Is Pre-Algebra necessary?

[loftmama]

This may sound silly, but I've been thinking lately about my own public school math education and I don't recall ever taking a pre-algebra class nor does my husband. I went to a school with about 25 people in my grade and only one math option. During my 8th grade year we moved to a school with about 80 in my grade and more than one math option. I went into regular math but in order to be on a college track, I had to take both Alg I and Geometry my 9th grade year. I had never had anything other than 8th grade math. So I'm just wondering, is Pre-Algebra a new thing? Is there something wrong with going straight into Algebra? We didn't have "gifted" or "AP" although I suspect there was "tracking." I did ask a friend today what the difference was between Saxon Math Algebra 1/2 and Algebra I and she mentioned that Alg I has Geometry in it. Still, I don't understand why a kid has to take Pre-Algebra. Any thoughts on this from you experienced homeschool parents? Thanks!

[jennynd]

There is no pre A in many Asian countries. From what I saw, preA just review and strengthen the problem solving skills, which are done at 6th grade in most Asian country . Then we jump right into algebra. I remember the section 7 in the first chapter was complex number when I was 1st year (7th grade) in middle school ( I was goofing around and got caught by the teacher.so I had traumatized memory about complex number.. :).

Anyhow, DS used Singapore and I do think the 6 th grade material had enough complex problem solving problems that is sufficient to be used as PreA. However, I can't say the same about most US curriculum simply because I did not have the experience

[mom2bee]

Removed by the Author.

[Chrysalis Academy]

From what I can see, everything after 5th grade math and before algebra is just deepening and extending (or reviewing, or learning in the first place) basic arithmetic, and then starting to work with variables. I don't think formal PreA is necessary. I'm planning on using an enriched MM6 as "preAlgebra" and then moving into algebra.

 

I do remember back in when I was in school, I was on the "accelerated" track, and what we did in 7th grade was called PreAlgebra, and then we did Algebra in 8th (this was in CA). I don't recall that I learned anything new in 7th grade, it was basically a review of what I'd learned in 6th grade. FWIW.

[ErinE]

I went from an accelerated 7th grade math to Algebra in eighth. It wasn't called Pre-Algebra. I think the re-naming comes in so the student (and parent) can see an end goal. In high school, the year before Calculus was called Pre-Calc, which sounds much better than "A Whole Year of More Algebra Before You Get to Calculus."

[Targhee]

I think PreAlgebra was the name they gave to the math class before algebra that was taken out of the normal sequence (ie early, or late as in high school) in order to distinguish it for the grade level math. I think if you are going into algebra early a PreAlgebra class is a good because you will be certain to cover all topics necessary to start algebra in the next year. You could use a regular grade level text and be ready to take algebra in 8th or 9th grade without the "PreAlgebra" course.

[regentrude]

No. Actually, there is no such thing as "prealgebra".

What is necessary as a prerequisite for algebra is a thorough mastery of arithmetic, i.e. addition, subtraction, multiplication and division with positive and negative integers and fractions, including decimals and percent. This does not have to be taught in a "prealgebra" course (and most definitely does not need eight school years to accomplish!)

[Arcadia]

It depends on a few factors:

Firstly, whether the child needs the review and consolidation.

Secondly, what textbook/curriculum you are using for prealgebra.

Thirdly, what you as the tutor wish to use prealgebra for.

 

If your child needs review, skipping prealgebra obviously makes no sense. If a child is mathematically strong, doing prealgebra may seem like a waste of time.

Prealgebra textbooks are not created equal. I have read through all of california's prealgebra public school textbooks as my libraries have copies. Algebra school textbooks are not created equal too, again I have read through those.

My older finished SM6 before he turned 8. I am using AoPS prealgebra for review and consolidation. At the same time I am "training" him to be more careful with his work.

 

I agree with Regentrude though, I only heard of prealgebra in the states. We don't have that in Asia. We don't have precalculus either, it is all intergrated. I agree with Jenny, you goof in math class and you likely get "tortured" by complex numbers.

 

 

ETA:

Can't find when prealgebra started in the states except the old textbooks are in the 70s. However I found some algebra readiness test in case anyone wants to have a go.

