Geometry in 8th Grade??

[Krystan]

Dd did Foerster's Algebra 1 last year in 7th grade and did fine.  Plan was originally for her to do geometry in 8th and then Algebra 2, Pre-Calc, Stat, Calc, or whatever her interests determine.  She is very good at math, but does NOT love it.  In fact, she was looking forward to geometry as a break from algebra (though we were planning to do LoF algebra on the side as review).  I was going to post a Jacobs vs. Holt Geometry question, but have been reading other threads about going too fast in math, and it possibly being a mistake to do geometry in 8th.  I am now considering doing an algebra review/pre-geometry year.  I'd love some input though.  What are your thoughts?  Here are my concerns:

 

- I do not think she is fully confident in her algebra, despite scoring very well.  Foerster's had some review, but not tons. Algebra review has already been heavily planned for this year during geometry.

- Do colleges only let you count credits from 9th grade and up? Is it okay to have geometry completed before 9th?

- Although she is very intelligent and has done well so far, is it better to solidify basics before moving on? Is there a downfall to speeding ahead fast? I am wondering if there are others who have done geometry in 8th grade and have had it backfire.

- On the other hand, is there anything to lose by NOT plowing ahead? She should still get at least a full year of calculus in with geometry in 9th grade. However, she would have less time for math electives like stats.  She's not a math lover and probably wouldn't mind this?

- Have others done an "extra" year of algebra/pre-geometry? If so, have you regretted it? And what resources did you use and like?  If we go this way, I'd love to bring a little more fun to math, so she feels nice and confident going into geometry. She thinks she is "bad" at math right now, which is simply not true.

- I know my husband likes the idea of her being "ahead" and would probably rather see her go farther instead of deeper, but I'm not sure I agree with that one.

- Another option might be spending the fall "finishing up" algebra, then starting geometry in January, and taking as long as needed, with algebra review insterspersed.

 

Anyway, you can see I'm rambling with indecisiveness, so I'd love to hear if anyone has BTDT, and has words of wisdom or examples either way.  Thanks!

[Luckymama]

What parts of algebra is she not confident with? Can she manipulate equations with ease? How are her ratio skills?

 

My dd did geometry from March of 7th grade through September of 8th grade (online Art of Problem Solving class). She would have been sunk if her algebra wasn't automatic.

 

No time now--running out. I'm sure others will have much to share :)

[freesia]

What we did was have my ds go through Teaching Textbooks Geometry 4 days a week and do Algebra review one day a week. We used a NY Regents review book, but I wouldn't say that was the best resource--it worked fine, but I'll use something else with the next child. I am much more confident about him heading into Alg 2 now. He also did well in geometry and I feel TT covered the topics well.

[NittanyJen]

Another way to go might be to spend a year with AoPS Number Theory and Probability books in 8th, then hit geometry in 9th, you could still review algebra throughout the year to shore up any areas where she needs more confidence.

[MinivanMom]

It's fine to complete Geometry before 9th grade. In fact, this has become the standard for advanced students in my area. Local kids like it, because they have Calculus BC scores from 11th grade to report when they apply to college and they can have an "easy" math year taking AP Stats in 12th. There's no downside to doing this as long as your kid is solid before moving forward.

 

What do you mean by "not fully confident". Does that mean she's making mistakes? Are there algebra topics she hasn't fully mastered? If that's the case, then I wouldn't move onto geometry yet. I would use 8th for reviewing algebra along with a side course (perhaps number theory). It sounds like maybe she's scoring well in algebra, but you don't feel like she completely owns the knowledge yet. If that's the case, then I would probably move onto Geometry, but build some algebra review into the week. It's hard to say without knowing which algebra topics she isn't confident in and what you mean by "not fully confident."

[Arcadia]

I was going to post a Jacobs vs. Holt Geometry question, but have been reading other threads about going too fast in math, and it possibly being a mistake to do geometry in 8th.

...

Is it okay to have geometry completed before 9th?

...- I know my husband likes the idea of her being "ahead" and would probably rather see her go farther instead of deeper, but I'm not sure I agree with that one.

Jacobs and Holt has a different style. My kids read all the comics in Jacobs geometry (hardcover library copy) and that was all that interest them. Holt is a typical get it done public school textbook.

 

In general, there is nothing wrong in completing geometry in middle schools. Some local public middle schools here has long offered geometry for 8th grade or before 8th grade. Whether it is what your child wants to do is up to your child and you.

 

It would be possible to do geometry at a slower pace for 8th and a review of algebra as well as probability and statistics.

 

How have you intended to go deeper? MathCounts, AMC8?

[Crimson Wife]

Colleges are used to seeing applicants with Algebra 2 as the first high school math credit. Many schools offer a post-AP math course in 12th for students who took algebra 1 in 7th.

[wapiti]

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Edited September 15, 2016 by wapiti

[Krystan]

Thanks for feedback so far!  I am feeling a little better about moving on.  When I say "not fully confident", I mean that she feels she is doing poorly because it is the first math course she's really had to work at.  She is used to getting 100s on everything without studying, and in Algebra it was more like low 90s on average, and the work took a lot longer.  I think I panicked reading a few older threads where some people (Jann in TX for one) thought 8th graders are just not ready for geometry, and were encouraging an extra review year.  Thinking about it though, dd would probably go crazy if we just reviewed the same material again.  I guess my concern is that she feel successful.  It's hard explaining to her how well she is doing when she has no one to compare herself to!

 

I really like the look of the Jacob's geometry text, and dd has always said she does better just reading from a book without flashy games, pictures, and videols.  However, our one big issue with Foerster was the feeling that I could have used more back-up material.  She would get frustrated if she didn't understand things perfectely the first time, and I sometimes wouldn't be able to explain it another way.  We did use Khan for things that needed more explanation, and that worked well, but it obviously would be easier to have some matched to the lesson (but not verbatum a la MWB).  The Berger videos (Holt) sound great, and I like that algebra review is pretty thoroughly integrated in Holt.  The pages are busy, which will turn her off, but I do feel like Foerster alone wasn't *enough* for Algebra, and I worry about the same thing with Jacob's.  I think I'll have to start another post on this one...

