by Sugi Sorensen, June 6, 2024
Back in January of 2023, La Cañada Math Parents published an article notifying the community of upcoming changes to the La Canada High School (LCHS) math pathways and course offerings. As we noted in the article then, LCHS and district administration indicated that the transition to the new advanced pathway would be a phased transition, meaning one new class would be added per year while one old pathway course would be retired per year. As the 2023-24 school year closes, we are in year one of the pathway transition.
Unfortunately, recent developments indicate staff impatience with the pace of the transition, and attempts to accelerate it are resulting in shortcuts that may harm certain cohorts of LCUSD students. Students were given questionable advice about which math courses to take next year by both counsellors and teachers.
Background
As a reminder, here are the old pathways (no acceleration) that are being phased out:
Figure 1: Old pathways prior to 2023-24 school year. Phasing out one year at a time during transition to new pathways.
Some students accelerate one or two years, having passed one or both parts of the middle school math placement exam entering 7th grade. Below is the old pathway with the bottom row showing what a student who passed just the 7th grade part of the middle school math placement exam in 2023 or before would take:
Figure 2: Old pathways with one-year acceleration added on bottom row.
The revised, new math pathways that were deployed starting this year (i.e. 2023-24 school year) will look as follows after fully deployed:
The College Prep Pathway is identical to the old College Prep Pathway, except that the courses have been renamed to their subject-based descriptive names. Note also the introduction of a new course (in pink) — AP Pre-Calculus — taken after Algebra 2 or Honors Algebra 2. The main differences between the old and new pathways is in the old Advanced College Prep Pathway, four years of standard high school math prior to Calculus were compacted into three years. The new Advanced College Prep Pathway uncompacts those courses into four standard traditional pathway high school mathematics courses that should be compatible with standard traditional pathway math courses offered at other schools and institutions up and down California. Uncompacting the four courses in the Advanced College Prep pathway means it will be easier for teachers to cover the material in a single year (one of the motivations to change the pathways in the first place), and they should be less difficult for students who previously found it hard to keep up with the pace of instruction in compacted courses.
Transition Trouble Begins
The rollout of the new Advanced College Prep Pathway began this year with little fanfare. Unfortunately confusion has reigned over the second semester with much misinformation circulating amongst students, parents and staff. There are several bumps in the road to warn parents about.
The first sign of trouble began last school year when another parent and I were invited to a meeting on December 16, 2022 to provide feedback on a plan by LCHS staff to accelerate the transition from the old to the new Advanced College Prep pathway. We were shown the following plan to accelerate the transition to complete in two years, instead of the originally promised four years:
Rather than phase out one old pathway and phase in one new pathway course per year, administration and staff wanted to have all new courses phased in by the 2025-26 school year.
Page 11 of the presentation slides showed staff’s plan to accelerate the transition by first having students in the present Math 8 Advanced class (old pathway) in the 2023-24 school year skip LC Math 1 Advanced next year in the 2024-25 school year and jump ahead into the new Honors Geometry course instead:
As my colleague and I pointed out to LCHS/LCUSD staff at the December 16, 2022 meeting, this was a terrible idea because they were proposing that this cohort of students skip Algebra 1, which is the most important math course for students to master in high school. The rationale given by staff was that they believed the Math 8 Advanced (old pathway) course was really an Algebra 1 course and all these years it’s been in use everyone has misunderstood its true nature. This claim was ridiculously false, staff’s protests to the contrary notwithstanding.
