Looking for help with AOPS planning for HS

[Guest MumofJ&K]

I'm trying to map out a 4 year plan for my son (14, entering 9th grade) so that he can complete Calculus in 12th grade.  He only started AOP Intro. to Algebra partly through 8th grade and has completed through Ch. 13.  He will not be taking any AOPS classes, but working through the books independently.

 

This leaves the rest of Intro. to Algebra, Intro to Geometry, Intermediate Algebra, Pre-Calculus, and Calculus.  (We are figuring on doing Intro. to Counting and Probability as an elective one year in addition to the primary math sequence.) Still seems like a lot to fit in!

 

I'm wondering how to strategically eliminate certain "extra" and/or "competition math" chapters from any of the above books so that he can get through this sequence and hit calculus by 12th grade.  Any suggestions you have would be very welcome!  Thanks!

 

[regentrude]

You could do Intermediate Algebra and Precalculus in one year, or you can start Geometry concurrently with the second half of Intro to Algebra.

 

Intermediate Algebra contains  material typically taught in precalculus, and precalculus contains some material often not taught at all in high school. In this thread

http://forums.welltrainedmind.com/topic/361425-aops-or-college-algebratrig/?do=findComment&comment=3742293

in post #5, Kathy is giving a possible outline for a precalculus course combining teh two books and omitting the topics not aligned with traditional precalculus.

Intermediate Algebra chapters 17-end contain topics mainly relevant for students interested in competitions. Precalculus covers more on 3-d vector and matrices than usually taught in high school.

 

 

[daijobu]

 

I'm trying to map out a 4 year plan for my son (14, entering 9th grade) so that he can complete Calculus in 12th grade.  

I'm wondering how to strategically eliminate certain "extra" and/or "competition math" chapters from any of the above books so that he can get through this sequence and hit calculus by 12th grade.  Any suggestions you have would be very welcome!  Thanks!

 

 

Are there Challenge Problems at the end of each chapter?  (PreAlgebra and Algebra texts have them.)  You will save time by skipping those.

 

But really, if you are aiming to skip the "competition math" aspect of AOPS, that's really all of AOPS.  Maybe you should use a different curriculum?

[Julie of KY]

I wouldn't call AoPS just for "compitition math". It's good math that draws lots of insightful problems from math competitions. Why spend lots of time designing new problems when the work has already been done?

 

As regentrude said, the last few chapters of int. algebra are geared toward competition math and are okay to be skipped according to the introduction.

[regentrude]

But really, if you are aiming to skip the "competition math" aspect of AOPS, that's really all of AOPS.  Maybe you should use a different curriculum?

 

I disagree. AoPS teaches the content of the standard high school math sequence and can serve as a great stand-alone math curriculum for a student who is really only interested in mastering the regular material. Such a student could omit certain chapters that contain material not typically taught in high school and not prerequisite for any further math courses the student will take. He will still benefit from using AoPS as his math curriculum, even if he has no interest in competition math. The critical thinking about math is something every student should develop, not just competition participants.

 

None of my children care at all about competition math. Our goal for them is to master and understand the math needed to be prepared to be successful as a science major at university.  AoPS serves this purpose perfectly.

[8filltheheart]

Are there Challenge Problems at the end of each chapter? (PreAlgebra and Algebra texts have them.) You will save time by skipping those.

 

But really, if you are aiming to skip the "competition math" aspect of AOPS, that's really all of AOPS. Maybe you should use a different curriculum?

I am posting from the perspective of not really understanding or even knowing **what** my ds studied in math from 8th grade on other than the names of the courses and AoPS course descriptions. It is all way beyond me.

 

However, I do know what I see. Ds is not interested in math competitions and the last time he participated in one was Math Counts in 8th grade. This is mainly bc his love is for theoretical physics. He really enjoys math, but it isn't where his heart is.

 

That said, AoPS has prepared him for college level math courses in ways traditional math texts simply don't. He understands the process behind what they are doing in the classroom that has his college professors talking to him in a way that shows they recognize something different about his mathematical abilities. He has made the highest grade in every college math class he has taken (and it distresses me, not him, that he has done so with essentially very little effort.......definitely concern on my part bc I do NOT believe all educations are equal, so I wonder just how adequately these classes are preparing him but have zero way of gauging.) He has math professors trying to convince him to major in math.

 

For ds part, he says that the topics he learned in AoPS alg 3, precal, and cal have all made portions of his upper level classes review or have provided such a strong foundation for the classes that learning the new material has been simple.

[daijobu]

I disagree. AoPS teaches the content of the standard high school math sequence and can serve as a great stand-alone math curriculum for a student who is really only interested in mastering the regular material. Such a student could omit certain chapters that contain material not typically taught in high school and not prerequisite for any further math courses the student will take. He will still benefit from using AoPS as his math curriculum, even if he has no interest in competition math. The critical thinking about math is something every student should develop, not just competition participants.

 

None of my children care at all about competition math. Our goal for them is to master and understand the math needed to be prepared to be successful as a science major at university.  AoPS serves this purpose perfectly.

 

We'll have to agree to disagree.  I don't have the higher level books, but in looking at my PreAlgebra book, I see that out of the 14 Review Problems (pp. 438-9) for Chapter 11, half are competition math problems.  That is, the cited sources are MathCounts, MOEMS, AMC, etc.  