[kiana]

Thanks for feedback so far!  I am feeling a little better about moving on.  When I say "not fully confident", I mean that she feels she is doing poorly because it is the first math course she's really had to work at.  She is used to getting 100s on everything without studying, and in Algebra it was more like low 90s on average, and the work took a lot longer.  I think I panicked reading a few older threads where some people (Jann in TX for one) thought 8th graders are just not ready for geometry, and were encouraging an extra review year.  Thinking about it though, dd would probably go crazy if we just reviewed the same material again.  I guess my concern is that she feel successful.  It's hard explaining to her how well she is doing when she has no one to compare herself to!

Oh, in that case I would definitely not spend a year reviewing. She'll get used to having everything be easy again, and then 9th grade geometry will be back to working!

 

8th grade geometry or 8th grade AOPS discrete math (nt/c+p) would both work. I loathed geometry and changed my major to math because of a discrete math course, so I'm personally a little biased towards the discrete, but quite honestly if she has been looking forward to geometry I would go ahead with that.

 

If she starts struggling a lot with the proofs then I would sidestep and do discrete math instead for the year. The nice thing about discrete is that you don't have to feel compelled to finish any sort of scope and sequence, and since it's outside the normal course sequence you don't have to worry about half-understood bits cropping up in future courses, if it doesn't go well. It'll also review algebra.

[Arcadia]

The Berger videos (Holt) sound great, and I like that algebra review is pretty thoroughly integrated in Holt. The pages are busy, which will turn her off, ...

If you have an iPad, Prof Edward Burger's Geometry is available as an iBook for $14.99. You can download the sample and see if your daughter likes it. The videos are in the iBook.

 

If your daughter have already seen the Holt geometry book, then don't bother if she doesn't like the book. The iBook version is similar but less busy.

[Matryoshka]

My dd is taking Geometry next year in 8th.  I'm not sure how 100% solid her Algebra skills are in spite of having gone through AoPS Algebra - she could do it as she was going through it, but I'm not sure she had quite enough review to really own it.  But I can't imagine making her go through Alg1 again - with an easier text?  So instead she's moving on to Geometry (online with Wilson Hill/Jacobsen) and using Khan Academy to review Algebra 1, which she's been doing all summer and will continue to do over the year.  When she's got Khan-approved mastery of their Algebra 1, i'll probably add in either Geometry or Algebra 2 for her to work on in Khan (she actually touched on a lot of Algebra 2 topics in AoPS already - I'd rather have her review them so she has some memory of them when she gets to a complete Alg2 course in 9th).

[foxbridgeacademy]

DS did Alg. 1 last year for 7th, but it was an easy text (had breadth, no depth).  So for 8th we are doing "Integrated Math".  We're going to use Lial's Beginning and Intermediate Algebra (all in one, which is faster paced) and Keys to Geometry.  Hopefully by Christmas we will be well into the Alg. and Done with Keys.  Then we'll begin to focus on Geometry (probably Jacobs or Jergensen?) and Alg will only be 1-2 times per week.  For 9th we'll switch this up a bit and focus on Algebra again(Geometry 1-2 times per week).  For 10th grade, 1st semester we'll finish up anything he's weak on (to the best of my ability) then he'll take College Algebra or Pre-Calc at CC (depending on what he tests into) for 2nd Semester.  At that point I'll be done with Math!  The State Uni's Engineering Program only requires Pre-Calc. for Freshman year so he should be well ahead of the schedule. He's also one of those that is good at but doesn't like Math. If he hits blocks I am more then happy to slow down too. 

[Mike in SA]

DS12 did geometry in 5th prior to starting algebra.  We did that because he was clearly gifted, but lacked the techniques to structure his reasoning.  It has worked out beautifully for him.  He'll be in precalc next year (7th grade), and while we'd like for him to take a deeper dive into some of his material, it just isn't going to happen for him.  So, we enrich between subjects, and let him move along as he is driven to.  This summer, he is doing AoPS Counting and Probability.  Next, we'll pull out the trusty Lethold Calculus, and do a summer of math theory.  After a year of applied calculus, we'll be back to a deeper dive in number theory or elementary abstract algebra, and then fly into linear algebra, et al.

 

Unless you are using a spiral program, you can be very flexible with your math sequences.  Plowing ahead just for the sake of being ahead is generally not wise.  But there certainly is no harm in jumping into geometry earlier.  It is one of those classes that provide depth.  Use AoPS and go slowly with it, or supplement with Kiselev.  Holt is not a bad text, either (just not quite as deep).  If you want more, you can do symbolic logic when you are done, or number theory, or whatever you please.

[giraffefamily]

:bigear:

 

We are in a similar place to your dc - finishing up alg 1 / starting geometry.

[Ali in OR]

I'm one of those people who think too many people take geometry in 8th grade. It is appropriate for some, but for me that "some" are the kids who live for math. The ones who want to get to college level courses in high school. I've seen too many kids accelerate and then quit after calculus. In that case, you are going to have a better understanding of geometry, algebra II, trig, and calculus by taking them when you are a year older. I come at this as a former high school math teacher and having earned an engineering degree from a top university. At that top university, most students didn't really want to start off in the more advanced math classes; the standard calculus for engineering majors was challenging enough. But to claim that AP calc credit, you have to start in the harder courses. Great for those real math wizards out there, but for the more typical "strong at math" student, it would have been too much. And those engineering students took calculus in high school and still found the university's calculus program enough of a challenge.

 

I taught honors geometry to 9th graders, and understanding the concept of proof was definitely a cognitive jump for many students (all strong students in honors math). We taught a rigorous course. If I had to teach geometry to kids who were all a year younger, I don't think it could have had the same rigor. Yes, some math whizzes are ready for the jump earlier. But for someone who is just a typical good student, strong in math but not likely to get into conversations about math problems for fun, I prefer to put geometry at 9th grade. Where I taught, students who wanted to take AP stats took it on the side in addition to whatever other math class they were taking.