To prove the falsity of staff’s claim that Math 8 Advanced (old pathway) is really an Algebra 1 course in disguise, I spent the ensuing winter break analyzing the Math 8 Advanced (old pathway) course outline and mapping all topics to the California Common Core State Standards in Mathematics (CCSS-M.) In fact, I wound up analyzing and classifying the content of most of the LCHS math courses as well as the old Math 8 Advanced and new Math 7 Advanced courses. My intent was to give staff the benefit of the doubt, and objectively evaluate their claim that Math 8 Advanced (old pathway) was really an Algebra 1 course, as well as other reinterpretations they made later in our meeting. Here’s the summary table of all Math 8 Advanced (old) course topics mapped to CCSS-M standards:
To interpret the above summary table, the first column shows the CCSS-M grade-level or subject standards, the second column sums how many of those topics are taught in the course, and the third column reflects the percentage of those grade-level or subject standards covered in the entire course by number of topics, not by time spent on the standard area. Thus you can see that the Math 8 Advanced (old pathway) course contains 75% grade 8 standards, and less than 20% Algebra 1 standards. This shows beyond question that staff’s claim that the course is really an Algebra 1 course is wildly exaggerated. To see my detailed mapping of every topic in the course syllabus to CCSS-M standards, see my detailed analysis here.
Reinterpretation of Old Math Courses Gets Even More Ridiculous
Later in the same Dec 16, 2022 meeting with LCHS/LCUSD staff, they showed the following slide:
Note in the highlighted areas that staff was recommending that several cohorts of LCHS students in the Advanced College Prep Pathway skip LC Math 3 Advanced entirely and move from LC Math 2 Advanced directly into the new AP Pre-Calculus class instead. Remember that LC Math 2 Advanced is primarily a Geometry course, and LC Math 3 Advanced is primarily an Algebra 2 course with some Trigonometry and Pre-Calculus compacted into it. My colleague and I explained that we thought this was a terrible idea as well, because students should not skip Algebra 2 material just to get to AP Pre-Calculus sooner than normally prescribed.
Staff defended this idea by re-interpreting the content of the LC Math 1 Advanced and LC Math 3 Advanced courses from the old Advanced College Prep Pathway. They claimed that LC Math 1 Advanced is really an Algebra 2 course and LC Math 3 Advanced is really a Pre-Calculus course. This contradicts the naming of the courses in the LCHS Course Catalog, the certification of these courses by the University of California Office of the President (UCOP), and the description of these courses used by the district for the past 10 years.
The breathtaking nature of these claims stunned my colleague and I when first presented to us. However, we contained our shock and I told staff at the time that I would do further investigation to evaluate their reinterpretations of course content more closely.
Thus, over winter break after the December 16, 2022 meeting, I analyzed the course syllabi for all LCHS math courses for which course outlines were provided, and mapped them to the CCSS-M standards. In order to do that, LCHS Principal Cartnal provided me with the course outlines for LCHS courses, though in several cases he provided me with old or incomplete course outlines, or skipped them altogether. In spite of the incomplete nature of material provided, I was able over a span of two weeks to complete course-to-standards mappings of all of the courses in dispute. Here was the result of my analysis of Algebra 1 level courses:
It is plainly clear that staff’s claim that the LC Math 1 Advanced course is really an “Algebra 2” course is demonstrably false. Only 17.9% of topics taught are CCSS-M Algebra 2 standards, and nearly 3/4ths of the course is Algebra 1 standards. The mischaracterization of LC Math 1 Advanced as really an “Algebra 2” course has been quite prevalent among LCHS staff this school year coincidentally.
And below is my mapping of the Algebra 2 level courses in the LCHS math department (you can access the full mapping here):
Note that the LC Math 3 lower College Prep Pathway course outline was not provided by Cartnal, and the new AP Pre-Calculus course outline was too general to be able to map. However, my analysis was able to answer the question, “Is LC Math 3 Advanced (old) really an AP Pre-Calculus course?” Given LC Math 3 Advanced contains 85.3% Algebra 1 and Algebra 2 standards, it’s incontrovertibly NOT a Pre-Calculus course.
Though no more evidence need be presented, here is how these reinterpreted courses were described in the 2022-23 LCHS Course Catalog:
Notice the third column (i.e. “UC/CSU Transcript Abbreviation”) describes LC Math 1 as Algebra I and LC Math 1 Advanced is Algebra I Advanced. LC Math 3 is classified as Algebra II/Trig(onometry) and LC Math 3 Advanced is classified as Algebra II/Trig HR. As an aside, the values shown in the above table do not match the classifications shown on the UCOP’s Course Management Portal (CMP) page for LCHS courses. The 2023-24 and 2024-25 editions of the LCHS Course Catalog maintain the same course mappings shown in the table above.
