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AoPS vs. Lial Algebra/ Jacobs Geometry


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I have a ds who is really good with math and getting bored... I used Lial Introductory Algebra this year and am planning to use Jacob's Geometry next year. I just encountered AoPS--sounds like it may be good for him, but I wanted some input on that program. How is it different from Lial and Jacob's?

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Hi! I know there are going to be many people that are going to chime in after me that know lots more than I do, but here's our experience.

 

According to my eldest daughter (who has taken Algebra I, Algebra II, Number Theory, and Geometry through the AoPS online classes and self studied using the Counting and Probability books), AoPS makes you think about the "why" of problem solving, not just the "how." They delve deeply into the theory behind the algorithms of problem solving, and also present a variety of problem types for each topic... some get rather challenging.

 

Dd loves this approach --- and she has had fantastic teachers and teachers' assistants at AoPS. (Insert shout out here to Lady Knight --- I'm sure her mom will be by to describe AoPS much more skillfully than this...) It has been terrific for us as a family because my daughter very much wishes to go into math and/or science, and I am of little help in this area - having dropped math after 11th grade and made a run for the safety of the band room. Dd and I are hoping she can take every available class at AoPS before it is time for her to head off to college. Algebra III starts at the end of May and she can't wait to do math all summer. (That's not a joke! :) )

 

HTH!

Edited by Jen in NY
:o) self editing vocabulary
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Hi! I know there are going to be many people that are going to chime in after me that know lots more than I do, but here's our experience.

 

According to my eldest daughter (who has taken Algebra I, Algebra II, Number Theory, and Geometry through the AoPS online classes and self studied using the Counting and Probability books), AoPS makes you think about the "why" of problem solving, not just the "how." They delve deeply into the theory behind the algorithms of problem solving, and also present a variety of problem types for each topic... some get rather challenging.

 

Dd loves this approach --- and she has had fantastic teachers and teachers' assistants at AoPS. (Insert shout out here to Lady Knight --- I'm sure her mom will be by to describe AoPS much more skillfully than this...) It has been fantastic for us as a family because my daughter very much wishes to go into math and/or science, and I am of little help in this area

 

HTH!

 

:iagree: My ds has taken alg 3, counting/probability, pre-cal, computer programming, and has worked through parts of their volumes on his own. He absolutely LOVES them and highly recommends them. He spends hours exploring math topics

 

My one caveat is that it is more of a discovery learning type approach vs. direct teaching. My 6th grade dd that is pretty good in math (only a yr behind where her 9th grade brother was at this age) does not "think" like him and I am not sure AoPS will be a good fit. She is working with me right now in the alg 1 book and most of it is review. Even so, as we discuss what is in the book, I can tell she wants them to flesh out and explain more instead of pondering her way through where they are attempting to lead her. I guess I won't really be able to tell until she reaches something she doesn't already know whether or not the frustration I sense now will increase or decrease.

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:iagree: My ds has taken alg 3, counting/probability, pre-cal, computer programming, and has worked through parts of their volumes on his own. He absolutely LOVES them and highly recommends them. He spends hours exploring math topics

 

My one caveat is that it is more of a discovery learning type approach vs. direct teaching. My 6th grade dd that is pretty good in math (only a yr behind where her 9th grade brother was at this age) does not "think" like him and I am not sure AoPS will be a good fit. She is working with me right now in the alg 1 book and most of it is review. Even so, as we discuss what is in the book, I can tell she wants them to flesh out and explain more instead of pondering her way through where they are attempting to lead her. I guess I won't really be able to tell until she reaches something she doesn't already know whether or not the frustration I sense now will increase or decrease.

 

I think I am just following you around on the math threads. In your opinion, if a child responds well to the type of instruction in Foerster, will AofPS be too "loosey goosey." While everything I have read about AofPS is very positive, my knees tremble and my hands shake when I see "discovery learning type math." That is the type of math touted in elementary and middle school in my neck of the woods and my older kids have to yet recover from it. Not only do they not have the "why" but they don't have the "how." It is why I started homeschooling in the first place.

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Hi Lisa,

 

I understand your trepidation. It's really not loosey goosey in that way at all... all the solutions are extremely well written and technical. There's no "new math" in there as far as I can tell. The discovery part is that the student is presented with a problem and given the opportunity to use former knowledge/intuition/esp ;) to solve it first --- then a detailed solution is presented immediately. Most of the axioms and "rules" are presented through worked examples and engaging text, and then highlighted in a text box marked "important!" --- so the essential points are hard to miss.

 

Also, there are no "answers" in the solution manual without an explanation, which is helpful for me, because I am not that strong in math yet. (Dd is helping me along, though.) :001_smile:

 

Here's what my daughter has done. (Some kids don't feel the need to do all the problems in the books, but she does just about all of them.) She attends the interactive class "lecture" when she can, but many times she has dance during the class time. If she misses she reads the transcripts because they are informative and funny. She reads the text, and does the worked examples. There is then a series of exercises with solutions in the separate teacher's manual, so it's not so easy to give in and take a peek. She does those, and checks her own work. If she misses any she reads the solution, sees where her error was, and tries again the next day. She posts answers to the weekly questions in the forum for whatever class she is taking at the time.