 

Another materials source to look at would be Singapore's Discovering Mathematics series as it has both algebra and geometry topics. And the application problems are appropriately challenging; if your daughter can do them, you will know she has a good understanding of the topics.

[kiana]

I have NO clue if this text is 'enough' for a 'standard' Geometry course in the USA.

But we use Understanding Geometry from Critical Thinking Company during grade 7/8.

It is what we need to cover our (Belgian} Geometry requirements in Middle School.

This is a good idea too. It covers enough to be a HS course, but really it's intended for bright middle schoolers who are going to take a very rigorous geometry in high school. It does do proofs.

[bluedarling]

I was not ready for geometry in 8th (took it at the high school while in jr. high).  I passed the class, but I couldn't generate the proofs, and socially was too shy to be put in a class of older students.  That said, I had totally mastered algebra.  Your dd, however, seems to look forward to geometry!  It seems some people like geometry better (but I wasn't one of them!)  If she likes it, I'd go for it.  If she doesn't I  think doing another math first makes sense.  I might have liked geometry better if I had encountered it a bit older....my oldest two are just starting geometry this year, so I guess I'll find out how I'll do with it more than a bit older!!   (Geometry was the only math class I ever hated.  I took advance math classes in college...and physics as electives, so even if its difficult for her now, its not the end of the world to make it the one class not totally mastered, either.  She'd still get the basics of it that she needs to progress in math.)  OK, so I'm guess I'm saying its fine either way....guess I'm not that helpful!!

[regentrude]

 At that top university, most students didn't really want to start off in the more advanced math classes; the standard calculus for engineering majors was challenging enough. But to claim that AP calc credit, you have to start in the harder courses. Great for those real math wizards out there, but for the more typical "strong at math" student, it would have been too much. And those engineering students took calculus in high school and still found the university's calculus program enough of a challenge.

 

Why do you conclude that this was because they took the course too early, and not because the quality of instructor had been lacking?

 

I taught honors geometry to 9th graders, and understanding the concept of proof was definitely a cognitive jump for many students (all strong students in honors math).

 

I am curious about this, because formal geometry proofs were taught in 6th grade in the country where I grew up, and the current 6th grade curriculum in college prep (ETA which means 50% of all students) public schools in my home state includes proving theorems about triangle geometry such as congruency theorems, angle sum, triangle inequality, plus formal construction with straight edge and compass. 7th grade covers proofs that include case differentiation and theorems like Thales' theorem and a whole bunch of others.

 

Why should students in this country be less mature cognitively that they can not, in 9th grade, do what elsewhere in the world is expected from students several years younger? Again, could it have to do with the quality of math instruction in the years preceding geometry, rather than inherent cognitive ability?

[NittanyJen]

I think in the US we need to be careful about using our own frame of reference when thinking of what kids can or should do in math.  The fact is, traditional math instruction here has been pretty poor-- it has moved at an intolerably slow pace for no good reason (really-- in the traditional sequence into the early 80's at least, kids were still working on arithmetic into the 8th grade; only the very cream of the crop got to try algebra by then, and the general math courses did not introduce much in the way of algebraic thinking).

 

So of course to many kids, even good ones, algebra and geometry felt like "a jump" in cognitive skills and thinking.

 

I think that is why Singapore Math and a few related programs feel so Earth-shattering to us (and is one reason why there is so much blow-back on the Common Core).  Not only do these programs offer much better gradual buildup of numeric literacy and mathematical logic from the beginning than traditional US instruction typically did, but in the Asian classrooms, the methods of instruction were very different, as were the methods of teacher development.  I just read a WSJ article from a Japanese teacher, describing how kids were encouraged to talk in class, interact with one another, and be generally noisy in math class, rather than sitting at their desks absorbing from the teacher, developing multiple strategies and helping each other find the problems in their solutions-- things people in the US are crying foul over as being developmentally inappropriate and not possible-- because our teachers have not received the critical support and training they need to see how this works, in order to be productive and instructive rather than chaotic.  Apparently, kids really can do this stuff.  Those of us who use Singapore's Primary Math series already know that teaching kids multiple strategies works wonderfully, as does introducing algebraic thinking and more advanced geometry earlier (though even in 7DM, I am seeing foundations for formal proofs rather than line by line actual proofs, though I could easily adapt the program to make it that way-- I don't because I see that step developed more in the Additional Math program that hits later on).

 

I get that people had these experiences.  I think we need to remember that our experiences were based upon our baseline educations, which even in good schools, was maybe not the most up to date model available to us today.  It could be a mistake to hold our kids back because of what we experienced.  I make an effort to teach the programs written, not the programs I recall-- yes, I tweak here and there, and I am in charge, not the book-- but if I change something, I try to make sure it is for sound reasons, and not because I'm being a stick in the mud.  I need a better reason than, "WEll that's how I larned it, and I done did good!"  I think that goes for both sides--whether we feel our background was lacking or superior.  No matter who you are, there is probably something that could be learned.

 

 

[Mike in SA]

I'm one of those people who think too many people take geometry in 8th grade. It is appropriate for some, but for me that "some" are the kids who live for math. The ones who want to get to college level courses in high school. I've seen too many kids accelerate and then quit after calculus. In that case, you are going to have a better understanding of geometry, algebra II, trig, and calculus by taking them when you are a year older. I come at this as a former high school math teacher and having earned an engineering degree from a top university. At that top university, most students didn't really want to start off in the more advanced math classes; the standard calculus for engineering majors was challenging enough. But to claim that AP calc credit, you have to start in the harder courses. Great for those real math wizards out there, but for the more typical "strong at math" student, it would have been too much. And those engineering students took calculus in high school and still found the university's calculus program enough of a challenge.

