Algebra II next or Geometry?

[King's Kid]

My dd14, 9th grade, will finish her Alg. I by mid-Jan. I can't decide if she should go on to Geometry next, or Alg. II.

Which do most of you WTMers have your high schoolers do after Alg. I?

TIA!

[jayfromcleveland]

My son went straight into Saxon Algebra 2, and I feel this the way to go. IMHO, classical Euclidean geometry should be a math elective. I don't agree that it should obstruct the path to trig and calc, which are algebra based. I'm sure rote memorization of theorems is fine mental discipline, but the traditional approach of formal proofs, etc goes away forever after Geometry, and does not help a student prepare for higher level math classes.

From my experience, geometry was a "weed out" class. I bombed out, thus terminating my public high school math sequence. But I made up classes at community college and geometry was not on the path from algebra to calculus and beyond. I got mostly As and Bs in college. In getting my physics degree, we took a few courses in calc-based vector analysis, which essentially comprised everything from Euclidean geometry.

So IMHO, geometry is a useless waste of time, but perhaps I'm biased.

my two cents, jay

[kiana]

Taking Algebra II in 10th grade and pushing Geometry to 11th might cause her standardized test scores to be slightly lower, if that's important to y'all. Otherwise, really, either's a legitimate path -- Geometry programs often, however, have Algebra I review incorporated but not Algebra II, so she'd have to review a lot more if she went that path.

To JFC: Geometry is not actually about "rote memorization of theorems", but rather understanding why the theorems work so that one can construct the proofs without needing to memorize them. Perhaps your class was taught as a rote memorization class -- if so, this would certainly explain your struggle and disillusionment. It's also possible to find bad teachers. The college sequences I've seen seen don't list geometry as a separate course because they incorporate it into the algebra/precalculus/calculus sequence. I assume, also, that if the OP's daughter struggles in Geometry, she will not terminate her math sequence.

[Lori D.]

Our math progression is to put Geometry between Algebra I and II, to be doing Algebra II in the junior or even senior year, closer to the time the student will be taking SAT testing. I understand that the SAT test questions are far more about Algebra II than Geometry, so you'd want to be "fresher" with the Algebra II.

Also, FWIW, we used Jacobs Geometry which is fairly proof heavy and have found that is has been of great value in helping the student develop sequential logical thinking, which helps in writing essays and in discussing issues. : ) Jacobs Geometry also covers area and volume of various solids.

BEST of luck, whatever you go with! Warmest regards, Lori D.

[LisaK in VA]

Most places I've been, taught or gone to school had the Alg. 1, Geometry, Alg. 2 sequence.

I was one of those kids who struggled and fought her way through Algebra I, and flourished in Geometry. By the time I got to Alg. 2, I really understood it -- my dad was the same way.

[Michelle in MO]

I believe that most kids fare better if they do Algebra I, then Geometry, and then Algebra II. Many kids are not ready for the more difficult concepts in Algebra II right after Algebra I.

My oldest did fairly well with Algebra I in eighth grade. Then I had her do Algebra II in ninth grade. For us, that was a huge mistake. She completely failed all of her tests the second half of that year, and this left her with a hatred of math for that entire year. The next year (tenth grade) she did Geometry (Chalkdust) and that went much better for her. This year she's repeating Algebra II and she's getting it!

Everyone has their own opinions on this subject, and I've read arguments for both ways. However, IMO, Algebra I is the first stepping stone. Geometry reviews and uses some of the concepts in Algebra I and also is a good preparation for trigonometry. Algebra II takes the concepts from Algebra I and Geometry and helps launch the child into trigonometry and then calculus. Personally, I would not recommend skipping Geometry. I believe there is great value in learning those principles from Geometry: 1) the introduction to trigonometric principles; 2) giving the child a break from the more abstract Algebra; and 3) learning to develop proofs and theorems, which is applicable to many fields of study. To name a few: logic, philosophy, writing research papers, economics, history (for the latter three, the study of cause and effect), etc. Yes, those are not fields of "math", but the logical thinking and development of proofs can help the developing logical thinker learn to reason more thoroughly.

Plus, I liked Geometry in high school! It was the one math class that I carried almost a 100 average for the entire year.