 

Saxon homeschool algebra

http://saxonhomescho...r_placement.pdf

Jacobs Algebra test written by Dr Callahan

http://www.askdrcall...iness-Exam.html

MathUSee

http://www.mathusee....adinesstest.pdf

AoPS pre-test

http://www.artofprob...bra/pretest.pdf

[dereksurfs]

I look at Pre-Algebra as a method for building a mental bridge from Primary to Secondary Mathematics. This is a critical stage in a child's life as they move developmentally from concrete operations to abstract reasoning. Can a child jump right from decimals and percents to formulas and multivariable equations without any introductions? Sure. But is it painful or difficult for some? Of course it is.

 

Now some programs may lay an earlier foundation including introductions to variables and equations. But IMO that is the beginnings of Pre-Algebra. Its simply preparation for more difficult, abstract subject matter to come. To continue in that same fashion at the end of primary math further builds this mental bridge to the abstract world of math soon to follow. As was said earlier there is a *big* difference in Pre-Algebra as well as Algebra programs out there from the easy to the very challenging.

 

So I don't think lines can be that easily drawn to say absolutely, Pre-Algebra is or is not needed, though one could argue not in its traditional US sense as a single course in time. I don't think early algebraic concepts should be left out until Algebra 1 has formally begun. The answer to this question also depends on many factors including the child's unique learning needs, abstract reasoning skills, maturity level, previous training, retention of primary mathematics, etc... I think Pre-A can begin early and then tailored to the individual child's development. This tailoring includes varying the rate at which new abstract concepts are presented as well as their level of difficulty. For the very bright math student the process can obviously be accelerated and so on.

 

Lastly I must also mention that after growing up in the US and taking traditional primary math *without* Pre-Algbera of any kind I was not ready for Algebra 1. After struggling through all the abstract concepts quite a bit the lights eventually turned on. Then math became easy, relatively speaking of course. But I am purposely doing the opposite with our kids to avoid that abrupt introduction to the world of the abstract. In fact I think Algebraic reasoning is so important I want to devote up to two years really solidifying these concepts. For us that started in earnest with TabletClass Pre-A which had a lot of Algebraic content in it. Though it really started earlier with things like Hands on Equations during the elementary years.

[Arcadia]

Found a 2009 thread "Can you skip Pre-Algebra" http://forums.welltrainedmind.com/topic/123487-can-you-skip-pre-algebra/

Saxon 8/7 or prealgebra http://forums.welltrainedmind.com/topic/270637-saxon-users-87-or-pre-algebra/

Who skips TT Pre Algebra http://forums.welltrainedmind.com/topic/404105-who-skips-tt-pre-algebra/

[Lilaclady]

I don't think you have to have a class named prealgebra as long as you cover all of arithmetic, decimals, percents, ratios, negative integers and the like. Some curries don't call it preA and over here, they are even starting an integrated math curriculum and so labeling all math classes by the grade name ie. math 8, math 9 etc.

[Tess in the Burbs]

I don't remember preAlg either in school and I really struggled with our choice for next year. Ds is ahead in math and hitting algebra in the fall at 11/12 seemed too early. He doesn't love math. At first we were going to go into it and do algebra slowly but his personality just isn't one to accept challenges, so we decided to do a 'prealg' year next year with the Derek Owens pre algebra. Mostly to cement his knowledge and give him another year to mature before trying algebra. He really wanted this more than I did. And with his input I hope it's a successful year!

[K&Rs Mom]

I don't think it's necessary, but I wanted to delay my 10yo a little before jumping into Algebra, and try to fill any gaps, so taking a half-year to do it was right for her. I see my 8yo going in the same direction, so I guess maybe it's necessary in my house. I don't think I'd spend an entire year unless they really needed a lot of review - as others have said, it's pretty much just a roundup of all the earlier arithmetic topics.

[loftmama]

Thanks, everyone, for sharing your experiences with PreAlgebra. Regentrude, I appreciate you chiming in, too. Arcadia, thank you for those links!

 

I wouldn't entertain *skipping* anything lightly. I don't want to rush him if he'll miss something essential but I also don't know why he can't just go straight to Alg 1 like we did back in the old days. I will spend more time examining the differences between SM Alg 1/2 and SM Alg 1 as soon as I get the Alg 1 book from my friend. I can't find a table of contents online for Alg 1. Do any of you know of a link with that listed?

 

I clicked with Algebra in school and have been playing Algebra games with him since he was 8 or so. So I think he is just as ready for Alg 1 as he is for Alg 1/2 - especially if there's more Geometry in it, which is what he really loves. But I definitely don't want to push him if he's not ready. I'd rather he get there at his own pace loving it than push him before he's ready and resent it. I just don't want to hold him back unnecessarily.