 

I taught honors geometry to 9th graders, and understanding the concept of proof was definitely a cognitive jump for many students (all strong students in honors math). We taught a rigorous course. If I had to teach geometry to kids who were all a year younger, I don't think it could have had the same rigor. Yes, some math whizzes are ready for the jump earlier. But for someone who is just a typical good student, strong in math but not likely to get into conversations about math problems for fun, I prefer to put geometry at 9th grade. Where I taught, students who wanted to take AP stats took it on the side in addition to whatever other math class they were taking.

 

Another materials source to look at would be Singapore's Discovering Mathematics series as it has both algebra and geometry topics. And the application problems are appropriately challenging; if your daughter can do them, you will know she has a good understanding of the topics.

 

It IS a bit of a jump in thinking processes, which is all the more reason why it can be good to start earlier.  Instead of cramming it into one educational session, it can be taught and reinforced over many.  Much more effective that way (and how many foreign programs work)...

 

Where my wife is from, all kids did formal geometry with proofs starting in the 6th grade.  There's no reason kids CAN'T do it, but it does require a lot of work on the part of the teacher at any age.

[Ali in OR]

Why do you conclude that this was because they took the course too early, and not because the quality of instructor had been lacking?

 

My point from this anecdote (college freshmen who did not want to be placed in more advanced math classes as their first college math experience) is that even students who could claim credit for calculus via the AP (and would then need to take a harder classes to fulfill the university's requirement of taking a math class) chose to take calculus again. Not all students, but many of them chose this path. Accelerating in math in high school is appropriate for students who want to get to advanced courses. Many don't want that, so what is the point of taking calculus earlier if you don't want to go beyond calculus? Just to get it done early? It's not an easy course for most people, and it may be more understandable if you don't rush math each year to get to it as early as possible.

 

I am curious about this, because formal geometry proofs were taught in 6th grade in the country where I grew up, and the current 6th grade curriculum in college prep (ETA which means 50% of all students) public schools in my home state includes proving theorems about triangle geometry such as congruency theorems, angle sum, triangle inequality, plus formal construction with straight edge and compass. 7th grade covers proofs that include case differentiation and theorems like Thales' theorem and a whole bunch of others.

 

Why should students in this country be less mature cognitively that they can not, in 9th grade, do what elsewhere in the world is expected from students several years younger? Again, could it have to do with the quality of math instruction in the years preceding geometry, rather than inherent cognitive ability?

I have trouble imagining all 6th grade students mastering proof to the degree we expected of 9th grade students. Maybe that's just the American math background they have, but I also think that developmentally, 14 year olds are going to be better able to understand how to justify each proof step with theorems and axioms. We've been using the Singapore Discovering Mathematics books, and while they will sometimes informally explain why certain steps follow, they also do not do any formal proof at least through book 3A which I think would be a 9th grade book (they're changing their system over from DM 1,2,3 to DM 7, 8--don't know if 9 is coming. 7 is a 7th grade book, etc). So it doesn't look like Asian math does proof at a young age either. CA and OR do not teach proof in 6th or 7th grade (advanced students are splitting algebra over those two years as algebra comes before geometry in the American math world). Even our 8th grade geometry class is a small percentage of all math students--one class period at each middle school, and typically a small class--maybe 15 kids.

 

Strong math students in our town do have the option of taking geometry in 8th grade. Anecdotally (chatting with their moms), many of these kids bog down in high school. They do not really wish to take the hardest math classes at a younger age any more, but there's no easy way off the path they're on. I think these classes are great for kids who want to dive into the math. But I think parents can somehow get the idea that their children have to be in the hardest class possible to get into the college of their choice or to be a serious student. You can be a successful engineer, doctor, scientist, even a math major WITHOUT taking geometry in 8th grade. And you just might enjoy the math more if you're a little older and more developmentally ready for the challenge.

 

[Mike in SA]

*** NOT complaining about Dolciani ***

 

As always, there are some misunderstandings here.  Most would agree that rushing just to get there is not a good idea.  It doesn't help achieve anything in the long run.

 

Where geometry is taught earlier, it usually isn't done so that one gets to calculus sooner.  Instead, it's typically taught over a number of years, often in an integrated fashion with what we would call prealgebra and algebra.

 

Kids have a surprising capability to follow proofs, just as long as they don't have preconceptions blocking their path.  I often worry about doing prealgebra before geometry, just because it creates those preconceptions about what "advanced" math is.  Geometry is completely different than algebra.  Where it is difficult, it is because the Dolciani method doesn't work very well.  We have had the Dolciani approach so crammed into our heads that we forget that it is one approach.  i appreciate Dolciani and what she brought to math education -- she really did great things -- but classical geometry education was an unfortunate casualty of her system.

 

I have taught elementary abstract algebra to six year olds (yes, upper-division college concepts, to first graders), so I know that a 10 year old is fully capable of learning geometry.  It IS tougher for some kids than others.  But, they are all capable of succeeding.

 

Sometimes, I really believe it is more the parents' and instructors' fears that hold kids back, rather than the abilities of the kids themselves.

 

 

[kiana]

Strong math students in our town do have the option of taking geometry in 8th grade. Anecdotally (chatting with their moms), many of these kids bog down in high school. They do not really wish to take the hardest math classes at a younger age any more, but there's no easy way off the path they're on. I think these classes are great for kids who want to dive into the math. But I think parents can somehow get the idea that their children have to be in the hardest class possible to get into the college of their choice or to be a serious student. You can be a successful engineer, doctor, scientist, even a math major WITHOUT taking geometry in 8th grade. And you just might enjoy the math more if you're a little older and more developmentally ready for the challenge.

 

But one of the really cool things about homeschooling is that we have the ability to step kids back a notch. A kid who does geometry in 8th grade and wants to slow down from the advanced math track has a lot more options than one in public school. Off the top of my head:

 

Do alg 2 in 9th, then a two-year precalculus using something like the UCSMP program in 10th and 11th.

Do discrete math in 9th using all or part of the AOPS number theory/counting and probability books, then move to alg 2 in 10th.

