Anonymous
06/01/2023 17:52
Subject: Re:Algebra I, geometry, algebra 2
no prep ever if your kid struggles drop down a course
enough with the math arms race. It's pathetic
enough with the math arms race. It's pathetic
Anonymous
06/01/2023 17:06
Subject: Algebra I, geometry, algebra 2
Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student (e.g., no complex numbers in Algebra 1, no linear programming). Fourth, school math is much less fun.
In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.
Is this a joke? Why would there be complex numbers in Algebra I? You sound nutty.
When covering math at a level appropriate for mathematically gifted students you introduce complex numbers before the quadratic formula. For instance, AoPS's textbook does so in Chapter 12.
Complex numbers have never been part of Algebra I. If you want to pay money to have someone teach your DC ahead, fine, but it's not "abridged" or "appropriate".
You have to realize the division between algebra 1 and 2 is somewhat arbitrary, although it’s true that national curriculums like common core omit complex numbers in elementary algebra.
On the other hand elementary algebra textbooks for college are better structured and start with numbers (including complex) and arithmetic, then move to equations and then systems.
Most good students can handle complex numbers when doing quadratic equations and I thinks it’s even recommended to do so, since it’s a more complete treatment of the topic.
Also, some people choose enrichment to go deeper, broader and different then the worksheets kids do at school.
College algebra has a prerequisites of a high school diploma or GED, and/or remedial Algebra class. A high school diploma has a prequisite of....Algebra 1.
GED includes solving quadratics but not imaginary/complex numbers/roots.
Anonymous
06/01/2023 15:48
Subject: Algebra I, geometry, algebra 2
Anonymous wrote:Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student (e.g., no complex numbers in Algebra 1, no linear programming). Fourth, school math is much less fun.
In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.
+1. This is a really thoughtful comment. Teaching to the class average is built in, that’s not necessarily wrong because this is the role of the public school, but it should be pretty obvious that the extremes of the mathematical skills distribution won’t benefit much. For a top 1% student you simply need to find alternate forms of instruction , not to prepare for the regular school class, but just to cover what is not taught. But that’s probably true for any subject.
Anonymous
06/01/2023 15:35
Subject: Algebra I, geometry, algebra 2
Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:On the other hand elementary algebra textbooks for college are better structured and start with numbers (including complex) and arithmetic, then move to equations and then systems.Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student (e.g., no complex numbers in Algebra 1, no linear programming). Fourth, school math is much less fun.
In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.
Is this a joke? Why would there be complex numbers in Algebra I? You sound nutty.
When covering math at a level appropriate for mathematically gifted students you introduce complex numbers before the quadratic formula. For instance, AoPS's textbook does so in Chapter 12.
Complex numbers have never been part of Algebra I. If you want to pay money to have someone teach your DC ahead, fine, but it's not "abridged" or "appropriate".
Can you name one such book?
Stewart, College Algebra
Openstax, College Algebra
All college algebra books, I’m not aware of a single one that doesn’t use complex numbers in the treatment of quadratics.
The division between algebra, geometry and pre calculus is also quite arbitrary, with many areas of overlap. Of course arithmetic, equations and systems belong in algebra, shapes, angles, lines belong to geometry, and vectors and matrices traditionally taught in precalculus. But functions are thought in both algebra and precalculus, analytical geometry are taught in algebra, geometry and precalculus, etc. trigonometry is another one that can be taught alone, or almost any high school math class.
I found it somewhat amusing when posters decree that complex number are taught in Algebra 2. What exactly is Algebra 2? Then why are they taught again in precalculus. There’s an apt analogy that math is a spiral, it’s up to the individual how fast one goes around and the breath and depth of the material studied.
I don't remember if it was algebra 2 or algebra 1, but matrices came up in at least algebra 2, with Cramer's rule and determinants.
Agreed, precalculus is a collection of topics borrowed from other areas. Still it shows how blurred the demarcation between these classes really is.
Anonymous
06/01/2023 15:14
Subject: Algebra I, geometry, algebra 2
Anonymous wrote:Anonymous wrote:Anonymous wrote:On the other hand elementary algebra textbooks for college are better structured and start with numbers (including complex) and arithmetic, then move to equations and then systems.Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student (e.g., no complex numbers in Algebra 1, no linear programming). Fourth, school math is much less fun.
In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.
Is this a joke? Why would there be complex numbers in Algebra I? You sound nutty.
When covering math at a level appropriate for mathematically gifted students you introduce complex numbers before the quadratic formula. For instance, AoPS's textbook does so in Chapter 12.
Complex numbers have never been part of Algebra I. If you want to pay money to have someone teach your DC ahead, fine, but it's not "abridged" or "appropriate".
Can you name one such book?
Stewart, College Algebra
Openstax, College Algebra
All college algebra books, I’m not aware of a single one that doesn’t use complex numbers in the treatment of quadratics.
The division between algebra, geometry and pre calculus is also quite arbitrary, with many areas of overlap. Of course arithmetic, equations and systems belong in algebra, shapes, angles, lines belong to geometry, and vectors and matrices traditionally taught in precalculus. But functions are thought in both algebra and precalculus, analytical geometry are taught in algebra, geometry and precalculus, etc. trigonometry is another one that can be taught alone, or almost any high school math class.
