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Anonymous wrote:
pettifogger wrote:
Anonymous wrote:OP. We have been doing AOPS's Contest Math for Middle School (small paperback) after the intro series. It was a good book to practice, but DC is sick of it (we repeated the missed questions up to 4 times). Then, I randomly purchased from Amazon Learn or Review Trigonometry Essential Skills, but it is too easy.

DC is not math genius, and we are not that interested in pushing for the contest math direction. DC recently took AMC8 at school though.

I looked at the AOPS's Intermediate Algebra book, and it seems too difficult/unnecessary. Alcumus is recommended, and we will do, but I am looking for a next book to work on.

Is AOPS's precalculus book a bad idea (wondering this book may be easier than Intermediate Algebra?), or do you recommend just repeat Intro to Algebra book for a second round?



While starting to learn the beginning of AoPS Precalc would not be a bad idea, I would personally not recommend it until they have a very good grasp of algebra. Despite its smaller size, the precalc book has more difficult material than Intermediate algebra (for the most part). The book is very different from a typical K12 precalculus book. It essentially teaches three topics in great depth, connecting them all together: 1) Trigonometry in the first third of the book, 2) Complex Numbers in the second part of the book, and 3) Fundamentals of Linear algebra (vectors, matrices in both 2D and 3D) as well as a final chapter on solving tough geometry problems using vectors and other tools learned in the book. Some of the problems (not all) can be very difficult, and a few have appeared in past high school Olympiads such as the USAMO, etc.

I think the most important principle is that your DC should enjoy math (CMMS is a lovely little book, but I don't think it was a great idea to have made them repeat problems they missed 4 times, as that is not a recipe for enjoyment...) One way to do that is to solve lots of interesting problems at an untimed and relaxed pace. A few ways that could be done is by perusing the AoPS site and cherry picking problems that look interesting to them (i.e from the past AMC 8 or even AMC 10 questions) or perhaps via playing Alcumus (which itself contains a very large collection of problems, many from past contests).

Earlier in this thread I have recommended for you Anna Burago's Mathematical Circle Diaries. If your DC finished the Intro series, Year 2 (the second book in the two book series) would be more appropriate. It contains many interesting problems organized by various topics, that are excellently curated, similar to AoPS. It introduces students to some difficult ideas that most don't see until a discrete math course in college (i.e Pigeonhole Principle, Invariants, Parity, Combinatorics, Graph Theory, etc) via approachable problems aimed at advanced middle schoolers. Some of these topics are really very lovely, but sadly AoPS did not include them in their books (other than perhaps in their Intermediate Counting and Probability book, which is an amazing but challenging book, on par with their Precalculus or Calculus book).


hello, we interacted previously about DC but i couldn't find that thread. it's was about AOPS algebra 2, so it's relevant. DC is taking that class now and yesterday told me this is the best thing ever and they nowhere learned so much. when i wrote to you here several months ago i wasn't sure whether DC was ready and if they will be able to take advantage of the advanced content. DC was well behind in math (100% on all tests obviously but superficial knowledge) with little capacity to work on the same problem for extended amount of time. this class lit up the math fire in DC.

we had no idea how good it was, either. thank you.


No problem, glad to hear they are enjoying math and being challenged!
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Anonymous wrote:It’s very hard to compete with Asian kids on AMCs who have been prepping since elementary school.

How many hours a week do they prep? 10? 20?

If my kid likes math I don’t want to kill it with drilling for competitions.


Some prep that much. Others are just good. My kid maybe spends 3-5 hours per week on extracurricular math. He just received his AIME score and will almost certainly qualify for JMO as a 9th grader.


My 7th grader loves math and did AMC 8 last yr and this year for fun. He has no interest in enrichment outside of school but does enjoy taking the test to challenge himself. He scored both equal to, and better than, a number of friends who prep many hours a week. So I’d say he’s “competing” just fine, although he’s really just doing it for himself and not to do better than anyone else.


The funny part for my kid is that he backed away pretty significantly from contest prep and instead focused on a much deeper understanding of the math itself. He only did maybe 2 AIME mocks and no AMC 10 mocks. But, this is the year he got a 12 on AIME.


What does that look like? Courses? Books? Videos?

The focus of AIME prep is, of course, much deeper understanding of the math itself, as that is what the AIME tests.

Each year, fewer than about 50 people in the entire USA score 12+ by 10th grade, so strategies for doing so are not very generalizable across the wider population.

Yes, but many kids prep for AIME by just grinding AIME problems. This can be somewhat helpful, because MAA sometimes recycles problems or has problems that use the same trick, but the value is pretty limited.

My kid instead focused on more olympiad style proofs and understanding a bunch of theorems that appear in olympiad level problems. Geometry was a weakness, so he spent time with the Euclidean Geometry in Mathematical Olympiads book.

Makes sense, EGMO is a very legit book and might even be considered "the" one book to have for oly geo problems.