In addition, the LCHS Math Department home page describes LC Math 1 as:
“LC Math 1, for instances (sic), is LCHS’ new standards aligned Algebra 1 class, while LC Math 1 Advanced is a course based upon Algebra I and will include concepts taught in Algebra II and Pre-Calculus.”
The sudden reinterpretation of the LC Math 1 and LC Math 3 courses as something they never were was baffling.
Why Should You Care?
If you are still reading, you may ask yourself, “why should I care what the courses are called and how does it affect my child?” The major problem is that the LCHS staff recommended that at least three cohorts of students skip an essential course in the high school math sequence. This could have been seriously damaging to students’ mathematics education. K-12 mathematics is a cumulative domain of knowledge where the learning of new topics and concepts depends on understanding and mastery of earlier topics, with some exceptions. Algebra 1 is widely considered to be the keystone course in high school (or middle school for kids capable of reaching it earlier.) Skipping it so you can avoid having to teach two sets of courses is simply a bad decision.
Further, Algebra 1 is a prerequisite for a number of science courses, including Physic of the Universe Advanced (SC8026) taken in 9th grade:
…and Honors Chemistry (SC8110), taken in 10th grade:
LC Math 2 Advanced requires successful completion of LC Math 1 Advanced with a grade of B or higher, or successful completion of LC Math 1 with a grade of A, as well as teacher recommendation. Thus neither Conceptual Physics Advanced (9th grade) nor Honors Chemistry (10th grade) could be taken unless LC Math 1 Advanced (or LC Math 1 with a grade of ‘A’) was completed in 9th grade. So why on Earth did staff think skipping Algebra 1 was a good idea for anyone needing to take honors science courses?
Thankfully, LCHS staff seemed to understand the gravity of our objections. After my colleague and I articulated our serious concerns about staff’s proposed accelerated pathways implementation plan, and the fact it would skip foundational math courses for certain LCHS grade level cohorts of students, we were promised that the pathway acceleration plan would be shelved and staff would not present it to parents. We were told that they would continue with a phased implementation over four years.
Back from the Dead…
Thinking all was well and a disaster had been averted, the 2023-24 school year started off and early reports were that the first year implementation of the phased deployment of the new LCHS math pathways went smoothly. Reports from students taking the new accelerated Math 7 Advanced course were positive. Then mysteriously parents started contacting me in March of 2024 saying they heard some LCHS math teachers were recommending that students presently taking LC Math 2 Advanced in the old pathway were being told by their teacher and counselors to skip LC Math 3 Advanced next year and go directly into AP Pre-Calculus.
After hearing the same story multiple times, and the resulting confusion it created, I reached out to LCHS Principal Jim Cartnal and LCUSD curriculum czar Anaïs Wenn in mid-April to ask why students were being advised to skip LC Math 3 Advanced. Cartnal responded on Apr. 15, 2024:
“Our approved math counseling position is as follows: If a student is considering taking AP Calculus BC as a senior, students would be wise to enroll in AP PreCalculus. If students were considering taking AP Calc AB, they should enroll in LC Math 3 Advanced.”
Befuddled at the seeming amnesia about our concerns expressed and presumably received the previous year, I did some investigation. Lo and behold, it turned out LCHS staff had decided to ignore half of our advice from the previous year and instead to advise that all students in the old Advanced College Prep Pathway skip LC Math 3 Advanced and proceed directly into AP Pre-Calculus after LC Math 2 Advanced. I found the following math pathways slide on the Academic Planning page of the LCHS website in the slides for the Course Selection (for) Rising 10th Graders presentation:
Note how the second and third pathways show students skipping LC Math 3 Adv and going directly into AP Pre-Calculus after completing LC Math 2 Adv. The Course Selection presentation for grade 9 contains the same errant slide dispensing the same bad advice. Here’s the same slide from the Course Selection (for) Rising 9th Graders presentation:
Again note the second and third paths show students skipping LC Math 3 Adv and going straight into AP Pre-Calculus after LC Math 2 Adv. Concerned that the LCHS counseling department was advising students to skip an important math course, I responded to LCHS Principal Cartnal on April 17, 2024 to inform him that it was no wonder so many students were signing up to take AP Pre-Calculus after LC Math 2 Advanced — LCHS counseling staff was telling students to do so! In that email I showed him Figure 12 above from the Academic Planning link on the LCHS website.