 

The OP wanted to eliminate the competition math problems.  Actually, that would not be hard to do, since those problems are clearly labeled and easy to skip.  But why skip half of the problems?  And really, is there anything materially different between those problems labeled as originating from MathCounts, and those just made up by the author?  

[regentrude]

We'll have to agree to disagree.  I don't have the higher level books, but in looking at my PreAlgebra book, I see that out of the 14 Review Problems (pp. 438-9) for Chapter 11, half are competition math problems.  That is, the cited sources are MathCounts, MOEMS, AMC, etc.  

 

The OP wanted to eliminate the competition math problems.  Actually, that would not be hard to do, since those problems are clearly labeled and easy to skip.  But why skip half of the problems?  And really, is there anything materially different between those problems labeled as originating from MathCounts, and those just made up by the author?  

 

I have used all books of the main sequence through calculus.

Just because the problems originate from a math competition does not mean that the material they cover is not part of the traditional canon of high school material. The way I understand the OP, she did not want to eliminate competition math problems, but chapters that were content geared towards competitions and not required material for high school.

 

I believe that quite frequently the competition problems would have been given to students below the grade in which the material would have been taught sytematically. For example, a challenging competition problem for middle schoolers might be easy to solve for a student who has algebra tools, but a challenge for a student who had not. Many of the competition problems are problems that are well placed in their sections, maybe a bit more original, but by no means a lot harder than what the problems should be for mastery.

 

The material of the competition problems in not necessarily different from the problems designed by the author. It is very time consuming to create math problems, so it is only sensible that they have used previously constructed problems. But there are entire chapters in the later books that contain math topics not usually taught at all through the  first semesters of math at the university, but that will be used frequently in the high level competitions.

 

There are, of course, some of the challenge problems in each section that could be omitted. But  I would discourage anybody aiming to streamline math from simply eliminating all problems originating from competitions; this will greatly diminish the learning of the regular material.

[Guest MumofJ&K]

Thank you Regentrude and 8FillTheHeart for your thoughtful replies and threads.  I was actually hoping that one of you would reply since I've followed your input on AoPS for awhile now!  That's exactly what I was looking for - a feasible plan for covering the sequence through HS, by eliminating the non-essential chapters.  I'm not trying to eliminate "competition" problems from each chapter.  We have found AoPS an invaluable resource to advancing our son's problem solving abilities.  Yes, we would love to do it all, but time is the issue.  Thank you Kathy for sharing your plan for combining Inter. Algebra and Pre-Calc.

 

Another question... if there is only time to do Intro. to Number Theory or Intro. to Counting and Probability, which one did your children find more helpful to later math/computer studies?  Is one a lot more time consuming than the other?

[regentrude]

Another question... if there is only time to do Intro. to Number Theory or Intro. to Counting and Probability, which one did your children find more helpful to later math/computer studies?  Is one a lot more time consuming than the other?

 

Each of the textbooks can be covered in one semester.

My DS did probability because that was what he was interested in; my DD was not interested in either. The probability concepts are rather important in many fields, but do not really require such an extended coverage of discrete probability. Number theory would be useful for a student interested in cryptography and computer science.

I would let the student pick what appeals more to him.

 

[Kathy in Richmond]

Both number theory and counting/probability would be useful for future mathematicians and computer scientists, as regentrude said. If I had to choose one, though, I'd select number theory for a future mathematician and counting/prob for a future computer guy. Here's the syllabus for CS 6.042, a required "math for computer science majors" class at MIT (They take this class in addition to the usual calc, multivariable, linear algebra, and differential equations). You can see that a substantial part the class (the last 5 or so weeks) covers counting, prob, and statistics. The rest involves proof writing, sets & logic, graph theory, asymptotics & approximation theory, and one week of number theory.

[oscilatorium]

Both number theory and counting/probability would be useful for future mathematicians and computer scientists, as regentrude said. If I had to choose one, though, I'd select number theory for a future mathematician and counting/prob for a future computer guy. Here's the syllabus for CS 6.042, a required "math for computer science majors" class at MIT (They take this class in addition to the usual calc, multivariable, linear algebra, and differential equations). You can see that a substantial part the class (the last 5 or so weeks) covers counting, prob, and statistics. The rest involves proof writing, sets & logic, graph theory, asymptotics & approximation theory, and one week of number theory.

 

I agree, for computer science, the Counting/Probability material is extremely useful to learn as early as possible in order to have a leg up in today's challenging CS college curriculums. If they will go into CS, it's imperative they learn this stuff asap, because in my experience being able to 'count' properly (i.e. combinatorics) takes a couple of passes before it really registers in the brain, so doing this book at the earliest possible age will provide the greatest benefit later. To me counting, and probability to a lesser degree, seemed quite murky the first time I wrapped my head around them, and I felt I only really understood the concepts well, when I had seen them 2 or 3 times, unlike the standard algebra/geometry/calc stuff.

 

Number Theory is beautiful but not as applicable as the other book; definitely great for a math major, but in my opinion probably less important in terms of overall applicability. Wonderful stuff to know for high school competition math contests, though.