Do alg 2 in 9th, then do an advanced geometry in 10th before precalculus in 11th.

Do alg 2 in 9th, then do a year of stats before precalculus.

Do a year of problem-solving using something like the AOPS intro to problem solving book, then move to alg 2 in 10th.

 

I'm sure I could come up with more if someone had something specific, but it doesn't make sense to me to hold back a kid who is interested now (like the OP's kid, who is apparently looking forward to it) based on what might happen in the future.

[Matryoshka]

Kids have a surprising capability to follow proofs, just as long as they don't have preconceptions blocking their path.  I often worry about doing prealgebra before geometry, just because it creates those preconceptions about what "advanced" math is.  Geometry is completely different than algebra.  Where it is difficult, it is because the Dolciani method doesn't work very well.  We have had the Dolciani approach so crammed into our heads that we forget that it is one approach.  i appreciate Dolciani and what she brought to math education -- she really did great things -- but classical geometry education was an unfortunate casualty of her system.

 

Could you elaborate on what you mean here?  Was Dolciani the one who started us down the Alg1/Geo/Alg2 path?  Or do you mean something else? 

 

We've never used Dolciani before, but next year dd will be taking her Geo class with Jurgensen/Brown, which leads into Dolciani Alg2, so this makes me more curious. :)  Dolciani didn't write a Geometry text herself, did she?

 

 

 

 

[Mike in SA]

Could you elaborate on what you mean here?  Was Dolciani the one who started us down the Alg1/Geo/Alg2 path?  Or do you mean something else? 

 

We've never used Dolciani before, but next year dd will be taking her Geo class with Jurgensen/Brown, which leads into Dolciani Alg2, so this makes me more curious. :)  Dolciani didn't write a Geometry text herself, did she?

 

*** NOT complaining about Dolciani ***

 

Dolciani was the proponent of the modern mathematics education approach, where axioms were replaced by drills.  She was a very well respected mathematician, and definitely revolutionized mathematics instruction.  I have absolutely nothing against her or her books.  It was more of a comment on eras in math education, and the impact the shifting styles have had on both teachers and students.

 

If you pick up a pre-Dolciani textbook, you will see that they look an awful lot like an AoPS one, with just a handful of very specific problems, but maybe without some of the tougher ones.  Algebra used to be taught very similarly to geometry now.  Post-Dolciani, you see textbooks with 100 algebra problems of the same basic type.  You will also notice that textbooks became about 4-5 times thicker.

 

For algebra, by and large, the effect has been positive in that more students graduate school with essential math skills.  For geometry, the effect has been somewhat negative, in that most students have little to no exposure to math theory by the time they hit geometry.  Proofs, then, became a jump instead of a step.  Unfortunately, that means that it has started to lose its place in our educational system.  It is either getting pushed farther and farther back because "it's hard," or it is being removed from curricular requirements altogether (Texas, I dislike that you did this!).

[Matryoshka]

Dolciani was the proponent of the modern mathematics education approach, where axioms were replaced by drills.  She was a very well respected mathematician, and definitely revolutionized mathematics instruction.  I have absolutely nothing against her or her books.  It was more of a comment on eras in math education, and the impact the shifting styles have had on both teachers and students.

 

If you pick up a pre-Dolciani textbook, you will see that they look an awful lot like an AoPS one, with just a handful of very specific problems, but maybe without some of the tougher ones.  Algebra used to be taught very similarly to geometry now.  Post-Dolciani, you see textbooks with 100 algebra problems of the same basic type.  You will also notice that textbooks became about 4-5 times thicker.

 

I only know about Dolciani what I've read here, but I thought people kept saying she was part of the 60's "New Math" revolution that moved away from traditional drill and did "wacky" things like talk a lot about theoretical/conceptual stuff like set theory, and that's why everyone's hunting for her older textbooks as if they were nuggets of gold, as apparently the modern revisions have taken some of that stuff out?

 

For algebra, by and large, the effect has been positive in that more students graduate school with essential math skills.  For geometry, the effect has been somewhat negative, in that most students have little to no exposure to math theory by the time they hit geometry.  Proofs, then, became a jump instead of a step.  Unfortunately, that means that it has started to lose its place in our educational system.  It is either getting pushed farther and farther back because "it's hard," or it is being removed from curricular requirements altogether (Texas, I dislike that you did this!).

 

Now you're making me glad dd's background was Singapore/AoPS...  As I said upthread, though, I think AoPS might not have had enough review-type stuff for her, which is why the switch this year.  Dd seems to pick stuff up quickly, but doesn't seem to retain it if she doesn't keep seeing it.  I think she'd just shut down with Saxon-type drill, but she's apparently not the über-gifted "see it once, know it forever" types that AoPS seems made for.  I thought from previous talk here that Dolciani texts were more theoretical than more modern texts.  Now I'm just confused. :tongue_smilie:

[Mike in SA]

I only know about Dolciani what I've read here, but I thought people kept saying she was part of the 60's "New Math" revolution that moved away from traditional drill and did "wacky" things like talk a lot about theoretical/conceptual stuff like set theory, and that's why everyone's hunting for her older textbooks as if they were nuggets of gold, as apparently the modern revisions have taken some of that stuff out?

 

 

*** NOT complaining about Dolciani ***

 

Yep, the older, the better.  :)

 

If you get a really old book, they really read like a Schaum's Outline:

 

1. Definition

2. Proof

3. Example

4. Exercises

 

Nothing like today's books!

[NittanyJen]

Hmmm one of these posts made me wonder...

 

When I took algebra 1, we were not allowed to use anything until we had proven it to our instructor. I wish I knew which text we used! So geometry was a piece of cake. Now it seems algebra is being presented with less reliance on proofs. Is this generally true?

[Matryoshka]

Hmmm one of these posts made me wonder...

 

When I took algebra 1, we were not allowed to use anything until we had proven it to our instructor. I wish I knew which text we used! So geometry was a piece of cake. Now it seems algebra is being presented with less reliance on proofs. Is this generally true?

