame you because one has to experience this to fully understand and believe — is that our placement process is broken. PAUSD systematically misplaces kids that are more than full grade level, sometimes two grade levels ahead. For example, our 6th graders can place into Algebra, but not into 7A. This means that 6th grade is crowded with kids for which the most suitable course is 7A or that are already proficienty in most of 7A (!). Moreover, even kids ready to Algebra are egregiously misplaced in math 6. This harms everyone.

So if you carefully look over everything, you may see the point (which I think you are still missing). It is not that we have to choose between supporting the SED kids, or the white kids, or the Asian kids. A broad program with accurate placement can support everyone better and be implemented with lower cost.

We do not need that many different pathways to implement a broader program. It is not that complex or expensive. We need the additional support for those well below grade level. This is best done in the form of 2 math periods in a homogenous group. Other than that, we can do a lot with one additional course (as done in Los Alto or Saratoga) and better placement.

@criteria-for-geometry

You say
“…. and instead chosen to do game design or logic puzzles or maze art or cryptology or almost anything else that is challenging and interesting but not skip-ahead tutoring like memorizing the quadratic formula. That’s my 2c.”

I find your statement to be an under-informed, demeaning, and a mis-representation of a large group of our students. I suggest that you explore this by talking to the kids and families you are referring to here.

I do understand your frustartion with the presence of already-proficient students that impede your kids’ learning. But the only fair solution is to place these kids correctly at school. At our and demographically similar district, the number of students that needs a higher lane is about the same as those for which the 7A-Algebra8 pathway is suitable. Neither pathway is required by the state. Why serve one group while completely sidelining another? Especially that all evidence is that a broader program that supports everyone better is easily within reach with lower cost.

Thes kids (30-40%of our students) you are refering to are grossly misplaced at school (the program is not adequate in level or pacing) and respond by compensating after school. This is not “memorizing the quadratic formula” — most take solid programs (AoPS, Russian math, ….). Specifically for quadratics, AoPS builds it up beautifully. First gaining mastery of factoring, completing the square, complex arithmetic, and then guiding students to derive the quadratic formular themselves.

You suggest that these kids take instead courses that “bypass” the curriculum (cryptography, logic, advanced coding) but these courses are rare and more expensive than quality basic math courses and also make less sense in terms of sequencing than first covering (pre)algebra basic. Moreover, this will not resolve any issue, since it is not unsuitability of level alone but unsuitability in depth and pacing that makes kids “bored”. Do you see the point?

@Greene and Paly Parent

I hear your optimism, but when I look at the specifics, I only see goals tied to the state standards. I don’t see anything to help ALL students. The meeting to discuss this is tomorrow.

The KPIs (Key Performance Indicators) are:

Maintain standards aligned instructional materials for all subjects
Increased number of course-alike teams self-reporting progress on the alignment implementation rubric
Increase the percentage of teachers implementing standards/evidence-based grading
Increase the percentage of students performing at or above standard on CAASPP assessment
Increase the percentage of students meeting A-G eligibility requirements
Increase the CAASPP participation rate (target = 95%)

Curriculum Standards:

Develop a curriculum evaluation and renewal cycle to be used for all disciplines.
Review and revise elementary progress reports and secondary report cards to reflect new standards and provide meaningful feedback on academic and social-emotional growth.Identify and scale dyslexia instructional and assessment practices for early literacy.
Provide and build capacity for diverse pathway options for student success. Analyze computer science and digital citizenship implementation practices.
Adopt and implement Next Generation Science Standards (NGSS) aligned curriculum.
Increase dual enrollment opportunities.

Instructional Practices:

Analyze formative and summative data to inform instructional next steps.
Identify and scale up impactful instructional practices for students who were once below benchmarks and have demonstrated significant growth in core subjects.
Ensure course-alike teams have common grading practices, with increased use of evidence-based grading; revision/retake opportunities; and scaled rubrics based on learning targets, homework load awareness, etc.Pilot alternative homework strategies that result in reduced homework load for students.
Ensure course-alike teams have common Learning Targets; common formative and summative assessments; and that teachers communicate Learning Targets to students, both orally and in writing.
Expand blended learning opportunities.
Teach students to self-assess progress and set goals for next steps.

@fact checker

yes, I looked for substance in the promise and now I am much less positive. There are multiple issues taht quickly surface.

In particular, I saw no indication for performance indicators that will support the promise of “unobstructed access to rigorous courses.” The current major “obstructions” to students reaching their potential at PAUSD are:
— Limited and faulty “measurements” of where students are currently at that lead to wide spread misplacement
— Unbalanced and limited pathways and obstacles that tripp students that do not have private after school support

The first might be easier to remedy and a good starting point as there are established normed third party tools. BUT the assessment tools and metrics specified in the “promise” are all focused on grade-level standards. This is not enough in our district with so many students exceeding grade level. We need to have granularity that is suitable to the distribution of our students.