 

Thanks!

[Crimson Wife]

Ds is ahead in math and hitting algebra in the fall at 11/12 seemed too early.

 

You are obviously in the best position to judge your child's readiness for algebra 1 vs. pre-algebra, but in many districts, algebra 1 in 7th is now the standard "honors" track. My entire state has algebra 1 in 8th as the standard, and in my district 75% of students take it before 9th. 20% take geometry before 9th. I have to personally keep in mind the "signaling" effect of when my kids take algebra 1. If I don't have them in algebra 1 by 7th, then I am signaling to colleges that they are not in the top 20% of students.

 

It isn't just a California thing, either, as the secondary school in my hometown in MA shifted their "honors" track to have algebra 1 in 7th rather than 8th a few years back.

[loftmama]

Wow, 8th grade is the norm for Algebra in CA! Well, I guess my 12yo is right on track for average then. I'm glad he's not being tracked! I guess I'll just quit sweating it, then, and move him from SM 76 to Alg 1. If I didn't like Algebra so much, I might be worried about the big jump. But I love it and know I can teach it. (I tutored high school Alg and College Alg.) And I am completely confident in his math skills, so leap we will. Thanks!

 

Now I wonder when students in Texas take Algebra...

[Lanny]

<snip>

Now I wonder when students in Texas take Algebra...

 

 

No idea if this applies to all Public School Districts (ISDs) in Texas or not.... I believe TTUISD normally has them taking Algebra 1 in 9th grade. Algebra 1 is a High School course in Texas, and there is an EOC (End of Course) examination required. If Governor Perry signs the Bill that passed, unanimously, 2 days ago, there will still be an EOC examination required for Algebra 1, if they reduce from the current 15 EOC examinations to 5. So, Algebra 1 is critical in Texas for High School graduation....

 

DD is in 6th grade and if she continues above 90% for the second semester Math, she will probably be allowed to take what is normally 8th grade Math (Pre Algebra), when she is in 7th grade. The Principal explained to me that they really suggest not taking Algebra 1 before 8th grade, so the students are more mature, and that is a critical course, because of the EOC examination for High School graduation.

 

That said, I correspond with a TTUISD family that is temporarily in Europe and I believe their older daughter had been accelerated in the Houston area and that she took Algebra 1 in the 8th grade in TTUISD. She had to wait until she was in the 9th grade, to take the EOC examination for Algebra 1, which was difficult for her, since she had finished Algebra 1 many months before...

[loftmama]

Thanks for chiming in, Lanny. I just read something about Texas dropping Algebra 2 as a requirement for graduation and didn't know about the EOC tests although I guess we're waiting to see if Perry passes it. I'm pretty sure Algebra 1 is a 9th grade course where I live.

[dereksurfs]

I would be very hesitant to base these decisions upon what the public schools do in any particular state. Although it is interesting to hear about the differing standards. The reason for this is that each child is so different with a unique set of gifts and abilities. I would especially not want to hold back a gifted math student from starting Algebra until 8th or 9th grade if they are clearly ready to start it earlier. There are so many paths one could take if advanced as we've seen on the forums here. For example they can take calculus based sciences while still in high school at a university or as an AP course. I would be more concerned with college readiness vs. state standards which are ever changing and lower than most other developed nations.

 

One exception would be if a child is planning on attending public school in high school. Even in that case the student could do a review prior to testing if advanced beyond their state peers. Another option would be to study both courses concurrently such as Algebra and Geometry over an extended period of time. I would like to spend more time with ds11 in Algebra 1 since he started during the 6th grade this year. So I plan to extend it out with some Geometry work.

[texasmama]

In Texas here. :D

 

I took Algebra in 8th grade. I don't recall what my 7th grade math class was called. That was back in the early 80's. Ahem.

 

In a local public school district, a 6th grader I know is on the fast track and is taking pre-Algebra. He will take Algebra in 7th. This is a smallish school district, BTW, not one of the large metroplex ones.

[texasmama]

I felt so strongly about this topic, I posted twice. :)

 

But I could add that both of my boys (5th and 7th grades next year) will be working their way through pre-Algebra using two very different programs. Algebra will follow for both of them the year after if all goes as planned.