Cartnal responded on April 23, 2024 that the slide from the Academic Planning guide was a mistake:
“The slide you included is from the rising 10th grade registration guide. It is in error. From the rising 11th grade presentation, this is the slide that was included and this is the correct image and the message was in alignment with what I shared in my earlier response – AP Calculus AB bound students were advised to take LC Math 3 Advanced while BC bound students were advised to go to AP Precalculus. I will work to get the 10th grade presentation fixed.”
He then included the following “corrected” slide from the rising 11th grade academic planning presentation:
Note the difference from the presentations given to rising 9th and 10th graders — students are advised to take LC Math 3 Adv after LC Math 2 Adv, but only if they are ultimately headed to AP Calculus AB, AP Statistics, or Financial Literacy. But students headed for AP Calculus BC are told they should take AP Pre-Calculus after LC Math 2 Adv instead.
The different recommendation seems to reflect Cartnal’s statement from his April 15, 2024 email that, “If a student is considering taking AP Calculus BC as a senior, students would be wise to enroll in AP PreCalculus. If students were considering taking AP Calc AB, they should enroll in LC Math 3 Advanced.” No explanation is given why students completing the same LC Math 2 Advanced course, but headed for different courses senior year, should take different classes in between. There should at least be some mathematical related reasoning for the differential decision. None is given.
Cartnal’s April 23, 2024 email said he would, “work to get the 10th grade presentation fixed.” That never happened. As of the last day of the 2023-24 school year, the 10th (and 9th) grade presentations remain with the errant slide. Thus bad advice was allowed to remain in circulation and dozens of students remain misplaced into the wrong math course for next school year.
Why Skipping LC Math 3 Adv is Bad Advice
None of this would matter if a sound explanation was behind the differential advice given in the academic planning documents, which to this day remain contradictory and in error. But there is no sound explanation. In my email to Cartnal on April 17, 2024, I enumerated four reasons why I thought skipping LC Math 3 Advanced after completing LC Math 2 Advanced was a bad idea:
- Students will miss key Algebra 2 / Trigonometry topics that are (or were at one time) taught in LC Math 3 Advanced that aren’t taught in AP Pre-Calculus according to the course outline approved by the LCUSD Governing Board at its April 2023 meeting. I then listed 22 Algebra 2 and Trigonometry topics I had identified that would be missed by skipping LC Math 3 Advanced.
- Additionally, students in the old Advanced College Prep pathway who had completed LC Math 1 Adv and LC Math 2 Adv will have already learned much of the material taught in the AP Pre-Calculus course since the courses were intentionally designed to compact 4 years of math into 3, and the means of compaction was taking the old LC Math 4 course, which contains Pre-Calculus/Trigonometry, chopping it up and inserting the pieces into the LC Math 1 Adv, LC Math 2 Adv, and LC Math 3 Adv courses. I reasoned forcing students to re-learn Pre-Calculus topics already taught to them in LC Math 1 Adv and LC Math 2 Adv was a sub-optimal use of classroom time.
- The UC/CSU Area C requirement in mathematics is 3 years required, 4 years recommended. Of the 3 years required, students must “include the topics covered in elementary and advanced algebra and two- and three-dimensional geometry,” (source) which is translated to mean Algebra 1, Geometry and Algebra 2 in a traditional pathway course sequence, or Math I, Math II, and Math III in an integrated math pathway course sequence. Skipping LC Math 3 Adv jeopardized the ability of all students who intended to apply for admission to UC and CSU campuses senior year. I surmised when students went to fill out their UC applications, they don’t just send their transcript, they have to enter each class they took and the grade they received. I asked what will those students do when filling out the third year math question?