[YJ in AL]

I have had the same experience as Lori. Jacob's Geometry really helped my middle ds with his logical thinking.

Yvonne in Alabama

[jayfromcleveland]

To JFC: Geometry is not actually about "rote memorization of theorems", but rather understanding why the theorems work so that one can construct the proofs without needing to memorize them.

Thanks, but after getting a college minor in math, I think I have a glimmer by now of what geometry is about.

Rather than bothering with canned curricula, I would recommend that anyone get a copy of Heath's translation of Euclid's Elements from Dover and drink from the source.

[Kareni]

The path here:

My teen did Algebra I in 8th grade using Lial's Beginning Algebra. The following year, she did Jacobs' Geometry. In 10th grade, she did Algebra II using Lial's Intermediate Algebra.

In 11th she took College Algebra and Trigonometry (with Sullivan's Pre-Calculus) at the local community college.

This year, as a 12th grader, she's taking AP Statistics through PA Homeschoolers.

Regards,
Kareni

[Beth in SW WA]

I'm not planning to commit an entire year to Geo. It will tag-team w/ Alg 1 & 2. Ds is doing a bit this year in 8th but will finish up in 9th, so we will put Alg 2 & Geo in 9th (for transcript purposes).

This plan could be thrown out the window at a later date. :)

[kiana]

JFC: I honestly wasn't intending to snark in my original comment, as many people have been taught in the past that Geometry IS about rote memorization.

But it's not. And a college minor barely begins to qualify you as to "what math is about", since from your own description I doubt you touched on any of the actual proof-based classes, which is all you find in math after a certain point.

Again, I'm not meaning this to devolve into a flamewar, but simply was contradicting misinformation.

[yeongil]

There really should be a sticky on the question about math sequence. It sure gets asked often here. ;)

I'm teaching at a school where the sequence is Alg1-Alg2-Geom, and I'm leading the charge to get that changed to the normal Alg1-Geom-Alg2 sequence. You can see the stuff I collected that supports my argument here: http://www.welltrainedmind.com/forums/showthread.php?t=67580

Anyway, to answer the OP's question another vote for Geometry here.


01

[Jane in NC]

Thanks, but after getting a college minor in math, I think I have a glimmer by now of what geometry is about.

Rather than bothering with canned curricula, I would recommend that anyone get a copy of Heath's translation of Euclid's Elements from Dover and drink from the source.

(Gently now...)

As a new poster to this board, Jay, you may not realize that there are a number of participants with BS and MS degrees in Math, Stats and Math Ed. Further, if you were to read through the archives, you would see that there is no agreement on a correct path.

I know what worked for me and my son. Hence I recommend a solid geometry course centered around proofs and constructions. Most high school students (frankly most students who only study mathematics through differential equations) only see an algorithmic side to the subject. Real Mathematics, as you know, is about proof. Most American high school students do not prove much in algebra courses or precalc. They might do some verifications of identities in trig. But that is about it.

Geometry is not only an introduction to the Mathematics as it really is but also an opportunity for an examination of logical arguments.

Some posters on this board study Logic as a separate course. Particularly for those who do not, I feel that the rigors of a proof based geometry course will help that student not only down the road in math and science but in rhetorical work as well.

Finally, as everyone knows, not all text books are equal or standard in their approaches.

To answer the original question: I recommend Algebra, Geometry, then Algebra II, etc. Call me a Traditionalist.

Best,
Jane

[Nan in Mass]

You can add soft-ware engineering to the fields in which proof-based geometry is applicable.

[Nan in Mass]

I'm not a mathematician, but if I had to keep only one class from high school, that is the one I would keep. That is the class that taught me to think. My class wasn't just memorizing. If it had been, I would certainly have flunked LOL. In mine, there wasn't any memorization (that I remember); instead, it was almost pure thinking/problem solving. I learned to break a bigger problem into parts and solve them one by one. I learned to think back to the roots of things. I learned to spend time sort of gazing at something until suddenly the answer occurred to me (an amazingly useful skill). I learned to back up and try again when something didn't work. And again. And again. I learned how to define a problem... and lots of other useful stuff.
-Nan