[jennynd]

Now I wonder when students in Texas take Algebra...

 

 

It will be varied from one school district to another. I live in NY capital region. One of the lady on this board I believed lives very close from me. From her post I gathered her school district offers no acceleration in math whereas my school district does double acceleration for qualified kids. They accelerated 1 level max for elementary kids and combine 7/8/algebra in 2 years. So kids can do algebra in 7th grade.

Just want to say there is big variation between districts.

[loftmama]

TexasMama, I'm curious what book you will use for your 5th grader. I'm starting Algebra "games" with my 9yo - just fun ways to play with numbers that I make up.

 

There is a lot of variance around the state, not to mention around the country!

[Trish]

 

 

You are obviously in the best position to judge your child's readiness for algebra 1 vs. pre-algebra, but in many districts, algebra 1 in 7th is now the standard "honors" track. My entire state has algebra 1 in 8th as the standard, and in my district 75% of students take it before 9th. 20% take geometry before 9th. I have to personally keep in mind the "signaling" effect of when my kids take algebra 1. If I don't have them in algebra 1 by 7th, then I am signaling to colleges that they are not in the top 20% of students.

 

It isn't just a California thing, either, as the secondary school in my hometown in MA shifted their "honors" track to have algebra 1 in 7th rather than 8th a few years back.

 

 

I'm sorry but I can't agree that just because a student is not ready for algebra in 7th grade, that they are "not in the top 20 percent of students" ability-wise. I think algebra is VERY MUCH a developmental thing, and pushing a student into algebra before his/her brain is ready for it can set them up for failure down the road.

[texasmama]

TexasMama, I'm curious what book you will use for your 5th grader. I'm starting Algebra "games" with my 9yo - just fun ways to play with numbers that I make up.

 

There is a lot of variance around the state, not to mention around the country!

 

I chose AoPS pre-Algebra for my 5th grader because it seems to be a fit for his personality/learning style. This is our first trip down the AoPS road so I don't have any concrete feedback on it yet. If the program works for him, we will continue with Algebra the next year. I will be using a Dolciani (1985) text with my 7th grader so if AoPS falls flat with my 5th grader, I have the option of switching him to another program, either Dolciani or SM level 6, which I already have. I like my plan, but I have no idea if it will work for my kids. Time will tell. :)

 

There is a good thread started by WendyK (I think?) regarding AoPS pre-A which you might want to check out.

[Trish]

 

 

 

They may be in the top twenty ability wise at a later point, but they've missed the boat in many districts because there are no honors classes offered to students who didn't board in seventh. Some progressive districts do offer a catchup with summer work so that they can cross over to honors at a later point, but that is a rarity.

 

 

That is a failure of the district, not the student. It is unfortunate if districts and parents alike are signaling to children that they've "missed the boat" if they are not ready for algebra in 7th grade. Many are not, and that is no reflection of their math ability or potential future performance. Or the promise of a STEM career, for that matter.

[wapiti]

You are obviously in the best position to judge your child's readiness for algebra 1 vs. pre-algebra, but in many districts, algebra 1 in 7th is now the standard "honors" track. My entire state has algebra 1 in 8th as the standard, and in my district 75% of students take it before 9th. 20% take geometry before 9th. I have to personally keep in mind the "signaling" effect of when my kids take algebra 1. If I don't have them in algebra 1 by 7th, then I am signaling to colleges that they are not in the top 20% of students.

 

It isn't just a California thing, either, as the secondary school in my hometown in MA shifted their "honors" track to have algebra 1 in 7th rather than 8th a few years back.

(Disclaimer: if a student isn't shooting for top-tier colleges, I think this discussion is unlikely to be relevant.)

 

In the past, I too have wondered about this based on our local middle school's tracks ("gifted math" students - 98th percentile - take alg in 7th, other advanced in 8th and regular in 9th; even more complicated, my dd's private middle school teaches algebra 1 only to the advanced students over two years - 7th and 8th - though my dd ended up starting alg 1 this year in 6th so she'll finish next year in 7th).

 

However, my personal guess is that colleges - even top-tier ones - do not care at all what grade level the student took algebra 1. Instead, I think they'll care what the student did in late high school. I'd be interested to hear what the usual math track is in these high schools, specifically for junior and senior years, for the students who took alg 1 in 7th. Will most of the advanced math students end up taking a course that's sequentially beyond AP Calc BC or some alternative, rigorous math course that makes them interesting applicants for top-tier schools? If they're not taking math beyond AP Calc BC, I doubt it matters for all but the likes of MIT/Caltech (and even then, from reading the MIT admissions math jam at aops, it seems that there's flexibility in how they view things).