What's even more amazing to me, is that Evan wrote the book during his high school senior year.
Anonymous wrote:Algebra I part B aligns to which FCPS class?


The topics include the latter portions of Algebra I, as well as a good chunk of Algebra 2.
Anonymous wrote:It's not extra, it's the second half of Intro Algebra.

You can start synthetic Geometry (construction and similarity, not measurement and Pythagorean theorem) without Algebra B, but I wouldn't recommend doing all of Geometry before intro Algebra B.


pettifogger?


This is correct. For example, my son is currently taking their geometry class and he's only worked through about half of the Intro to Algebra book (corresponding to most of the Algebra A class online). He's doing perfectly fine in geometry, but he's taking it at the local aops academy, which does go slower than the online version (36 classes at 1.75 hrs per class). By comparison, the online text based Aops course covers the whole geometry book in just 24 weeks/classes at 1.5 hrs per class each week.. a blistering pace in my opinion.

While you can start geometry without covering Algebra B (the 2nd half of the Intro to Algebra book), the geometry material is significantly more challenging and requires more mathematical maturity to really pick up the concepts. As such, I would recommend to take a cautious approach if wanting to do this and the child only has experience with the first half of algebra book (i.e everything up to about chapter 10, the start of quadratics). While it is true that they wouldn't be seeing much, if any, of quadratics and this more advanced algebra material in geometry (at least not until around halfway or later in the course, during the analytic geometry portions), the geometry material itself is quite deep. It covers things such as proofs, tight logical reasoning, creative use of adding new objects such as segments to diagrams, and using variables to angle/length chase, etc. These tools and many others are introduced pretty quickly in the geometry course, so ability to follow and develop logical reasoning is critical to understanding the concepts. I would suggest that kids have some other math experiences, to compensate for the lack of a full blown Aops algebra course, such as math contests, or maybe having worked through one of their other Intro books (Intro to Counting and Probability, or Intro to Number Theory). If they don't have this type of experience or similar, and are just coming in with some algebra, then I would not recommend taking the online text based version as it would be very, very, challenging. Better options would be either virtual aops academy, a local aops academy, or just working through the book at their own pace at home. These would all be less stressful and more manageable, although Aops geometry will still be significantly more challenging than any of the other Intro Aops books.

And a side note, since online placement tests came up in the thread: Their pre test is pretty much the bare minimum needed to place in a course, while their post test questions are much more involved. The post test questions would typically show mastery of the material in a class. While I haven't looked, I am pretty sure that you'll find for example their Prealgebra post test to be more difficult than their Algebra pre test.
First of all, why would you believe that kids should be able to understand any textbook 'cover to cover', nevermind this particular AoPS book?

To your questions:

- Yes, the Precalculus book is challenging and tries to go deeper into trigonometry than in a standard precalc book. That isn't necessarily a bad thing; one can take it as an opportunity to write down questions and try to resolve them by asking teachers/peers, or looking things up online and/or from other books.. basically an opportunity to learn how to learn.

- You cannot compare the Schaums series with a textbook, especially the AoPS precalc book. The Schaums series are meant for review of concepts for those who have already seen most of the material before. They're not meant to be used as first time teaching tools.

- The AoPS precalc book could be useful for some aspects of math contests, particularly ones that may contain trigonometry concepts. But that is not even remotely close to its main goal, which is to do a deep dive into 3 main topics and connect them together: trigonometry, complex numbers, and linear algebra basics (i.e vectors in 2D and 3D).

If your main goal is to have your child understand standard precalcus material (such as from the school AP precalcus course you mentioned), the AoPS book could be good for certain topics, such as the first few chapters on trigonometry. But that's likely to be a more difficult experience, due to the depth, as well as specific focus on the 3 topics I mentioned above, which may not quite match the typical precalculus curriculum found in schools.

If on the other hand, your goal is to have your child develop a deep understanding of important precalculus topics and how they are connected to each other, as well as to develop problem solving skills in the process (and even perhaps try out some problems that are either similar to, or actual from some past math contests), then the AoPS precalc book is a good choice. However, it is one of their more difficult books, so the bar is pretty high. If your child does not have any previous experience with other AoPS material, starting with the precalc book could initially feel like a very frustrating experience.
Anonymous wrote:Thank you very much. I was once quite good at math competitions, I knew a few tricks, and I was surprised I hit the wall so quickly. I was going through this with my child - he was doing the problems and I helped him when he got stuck. Until I got stuck myself. So my worry now is that he won't be able to handle AoPS class. School math is easy for him; we tried RSM this summer and it is very repetitive and a lot of kids struggle even with that. So he clearly needs something more challenging. I know RSM has more challenging classes but it sounds like it will take some time to qualify for those and he already lost a lot of time. Thus AoPS.