 

One of my older dds used Foersters for Algebra - it had proofs for everything.  I don't think this is the case for most texts, though.

 

AoPS also proves everything, but it's much more wordy - I sometimes wonder if younger dd didn't internalize some of the stuff as much as I would have hoped because of that...

 

[EKS]

You can list geometry taken prior to 9th grade on the transcript.  Even b&m schools do this.

 

Jacobs Geometry has an algebra review section in just about every chapter.  Also, most Algebra II books have a review of Algebra I built in. 

 

The thing I would be most concerned about in doing geometry early (and 8th grade is really only a year early) is that her geometry skills might be rusty when it comes time to take the SAT/ACT.  But, apparently, the SAT is eliminating problems that require geometry knowledge in 2016, so that might be less of a concern.

[Mike in SA]

Hmmm one of these posts made me wonder...

 

When I took algebra 1, we were not allowed to use anything until we had proven it to our instructor. I wish I knew which text we used! So geometry was a piece of cake. Now it seems algebra is being presented with less reliance on proofs. Is this generally true?

 

Yes, this is unfortunately true.  Math continues to be watered down.

[Mike in SA]

You can list geometry taken prior to 9th grade on the transcript.  Even b&m schools do this.

 

Jacobs Geometry has an algebra review section in just about every chapter.  Also, most Algebra II books have a review of Algebra I built in. 

 

The thing I would be most concerned about in doing geometry early (and 8th grade is really only a year early) is that her geometry skills might be rusty when it comes time to take the SAT/ACT.  But, apparently, the SAT is eliminating problems that require geometry knowledge in 2016, so that might be less of a concern.

 

Yep, and it's one of the reasons that Texas dropped it from their graduation requirements.  The scary thing is that Texas has a LOT of influence on textbook publishers, so other states are likely to follow suit.

[regentrude]

Hmmm one of these posts made me wonder...

 

When I took algebra 1, we were not allowed to use anything until we had proven it to our instructor. I wish I knew which text we used! So geometry was a piece of cake. Now it seems algebra is being presented with less reliance on proofs. Is this generally true?

 

In school, yes. Students are frequently taught formulas without conceptual understanding where they are coming from.

I see the fallout in college. The students expect physics to be a grab bag of equations to plug things into because that's what they have  know from school; they are complaining when I spend time deriving the relationships so that they know where they come from (and thus won't have to memorize but can re-derive what they need). They'd rather have to memorize stuff than understand.

 

AoPS is a wonderful exception: they prove or derive every relationship before it is being used. So the idea of a geometry proof is really nothing special after you have derived all relationships in algebra1.

[regentrude]

AoPS also proves everything, but it's much more wordy - I sometimes wonder if younger dd didn't internalize some of the stuff as much as I would have hoped because of that...

 

I think the reason AoPS is perceived as "more wordy" is that it is written to be used without a teacher. Thus the text must contain every word a good teacher would say orally when explaining a concept to the class.

I believe most other math texts are not originally designed for independent study, but for use with an instructor.

 

[Sebastian (a lady)]

Could you elaborate on what you mean here?  Was Dolciani the one who started us down the Alg1/Geo/Alg2 path?  Or do you mean something else? 

 

We've never used Dolciani before, but next year dd will be taking her Geo class with Jurgensen/Brown, which leads into Dolciani Alg2, so this makes me more curious. :)  Dolciani didn't write a Geometry text herself, did she?

 

I have seen two geometry books in the same line as Dolciani algebra.  Jurgensen/Brown is the more recent edition that I think was published by Holt (or HBJ).  But I also have a book titled School Mathematics Geometry by Anderson, Garon & Gremillion that is part of the Houghton Mifflin Modern Mathematics Series.  My 1962 & 1965 Dolciani Algebra books are part of this same series.  I suspect that as various publishing houses consolidated, there was a tendency to drop titles.  The 1966 Anderson School Mathematics Geometry definitely has proofs.

 

I'm not understanding the critique of Dolciani as being just drill.  At least in the older editions, there are definitely descriptions, diagrams and other explanations of the concepts.  The problems that follow are often progressively harder, such that a student would see that a concept could be applied to whole numbers, fractions, decimals, variables, etc.  (I personally think the word problems and practical problems are also a lot more interesting than what appear in many more recent texts.  They have a lot in common with AoPS imho.)

 

As for the number of problems, the teacher's editions typically have three tracks through the course (minimum, average, and maximum).  A student isn't expected to do all of the problems in a lesson.  Instead, they might do just the odd problems or all of the A problems; half of the B level problems and none of the C level problems; or skip all of the A level problems, a couple of the B level problems and all of the C level. 

 

I did read an interesting discussion of New Math and the CSMP that suggested that part of the problem with the introduction of New Math is that they started with algebra and districts were willing to send high school and junior high school math teachers to the teacher training sessions.  But then they started to write material for younger and younger grades.  Elementary schools didn't have specialized math teachers and weren't willing or able to send all of their teachers to training.  The materials for the early grades had included information on sets, because they wanted students to have heard of sets when they hit later grades.  But absent the training, elementary teachers concluded that what came first in the book had to be mastered before moving on.  This led to some of the (over)emphasis on set theory for elementary.

 

I don't have first hand New Math experience.  Somehow I dodged that bullet in my schooling.  I don't remember if I used Dolciani for algebra, but if not, it was a similar book.  As I've moved between AoPS and Dolciani with my older kids, I've found them more complementary than in conflict.

 

Of course, your mileage may vary.  And it grows harder to get copies of even the later editions of Dolciani.  I guess there was more money in a glossy, full color math book with lots of online supplemental material. 

[Mike in SA]

 

I'm not understanding the critique of Dolciani as being just drill.  At least in the older editions, there are definitely descriptions, diagrams and other explanations of the concepts.  The problems that follow are often progressively harder, such that a student would see that a concept could be applied to whole numbers, fractions, decimals, variables, etc.  (I personally think the word problems and practical problems are also a lot more interesting than what appear in many more recent texts.  They have a lot in common with AoPS imho.)