 

Eta, my assumptions include the fact that a student taking algebra 1 in 8th can most likely work their way into calc BC senior year if they so desire.

 

Eta, sorry OP, for going so far off-topic. Regarding prealgebra, programs that don't list a "prealgebra" usually cover the same topics in 8th or 7th/8th, just without that title. (My kids have used/are using AoPS Prealgebra.)

[Arcadia]

I really don't know though - I'd be interested to look at a top high school's website that discusses math tracks, if someone can recommend one. My kids will probably attend a Jesuit high school that has certain "usual tracks" based on one's math level upon entering (eta, and of course peformance).

 

These are from the "top" high schools in my area.

http://www.paly.net/academics/math/mathPausdFlowChart.pdf

http://lynbrook.schoolloop.com/file/1346928306289/1226804937203/5186278870320010832.pdf

http://www.debratroxell.com/MathDept/images/MathScopeAndSequence.jpg

 

My school district is middle of the road and has dual enrollment arrangements with the community college near my home. So I don't know how that affects the accelerated math track.

[wapiti]

These are from the "top" high schools in my area.

http://www.paly.net/...sdFlowChart.pdf

http://lynbrook.scho...70320010832.pdf

http://www.debratrox...AndSequence.jpg

 

My school district is middle of the road and has dual enrollment arrangements with the community college near my home. So I don't know how that affects the accelerated math track.

 

Ah, thank you, Arcadia, ever the font of useful links!!

Edited March 15, 2016 by wapiti

[Dmmetler]

I don't think you need it-SM 6a/b is essentially pre-algebra, as, I suspect, is MM 6. Having said that, my DD really, really wanted to start "Algebra"-so doing a year of "Pre-Algebra" gave her a book with that word "Algebra" on the cover while still actually being a year of reinforcement, and fit what she wanted/needed better than SM 6 would have (I had her do a lot of the CWP for SM 6 anyway ;) ).

 

I do think, looking at AOPS Pre-Algebra, that it's a good book to go through if you've got a kid inclined to the math competition route, because it contains so much that's not in the typical K-6/K-7/K-8 math sequence.

[Dmmetler]

FWIW, to be eligible for Algebra in middle school here, you have to be in the top 10% of the state test or the top 25% on the EXPLORE in the grade before-so you had to be in the top 25% of 8th graders taking the Explore in 6th or 7th in order to take Algebra in 7th or 8th. And you won't be eligible for the STEM magnet or the IB high school if you haven't taken it by 8th.

 

They're really trying to return to Algebra 1 for a majority of 9th graders here because the passing rates on the state Algebra exit exam are so abysmal. Which is kind of sad-based on released tests, I think a kid who had finished SM 6 or something equivalent could very, very easily pass it-a lot of the test doesn't require any Algebra to solve whatsoever.

[wapiti]

I don't think you need it-SM 6a/b is essentially pre-algebra, as, I suspect, is MM 6.

 

 

IMO, the not-yet-Common-Core-aligned, current version of MM6 is roughly half prealgebra. There definitely are topics I'd add to it, and expand on, if I were using it as a prealgebra. When MM7 (prealgebra) comes out next year, that should solve the issue for a lot of people.

 

I do think, looking at AOPS Pre-Algebra, that it's a good book to go through if you've got a kid inclined to the math competition route, because it contains so much that's not in the typical K-6/K-7/K-8 math sequence.

 

 

FWIW, I think the usefulness of AoPS goes far, far beyond kids inclined to math competitions (my 10 y.o. boys, for example, aren't currently interested because they equate competition with speed - they'll find out more later :)). The problem-solving perspectives and deep concept understanding that can be had with AoPS are important for more long-term reasons (the same long-term intellectual development to be had from certain secondary-level math competitions).

[Arcadia]

As I suspected, there doesn't seem to be anything that's "beyond" calc BC that's offered *at* these high schools, though the one school has some sort of elective in advanced problem solving.

 

For the students who took AP Calc BC in 11th grade, I believe they take AP statistics or AP Computer Science for 12th grade. Both AP are two semester courses.

