Assuming you mean physics for physics and engineering majors, the sequence typically starts with a prerequisite of calculus 1 (or AP calculus AB) and a corequisite of calculus 2. Students are expected to start in frosh spring, but may start in frosh fall if they start in calculus 2 or higher for math.
So a high school that offers math up to precalculus should have students ready for calculus 1 in frosh fall in college, so that they can take physics 1 and calculus 2 in frosh spring. This is considered the normal sequence. A high school that offers calculus should have those students who take it ready for physics 1 and calculus 2 (or higher) in frosh fall.
So that suggests that the high school in question is a very low performing one that does not even offer precalculus. How many college-intending high school students attend high schools that do not even offer precalculus? (Note that only 14% attend high schools that do not offer calculus, so those which do not offer precalculus is a subset of that 14%.)
The âusual sequenceâ is often not found among students at T20 schools, many of whom have taken both sections of AP physics C, BC calculus, and often MVC before heading to college, and who
then retake those courses, as many colleges suggest.
The math acceleration race only to repeat with regular (not honors or proof-heavy) courses in college seems like a big waste. Also, the true math talents would highly resist doing such a thing â they would either move on to the next course, or take an honors or proof-heavy course instead of repeating what they already know in a regular course.
I completely disagree. Many kids can learn math early, and well, but hit the wall at a certain point. I was very good at math early on, but hit the wall in second semester calculus. It wasnât a brain maturation thing, and it certainly wasnât predicted by my 99th percentile math aptitude and SATs. In fact, I think I would have done better if Iâd been allowed to move as fast as I could in math. My brotherâs math aptitude was even better, and he hit the wall after second year college math at Columbia.
Just because a child is going to eventually hit the wall with math, does that mean that he should be held back in arithmetic? Why not let them move ahead and learn as fast as they can, as long as they can do it? Because theyâre going to have trouble with Calculus, they should not be allowed to progress to Algebra? And if you make them sit there bored in math class since they already know the material, is that going to help them to do better when they eventually hit material that they havenât yet mastered?
That many +2 students seem to be hitting the wall in algebra 2 or precalculus or earlier in high school (as opposed to real analysis in college) suggests that their acceleration was due to parental pushing, rather than ânaturalâ placement into the level that the student was best suited for.
So if a student has done well in accelerated math up until hitting precalculus, would they have done better if they had been held back in math? Math ability is not a late-developing skill. Whatâs the big deal if they drop down to the regular track from the honors track, once they hit their limit in math? Does their later inability to get easy Aâs in honors precalc devalue their past Aâs in Algebra I and Geometry?
This seems to be the issue VA is seeking to address. How should placement occur? Natural aptitude seems like the best course but apparently thatâs either not happening or itâs not happening in the âcorrectâ percentages.
To me the biggest problem with math in the US is that itâs all about advancing in the sequence rather than adding depth. I grew up in a system (the UK) that does the opposite, there is no acceleration (apart from a very few, say 1%, of the most able kids being able to skip an entire year in every subject in elementary school). But the depth to which they go, especially at A level in the last two years of high school, is vastly greater. It is about solving novel problems, not turning the handle, and learning proofs. Much closer to the type of skills taught in AOPS.
Of course you choose your A levels, so only kids who do well in math choose to explore that greater depth. But I see plenty of US kids who are significantly advanced in the math sequence without the depth of understanding to solve novel problems. Then they may âhit the wallâ when their foundation is insufficient to move onto the next level. And I even see graduates whoâve majored in math who canât do the STEP entrance exam questions that a strong 18 year old is taught to tackle in the UK.
So my objection would not be to stopping acceleration, but to not replacing that with a choice of enriched math courses that teach the same material at a deeper level. Thatâs what happens in English, you donât accelerate (since everyone does 4 years of English in high school) but instead choose the honors/AP track or the regular track. It could just as easily happen in math. But without that, the wealthier parents will take their kids off to AOPS and leave the rest without any option to get that enrichment in their public schools.
A long time ago, placement occurred by natural ability, because kids were allowed to move ahead to the next class once theyâd mastered the material. It was called skipping. NYC many years ago had a semester system starting as early as kindergarten. When the child had mastered the material in one level, they were simply moved up a half-year, until they reached high school. In this way, most bright kids finished high school at age 16. My mother was skipped this way so many times that she began high school at age 11, and was graduated at age 14. Iâm not saying that this was a good thing. Socially, it was a tremendous strain on the kids. But having a group of kids with similar math ability move ahead in one subject, as a group, while staying in the same grade, was the perfect solution. Virginia has just essentially said that theyâre going to deny their brightest kids math education. How is a teacher supposed to âdifferentiateâ a math lesson, to teach simultaneously the kid who isnât doing two digit addition, and the kid who is ready for decimals, percentages, fractions, and all the levels in between?
Yes, if youâre teaching an entire grade level of kids but supposed to be tailoring the curriculum to each kids abilities, what do the tests look like? Does everyone get a dumbed down version of the test so all can do well? Are there multiple versions of the test? Is different homework assigned to each individual student? What is taught at the front of the class everyday?
