Epic Thread of Geometry Programs! (OR Geometry Thread of Epic Proportions!)

[Courtney_Ostaff]

Every time I come up with something vintage I'm sure to get told how dreadfully wrong it is! :laugh:

OK.

It's First Lessons in Geometry by Thomas Hill, 1878. He wrote it because he was looking for a geometry study for his kids. They were 5 years old and I think one must have been 7, given the intro. It is very old fashioned, but it has such an imaginative quality to it that I think I can get into it. Since I'm looking to do geometry for myself NEXT year, I thought I'd play around with the ideas this year. Probably not at all what Gil would be looking for. Not problems, just discussion.

 

Here ya go:

First Lessons in Geometry

 

 

Also:

Geometry without proofs exists?!!  I didn't think I was that old, but now I feel positively ancient. How on Earth could you call it a geometry course without the proofs?!

[Crimson Wife]

 

Geometry without proofs exists?!!  I didn't think I was that old, but now I feel positively ancient. How on Earth could you call it a geometry course without the proofs?!

 

Singapore Discovering Mathematics is an integrated program. The sequence is not pre-algebra, algebra 1, geometry, algebra 2 but rather a mix of topics each year. The geometry chapters cover a lot of the same topics as in an American geometry text, but the focus is purely on calculations. It is an academically rigorous program with challenging problems, but the student does not have to write proofs.

[lewelma]

Gil, I haven't been following this thread, but I did not see in your first post what my ds is using right now.  He has finished AoPS Intro Geometry. And because they don't have an intermediate book or class, and because their Olympiad Geometry class is supposed to be super hard, he is doing all the geometry chapters in AoPS's Volume 2: And Beyond, which look to be about a half-year class. The material is of contest level, and quite a bump up from AoPS Intro Geometry, which of course is quite hard.  It has been a fun challenge for him and he has really enjoyed it.

[Courtney_Ostaff]

Singapore Discovering Mathematics is an integrated program. The sequence is not pre-algebra, algebra 1, geometry, algebra 2 but rather a mix of topics each year. The geometry chapters cover a lot of the same topics as in an American geometry text, but the focus is purely on calculations. It is an academically rigorous program with challenging problems, but the student does not have to write proofs.

 

Off to look at DM....back. Apparently they don't get to proofs until "Additional Mathematics", which is supposed to be used after DM.  Hmmm.  I feel more comfortable with my traditional sequence: Alg I, Alg II, Geometry, Alg III/Trig/Pre-Calc, Calc. Which is probably just my comfort level, but still.

[Crimson Wife]

Off to look at DM....back. Apparently they don't get to proofs until "Additional Mathematics", which is supposed to be used after DM.  Hmmm.  I feel more comfortable with my traditional sequence: Alg I, Alg II, Geometry, Alg III/Trig/Pre-Calc, Calc. Which is probably just my comfort level, but still.

 

I think there is a case to be made for integrated math, assuming that it's done using a strong program. Most (all?) of the top-performing Asian and European countries do it that way.

 

Apparently in Singapore, the students who are aiming for STEM majors at university do the Additional Math book in conjunction with DM 3 & 4. So they finish up through intro calculus by the end of 10th grade.

[dereksurfs]

Since we're well into Geometry this year I'll add in Wilson Hill Academy's Geometry course which we really like.

 

With geometry one of the first aspects to consider is how much you want the course to cover proofs.  Many of the more modern Geometry texts are very 'proof light' to make it easier for both student and teacher.  But easier isn't always better when it comes to cognitive development.  Quite a few mathematicians and educators disagree with this watered down approach.  The reason is that it lacks what was once fundamental to mathematical and logical reasoning development during this stage.  If you look at what most private schools and academies use they definitely favor including more proof based Geometry.

 

There is a good article discussing the current problem here:  The Modern Day High School Geometry Course: A Lesson in Illogic

 

We selected Wilson Hill Academy this year because I specifically wanted a more proof based Geometry.  They use Jurgenson Geometry which is a highly regarded classical Geometry texts.  The book masterfully weaves proofs throughout the text from the very beginning.  In addition the 'teacher' grades them which is a big plus considering proofs can have more than one correct answer/approach.  ds13 has really been enjoying it:

 

Wilson Hill Academy Geometry:  http://www.wilsonhil...emics/geometry/

[crazyforlatin]

Thanks, Derek, for keeping us posted about Wilson's Geometry class. It's what I would like for DD next year.

 

But what I'm wondering is whether it will be fine (feasible, doable, etc.) for us to continue using AOPS Algebra and Wilson's Geometry. We may be able to finish half of Algebra by the summer, but I'm also thinking I would like to add in geometry. Or better to wait until Algebra is finished so that DD can focus on geometry? What is the workload like? Like how many hours is expected per week? I'm hoping for a slow-paced class, but that's probably not the case with an online class.