This one is from Lowell High, a top school in San Francisco. It is not in chart format but the details for each course are clear enough.

http://lhs-sfusd-ca.schoolloop.com/cms/page_view?d=x&piid=&vpid=1275747746574

[wapiti]

For the students who took AP Calc BC in 11th grade, I believe they take AP statistics or AP Computer Science for 12th grade. Both AP are two semester courses.

This one is from Lowell High, a top school in San Francisco. It is not in chart format but the details for each course are clear enough.

http://lhs-sfusd-ca....d=1275747746574

 

 

That's what I figured. I could use some enlightening, however, on how those two APs particularly enhance an application to a top-tier school with regard to the math sequence - is calc BC even a prerequisite? Nevermind, I guess it must be for AP stats - nope, that just requires alg 2. I just don't see the competitive edge.

 

eta, competitive edge beyond the AP score for calc BC being available prior to admissions, taken spring of junior yr

[Arcadia]

That's what I figured. I could use some enlightening, however, on how those two APs particularly enhance an application to a top-tier school with regard to the math sequence - is calc BC even a prerequisite? Nevermind, I guess it must be for AP stats... I just don't see the competitive edge.

 

Since the public high schools in my area need to fulfill UC A-G requirements, the AP Stats fall under the math category while AP Comp Sci falls under the elective category. AP Calc BC would be a norm in the top area schools. Silicon Valley is probably a skewed student population though with many parents in STEM fields so there is parental pressure on the schools.

We are de-railing the thread :001_unsure:

[Crimson Wife]

I'd be interested to hear what the usual math track is in these high schools, specifically for junior and senior years, for the students who took alg 1 in 7th. Will most of the advanced math students end up taking a course that's sequentially beyond AP Calc BC or some alternative, rigorous math course that makes them interesting applicants for top-tier schools? If they're not taking math beyond AP Calc BC, I doubt it matters for all but the likes of MIT/Caltech (and even then, from reading the MIT admissions math jam at aops, it seems that there's flexibility in how they view things).

 

The honors track kids take AP Calc in 11th and "Post-AP Math" in 12th. I'm not 100% sure what that entails but I think it covers 3rd semester calculus, some DiffEq, and maybe an intro to linear algebra? Students have to score well on the AP Calc exam in order to continue on to it. The alternative 12th grade math is AP Stats.

[Trish]

I would say for those parents whose children are able to sail through math and grasp algebra, there's absolutely no reason to hold them back. (After all, that's one of the primary benefits of homeschooling -- going at your child's pace!) But, the national push to have students take algebra in earlier grades hasn't exactly yielded the results they've hoped for. And that's because kids' brains mature at different rates, and not everyone is ready to take it in 7th grade, or even in 8th. And no one should feel pressured to take algebra early because it will somehow "affect college admissions" or "signal to colleges" that you aren't a good student.

 

It's bad enough that school districts are pressuring kids on this, but we as parents shouldn't be following that flawed lead. We know our kids best, and if they aren't ready for algebra, pressuring them to take it early can be a big mistake. And when I see that pressure on a forum like this (some subtle, some not-so-subtle) I have to object to that viewpoint. For example:

 

 

A new study from the Brookings Institution questioned the national push toward algebra-for-all by eighth grade, and found that the equation is a simple one: teaching algebra and other advanced math courses earlier than the ninth grade does not equal improved achievement.

 

... research suggests that teaching algebra to students who aren't ready to learn it brings unfortunate results.

 

A 2012 North Carolina study of 141,000 students found students taking algebra early scored significantly lower on end-of-course tests in Algebra I. And, they were less likely to pass standard follow-up courses.

 

That suggests that though strong math students can benefit from taking algebra in eighth grade, it is "decidedly harmful" for weaker math students to be rushed into advanced math concepts, Loveless said.

 

http://www.deseretnews.com/article/865577774/New-research-says-the-push-to-have-students-take-algebra-by-8th-grade-has-hurt-not-help-students.html?pg=all

[regentrude]

I would say for those parents whose children are able to sail through math and grasp algebra, there's absolutely no reason to hold them back. (After all, that's one of the primary benefits of homeschooling -- going at your child's pace!) But, the national push to have students take algebra in earlier grades hasn't exactly yielded the results they've hoped for. And that's because kids' brains mature at different rates, and not everyone is ready to take it in 7th grade, or even in 8th. And no one should feel pressured to take algebra early because it will somehow "affect college admissions" or "signal to colleges" that you aren't a good student....