I think he will be ok with AoPS provided he has a couple of hours per week to work on the concepts he learns by reading the book/practicing problems. I assume he's taking the geometry class, which is significantly more challenging than the other introductory AoPS courses. However, it does start from the very beginning and does not assume anything more advanced than some algebra (i.e Pythagorean theorem, radicals, and a bit of quadratics/factoring but not too much). AoPS is also much higher ceiling as it is focused on developing deeper problem solving skills; this means there is lots of wiggle room where an 'A' could mean just being able to solve around 60-70% of the material. For some students this is great, as the focus is not on minimizing silly mistakes and being "perfect" on one/two step problems, but rather focusing on the higher order thinking needed to solve more difficult problems.

I believe that as an engineer you'll quickly find the AoPS type of thinking very closely related to what you're used to in the real world. One of the main goals of AoPS courses is to teach students to take basic tools and use them effectively to solve many problems in a variety of ways. So rather than introducing a whole bunch of tricks/formulas for various types of problems, AoPS prefers to focus on a smaller set of ideas/principles and show how to apply them to a wide variety of problems. In this way students develop flexibility and creative approaches to problems, to the point where eventually they become comfortable with working on problems they don't (initially) know how to solve. In my opinion, this approach is super valuable because it's very transferable to many other areas in STEM and also beyond.
Anonymous wrote:Thank you. I wanted to enroll my child in AoPS but Alcumus got me worried.


I wouldn't worry much about it. As others above said, it's a great resource with a huge range of difficulty on the problems. But most importantly, in your child's case (and yours as well), it's actually more efficient to work systematically through the AoPS geometry book. After that, many of the geometry Alcumus problems become quite doable. It's not a surprise that you are hitting a wall relatively quickly but that is only because you are attacking them cold without having a math contest background and/or training. As you get used to the various types of techniques and ideas, they become quite manageable. Again, I'd highly recommend working through the book first, as it's really fantastic. Alcumus works best when you are already somewhat familiar with the topic, so you could then use it as a source of extra problems.
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Why did you take Math 3 this year after already taking Precalculus last summer?



I thought my child wouldn't be able to handle geometry over the summer, so I didn't sign him up. But he quickly learned geometry over the school year during 8th grade, and learned algebra 2 in the second semester of 8th grade year.

I'm not sure why I didn't sign him up for summer algebra 2 but I didn't, and instead enrolled him in AOPS precalculus during the summer after 8th grade.

AoPS precalculus is not as rigorous as TJ math 4 & 5. Without TJ math 4&5 or tj calc ab, taking on Tj calc bc may be challenging

On what basis do you make this claim? I have worked through a large number of problems from the AoPS precalculus book. Many are very difficult, drawing from AIME and other past contests. A select few are from USAMO and/or other olympiads.


AoPS has hard problems, but they focus on pure math puzzle problems, not engineering applications. You miss a lot if you only do AoPS.

A word problem by definition is an application of mathematical concepts. As long as it highlights the how the math is used, it doesn't matter whether it's about engineering, horses, or flying sheep. I will also dispute your claim about missing a lot. It's far more likely that the opposite is true, where there are many ideas found in AoPS which are not taught in the school classes.


AoPS doesn't have many word problems, and the ones that are are silly window dressing. Most of AoPS is abstract expressions and equations.

AoPS is aimed at students on a pure math track. It comes from a contest math pedigree of tricky puzzles and proofs.
TJ and school math in general is aimed at a more general/broad engineering track.
I've seen very high caliber AoPS students struggle with the sort of engineering type problems (modelling a real world situation mathematically like building a roof for a house) that schools emphasize.

It's a different focus.

Also, AoPS teaches about set theory, where you can learn that it's possible for for two different things to both be missing a lot from each other

I will again dispute your concept of word problems. You seem to be myopically focused on a very stringent definition of a word problem as having to do with "real world application". Speaking of set theory, I will relax your restrictive definition and define a word problem as anything that is an application of mathematical concepts. So yes, your "building a roof for a house" type of problems qualify, but are just a small subset of word problems. It's very important to understand that math is not just about engineering, modeling, or finding a "real world application". It can be about anything as long as it involves applying and connecting mathematical ideas and patterns.

As for your two statements "most of AoPS is abstract expressions and equations" and "AoPS is aimed at students on a pure math track. It comes from a contest math pedigree of tricky puzzles and proofs" -- The first one is meaningless because all math (and even languages) are abstract expressions and equations, which says nothing. The second is completely contradictory because contest problems and pure math are about as different as Earth is from Pluto. Sure, students who enjoy AoPS would likely do very well as pure math majors, but that doesn't mean that is the goal.