- Students would be less prepared for the SAT and ACT standardized tests because both exams expect knowledge of math standards through the end of Algebra 2, and skipping LC Math 3 Adv, which is ostensibly an Algebra 2 course, would deprive students of the knowledge of those missed Algebra 2 topics.
Cartnal’s response to these concerns was essentially hand waving and vague claims. In an earlier email, Cartnal had claimed that LC Math 3 Adv and the new AP Pre-Calculus course were “very similar in standards.”
On April 26, 2024, Cartnal sent an additional follow-up email response that included a detailed response to my reason #1 above from the LCHS math department staff. They claimed that of the 22 Algebra 2 / Trigonometry topics that I claimed would be missed by skipping LC Math 3 Adv, almost all of them would be covered in LC Math 1 Adv, LC Math 2 Adv or AP Pre-Calculus. I strongly contest many of these claims.
The Phantom AP Pre-Calculus Unit
Bolstering this view, I contacted the current teacher of the new AP Pre-Calculus course — Tyler Fernandez — on April 17, 2024 and asked him if he intended to teach Unit IV of the AP Pre-Calculus course outline that had been approved by the LCUSD Governing Board on April 18, 2023. For reference here is Unit IV from the AP Pre-Calculus course outline:
Mr. Fernandez responded via email on Apr. 19, 2024 and said that up to the date of his response, he had not taught any topics out of Unit IV and did not plan to, but after his students took the AP Pre-Calculus exam in mid-May, he planned to teach “a few topics suggested from the current Calculus teachers.”
The reason I asked Fernandez if he planned to teach any Unit IV topics is because I knew that the AP Pre-Calculus exam only covered material on Units I through III of the College Board’s model syllabus, which LCUSD had copied exactly when creating its proposed course outline presented to our Governing Board. Thus I reasoned he would have little incentive to teach Unit IV topics if they weren’t going to be tested on the AP exam itself. Sure enough, I was correct in my speculation.
The reason this is important is that the LCHS math department response to my concern about 22 missing Algebra 2 / Trigonometry topics from skipping LC Math 3 Adv assumed that all four units in the AP Pre-Calculus would be covered in class, an assumption that turned out not to be true. Remember that the LCHS math department response to my concerns was drafted sometime in early April, before Fernandez had gotten to Unit IV. So unless they had spoken to Fernandez directly, they formulated their response to my questions based on reading the AP Pre-Calculus course outline approved by the Board on April 18, 2023 and (wrongly as it turned out) assumed he would teach Unit IV topics.
The Bottom Line
The endpoint of this long, exhaustive account is that in my informed opinion, the LCHS and district staff made an ill-informed decision by advising its students to skip LC Math 3 Adv after completing LC Math 2 Adv in the old Advanced College Prep Pathway. As a result, dozens of students will be short-changed by missing Algebra 2 / Trigonometry concepts normally taught in LC Math 3 Advanced. Ask yourself why staff would advise half of its students to take LC Math 3 Adv after completing LC Math 2 Adv, yet at the same time advise the other half to skip it? Further, ask yourself why the understanding held by LCHS teachers, administrators, students, families, and the UCOP about the content of old Advanced College Prep Pathway courses for 10 years was suddenly deemed incorrect by a novel reinterpretation made in the last two years?
Parents whose students are in the old Advanced College Prep Pathway would be better served, in my opinion, by taking LC Math 3 Advanced after LC Math 2 Advanced. Parents and students concerned that they will miss out on the opportunity to complete another Advanced Placement test (i.e. AP Pre-Calculus), should instead consider taking the AP Pre-Calculus exam in May of the same year they complete LC Math 3 Advanced. Students are permitted to take AP exams in topics for which they have not taken the complete course. If they are concerned that they may have forgotten Pre-Calculus and Trigonometry topics taught in the preceding two years embedded in LC Math 1 Adv and LC Math 2 Adv, I would advise they buy one of the many AP Pre-Calculus study guides available on Amazon during winter break of the year they take LC Math 3 Advanced, and self study outside of school over the next five months before taking the AP Pre-Calculus exam in May.