 

A new study from the Brookings Institution questioned the national push toward algebra-for-all by eighth grade, and found that the equation is a simple one: teaching algebra and other advanced math courses earlier than the ninth grade does not equal improved achievement.

 

... research suggests that teaching algebra to students who aren't ready to learn it brings unfortunate results.

 

A 2012 North Carolina study of 141,000 students found students taking algebra early scored significantly lower on end-of-course tests in Algebra I. And, they were less likely to pass standard follow-up courses.

 

That suggests that though strong math students can benefit from taking algebra in eighth grade, it is "decidedly harmful" for weaker math students to be rushed into advanced math concepts, Loveless said.

 

The big question is, however: how do other countries manage to teach their children algebra at a much younger age than the US? Since we can all agree that it can't be inherent differences in intelligence between their kids and the American ones, it can only mean two things:

1. their elementary math instruction is of superior quality (the better teacher education contributing heavily)

and

2. the compartmentalizing and lumping together all of "algebra" into one year, which is a US idiosyncrasy and not practiced like this elsewhere, is counterproductive.

It may be beneficial to get rid of this compartmentalization and teach algebraic concepts organically as part of "math", introducing students to easier concepts earlier and to harder concepts later instead of waiting with teaching any algebra until every student is ready for the hard concepts.

 

I do not believe that US kids are developmentally behind kids from Russia or Germany - that would make no sense. If they are behind in math, the problem has to be math education, not developmental readiness. There is no biological reason why a German 6th grader's brain can be expected to understand geometric proofs while a US kid's brain is not considered ready until grade 10.

[texasmama]

2. the compartmentalizing and lumping together all of "algebra" into one year, which is a US idiosyncrasy and not practiced like this elsewhere, is counterproductive.

It may be beneficial to get rid of this compartmentalization and teach algebraic concepts organically as part of "math", introducing students to easier concepts earlier and to harder concepts later instead of waiting with teaching any algebra until every student is ready for the hard concepts.

I agree with both of your points, but I think this is particularly an issue. Also, many or most US kids become pretty engrained with the belief that "Algebra is hard", and this affects the ability to learn it because they are intimidated by it.

[Arcadia]

1. their elementary math instruction is of superior quality (the better teacher education contributing heavily)

 

The mindset of the teachers is different. My older had a Kindergarten teacher who is good in math and language arts. His class benefited from that since the teacher was confident and knows what she is teaching. She happen to have her first degree in economics. His first grade teacher who is math and science phobic had a relatively harder time teaching math but her language arts is her subject expertise.

I wish the education system would either improve the teacher education system or just let the K-5 teachers be subject teachers instead of having to teach language arts, math and science. That way we can compact grade 6 and grade 7 math since kids would hopefully reach middle school with a better foundation.

[boscopup]

When I was in school, they didn't call it "prealgebra", but that's basically what 7th and 8th grade math were. When we got to high school, the honors track kids took algebra in 9th, the regular kids also took algebra in 9th, but with a different text (I presume an easier/slower pace), and the "behind" kids took "prealgebra". But really, 7th and 8th grades were prealgebra, so it's not like you actually skipped it. It just wasn't named that.

 

And today, most math programs have 7th and 8th grade as their prealgebra programs. It may not be named that way, but that's exactly what it is. With some programs, there is more "prealgebra" in earlier grades. For example, Singapore 5 and 6 basically are prealgebra. I'm not sure about Saxon though... My son that just finished Singapore 5B a month or so ago would place in Saxon Algebra 1/2 according to their placement tests. That's prealgebra. So presumably, what he learned in Singapore 5B is equivalent to what Saxon teaches in 7/6 (that's not a slam on Saxon, btw - just a scope & sequence difference). We're going to do AoPS Prealgebra instead of Singapore 6. I do think going from Singapore 5B to Algebra would be a bit of a leap. I don't know about going from Saxon 7/6 to Saxon Algebra. If the child finds Saxon 7/6 super easy, I might consider it. If not, I'd probably do 8/7 or Algebra 1/2 (whichever is appropriate) first.

[dereksurfs]

Duplicate, sorry.