Incidentally, the goal of AoPS is to introduce and develop deep problem solving skills in kids, so that they can succeed in whatever path they choose to pursue in college and later in life, no matter how difficult; not to prepare students for a pure math track. Math was chosen as a the mental playground for that because there are many beautiful problems that can immediately expose kids to a rich variety of problem solving techniques. Don't believe me? Here's the transcript of a 2009 speech RR gave at Math Prize for Girls event, where he describes the value of problem solving. At the end he jokingly says that he would have chosen Swahili if it was the best way to teach how to solve problems one has never seen before, but he happened to choose math because he thought it was the best way to teach problem solving. This should be required reading for everyone on this forum:

https://mathprize.atfoundation.org/experience/past-events/2009/Rusczyk_Problem_Solving_Presentation_at_Math_Prize_for_Girls_2009.pdf
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Anonymous wrote:Kids are doing this everywhere at their base school. Heaven help you if your TJ Kid can't handle it.


Thanks for the advice. That’s encouraging. At TJ though kids are strongly counseled not to do this normally so I’m not sure if there are differences in how the classes are taught there that make it harder to do concurrently.


TJ BC is brutal. Far far beyond the AP exam and base school class. Same for Physics C. Only recommended for the truly gifted to take simultaneously junior year. Plenty of TJ kids with Cs in these classes who breezed through pre calc. Not just this year but every year. Proceed with caution.


Why do they torture kids like this?
Blair has a Magnet Analysis class that goes beyond Calc BC, so they give it a different name.

TJ calculus or any TJ math appears overwhelming because it's compared to base school math, where homework is kept very light and lot of time is spent on first few units, whereas last units, usually the advanced topics, are rushed through in final weeks or skipped altogether. At TJ, they keep consistent pace no matter what covering all units, and never hold back on homework or test rigor, even if half of class were to get a C.


But some teachers do curve routinely.


Not in Calc. They don’t curve even if average is a D. Which happens.

Thankfully they dont curve in advanced classes, else TJ would be no different from base school. However there is curving and grade inflation in beginner courses and we all know why.

Are you trying to make a coherent point here, or just spouting white noise? Not sure whether you realize that some of the hardest math/science courses at top colleges are very often curved (sometimes significantly), and the curve varies for each exam.

Curving is a tool that teachers use when they realize that an exam was more difficult than the performance they expected from their students.

The base schools in FCPS have provided us with ample firsthand experience of curving and inflated grades. Given TJ's reputation, one would anticipate the maintenance of high, strict standards, which is fortunately observed in the advanced courses. Hats off to those TJ Calc BC and Physics C teachers. However, the same cannot be said of TJ's beginner courses, as you also indirectly acknowledge through the justification of curving as a commonly employed tool. We expect stricter standards, even for beginner courses, at TJ. But alas!

You're spouting a bunch of claims that hinge on "curving is bad because it is used at base schools, therefore it is always bad, even at tj". If you were to do your research before making illogical claims, you will find that curving is widely used in many schools, specifically at places such as MIT, Caltech, and many, many, others. Does that mean those courses do not have high, strict standards? Does that mean that a course that doesn't curve (of which there are very many in base schools, where an 'A' is always 93% or above) is automatically rigorous? And conversely, one where the class average might be 50% (such as the AMT elective at TJ) might be lax and watered down?

Most TJ students, (even ones in the "beginner courses" that you are disparaging without any proof of your "lack of rigor" claim) could easily tell you that you've concluded nothing, from your highly fallacious argument.

If you wish to actually succeed in making the claims you seem to really want to make, you'll have to actually provide proof that a) grades are actually curved in beginner courses, and not curved in advanced courses, and b) that the material is more watered down in beginner courses, and more rigorous in advanced courses. You are completely speculating until you have information on these things.


Have you attended MIT? How can you claim that MIT curves as a standard practice? In fact, neither MIT nor any other reputable educational institution commonly employs curving. While there may be exceptional circumstances that justify curving, such as if the entire class scores below a C, indicating an issue with the instruction or evaluation, it should not be used when only a few students have mastered the material with an A and the rest have lower grades. If TJ were to adopt curving practices like other schools with competing interests besides academic excellence, it would tarnish its reputation for adhering to strict standards.


You are completely missing the main point. You keep pointing to the arbitrary grading criteria of K12 education of 93% A, 80% B.. and assuming it holds everywhere. It's does not, far from it. I have had courses where an 80% or even 75% and above was considered an A, and this was explicitly stated in the syllabus without any kind of curving.

So again, I'll emphasize that you don't understand the principle that curving is based on, which is the fact that exams can be highly variant in difficulty, with many factors to consider, such as major subject, specific topic at hand, specific teacher, specific cohort of students, etc. You can't just simply make the claim that curving is bad, and thus a system that curves is automatically not rigorous. That is a false claim.

The beginner math courses at TJ consist of the typical FCPS middle school geometry courses, which do not involve much variability or factors to consider. Therefore, grading on a curve should not apply unless there is an intention to inflate the lower grades even for these basic courses.