 

There is really only one situation where the kids are answering questions that they do not have solutions for: the challenge sets. These are 10-15 questions assigned every couple of weeks by the teacher, and returned in a private message to the teacher. Notes with detailed comments on the student's work come back within a week or so.

 

There are other aspects of the AoPS website that both of my daughters use... there is a neverending math quiz (sounds deadly but it's fun --- I do it too!) that keeps track of your progress and sends you problems of increasing difficulty called Alcumus, there are forums where people discuss any number of math problems, theories, and other fun stuff (that I don't have a prayer of understanding but my daughter likes....), etc., etc. Dd#2 is beginning with her first class at AoPS this summer, and I wish we had started sooner.

 

I am not advocating AoPS for everyone. The classes move quickly for some... there are people I know that have tried the AoPS books and just not liked them. But for a kid like my daughter, who likes to know the "why" of everything, and also likes to have very challenging work in math and science, it has been a perfect fit. I can't emphasize enough the depth of understanding she has gained as a result of using AoPS.

 

If you do sign up for a class and find it's not a good fit, you can drop it before the third class for a full refund.

 

HTH!

Edited by Jen in NY
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I think I am just following you around on the math threads. In your opinion, if a child responds well to the type of instruction in Foerster, will AofPS be too "loosey goosey." While everything I have read about AofPS is very positive, my knees tremble and my hands shake when I see "discovery learning type math." That is the type of math touted in elementary and middle school in my neck of the woods and my older kids have to yet recover from it. Not only do they not have the "why" but they don't have the "how." It is why I started homeschooling in the first place.

 

I agree with Jenn that it isn't anything like Everyday Math. :tongue_smilie:

 

I was talking to Kathy in Richmond yesterday about Foerster and I think her assessment is probably the easiest way to explain it. She said that Foerster gives lots of details and she personally does not learn that way. She likes to be given the big picture and fill in the details on her own.

 

My ds that thinks mathematically sees patterns which he likes to then dissect in order to find their relationships. He "fills in the details on his own." Quoting him, "Not only do they expect you to develop the little points through guided practice, they expect you to assimilate the information to see the big picture in order to allow you to truly understand the concepts that you are learning."

 

I do NOT think that way with math. I need to be taught the details in order to completely understand the big picture. Once I understand what I am being taught, I can think things over and make the connections in order to "own it." I am watching my dd and I know she does not think like my ds (only my oldest ds (so far) seems to think the same way he does). I do not know for sure how she will end up doing with AoPS, but I am very cognizant of their different thought processes and I have a gut feeling that she is going to want (and perhaps need) the details.

 

AoPS is absolutely fantastic and I am so thrilled for my ds that he finally has something to use that appreciates how he processes math. I just know that not all people think that way. (I am pretty sure that my 11th grader would have floundered in math if she were expected to learn math the way AoPS teaches.)

 

Does that help?

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Jen and 8FilltheHeart have done a super job of explaining the nuts and bolts of AoPS.

 

Don't worry, Lisa, it's *nothing* at all like the reform math texts that are frustrating so many in the school systems. Richard even says that the discovery method doesn't necessarily have to be used with his books. The teacher could just present the material in each section and let the kids go at the problem sets. But then I think you'd lose something of what's special about AoPS. It's perfect for those kids who *want* to be left alone to try out their ideas and intuition before the teacher steps in and explains everything. And the texts and classes do get to those explanations and all the technicalities! The solution manuals are absolutely wonderful and helpful to homeschool families where there might not be a math-experienced teacher to look over the kids' work.

 

Overall, AoPS worked very well for us with independent, motivated, math-loving students. We did use Jacobs for algebra and geometry (2nd edition) when my kids were young and AoPS intro courses weren't yet available. They were fine, too. AoPS reaches into more topics and the problems go to a (much) higher level of challenge. But I don't regret using Jacobs at all. It worked well with young ones who weren't quite ready to jump into the depths of AoPS yet. And AoPS makes a fine follow-up to a more basic algebra or geometry course.

 

About the online community and courses: the online classes move fast, but my kids adored them. You'll get the added benefit of a private online discussion board for the corresponding class, weekly problems posted on that board, "classroom" space online that the kids are encouraged to use for collaboration, and graded problem sets.

 

The kids online in both the classes and the forums are some of the nicest, friendliest, most motivated students we've met. My daughter actually made so many friends through AoPS that by high school they formed a traveling math team together to go to some of the math tournaments on the East coast.:001_smile: Both kids were AoPS TA's and graders & my dd (Lady Knight - gotta love how the name she made up in seventh grade sticks) still works for them in college. When she's doing her grading at home, I can see that she often spends over an hour reading and grading one individual problem set with detailed comments. She loves it.

 

ETA: 8FilltheHeart and I posted at the same time & again she nailed it. You'd think I could remember what I said yesterday but it's too early, and I haven't had my caffeine yet :tongue_smilie:

Edited by Kathy in Richmond
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