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Kimberleigh

Art of Problem Solving Math

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MIchelle asked in another thread about the Art of Problem Solving. My daughter's been using the books and online classes for a year now, and they've turned math from her least favorite subject to her favorite. She even wound up joining a local math circle and competing on the homeschooling MathCounts team (which came in first place in the region and 4th place in the state -- good representation of what homeschoolers can do!).

 

The Art of Problem Solving books are intended for kids who want a challenge. The problems are multi-step and very involved. Rather than baby steps, the books offer challenging problems up-front, then talk you through the solutions. The Introduction to Algebra book, for example, uses negative exponents and equations with fractions right from the start. Once you figure out how they work, it's just as easy to solve an algebra problem using negative exponents as one using positive exponents.

 

My daughter's also taken a couple of the AoPS online classes. They're done in chatroom fashion and cover a couple chapters' worth of material each week. There are additional problem sets posted on the related forum and others that are meant to be worked offline. My daughter likes the online classes because even though they cover the same material as the books, they keep her moving at a faster pace than she'd probably set otherwise and the instructors provide additional tips and problem-solving strategies.

 

Disclaimer: I have no affiliation with AoPS. I'm just a satisfied mom.

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My daughter did about 1/2 of the online course. We took a long vacation and missed a couple of weeks, and then it was hard to get back to it. She got kind of emotional when I wanted her to return to it, so I let it go. She was also doing a Dolciani course (U. of Missouri ) for HS credit at the same time. I think the two were kind of too much. I was surprised because I thought the course was designed as a supplement, but we had a hard time getting into the rythym of the class. One problem is that on our time she was always doing swimming during the class time, so she really couldn't attend the class. (for west coast, its kind of during the after school hours) At first it seemed too easy, but then the challenge problems seemed too hard! My daughter liked Dolciani better, but she did say she wanted to finish the AOP book after she's done with Dolciani. (I think AOP grows on you- it was just so new I didn't know what to think) I love the solutions manual---its excellent. I was hoping she might get interested in a contest--but our state has strict rules that homeschoolers must be academically linked throughout the year, not just for the contests; and there aren't enough in our local center in her grade to make a team. Then if you want to hook up with a school, it can only be your home school by geography. (it doesn't appear ours fields a math team, so I guess that's out too) It kind of seems like they point the kids to a contest--except how do you do it if you aren't on a team. I think I asked and they said, "homeschoolers have teams" except not in our area they don't. And you're not allowed to join a team unless you are in "school with them"

 

I also have the number theory book and I like that. I just don't know what is a good age where you're not pushing too much.

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Rebecca, my daughter completed the Introduction to Algebra book, but didn't take the online class for it. She's taken the Number Theory and MathCounts classes online and is thinking about doing Geometry online this fall. She might also take an AMC class because she came pretty close to qualifying for AIMEs last year and wants to make it this year.

 

The Intro to Algebra book was very thorough. I've never looked at Foerster or Dolciani, so I can't compare, but in comparing the AoPs book to Lial's and Saxon, the AoPS book seemed to cover a lot of material that isn't introduced until Algebra II in the others.

 

She's also used the Counting & Probability and Art of Problem Solving: The Basics, and both of those were also very good. She's hoping to move quickly through Geometry this year and tackle some of the Intermediate books in the spring before moving on to trig and calc.

 

Nancy, I think it's a matter of interest and learning style more than age. My kids are twins, but one is more creative and the other more logical. One is better at making connections in literary analysis and history while the other is stronger at finding the patterns of math and science -- and each needs more assistance with the opposite. One will push to go beyond even her own expectations while the other wants a guiding hand.

 

Sorry to hear your daughter can't find a MathCounts team. We certainly lucked out in location, which was unexpected when we moved here less than two years ago. Our group meets from October through April, and you can participate in the weekly warm-up sessions even if you don't compete. My son got a lot out of the group even as a non-competitor. It was also a great social outlet for both kids, as they met other academically-minded homeschoolers with common interests.

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Ds. took the Number Theory class last spring. He found it very challenging initially but loved it in the end. He recommends the textbook but not the online class. This particular class had approx. 30 students and probably that made it hard to allow sufficient time for interaction with the teacher. He said he understood most of it from reading the text. For us, this was a supplementary course to Foerster's Algebra I. These are meant to be supplementary courses. I am told that there are not enough exercises to ensure mastery.

HTH!

Nissi

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My ds also took the Number Theory course last spring, and enjoyed it, but wished he had more time (or at least *I* wished he had more time) to do more of the problem sets and really get all the learning out of it. I am hoping we can do the AMC course in the fall, but we may have time zone difficulties in the new place we're moving too... Oh well! But still, it is a great program, and really helpful.

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Sounds like a lot of our kids were in the same class. My daughter took the Number Theory class last spring, as well.

 

One thing my daughter likes about the online class is that it pushes her to respond quickly. She's good at the math, but she's very methodical and takes her time, which puts her at a disadvantage in competitions (and when trying to manage her course workload). She'll often answer every question she attempts correctly, but doesn't make it all the way through a test. Taking the online classes is helping her quite a bit in this area.

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I love AoPS, too! My older son did the Intro to Geometry book in 10th grade - this is a very complete course. I would be in total awe of anyone who thought this was just supplemental, unless someone really just "hits the high spots." My younger son, going into 9th grade, will use Life of Fred Adv Alg along with parts of AoPS algebra (intro and Intermediate) for Algebra 2 this year. These are great texts for stretching your thinking!

Another satisfied mom,

April

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Are these books (I'm thinking particularly of Number Theory and Probability) written to the student? How involved did you have to be?

 

Ds(16) liked the probability chapter in Foerster's Alg II better than all the others. Do you think he would like Intro to Counting and Probability?

 

Do you see Art of Problem Solving:The Basics as a prerequisite or do the other texts stand alone?

 

Did dc enjoy them as much without the on-line class?

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Thanks for the information about the Geometry-- I think 10th grade sounds like a good year for that. The T of C for the Geometry looks like it would give you an extremely solid geometry foundation. My daughter did say she liked the text.(Algebra 1) There's a few problems along with tips and warnings all throughout, so it seems "reader friendly" . The number of problems in each chapter is fairly small, so then you go on to the next chapter. The problems are interesting but only if you understand it because the book keeps moving.(she liked that) The latter part of the book is beyond most Alg. 1, I would say, and that's OK because the kids get a little taste of other skills. I would say the book with solution manual is a good value- I don't know what to think about adding the online course. I wouldn't know how the kids enrolled in full time school could manage this in addition to a High school curriculum! Question for the people that actually sent in the assigned problems-- were they happy with the feedback, and did you end up with the completion certificate? I think once you try an online school that has audio, (like the Potters school) to have only the rolling text doesn't grab the kids as much. Anyone else have ideas? I will say that the online samples of the books are very complete if you are interested in them. The algebra 1 book is HUGE, actually. (the Number theory and Probability are smaller) I'd be interested in knowing if anyone has purchased the new Int. Algebra book. He said they will keep going and have more and more new ones until they get to calculus.

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