 

*** NOT complaining about Dolciani ***

 

Dolciani herself wrote wonderful textbooks in the mid-60's.  That was the transition period from classical math to "new" math.  Her books had some of the old, and some of the new.  They were very good books.

 

The books since then focused on what she added: more piecemeal delivery and drill on each piece.  I didn't mean to criticize her or her texts in any way.  It was just a comment on the pre-Dolciani era versus the post-Dolciani era.  She really had that much of an impact on education.

 

If you can get one of her books from the 60's, it will be worth your time to use them.  I'm not so fond of newer "system" books, but each works well for a particular audience.

[raptor_dad]

We've never used Dolciani before, but next year dd will be taking her Geo class with Jurgensen/Brown, which leads into Dolciani Alg2, so this makes me more curious. :)  Dolciani didn't write a Geometry text herself, did she?

 

A predecessor to the Jurgensen/Brown book was Jurgensen/Donnelly/Dolciani Modern School Mathematics Geometry. So yes Dolciani did coauthor a Geometry text.

 

I have a 1969 copy and Chapter 1 is set theory and basic geometry definitions, Chapter 2 is induction and deduction( truth tables, venn diagrams, basic proofs), Chapter  3 onward dives straight into axioms and both 2-column and paragraph geomtery proofs.

 

I've only seen some of the other Jurgensen texts but I recall all the ones up until at least the late 80's being fairly similar. I'm not sure when the changes Mike in SA is complaining about happened.

[Mike in SA]

A predecessor to the Jurgensen/Brown book was Jurgensen/Donnelly/Dolciani Modern School Mathematics Geometry. So yes Dolciani did coauthor a Geometry text.

 

I have a 1969 copy and Chapter 1 is set theory and basic geometry definitions, Chapter 2 is induction and deduction( truth tables, venn diagrams, basic proofs), Chapter  3 onward dives straight into axioms and both 2-column and paragraph geomtery proofs.

 

I've only seen some of the other Jurgensen texts but I recall all the ones up until at least the late 80's being fairly similar. I'm not sure when the changes Mike in SA is complaining about happened.

 

*Drools*

 

As I said before, I have no complaints about Dolciani's books.  I suspect you confused my discussion of educational eras with her own books.  Not one and the same.  Her books were great.  Her work was also a major turning point in educational methods.

 

It's the authors who came AFTER that draw my ire.  There are still some good ones, but there's a lot of junk, too.  Imitations are rarely as good as the original.

[JadeOrchidSong]

NittanyJen,

I am interested in your reviews of Discovering Mathematics and AOPS that you use for your dc. Ds11 is doing Dolciani Prealgebra. I would like him to do integrated math and DM is one of them. I am also considering Jacob's Elementary Algebra. I grew up in China and remembered my math teacher encouraged us to find multiple ways to solve or prove math problems. We would go up to the blackboard and each did his or her own way and then we all compared them. We also had to copy all the math questions from the textbooks onto our own blank notebook. Workbooks were unheard of. My primary school and middle and high school were all together only 10 years. I remember we did all the integrated math that covered algebra 1, algebra 2, geometry, and trigonometry. I hope I can teach my kids the integrated way. Is DM the way to go? I really don't like the wordiness of AOPS. Thanks!

[Kathy in Richmond]

A predecessor to the Jurgensen/Brown book was Jurgensen/Donnelly/Dolciani Modern School Mathematics Geometry. So yes Dolciani did coauthor a Geometry text.

 

I have a 1969 copy and Chapter 1 is set theory and basic geometry definitions, Chapter 2 is induction and deduction( truth tables, venn diagrams, basic proofs), Chapter  3 onward dives straight into axioms and both 2-column and paragraph geomtery proofs.

 

I've only seen some of the other Jurgensen texts but I recall all the ones up until at least the late 80's being fairly similar. I'm not sure when the changes Mike in SA is complaining about happened.

 

Interesting! That might have been the edition I used back in high school.

 

I own a copy of the 1973 edition of Jurgensen & Donnelly, but with Maier as the 3rd author in place of Dolciani. The first three chapters you've mentioned above were combined into one at that point. Ch 1 covers basic definitions (point, line, plane, angle), reviews the postulates & theorems of algebra, then covers postulates, theorems, inductions and deduction, and proofs in geometry. No set theory or Venn diagrams, though.

[HSingThruMyLord]

Krystan~

Don't know if this is helpful but my otherwise bright son struggles with math as well. We used Chalk Dust Pre-Algebra this year. The DVD's are very thorough, not flashy, with an actual math teacher teaching and the text book is very clearly organized. We only watch the Section of the DVD for that day's exercises so it is not overwhelming.

He is doing better and we will continue with Chalk Dust's Algebra 1 this year. We did Singapore from K-6 so he had a challenging foundation and this is easier

Blessings!

Niessa

[raptor_dad]

*Drools*

 

As I said before, I have no complaints about Dolciani's books.  I suspect you confused my discussion of educational eras with her own books.  Not one and the same.  Her books were great.  Her work was also a major turning point in educational methods.

 

It's the authors who came AFTER that draw my ire.  There are still some good ones, but there's a lot of junk, too.  Imitations are rarely as good as the original.

 

Less so recently, but certainly in the pre-AoPS days, there have been many threads on the difficulty getting vintage math books. This is certainly true if you need ancillaries like TMs and WBs. However my drool-worthy copy is available currently for $0.25 + $3.99 shipping http://www.amazon.com/Modern-School-Mathematics-Geometry-Jergensen/dp/0395131022/ref=sr_1_2?ie=UTF8&qid=1407270743&sr=8-2&keywords=dolciani+geometry  Maybe there are other listings...