How do you know that the beginner math courses at TJ are typical FCPS middle school geometry courses? Again, without data this is pure speculation. I can give a test that covers the exact same specific set of geometry topics students have just learned, but will yield an average that is < 50% vs a more normal 80%. Simply by selecting harder problems.

Unless you've taken a specific test with a specific set of problems, you can't just make the claim that an A is only 93% and above. It completely depends.

Personally I believe that curving (as someone else upthread described) is a good thing because it not only allows students a chance to be tested on harder material without huge repercussions, it also gives very strong students a chance to really shine by scoring multiple SDs above the curve. Effectively, we're letting students pick what they can solve out of a selection of challenging material, vs watering down the exam content to the point where everyone has to cross their t's and dot their i's or they don't get an A. This by the way happens all the time in base schools content, including APs, where the A is simply gained by following specific procedure down to the method of how one shows their work and mimics like a monkey. E.g if they don't always rationalize the denominator, they lose points, which is extremely silly.

By the way, if you're complaining so much about curving, you should be aware that many teachers at TJ give extra credit to students all the time. Students often have a chance to do other things and gain points to offset some of the bad portions of their grade. Again, one can't just claim that this is not rigorous; it completely depends on context.

How do you know?

It's documented on the realtalk tj site, there's a teacher guide written by various students.
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pettifogger wrote:
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Anonymous wrote:Kids are doing this everywhere at their base school. Heaven help you if your TJ Kid can't handle it.


Thanks for the advice. That’s encouraging. At TJ though kids are strongly counseled not to do this normally so I’m not sure if there are differences in how the classes are taught there that make it harder to do concurrently.


TJ BC is brutal. Far far beyond the AP exam and base school class. Same for Physics C. Only recommended for the truly gifted to take simultaneously junior year. Plenty of TJ kids with Cs in these classes who breezed through pre calc. Not just this year but every year. Proceed with caution.


Why do they torture kids like this?
Blair has a Magnet Analysis class that goes beyond Calc BC, so they give it a different name.

TJ calculus or any TJ math appears overwhelming because it's compared to base school math, where homework is kept very light and lot of time is spent on first few units, whereas last units, usually the advanced topics, are rushed through in final weeks or skipped altogether. At TJ, they keep consistent pace no matter what covering all units, and never hold back on homework or test rigor, even if half of class were to get a C.


But some teachers do curve routinely.


Not in Calc. They don’t curve even if average is a D. Which happens.

Thankfully they dont curve in advanced classes, else TJ would be no different from base school. However there is curving and grade inflation in beginner courses and we all know why.

Are you trying to make a coherent point here, or just spouting white noise? Not sure whether you realize that some of the hardest math/science courses at top colleges are very often curved (sometimes significantly), and the curve varies for each exam.

Curving is a tool that teachers use when they realize that an exam was more difficult than the performance they expected from their students.

The base schools in FCPS have provided us with ample firsthand experience of curving and inflated grades. Given TJ's reputation, one would anticipate the maintenance of high, strict standards, which is fortunately observed in the advanced courses. Hats off to those TJ Calc BC and Physics C teachers. However, the same cannot be said of TJ's beginner courses, as you also indirectly acknowledge through the justification of curving as a commonly employed tool. We expect stricter standards, even for beginner courses, at TJ. But alas!

You're spouting a bunch of claims that hinge on "curving is bad because it is used at base schools, therefore it is always bad, even at tj". If you were to do your research before making illogical claims, you will find that curving is widely used in many schools, specifically at places such as MIT, Caltech, and many, many, others. Does that mean those courses do not have high, strict standards? Does that mean that a course that doesn't curve (of which there are very many in base schools, where an 'A' is always 93% or above) is automatically rigorous? And conversely, one where the class average might be 50% (such as the AMT elective at TJ) might be lax and watered down?

Most TJ students, (even ones in the "beginner courses" that you are disparaging without any proof of your "lack of rigor" claim) could easily tell you that you've concluded nothing, from your highly fallacious argument.

If you wish to actually succeed in making the claims you seem to really want to make, you'll have to actually provide proof that a) grades are actually curved in beginner courses, and not curved in advanced courses, and b) that the material is more watered down in beginner courses, and more rigorous in advanced courses. You are completely speculating until you have information on these things.


Have you attended MIT? How can you claim that MIT curves as a standard practice? In fact, neither MIT nor any other reputable educational institution commonly employs curving. While there may be exceptional circumstances that justify curving, such as if the entire class scores below a C, indicating an issue with the instruction or evaluation, it should not be used when only a few students have mastered the material with an A and the rest have lower grades. If TJ were to adopt curving practices like other schools with competing interests besides academic excellence, it would tarnish its reputation for adhering to strict standards.


You are completely missing the main point. You keep pointing to the arbitrary grading criteria of K12 education of 93% A, 80% B.. and assuming it holds everywhere. It's does not, far from it. I have had courses where an 80% or even 75% and above was considered an A, and this was explicitly stated in the syllabus without any kind of curving.