Blockquote So my objection would not be to stopping acceleration, but to not replacing that with a choice of enriched math courses that teach the same material at a deeper level.
Our current patchwork of math teacher training does not produce enough teachers with this level of depth. A lot of future math teachers attend our regional university. The ones who can teach at this level - not that many to begin with - find jobs at the top school districts in NJ, or leave for positions in industry. NJ , like CT and NY, is notorious for its micro-level, highly segregated school districts, where property values (aka wealth) dictate the K-12 public school experience.
None of this structural basis for inequity is going away with âdetrackingâ. In our school district, a small group of kids are tracked from 3rd grade. My DS2 benefited from this, but DS1 was not on that track. He was actually in a non-honors âadvancedâ track. Nevertheless, being in a âgoodâ school district, DS1 still was well prepared for his CS major in college. For me, the inequity in math prep is something I see everyday - from what my kids have to what my students have. To say it is jarring is an understatement. So I agree that there is some need for action - just not sure this is it.
âand nearly every child of a PTA parent was chosen for the advance classes.â
Sometimes this is because those parents are highly vested in the students academic life, both in and outside of school. Many parents are involved in schools PTAâs because they want to know about school programs and try their best to make the school the best environment for all learners.
To imply that these students only received their spots because of their parents is not based on facts.
Our district in IL is also âeliminatingâ accelerated math but if you look at the details, the path is still to calc in 12th grade and what they are really doing is eliminating the elementary age tracking. accelerated students more than one grade level ahead, still can take advanced math( our HS has an agreement with transportation to the local university.)
My D was tracked in third grade too. She was lucky to be advanced early, but we knew plenty of kids, mostly boys, that should have been moved up in middle school but because of staffing issues and classroom size constraints were not. IMO itâs nuts to be tracking kids at age 8. Seems to me that it make good sense to eliminate those barriers.
We really arenât âeliminatingâ accelerated math. We are removing barriers.
Are the elementary kids in your district all in the accelerated track? Or the regular track? Theyâll track them starting in 6th grade? How will the school figure out who ends up on the 12th grade calculus (or DE if higher math) track and who does not? What happens to the kid who would complete calculus by 10th or 11th grade? The one size fits all concept rarely works wellâŠitâs the same reason not all kids take all APs. Some take all they can, some donât take any, some mix and match class levels.
I donât know the solution, but agree that choosing kids for advance track in 3rd grade is not the answer. Here they test for âgiftedâ and there is no way that enough kids are testing high enough to have a class of 23 gifted kids at each elementary school.
Fast forward to HS and everyone is together in the same classes and these kids no longer need advanced curriculum?
I think that this is the area where this past year of online education shows its advantage.
The current In person education structure is too inflexible. In a country where the age of the last three presidents at inauguration have ranged from their 40s to 70s why on earth are we consigning kids academic potential at single digit ages? Thatâs nonsense.
Show me a 15 year old who is in the remedial math track but spends his free time fixing up cars with his dad and wants to study engineering at college. I say set him a Challenge. Give him access to the schools full set of math lectures through to pre-calc. Let him self study in the library during his normal scheduled math classes and say that he can contact a teacher at anytime if he needs to ask questions or requires explanations. Then give him all the required assessments. If he passes let him join the AP calculus class for his Junior year!
My understanding (from friends, neighbors, and reading the newspapers since my kid didnât go to school here and is in college) is that the regular track, where most kids are, gets them to 12th grade calc. Advanced track was MVC in 12th grade and that required tracking in elementary school and they are eliminating that pathâŠkind ofâŠbecause they are still allowing kids to test up at any point.
The big change is not locking kids into a track and being more flexible. My Dâs HS was like that. They did placement tests at the start of HS to determine which math track a student would start in. There were options of doubling up on math courses if a student wanted to jump a level, options of dual credit, etcâŠ
Again, my feeling is these changes are to avoid early tracking, not creating a one size fits all.
The standard math track in most places completes precalculus in 12th grade, while completing calculus in 12th grade is the +1 track. Donât believe it? Just look at the schedule plans at a state flagshipâs engineering majors. They start in calculus 1, based on the assumption of completion of precalculus (not calculus) in high school.
The idea of seeing the +1 track as ânot advancedâ seems to be a result of the parentally pushed math acceleration race. Remember that calculus in high school is considered an Advanced Placement subject.
That was my initial point. The curriculum here was already way advanced and âeliminatingâ accelerated is not accurate since the âregular trackâ is already advanced.
Thatâs why Iâm suggesting people look past the headlines and look at the curriculum details.
IMO, itâs media spin trying to create outrage about a non issue.
Hereâs the issue. It doesnât really matter that the median entering math, at for example Harvard, was completion of calculus. Most Harvard students will not be majoring in engineering or math or physics, so that is sufficient. For the 20% or so who are considering such a major, they may be surprised to find their classmates in frosh classes geared to such potential majors have already completed the class once. The top schools do ask their students to complete frosh level courses there ( albeit advanced versions), not rely upon prior course work. Can one catch up? Yes, but it is hard to do so.