 

I bought 60's copies of Dolciani Alg1/Geo/Alg2 for under $25 combined including shipping. I have a copy of the Dolciani/Beckenbach "Modern Introductory Analysis" precalc text that is supposedly in the mail for ~$10 including shipping. I bought a ~$15 like new copy of Allendoerfer/Oakley's "Elements of Mathematics", a precalc text, off of one Allendoerfer's grad students on ebay. If you want these books and are willing to wait a short time they are usually available quite cheap.

 

PS. If  you want my recommendation... I would get a 1st or 2nd edition of Jacobs. It is more kid friendly and still plenty rigorous.  I personally have a 1st ed which I bought on Amazon for ~$20 w/ shipping. Similar copies are available today http://www.amazon.com/gp/offer-listing/0716704560/ref=tmm_hrd_used_olp_1?ie=UTF8&condition=used&sr=8-3&qid=1407271548 If you need TMs it is expensive, if you can teach on your own books should be cheap.

 

ETA:

 

PPS: Various books I mention above were $50+ used when I first started looking. Lots of 3rd party vendors use automated pricing algorithms. Jacobs Geometry prices decayed roughly 0.30-40 a day. Around Dec/Jan it was $40+ , in late March it was ~$17 + $4 shipping.

 

This is typical. I have a White KF World History Encyclopedia that is also a cult item that I bought for ~$8 w/ free shipping in the last 2 years. If you are patient most items are cheap...Rare books like the CSMP Elements of Mathematics of Frank Allen's Algebra a Logical Approach are unfortunate exceptions :( .

[JadeOrchidSong]

raptor_dad, thanks to your link, I am just $15 +$3.99 happily poorer for Jacob's geometry! I am also sorely tempted by that $0.25 geometry book but decided I spent enough. Now I seriously need to find a Jacob's Elementary Algebra for that price, too. Can you help in any way?

I have been addicted to math books lately, watching eBay and such. I just won a bid on a Singapore secondary math set.

[NittanyJen]

NittanyJen,

I am interested in your reviews of Discovering Mathematics and AOPS that you use for your dc. Ds11 is doing Dolciani Prealgebra. I would like him to do integrated math and DM is one of them. I am also considering Jacob's Elementary Algebra. I grew up in China and remembered my math teacher encouraged us to find multiple ways to solve or prove math problems. We would go up to the blackboard and each did his or her own way and then we all compared them. We also had to copy all the math questions from the textbooks onto our own blank notebook. Workbooks were unheard of. My primary school and middle and high school were all together only 10 years. I remember we did all the integrated math that covered algebra 1, algebra 2, geometry, and trigonometry. I hope I can teach my kids the integrated way. Is DM the way to go? I really don't like the wordiness of AOPS. Thanks!

 

Hi Jade,

 

Sorry it took me so long to get back to you-- I have been assembling a chemistry co-op class for the first time ==:O  It has occupied a lot of my time.

 

We have been really happy with Singapore DM for the integrated approach to algebra/geometry/trig-- happy enough that I did go ahead and locate copies of the going out of print levels 3 & 4, and not sure if they're going out of print Advanced Mathematics, which introduces more trig topics and begins early calculus.

 

These books are the opposite of AoPS in terms of brevity.  They are written to the student, though I choose to continue to work with my son, because he studies better that way.  The workbook that accompanies these texts is actually not consumable-- there is not sufficient space inside to work in the workbook, and for this book as well as the text, the problems are to be copied into a separate notebook.  The workbook supplies additional problems that continue to develop the thoughts from the text, and I do recommend them-- the problem sets in the texts are excellent, but brief.  I have been using the workbooks for review a couple of months behind the text; again, that is how my son works best.  Others might work better by working through all the problems at once and learning it more solidly in the first place.

 

We often work together on a white board, or sometimes on the computer-- the textbook makes use of a program called Geometer's Sketchpad, for which you must purchase a subscription, but I have found the subscription worthwhile, as the program is very interesting to use and allows the student to develop geometric relationships as he goes before I present them to him formally, and he can see how the angles and lines and volumes and shapes all relate to one another in a dynamic way.  Just as with the earlier, Primary Math series, sometimes the books require hands-on activities such as cutting out shapes from paper to develop an appreciation of relationships, and the exercises let the student try different things to get an excellent sense of why the relationships work the way that they do.

 

I don't have experience with Jacobs, but for seeing different presentations of things, having a text that nicely facilitates discussion between teacher and student or alternatively allows a motivated student to work alone, and uses the integrated approach, I love Singapore DM series.

[JadeOrchidSong]

Thank you, NittanJen. Your response if very helpful. I bought eh whole set of DM 1 for $25. Now I hope I get lucky to get DM 2 for that price, too.

[angela in ohio]

All of my children do Algebra twice, no matter what year they first get to it. It is my rule; they also do Calculus I twice. :) I have done it with two so far - one confident and natural in math and the other not - and I haven't regretted it at all.

 

Yes, many schools only count courses taken in the four years of high school. You probably wouldn't want her to stop her math sequence anyway, so she could have four years, just higher. My oldest had Alg II, Trig, Calc, CC Calc. No problem with admissions for the courses that were taken earlier. My middle was in Calc her freshman year; I am not concerned, after talking to numerous college admissions folks, about the lack of Algebra and Geometry on her HS transcript.

[dovrar]

"Principles of Mathematcs"?

 

 

I bought a ~$15 like new copy of Allendoerfer/Oakley's "Elements of Mathematics", a precalc text, off of one Allendoerfer's grad students on ebay.

[kiana]

 

"Principles of Mathematcs"?

 

 

I bought a ~$15 like new copy of Allendoerfer/Oakley's "Elements of Mathematics", a precalc text, off of one Allendoerfer's grad students on ebay.

 

 

What's your question?

 

I believe I have a copy of this book -- at least, I have several precalculus-level books by Allendoerfer and Oakley -- if you have a question. 

[Janeway]

We used Foerster's for Algebra 1 and then Jurgensen's for geometry. Now we are doing Foerster's for algebra 2. I loved the choice of Jurgensen's.