One of our core challenges is prevalent misplacement. To address and measure misplacement, we need to accurately be able to measure the regime of 0-2 years above grade level standards. In particular, more than 80% of our Asian students exceed grade level standards and their average exceeds the standards of the *next* grade level. Many of these students are currently egregiously misplaced in their middle school math courses. Misplacement percolates down and harms (even more) everyone else placed in the same courses. Students compare themselves to others that don’t belong in their class and feel demoralized and inadequate. It is important to identify the already-proficient students and place them correctly or at a minimum provide them with an option to do independent work elsewhere instead of demoralize everyone else.

The district was piloting for 3 years now a tool (NWEA MAP) that is computer adaptive and accurate also above grade level. Our 5th and 6th graders were taking these assessments at school three times a year. Many other districts use these well-established diagnostic assessments both for intervention and to support placement in compacted accelerated pathways. But our “promise” seems focus on performance indicators based on the grade level “smarter balanced” tools. These are not adaptive and only very few questions exceed grade level standards.

Why not
— Share aggregate NWEA MAP test results with the community, so we understand where we are at now.
— Share over-time results of individual student with parents, so they are informed on where their students are at, track their progress, and provide support when the program is not effective.
— Construct a performance indicator for misplacement that is based on the gap between the student proficiency level and their school placement. That indicator can penalize gap that are more than a year of curriculum.

As promised:
Enrollment numbers in A or H advaced courses (7th-12th grade) based on 2018-2019 data (14th days of school) and combined across our middle/high schools. Since we are not looking over multiple years, this assumes some steady state.

The numbers are as fraction of the total enrollment for the respective grade level, and do not take “skipping” into account.

The A(dvanced) sequence: Math 7A, Algebra8, GeoA, Alg2/TrigA, Intro. An, AP AB calculus
The H(onors) sequence: Math 7A, Algebra8, GeoH, Alg2/TrigH, AnalysisH, AP BC calculus

grade %in A lane %in H total
7 66% 66%
8 70% 70%
9 25% 38% 63%
10 22% 39% 61%
11 23% 32% 54%
12 20% 26% 46%

We can see that
— the fractions are pretty steady 7-10th grades (the increase from 7A to AlgebraA due to skipping).
— The 10% drop from 8th to 9th is accounted for by skipping students already taking GeoH in middle schools. The drop actually occurs 9th to 10th (Almost Algebra8 students currently continue to GeoA/H but this might change for next year with the new B=pass rule for Algebra8)
— Into 11th grade: 10% drop in combined A/H enrollment and 20% drop in H lane.

Overall 69% of our students take Algebra8 and 2/3 of them continue to AP calculus. This suggest that Algebra8 is a critical step stone. I believe that more solid middle school pathways will give our students a better head start for high school: Balanced pathways to Algebra in 8th grade and no obstructions for those that need further acceleration can help all our student thrive.

This also bring as back to the questionable selection of performance indicators based on meeting grade level standards in the “PAUSD promise”. Why not make proficiency in Algebra in middle school a performance indicator? This will encourage the staff to strengthen the middle school program.

@C thank you for sharing!

The Einstein packets (stopped from this year) were never meant to prepare students for the 7A curriculum. They were used for at least two decades to provide a “challenge” for the many students that already master the math6 curriculum. This, as you say, without instruction time, discussion, or meaningful feedback. Even errors pointed out were never corrected and after two decades some of the content became even less politically correct (references to relative body weight) and culturally biased.

What I was refering to was a *different* packet program (dated back to the 20th century) that was stopped about 8 years ago. If you are still in high school then you did not even have that chance. (Your only path to placing in 8th grade Algebra was by taking a course outside on your own time and your parents’ expense). These packets were provided also for independent work but if you completed them you were more or less prepared for the “skip 7A” test. Again, these were stopped years ago without an equitable alternative. Instead of improving this (by providing more support and using modern tools that were already available 8 years ago) they stopped this altogether.

So when our then advanced math program was put into place in the 20th century, there were components that were put in place to support growth and opportunity to accelerate for students that needed it using material that was at least provided at school. These included the Einstein packets (challenge) and the “skip 7A” packets. These components are now all removed without modern (or any) replacements. This as the basic “math 6” curriculum (still two month on simple fraction) became even less adequate to more of our students and all districts around us offering stronger broader programs.

As to the number of students that are ready for “7A” (or a compacted accelerated pathway that covers 7A with no skipping). Your estimate was that among your peers there were many. But now we can obtain precise estimates, as these pathways are offered to 6th graders at neighboring districts with 30%-45% enrollment. Adjusting for demographics, it is safe to estimate that
— about 30-35% of our students are ready for a compacted accelerated 6th grade course (as you were in 6th grade) that also covers our math7A.
— That another 35% of our students would tremendously benefit from a 6th grade course that also includes *some* of “math 7” content. This will balance their pathway to Algebra in 8th grade (that currently compact many new common core math8 topics together with Algebra1 curriculum), allowing more to start high school with strong Algebra foundations.