So again, I'll emphasize that you don't understand the principle that curving is based on, which is the fact that exams can be highly variant in difficulty, with many factors to consider, such as major subject, specific topic at hand, specific teacher, specific cohort of students, etc. You can't just simply make the claim that curving is bad, and thus a system that curves is automatically not rigorous. That is a false claim.

The beginner math courses at TJ consist of the typical FCPS middle school geometry courses, which do not involve much variability or factors to consider. Therefore, grading on a curve should not apply unless there is an intention to inflate the lower grades even for these basic courses.

How do you know that the beginner math courses at TJ are typical FCPS middle school geometry courses? Again, without data this is pure speculation. I can give a test that covers the exact same specific set of geometry topics students have just learned, but will yield an average that is < 50% vs a more normal 80%. Simply by selecting harder problems.

Unless you've taken a specific test with a specific set of problems, you can't just make the claim that an A is only 93% and above. It completely depends.

Personally I believe that curving (as someone else upthread described) is a good thing because it not only allows students a chance to be tested on harder material without huge repercussions, it also gives very strong students a chance to really shine by scoring multiple SDs above the curve. Effectively, we're letting students pick what they can solve out of a selection of challenging material, vs watering down the exam content to the point where everyone has to cross their t's and dot their i's or they don't get an A. This by the way happens all the time in base schools content, including APs, where the A is simply gained by following specific procedure down to the method of how one shows their work and mimics like a monkey. E.g if they don't always rationalize the denominator, they lose points, which is extremely silly.

By the way, if you're complaining so much about curving, you should be aware that many teachers at TJ give extra credit to students all the time. Students often have a chance to do other things and gain points to offset some of the bad portions of their grade. Again, one can't just claim that this is not rigorous; it completely depends on context.
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Anonymous wrote:Kids are doing this everywhere at their base school. Heaven help you if your TJ Kid can't handle it.


Thanks for the advice. That’s encouraging. At TJ though kids are strongly counseled not to do this normally so I’m not sure if there are differences in how the classes are taught there that make it harder to do concurrently.


TJ BC is brutal. Far far beyond the AP exam and base school class. Same for Physics C. Only recommended for the truly gifted to take simultaneously junior year. Plenty of TJ kids with Cs in these classes who breezed through pre calc. Not just this year but every year. Proceed with caution.


Why do they torture kids like this?
Blair has a Magnet Analysis class that goes beyond Calc BC, so they give it a different name.

TJ calculus or any TJ math appears overwhelming because it's compared to base school math, where homework is kept very light and lot of time is spent on first few units, whereas last units, usually the advanced topics, are rushed through in final weeks or skipped altogether. At TJ, they keep consistent pace no matter what covering all units, and never hold back on homework or test rigor, even if half of class were to get a C.


But some teachers do curve routinely.


Not in Calc. They don’t curve even if average is a D. Which happens.

Thankfully they dont curve in advanced classes, else TJ would be no different from base school. However there is curving and grade inflation in beginner courses and we all know why.

Are you trying to make a coherent point here, or just spouting white noise? Not sure whether you realize that some of the hardest math/science courses at top colleges are very often curved (sometimes significantly), and the curve varies for each exam.

Curving is a tool that teachers use when they realize that an exam was more difficult than the performance they expected from their students.

The base schools in FCPS have provided us with ample firsthand experience of curving and inflated grades. Given TJ's reputation, one would anticipate the maintenance of high, strict standards, which is fortunately observed in the advanced courses. Hats off to those TJ Calc BC and Physics C teachers. However, the same cannot be said of TJ's beginner courses, as you also indirectly acknowledge through the justification of curving as a commonly employed tool. We expect stricter standards, even for beginner courses, at TJ. But alas!

You're spouting a bunch of claims that hinge on "curving is bad because it is used at base schools, therefore it is always bad, even at tj". If you were to do your research before making illogical claims, you will find that curving is widely used in many schools, specifically at places such as MIT, Caltech, and many, many, others. Does that mean those courses do not have high, strict standards? Does that mean that a course that doesn't curve (of which there are very many in base schools, where an 'A' is always 93% or above) is automatically rigorous? And conversely, one where the class average might be 50% (such as the AMT elective at TJ) might be lax and watered down?

Most TJ students, (even ones in the "beginner courses" that you are disparaging without any proof of your "lack of rigor" claim) could easily tell you that you've concluded nothing, from your highly fallacious argument.

If you wish to actually succeed in making the claims you seem to really want to make, you'll have to actually provide proof that a) grades are actually curved in beginner courses, and not curved in advanced courses, and b) that the material is more watered down in beginner courses, and more rigorous in advanced courses. You are completely speculating until you have information on these things.


