Anyone do pre-geometry before geometry?

[Mukmuk]

Ds is on the last 2 chapters of Algebra I for AOPS. Since we started, we've had a few changes in how we handle the text. At first, I went through the problems for about 15mins before setting him on the rest of the problems and exercises. Then it evolved into him doing the chapter by himself. When he started having problems, I realized that leaving him alone with the text was not a great idea. So I started working alongside. This is good overall because I'm up to speed with what's going on, and I feel a great connection with my son. On top of it all, I, the mathphobe, have actually been coping well.

 

Now though, I have concerns. I'm worried I can't hack it for geometry. Already, I'm not much help. We will take a break for Number Theory and/or Counting and Probability, but my question is for afterwards. The options going forward are:

 

1. Continue into the Algebra II section of the AOPS text. I'm likely to do this because, well, I've gotten through Alg I thus far without too much grief. He's doing Patty Paper and loves the book, so I'm wondering if I can pass the follow-on book, Discovering Geometry, to him to do on the side, without supervision from me. He wants to do this. When Algebra II comes to an end, he'd hopefully be able to help himself through AOPS Intro to Geometry?

 

2. Move into AOPS Geometry, but have him take an online class for instruction. He's now trying out for a contest prep class with AOPS. I picked it precisely because it has no text, to see if he could take the speed. Well, he loves the class, participates and does the homework, but I now realize that it may not be a good test case since a regular textbook based class will need pre and post prep (which could mean help from me :scared: ), and I don't know if he's able to communicate with the teacher's aides about what he doesn't understand.

 

I'm thinking that he has plenty of time, we can repeat classes easily, but he may feel like he's not moving with his knowledge base. This kid loves challenge to feel connected with his work, so AOPS has been a life saver for my/our sanity. Does anyone have advice for me? Should we consider a tutor? I have no idea about other textbooks, but ds really loves the style of questions that AOPS offers. Is Michael Serra's Discovering Geometry a lighthearted approach like PPG? Sorry about the mix of questions.

 

[Writing all this now, I wonder if I underestimate my value as a study partner and perhaps I should eeks soldier on.]

[Sunshine State Sue]

He's doing Patty Paper and loves the book, so I'm wondering if I can pass the follow-on book, Discovering Geometry, to him to do on the side, without supervision from me. He wants to do this.

I don't know if I can answer any of your questions. It sounds like you have a student who is motivated and passionate about math. I have a degree in math and ds is strong in math but he has no passion for math. I will say that we used PPG in 8th grade along with Foerster's Algebra and we used Discovering Geometry in 10th grade after a failed attempt at Jacob's. We enjoyed using both PPG and DG. You may read my review of DG here.

 

If your ds wants to use DG before AoPS, I'd certainly let him. Ds worked through it on his own. I checked homework, quizzes, tests, and provided occasional help.

 

Good luck!

[regentrude]

I have no advice about "pre-geometry" , but I can tell you that #2 will not work. Before he begins AoPS Intro to Geometry, he should have completed the entire Intro to Algebra book, not just the first part.

[Mukmuk]

Tks Sue! That was a good review, and the thread had interesting comments from Mathwonk. So it can be a pre-geometry course :).

 

Regentrude, that's great to know.

 

Looks like option 1 is good to go :001_smile:

[Julie of KY]

As long as he's started quadratics, I'm not sure why he can't do AoPS Geometry without having completed the Algebra text. My son did fine completing the geometry text before finishing algebra.

[regentrude]

As long as he's started quadratics, I'm not sure why he can't do AoPS Geometry without having completed the Algebra text. My son did fine completing the geometry text before finishing algebra.

 

 

Aside from the increased maturity and level of abstraction of the geometry book that makes completing the Intro to Algebra book desirable, especially for a young student:

I recall needing graphing quadratics and quadratic inequalities (chapter 14 and 15 of intro to Algebra) for geometry of curved surfaces and for analytic geometry. I do not fully remember, but I believe equations with radicals were useful, too (ch. 20 in algebra).

[Luckymama]

I have no advice about "pre-geometry" , but I can tell you that #2 will not work. Before he begins AoPS Intro to Geometry, he should have completed the entire Intro to Algebra book, not just the first part.

As long as he's started quadratics, I'm not sure why he can't do AoPS Geometry without having completed the Algebra text. My son did fine completing the geometry text before finishing algebra.

 

 

Aside from the increased maturity and level of abstraction of the geometry book that makes completing the Intro to Algebra book desirable, especially for a young student:

I recall needing graphing quadratics and quadratic inequalities (chapter 14 and 15 of intro to Algebra) for geometry of curved surfaces and for analytic geometry. I do not fully remember, but I believe equations with radicals were useful, too (ch. 20 in algebra).

 

 

Dd really wanted to take the online Intro to Geometry course before completing all of the Intro to Algebra book. I was quite concerned about her preparedness so I emailed AoPS, explaining her level of math (up to Ch 14 in algebra, 75% through Intro to C&P, Alcumus progress, all review and half challenge problems done) and her level of motivation. I asked why the course is considered the most challenging of all the Intro courses-----is it due to the subject difficulty, the workload, the length of the course?

 

Richard Rusczyk replied that the course is difficult because of the proofs, the subject matter, and the length of the course. He said they usually recommend that students complete all of the Intro to Algebra text before tackling Geometry. He however said that dd is a good candidate for taking the courses out-of-sequence because of her progress and her motivation, though her told me to keep an eye on her the first few weeks to make sure she isn't out of her depth.

 

I'll let you all know how it goes :)

 

I couldn't find anything in ch 15 (curved surfaces) requiring graphing of quadratics-----though I didn't go through all the challenge problems and solutions.

 

At the start of ch 17 (analytic geometry) there is a huge warning box:

 

"If you have not studied graphing lines and circles in the Cartesian plane, you may find the material in this chapter extremely difficult. If so, we recommend studying the fundamentals of graphing lines and circles [me: circles are in ch 14] in our Introduction to Algebra textbook.

 

Moreover, the algebraic manipulation required for parts of this chapter is considerably more complicated than in the rest of this text. Specifically, if you are not comfortable with completing the square, you may wish to study it in Introduction to Algebra (or another text) before returning to this chapter."

 

Completing the square is in ch 13 of the Intro to Algebra book, btw.

[Julie of KY]

Interesting replies. I always hear that the geometry book is so much harder, but in this household the algebra book has been the tougher book. I think it is because I have a very gifted visual spacial learner and he just sees the geometry. He can easily prove any of it and even the analytical geometry and trig sections were easier than the algebra book. I think some of what slowed him down in algebra is that is very dsygraphic and resists any writing. He is able to see the geometry and tell me elegant proofs orally, but sometimes it just takes some writing to not mix up the algebra numbers.

 

(My son started the geometry book early in his course of algebra and had only gone through chp.14 in the algebra book when he had completed the geometry book.)

 

Good luck and have fun with the geometry course.

[regentrude]

I couldn't find anything in ch 15 (curved surfaces) requiring graphing of quadratics-----though I didn't go through all the challenge problems and solutions.

 

 

OK, so my memory did not serve me right. I distinctly recall DD working problems that had intersections of parabolas with circles - so I guess these were either supplementary problems DH created for her, or they were in a different text. Sorry about that.

 

I do think that the study of functions in Algebra (ch. 17) was beneficial for understanding the trigonometric functions in ch. 18.