I would be interesting to hear your perspectives as a current high schooler on the number of your friends that could have benefitted from stronger middle school pathways. For example, it seems that many students struggle in Alg2Trig in highschool which could have been addressed with stronger Algebra1 foundations in 8th grade (obtained in a balanced pathway).

I graduated from Paly a few years ago, so I’m not all that invested in this. But I can say that it’s a shame that we “waste” so much time in middle school. If suitable students could enroll in 7A in 6th grade, then they could cover linear algebra during the senior year of HS. This is advantageous not only because it allows students to be challenged at the level they are at (what a novel concept) but it could allow the top two lanes an extra year to space out the existing material covered, perhaps reducing attrition rates. Or it could allow linear algebra to be taught in HS.

Thank you @C! You made a strong point as a recent graduate. We have amazing students here in Palo Alto and we need a broad program that meets them where they are and supports them in meeting their potential. Unfortunately, our district seems more focused insteady on fitting our students into very limited pathways (compared with neighboring districts). What we can see (comparing middle school math results with neighboring districts) is that this harms everyone, even the students for which our current pathways are suitable. Moreover, kids that do not have significant external means that allow them to compensate for anything from teacher mismatch, curriculum mismatch, or unsuitable pacing, are obstructed from getting to where they could be with a better program.

As @fact-checker pointed out, a key to improvements is to set up RPIs (performance indicators) that are compatible with our body of students: Meeting them where they are and supporting their growth. This will encourage district staff to improve our program. This is very important now as our new superintendent is working on a new vision for our district.

But… the current proposed RPIs are exclusively focused on meeting the minimum bar of state standards: Meeting common core standards and a-g UC graduation requirements. Having more students meet the minimum bar is important. But these RPIs mean continued lack of accountability for providing appropriate growth to 70% of our Palo Alto students that are well above the minimum bar. Additionally, data on middle school math shows that we should not think of it as a zero sum game. Better support for any cohort also HELPS other cohorts. Even if we focus on the struggling kids, but insist on placing them in the same standards-based classes with kids that are 0-2 years above the standard, it is ineffective for everyone.

The district does have in its disposable assessment tools that are compatible with measuring growth in the the top 70% of our students, but our current RPIs (intentionally?) are focused on the grade-level smarter balanced assessments. These assessments can only provide accurate feedback and data for the bottom 30% of our students. Surprisingly, despute very large spending we are failing to do well even for these kids.

Here are assessment tools from which we can derive performance metrics for the remaining 70%:

The MDTP tests, developed by the University of California, are very widely used to assess readiness and proficiency in CCSS standards of Algebra, Geometry, and more. They are available FREE to any California public school. Many schools use them at multiple points using the school year to assess student progress (in Algebra course) towards proficiency in a more accurate normed way than possible when only using course grades. PAUSD uses MDTP to place students that come to our high schools from outside the district but our students that stream from our middle schools are denied “fair and objective” placement checks and from this year will be failed with a course grade of “C+”.
https://mdtp.ucsd.edu

An RPI that is based on growth of students in our pathway to Algebra and more students meeting Algebra and Geometry proficiency at start of high school will encourage improvement of our middle school programs and also promote accurate placement compatible with the Math Placement Act (2015), which PAUSD is currently dodging.

The NWEA MAP assessments are computer adaptive (able to assess a wide spread of levels in same sitting), standards-aligned and normed over tens of millions of students. They are adequate for measuring growth in a meaningful way for all students. PAUSD had been piloting them at PAUSD for three years, but data is being withheld for parents. RPIs based on MAP grwoth data will again bring more accountability where it is needed.
https://www.nwea.org

@C the sentence is inaccurate (as you may have already observed from the chart). Trigonometry is still very much part of the curriculum also in common core. It is first introduced in the Geometry courses: At greater depth in our middle school GeoH courses and limited content (right triangles) at the high school GeoA/H courses. Then more (identities) in Alg2Trig A/H and also in following courses including AP calculus.

There were some changes with common core alignment in the high school sequence but they are not substantial. The article you point to also talks about the huge gap from the H lane to the A lane (we saw the drop in the H lane enrollment numbers from 10 to 11th grade) The H lane goes well above what is needed to know the AP BC calc curriculum (literally all students get a “5” in the exam). The A lane basically takes them to the AP AB calc curriculum. My opinion is that it is a shame that the emphasis on grades causes students to lane down and not be challenged, as the story in the article. One remedy could be weighted grades so that an H lane “B” can be equivalent to an A lane “A”. So students can sit in H lane courses without harming their (w)GPA and learn adequately.