I found it somewhat amusing when posters decree that complex number are taught in Algebra 2. What exactly is Algebra 2? Then why are they taught again in precalculus. There’s an apt analogy that math is a spiral, it’s up to the individual how fast one goes around and the breath and depth of the material studied.
I don't remember if it was algebra 2 or algebra 1, but matrices came up in at least algebra 2, with Cramer's rule and determinants.
Anonymous
06/01/2023 15:02
Subject: Algebra I, geometry, algebra 2
Anonymous wrote:Anonymous wrote:On the other hand elementary algebra textbooks for college are better structured and start with numbers (including complex) and arithmetic, then move to equations and then systems.Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student (e.g., no complex numbers in Algebra 1, no linear programming). Fourth, school math is much less fun.
In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.
Is this a joke? Why would there be complex numbers in Algebra I? You sound nutty.
When covering math at a level appropriate for mathematically gifted students you introduce complex numbers before the quadratic formula. For instance, AoPS's textbook does so in Chapter 12.
Complex numbers have never been part of Algebra I. If you want to pay money to have someone teach your DC ahead, fine, but it's not "abridged" or "appropriate".
Can you name one such book?
Stewart, College Algebra
Openstax, College Algebra
All college algebra books, I’m not aware of a single one that doesn’t use complex numbers in the treatment of quadratics.
The division between algebra, geometry and pre calculus is also quite arbitrary, with many areas of overlap. Of course arithmetic, equations and systems belong in algebra, shapes, angles, lines belong to geometry, and vectors and matrices traditionally taught in precalculus. But functions are thought in both algebra and precalculus, analytical geometry are taught in algebra, geometry and precalculus, etc. trigonometry is another one that can be taught alone, or almost any high school math class.
I found it somewhat amusing when posters decree that complex number are taught in Algebra 2. What exactly is Algebra 2? Then why are they taught again in precalculus. There’s an apt analogy that math is a spiral, it’s up to the individual how fast one goes around and the breath and depth of the material studied.
Anonymous
06/01/2023 12:20
Subject: Algebra I, geometry, algebra 2
Anonymous wrote:On the other hand elementary algebra textbooks for college are better structured and start with numbers (including complex) and arithmetic, then move to equations and then systems.Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student (e.g., no complex numbers in Algebra 1, no linear programming). Fourth, school math is much less fun.
In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.
Is this a joke? Why would there be complex numbers in Algebra I? You sound nutty.
When covering math at a level appropriate for mathematically gifted students you introduce complex numbers before the quadratic formula. For instance, AoPS's textbook does so in Chapter 12.
Complex numbers have never been part of Algebra I. If you want to pay money to have someone teach your DC ahead, fine, but it's not "abridged" or "appropriate".
Can you name one such book?
Anonymous
05/31/2023 22:29
Subject: Algebra I, geometry, algebra 2
Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student (e.g., no complex numbers in Algebra 1, no linear programming). Fourth, school math is much less fun.
In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.
Is this a joke? Why would there be complex numbers in Algebra I? You sound nutty.
When covering math at a level appropriate for mathematically gifted students you introduce complex numbers before the quadratic formula. For instance, AoPS's textbook does so in Chapter 12.
Complex numbers have never been part of Algebra I. If you want to pay money to have someone teach your DC ahead, fine, but it's not "abridged" or "appropriate".
You have to realize the division between algebra 1 and 2 is somewhat arbitrary, although it’s true that national curriculums like common core omit complex numbers in elementary algebra.
On the other hand elementary algebra textbooks for college are better structured and start with numbers (including complex) and arithmetic, then move to equations and then systems.
Most good students can handle complex numbers when doing quadratic equations and I thinks it’s even recommended to do so, since it’s a more complete treatment of the topic.
Also, some people choose enrichment to go deeper, broader and different then the worksheets kids do at school.
Anonymous
05/31/2023 08:12
Subject: Algebra I, geometry, algebra 2
My kid is now finishing Honors Algebra 2 in 9th grade (all As this year) and we never did any outside work. She says it is her favorite class, so she does like math.
Anonymous
05/31/2023 08:09
Subject: Algebra I, geometry, algebra 2
Anonymous wrote:Anonymous wrote:Anonymous wrote:Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student (e.g., no complex numbers in Algebra 1, no linear programming). Fourth, school math is much less fun.
In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.
Is this a joke? Why would there be complex numbers in Algebra I? You sound nutty.
When covering math at a level appropriate for mathematically gifted students you introduce complex numbers before the quadratic formula. For instance, AoPS's textbook does so in Chapter 12.
I remember covering this with DC in 4th or 5th grade shortly before quadratics.
pettifogger
05/30/2023 23:27
Subject: Algebra I, geometry, algebra 2
Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student (e.g., no complex numbers in Algebra 1, no linear programming). Fourth, school math is much less fun.
In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.
Is this a joke? Why would there be complex numbers in Algebra I? You sound nutty.