You're just saying this because 50% is an A on AoPS

Hah no, it's more of I'm fondly thinking back to some devilishly hard college exams where I could get away with an A at 65%
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pettifogger wrote:
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Anonymous wrote:Kids are doing this everywhere at their base school. Heaven help you if your TJ Kid can't handle it.


Thanks for the advice. That’s encouraging. At TJ though kids are strongly counseled not to do this normally so I’m not sure if there are differences in how the classes are taught there that make it harder to do concurrently.


TJ BC is brutal. Far far beyond the AP exam and base school class. Same for Physics C. Only recommended for the truly gifted to take simultaneously junior year. Plenty of TJ kids with Cs in these classes who breezed through pre calc. Not just this year but every year. Proceed with caution.


Why do they torture kids like this?
Blair has a Magnet Analysis class that goes beyond Calc BC, so they give it a different name.

TJ calculus or any TJ math appears overwhelming because it's compared to base school math, where homework is kept very light and lot of time is spent on first few units, whereas last units, usually the advanced topics, are rushed through in final weeks or skipped altogether. At TJ, they keep consistent pace no matter what covering all units, and never hold back on homework or test rigor, even if half of class were to get a C.


But some teachers do curve routinely.


Not in Calc. They don’t curve even if average is a D. Which happens.

Thankfully they dont curve in advanced classes, else TJ would be no different from base school. However there is curving and grade inflation in beginner courses and we all know why.

Are you trying to make a coherent point here, or just spouting white noise? Not sure whether you realize that some of the hardest math/science courses at top colleges are very often curved (sometimes significantly), and the curve varies for each exam.

Curving is a tool that teachers use when they realize that an exam was more difficult than the performance they expected from their students.

The base schools in FCPS have provided us with ample firsthand experience of curving and inflated grades. Given TJ's reputation, one would anticipate the maintenance of high, strict standards, which is fortunately observed in the advanced courses. Hats off to those TJ Calc BC and Physics C teachers. However, the same cannot be said of TJ's beginner courses, as you also indirectly acknowledge through the justification of curving as a commonly employed tool. We expect stricter standards, even for beginner courses, at TJ. But alas!

You're spouting a bunch of claims that hinge on "curving is bad because it is used at base schools, therefore it is always bad, even at tj". If you were to do your research before making illogical claims, you will find that curving is widely used in many schools, specifically at places such as MIT, Caltech, and many, many, others. Does that mean those courses do not have high, strict standards? Does that mean that a course that doesn't curve (of which there are very many in base schools, where an 'A' is always 93% or above) is automatically rigorous? And conversely, one where the class average might be 50% (such as the AMT elective at TJ) might be lax and watered down?

Most TJ students, (even ones in the "beginner courses" that you are disparaging without any proof of your "lack of rigor" claim) could easily tell you that you've concluded nothing, from your highly fallacious argument.

If you wish to actually succeed in making the claims you seem to really want to make, you'll have to actually provide proof that a) grades are actually curved in beginner courses, and not curved in advanced courses, and b) that the material is more watered down in beginner courses, and more rigorous in advanced courses. You are completely speculating until you have information on these things.


Have you attended MIT? How can you claim that MIT curves as a standard practice? In fact, neither MIT nor any other reputable educational institution commonly employs curving. While there may be exceptional circumstances that justify curving, such as if the entire class scores below a C, indicating an issue with the instruction or evaluation, it should not be used when only a few students have mastered the material with an A and the rest have lower grades. If TJ were to adopt curving practices like other schools with competing interests besides academic excellence, it would tarnish its reputation for adhering to strict standards.


You are completely missing the main point. You keep pointing to the arbitrary grading criteria of K12 education of 93% A, 80% B.. and assuming it holds everywhere. It's does not, far from it. I have had courses where an 80% or even 75% and above was considered an A, and this was explicitly stated in the syllabus without any kind of curving.

So again, I'll emphasize that you don't understand the principle that curving is based on, which is the fact that exams can be highly variant in difficulty, with many factors to consider, such as major subject, specific topic at hand, specific teacher, specific cohort of students, etc. You can't just simply make the claim that curving is bad, and thus a system that curves is automatically not rigorous. That is a false claim.
Anonymous wrote:
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Anonymous wrote:
Anonymous wrote:Kids are doing this everywhere at their base school. Heaven help you if your TJ Kid can't handle it.


Thanks for the advice. That’s encouraging. At TJ though kids are strongly counseled not to do this normally so I’m not sure if there are differences in how the classes are taught there that make it harder to do concurrently.


TJ BC is brutal. Far far beyond the AP exam and base school class. Same for Physics C. Only recommended for the truly gifted to take simultaneously junior year. Plenty of TJ kids with Cs in these classes who breezed through pre calc. Not just this year but every year. Proceed with caution.


Why do they torture kids like this?
Blair has a Magnet Analysis class that goes beyond Calc BC, so they give it a different name.

