LoF and AoPS. Help me think this through.

[LisaKinVA]

I have both of these series. Now, I'm trying to figure out how to implement them in the coming couple of years.

 

Right now my son is working through Foerster's Algebra 1 at a rapid clip (about an 8 week intensive class). I am planning on more beginning Algebra, alongside Geometry for 2012-2013, and here is where I get stuck.

 

LoF would like you to have completed Beginning and Advanced Algebra before their Geometry course, but Beginning Algebra is all that is really "needed." I see nothing along those lines with AoPS Geometry, but AoPS Geometry doesn't really have all of the formal proofs (statements/reasons) that are found in LoF.

 

I know we are doing Algebra "to-death" -- but my son has been enjoying the class, and he enjoys Fred, and he enjoys AoPS (all for a bit different reasons), so unless he just gets bored to tears, I was thinking of doing LoF after we finish Foerster's, and following LoF Beginning Algebra with AoPS Introduction to Algebra, and starting Geometry after we finish LoF Beginning Algebra.

 

My question is... which do you think my son would find an "easier" or "more fun" Geometry course...LoF or AoPS? I'm leaning towards LoF -- especially since my son will be working through AoPS Introduction to Algebra along side it. I'm thinking the difference in approach will make it easier to juggle the two subjects simultaneously.

 

After AoPS Introduction to Algebra, I figured we could start LoF Advanced Algebra and finish up Fred Geometry and then work through AoPS Geometry alongside Fred.

 

Does this seem workable (at this point)? After Geometry, I'm figuring my son will do some of the other AoPS books (counting & probability, number theory type things).

 

Thoughts (mostly regarding the Algebra 1&2 and Geometry work). Thanks!

[mumto2]

No advice other than to tell you dd did LOF Geometry directly after ABeka algebra 1. I didn't research so my fault totally. I was just thinking algebra 1, geometry, algebra 2. Anyway that was what i brought back to the UK for her 2 years ago. She had never seen a LOF book before. The first week or so was hard but more from a how to use this course perspective. Just so you know she was completing the NEM sequence at the same time. I don't know if that was any sort of an advantage.

 

Both dc's have gone back and done all the lof books because they love them. Ds12 is doing adv algebra lof with counting and probability. He does really like AoPS too.

 

I hope this helps you decide!

[Spetzi]

We use some of the same math curricula!

 

I had ds use TT Geometry alongside Fred Geometry. He said it was hard to go from one style of proof to the other. (I never realized just how differently we could present proofs!) He completed the exercises in both, but only did the proofs in Fred.

 

I have not used AoPS geo, but I would imagine it would be quite different from Fred. I'm certain w/imagination it can work; just be flexible.

[regentrude]

LoF would like you to have completed Beginning and Advanced Algebra before their Geometry course, but Beginning Algebra is all that is really "needed." I see nothing along those lines with AoPS Geometry, but AoPS Geometry doesn't really have all of the formal proofs (statements/reasons) that are found in LoF.

 

 

:confused:

 

There are PLENTY of formal proofs in AoPS! They are just written out, as mathematicians would do, and not in the school format. In fac, many of the end of section exercises are proofs, and some are pretty tricky.

 

AoPS Geometry requires completion of Intro to Algebra which does cover much of a traditional algebra 2 program.

 

I know we are doing Algebra "to-death" -- but my son has been enjoying the class, and he enjoys Fred, and he enjoys AoPS (all for a bit different reasons), so unless he just gets bored to tears, I was thinking of doing LoF after we finish Foerster's, and following LoF Beginning Algebra with AoPS Introduction to Algebra, and starting Geometry after we finish LoF Beginning Algebra.

 

Why do you want to use AoPS after he has learned the material with a traditional program? The best aspect of AoPS is the discovery method, but this will fall flat because there won't be anything to discover.