[wapiti]

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[EndOfOrdinary]

I think this might depend on whether your child leans toward geometry or algebra. I am algebra, but my son is geometry. He is very much visual. The geometry book is often touted as very difficult, but he does not find it so. I have a much harder time picking up on the thought process which the book is leading me.

 

Though we are not massively far through the book, and I have not done the online class' pace, I do not think it would be off the table for 7th graders who like to solve puzzles. It is proof based and some teachers are really not down with that. I think it is fabulous!

[dereksurfs]

Thanks, Derek, for keeping us posted about Wilson's Geometry class. It's what I would like for DD next year.

 

But what I'm wondering is whether it will be fine (feasible, doable, etc.) for us to continue using AOPS Algebra and Wilson's Geometry. We may be able to finish half of Algebra by the summer, but I'm also thinking I would like to add in geometry. Or better to wait until Algebra is finished so that DD can focus on geometry? What is the workload like? Like how many hours is expected per week? I'm hoping for a slow-paced class, but that's probably not the case with an online class.

 

Hi Crazyforlatin, ds13 finished AoPS Intro to Algebra (ch.1-13) before starting the WHA Geometry course this Fall.  That is what most consider Algebra 1.  I think if your DD can get through the first half before next Fall she should be fine in terms of preparation.  

 

Whether she can double up on Geometry and the second half of AoPS is really dependent on other factors.  For example how busy will she be with other subjects including extra curricular activities.  In addition how good is she with time management in balancing out her workload?  

 

For ds13 this was one of the huge advantages this year in taking a 'live' Geometry class with regular daily, weekly and semester scheduled assignments.  These all factor into a running overall grade.  They include homework, quizzes and chapter tests in addition to in-class participation with peers and note taking.  These skills are new to him and so he is learning a lot.  But it also takes more time I think to get a handle on, especially in the beginning.  So there are weeks when he has all his homework completed in all subjects before dinner.  Then there are other weeks where he needs to stay up and finish.  That is also something new for him.

 

With regards to the workload I think it follows a standard paced 'solid' High School level Geometry course.  He's given homework which usually includes the odd problems in Jurgensen.  Some of the problems can be quite challenging.  Though possibly not as much as AoPS challenge problems which can be off the charts difficult.  The Jurgensen proofs can take a long time to solve and involve many steps.  All this to say I wouldn't expect a 'light' course, more like a college prep Geometry course.  Just not an AoPS Geometry course which I hear is very difficult even on the AoPS scale.

 

I hope that helps some.  Let me know if you have any further questions regarding the course.    :) 

[wapiti]

I think this might depend on whether your child leans toward geometry or algebra. I am algebra, but my son is geometry. He is very much visual. The geometry book is often touted as very difficult, but he does not find it so. I have a much harder time picking up on the thought process which the book is leading me.

 

Though we are not massively far through the book, and I have not done the online class' pace, I do not think it would be off the table for 7th graders who like to solve puzzles. It is proof based and some teachers are really not down with that. I think it is fabulous!

 

I think you're right.  We are a very visual family.  It would probably be great as long as they're willing to put in the effort.  (That's part of the algebra issue; neither of them likes it as much, as a subject, and we've rotated material plenty, but they've got to get all the way through it to the point of acing placement tests before starting geometry at school; *sigh*.  They were more motivated with the Prealgebra text.)

[Wind-in-my-hair]

This looks like the book of my childhood dreams. 

 

Every time I come up with something vintage I'm sure to get told how dreadfully wrong it is! :laugh:

OK.

It's First Lessons in Geometry by Thomas Hill, 1878. He wrote it because he was looking for a geometry study for his kids. They were 5 years old and I think one must have been 7, given the intro. It is very old fashioned, but it has such an imaginative quality to it that I think I can get into it. Since I'm looking to do geometry for myself NEXT year, I thought I'd play around with the ideas this year. Probably not at all what Gil would be looking for. Not problems, just discussion.

 

[EndOfOrdinary]

I think you're right. We are a very visual family. It would probably be great as long as they're willing to put in the effort. (That's part of the algebra issue; neither of them likes it as much, as a subject, and we've rotated material plenty, but they've got to get all the way through it to the point of acing placement tests before starting geometry at school; *sigh*. They were more motivated with the Prealgebra text.)

Whatever bit of Geometry we do not finish this year is going to be rotated in with Algebra next year. Ds is very much not keen on the word, "Algebra." He is putting it off. I would most definitely suggest the $14 solutions manual. It has been pulled out a few times for a bit of a nudge in the right direction. If you are visual, you might be able to nudge without it, but I have very much enjoyed it being here as a support. I didn't need it with PreA, but it is worth the money.