When covering math at a level appropriate for mathematically gifted students you introduce complex numbers before the quadratic formula. For instance, AoPS's textbook does so in Chapter 12.
That's not The Correct Way handed down from God.
Chapter 10 is factoring, which has the same problem (some problems don't have solutions) that the quadratic formula has (chapter 13), until i is introduced.
i is very much a teaser in AoPS Algebra 1. Algebra 2 reintroduces i and covers it in a lot more detail.
I know
Still, one of the last writing problems in Algebra 1 was factoring z^4+1=0 using elementary means. Which I thought was really cool.
do you mean z^4 - 1 = 0? That can be factored using alg1 and introduces imaginary numbers. z^4 + 1 is much harder to factor.
Nope, I meant z^4+1=0. (Now that I think about it, it was actually z^4 + 4 = 0, which gives nice integer solutions.) Don't use the polar form, though. Set z=a+bi and see where this gets you.
Setting z = a+bi will work, but it's a quite lengthy to work through the algebra (expanding by binomial theorem, forming two separate equations and solving each of the cases). Much simpler is to rewrite the expression as the square of a binomial by completing the square, i.e:
z^4 + 4 = (z^2 + 2)^2 - 4z^2
Now apply difference of squares to turn the above into a product of two quadratics. The four roots are easily extracted with the quadratic formula, two for each of the quadratics. (Bonus for students who have studied polar/exponential form of complex numbers: Plot the roots of z^4 + 4 in the complex plane, and also plot the roots of z^4 - 4... what interesting observation can you make? Can you explain how they are related to each other and exactly why this is the case?)
Anonymous
05/30/2023 20:35
Subject: Algebra I, geometry, algebra 2
Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student (e.g., no complex numbers in Algebra 1, no linear programming). Fourth, school math is much less fun.
In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.
Is this a joke? Why would there be complex numbers in Algebra I? You sound nutty.
When covering math at a level appropriate for mathematically gifted students you introduce complex numbers before the quadratic formula. For instance, AoPS's textbook does so in Chapter 12.
That's not The Correct Way handed down from God.
Chapter 10 is factoring, which has the same problem (some problems don't have solutions) that the quadratic formula has (chapter 13), until i is introduced.
i is very much a teaser in AoPS Algebra 1. Algebra 2 reintroduces i and covers it in a lot more detail.
I know
Still, one of the last writing problems in Algebra 1 was factoring z^4+1=0 using elementary means. Which I thought was really cool.
do you mean z^4 - 1 = 0? That can be factored using alg1 and introduces imaginary numbers. z^4 + 1 is much harder to factor.
Complex numbers were first used to solve cubics. If they show up in the quadratic formula, then there is no real solution. However, in the cubic formula, you can get complex numbers in the formula while having a real solution.
Anonymous
05/30/2023 19:16
Subject: Algebra I, geometry, algebra 2
Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student (e.g., no complex numbers in Algebra 1, no linear programming). Fourth, school math is much less fun.
In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.
Is this a joke? Why would there be complex numbers in Algebra I? You sound nutty.
When covering math at a level appropriate for mathematically gifted students you introduce complex numbers before the quadratic formula. For instance, AoPS's textbook does so in Chapter 12.
That's not The Correct Way handed down from God.
Chapter 10 is factoring, which has the same problem (some problems don't have solutions) that the quadratic formula has (chapter 13), until i is introduced.
i is very much a teaser in AoPS Algebra 1. Algebra 2 reintroduces i and covers it in a lot more detail.
I know
Still, one of the last writing problems in Algebra 1 was factoring z^4+1=0 using elementary means. Which I thought was really cool.
do you mean z^4 - 1 = 0? That can be factored using alg1 and introduces imaginary numbers. z^4 + 1 is much harder to factor.
Nope, I meant z^4+1=0. (Now that I think about it, it was actually z^4 + 4 = 0, which gives nice integer solutions.) Don't use the polar form, though. Set z=a+bi and see where this gets you.
Anonymous
05/30/2023 18:37
Subject: Algebra I, geometry, algebra 2
Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Anonymous wrote:Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student (e.g., no complex numbers in Algebra 1, no linear programming). Fourth, school math is much less fun.
In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.
Is this a joke? Why would there be complex numbers in Algebra I? You sound nutty.
When covering math at a level appropriate for mathematically gifted students you introduce complex numbers before the quadratic formula. For instance, AoPS's textbook does so in Chapter 12.
That's not The Correct Way handed down from God.
Chapter 10 is factoring, which has the same problem (some problems don't have solutions) that the quadratic formula has (chapter 13), until i is introduced.
i is very much a teaser in AoPS Algebra 1. Algebra 2 reintroduces i and covers it in a lot more detail.
I know
Still, one of the last writing problems in Algebra 1 was factoring z^4+1=0 using elementary means. Which I thought was really cool.
do you mean z^4 - 1 = 0? That can be factored using alg1 and introduces imaginary numbers. z^4 + 1 is much harder to factor.
Anonymous
05/30/2023 14:27
Subject: Algebra I, geometry, algebra 2
The have an account on Khan Academy, that's all they need