 

If you do, be sure to plan plenty of time, since the AoPS Intro to Algebra is the longest of the AoPS texts, and many students take more than one school year to complete it (even if it is the only math program they do)

 

My question is... which do you think my son would find an "easier" or "more fun" Geometry course...LoF or AoPS?!

LoF is definitely easier; AoPS Geometry is very challenging. I can't tell you which he will find "more fun"; we did have a lot of fun with AoPS. It does already cover more than traditional geometry programs, and I would find adding a second program to be overkill.

Edited June 27, 2012 by regentrude

[boscopup]

There are PLENTY of formal proofs in AoPS!

 

I haven't seen the geometry yet, but yeah, I can't imagine there not being formal proofs in it. Going through the Prealgebra book, they're having the student prove every.little.thing. I have a hard time believing that would lessen in geometry. :D

[LisaKinVA]

I guess I didn't "see" the proofs, because they weren't arranged the way I'm used to seeing them. I did see theroms and postulates in little boxes...it was a cursory glance through the book ;)

 

As to why we don't use AoPS as "discovery" it's because my son does NOT like to struggle through concepts to discover them himself. If I tried to use AoPS with Algebra that way (in particular), he would probably throw the book across the room in utter frustration. After he has a grasp of the material, we use AoPS to present a different approach and much more challenging problems. I realize this is not the intended way to use the book -- but the way it's intended would *not work* with this young man.

 

We have found that there are still things he discovers, because the math is presented a bit differently, and because the challenge problems take things further than any other book he's used. Much like my friend's son who has completed Algebra 1 successfully, but can't do relatively simple, algebraic word problems (from ch. 4 of Foerster's). He's discovering how algebra actually works and is used vs. solving random equations. He has actually been surprised at how difficult he's finding the word problems, and is glad we're doing them.

 

Based upon what some of you are saying, it sounds like doing Fred Beginning Algebra and finishing up with AoPS Algebra (which will cover some of Algebra 2) will be good. and pair that with Fred Geometry and lead into Fred Advanced Algebra /Trigonometry, and AoPS Geometry...then probably AoPS Intermediate Algebra (timing on all of this will depend greatly on how my son gets through the material...I don't expect Algebra to take as much time, since he will have covered it once through Foerster's already...which will give him some familiarity). We're also going to start Alcumus, which should be another good thing for him to do.

 

Thanks, everyone!

[mathwonk]

I agree with others that AoPS has real proofs in it, but as you say in a different style from the "2 column" proofs in my high school geometry text. They are in the style a mathematician is used to. I might add I never learned anything from the ones in my high school book as they were sort of set up to memorize rather than understand. I have not seen LoF but I was impressed by the quality of writing in AoPS geometry.

 

Having said that, I want to support you LisaK in your awareness of your son's learning style and your conscious attempt to fit the material to him. Although not everyone agrees on this, I see no harm in relearning material from a more difficult or different point of view after seeing it before. I have myself relearned many subjects numerous times, and even last summer I learned some geometry from AoPS, more than 50 years after first taking the course.

 

Some people have believed (sometimes including me as a frustrated college teacher) that high school students are harmed by receiving shallow treatments of calculus in high school, and then being unmotivated to relearn it more deeply in college. I.e. they have already seen the "fun" parts, and see no reason to master the more difficult parts afterwards.

 

I agree that this poses a motivational challenge for the teacher but it does not have to be bad. Maybe it helps if one teaches the second course by focusing consciously on the aspects that were missing or "left hanging" in the first introduction. I think it is possible to make it interesting again the second time. You can say something like "previously we took this for granted, but how do we really know this is true?"

 

The key I think is what you are already aware of, the child should find it fun and interesting. If that is adhered to, the logical progression is perhaps less crucial, since the motivated child will likely be willing to go back and pick up needed elements in order to learn what he wants to learn now.

 

Just one observer's two cents - you are the ones currently on the "front lines".

Edited June 27, 2012 by mathwonk