TJ calculus or any TJ math appears overwhelming because it's compared to base school math, where homework is kept very light and lot of time is spent on first few units, whereas last units, usually the advanced topics, are rushed through in final weeks or skipped altogether. At TJ, they keep consistent pace no matter what covering all units, and never hold back on homework or test rigor, even if half of class were to get a C.


But some teachers do curve routinely.


Not in Calc. They don’t curve even if average is a D. Which happens.

Thankfully they dont curve in advanced classes, else TJ would be no different from base school. However there is curving and grade inflation in beginner courses and we all know why.

Are you trying to make a coherent point here, or just spouting white noise? Not sure whether you realize that some of the hardest math/science courses at top colleges are very often curved (sometimes significantly), and the curve varies for each exam.

Curving is a tool that teachers use when they realize that an exam was more difficult than the performance they expected from their students.

The base schools in FCPS have provided us with ample firsthand experience of curving and inflated grades. Given TJ's reputation, one would anticipate the maintenance of high, strict standards, which is fortunately observed in the advanced courses. Hats off to those TJ Calc BC and Physics C teachers. However, the same cannot be said of TJ's beginner courses, as you also indirectly acknowledge through the justification of curving as a commonly employed tool. We expect stricter standards, even for beginner courses, at TJ. But alas!

You're spouting a bunch of claims that hinge on "curving is bad because it is used at base schools, therefore it is always bad, even at tj". If you were to do your research before making illogical claims, you will find that curving is widely used in many schools, specifically at places such as MIT, Caltech, and many, many, others. Does that mean those courses do not have high, strict standards? Does that mean that a course that doesn't curve (of which there are very many in base schools, where an 'A' is always 93% or above) is automatically rigorous? And conversely, one where the class average might be 50% (such as the AMT elective at TJ) might be lax and watered down?

Most TJ students, (even ones in the "beginner courses" that you are disparaging without any proof of your "lack of rigor" claim) could easily tell you that you've concluded nothing, from your highly fallacious argument.

If you wish to actually succeed in making the claims you seem to really want to make, you'll have to actually provide proof that a) grades are actually curved in beginner courses, and not curved in advanced courses, and b) that the material is more watered down in beginner courses, and more rigorous in advanced courses. You are completely speculating until you have information on these things.
Anonymous wrote:If you want a more "normal" path through the books:

Intermediate algebra textbook:

Ch 1 - 4: review
Ch 5 - 6: all

Ch 7.1 - 7.5
Ch 9.1 - 9.2

Ch 10.1 - 10.5

Ch 11.3 -11.4

Ch 13.1 -13.3, 13.5-6

Ch 14.1

Ch 15.1 - 15.3

Ch 16.1 - 16.3



Precalculus textbook:
Ch 1 - 2

Ch 3.1 - 3.4

Ch 4 - 7

Ch 9 - 11


- I'd very strongly recommend 12.1 - 12.3 (first half of chapter) in Intermediate Algebra -- this is very important and fundamental material on inequalities.
- (Also, it's hard not to recommend Vieta's formulas in 8.3 as they're just too beautiful)
- Chp 12 in Precalc is pretty fundamental 3D material that builds on all the work done in the prior vector chapters... very useful later in calculus and physics (and it's usually good to see it more than once as it's not easy to learn it well the first time one is exposed to it).
Anonymous wrote:
pettifogger wrote:
Anonymous wrote:It's true thay AOPS Intermediate Algebra has a lot of more abstract math (like factoring and solving polynomials, conic sections, and functional equations), that isn't relevant to the STE part of STEM.

If you aren't focused on math for math's sake, you can skip a lot of the AOPS material and problems, and stick with Khan and Brilliant type stuff which focuses more on the math for engineering and technology.


Polynomials are not relevant in science and engineering?? I beg to differ.


"Polynomials" are covered in Intro Algebra. Professionals use calculators and computers for numerical methods, not Vieta's Formulas and rational roots.

Your comment is quite misleading. Polynomials were barely touched upon in the Intro book; there were only two sections of very basic material. The core and heart of polynomials, namely polynomial division, polynomial roots, including the Fundamental Theorem of Algebra, is all covered in the Intermediate Algebra book. In fact, a big portion of this material is standard K12 school material, required in an algebra 2 or precalculus class and is critical to STEM. This material is of course also found in Khan and any other algebra textbook or algebra course (though taught much more procedurally, and/or by rote). Where I do agree with you is that yes, in addition to what I just described, The AoPS Intermediate Algebra textbook goes way beyond a typical Algebra 2 course, even delving into high level math contest topics with chapters on advanced inequalities and functional equations.

The Intro to Algebra book, while very good, does not come close to covering all the algebra students need to be successful in STEM, that's why it is an intro course. While it may be ok to take a school based Precalculus course after taking the AoPS Intro series books, (largely because many algebraic topics are sometimes taught in a K12 typical precalc class), I would not recommend directly going into AoPS Precalculus just from the Intro Series.
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