[dereksurfs]

The big question is, however: how do other countries manage to teach their children algebra at a much younger age than the US? Since we can all agree that it can't be inherent differences in intelligence between their kids and the American ones, it can only mean two things:

1. their elementary math instruction is of superior quality (the better teacher education contributing heavily)

and

2. the compartmentalizing and lumping together all of "algebra" into one year, which is a US idiosyncrasy and not practiced like this elsewhere, is counterproductive.

It may be beneficial to get rid of this compartmentalization and teach algebraic concepts organically as part of "math", introducing students to easier concepts earlier and to harder concepts later instead of waiting with teaching any algebra until every student is ready for the hard concepts.

 

I do not believe that US kids are developmentally behind kids from Russia or Germany - that would make no sense. If they are behind in math, the problem has to be math education, not developmental readiness. There is no biological reason why a German 6th grader's brain can be expected to understand geometric proofs while a US kid's brain is not considered ready until grade 10.

 

Yes, it seems like many of the US Studies are based upon students' learning abilties in the US reflecting flaws within its own education system. Obviously if these algebraic concepts aren't introduced earlier, then abrubtly thrust on a young child they will become overwelmed, tuned out, perform poorly, etc... That is a foregone conclusion. But when one educates at home those same studies are not applicable since they are based upon a flawed system to begin with. This by no means is to say that some children do not develop abstract reasoning skills later than others. But it goes back to the question of nature vs. nurture or in this case nature + nurture? If given the opportunity (nurture) could some children (nature) rise to the occasion of a higher level of math proficiency earlier than what is standard in the US?

[Kathy in Richmond]

However, my personal guess is that colleges - even top-tier ones - do not care at all what grade level the student took algebra 1. Instead, I think they'll care what the student did in late high school. I'd be interested to hear what the usual math track is in these high schools, specifically for junior and senior years, for the students who took alg 1 in 7th. Will most of the advanced math students end up taking a course that's sequentially beyond AP Calc BC or some alternative, rigorous math course that makes them interesting applicants for top-tier schools? If they're not taking math beyond AP Calc BC, I doubt it matters for all but the likes of MIT/Caltech (and even then, from reading the MIT admissions math jam at aops, it seems that there's flexibility in how they view things). I really don't know though - I'd be interested to look at a top high school's website that discusses math tracks, if someone can recommend one. My kids will probably attend a Jesuit high school that has certain "usual tracks" based on one's math level upon entering (eta, and of course peformance). What seems odd to me is that the usual track described on the website for students who have taken geometry before high school has them taking calc AB junior year and calc BC senior year. I was under the impression that the first half of BC is AB.

 

(apologies in advance to OP for continuing off-topic)

 

Wapiti, it's the less thoughtful school systems that rush their brightest kids through algebra early, only to spend the last three years of high school dragging out Calc AB, Calc BC,and AP Stats. IMO, this does math-talented kids an injustice. When I was planning high school at home, I found math department web sites like IMSA's(residential STEM public boarding school in IL) to be very interesting and useful. Many of my kids' college classmates who are majoring in math or computer science had such backgrounds in high school. Those who were not fortunate to be able to attend a school like IMSA instead did lots of advanced dual enrollment math courses at local universities or else did lots of EPGY or AoPS classes.

 

Of course, their non math- and CS- major classmates generally stopped at AP Calc BC in high school (including many of the engineering majors).

 

At this point, I think I'm more concerned with convincing my kids to participate in the AMC :tongue_smilie:

:laugh: good luck!

 

FWIW, I think the usefulness of AoPS goes far, far beyond kids inclined to math competitions (my 10 y.o. boys, for example, aren't currently interested because they equate competition with speed - they'll find out more later :)). The problem-solving perspectives and deep concept understanding that can be had with AoPS are important for more long-term reasons (the same long-term intellectual development to be had from certain secondary-level math competitions).

 

:iagree: Exactly!

 

The big question is, however: how do other countries manage to teach their children algebra at a much younger age than the US? Since we can all agree that it can't be inherent differences in intelligence between their kids and the American ones, it can only mean two things:

1. their elementary math instruction is of superior quality (the better teacher education contributing heavily)

and

2. the compartmentalizing and lumping together all of "algebra" into one year, which is a US idiosyncrasy and not practiced like this elsewhere, is counterproductive.

It may be beneficial to get rid of this compartmentalization and teach algebraic concepts organically as part of "math", introducing students to easier concepts earlier and to harder concepts later instead of waiting with teaching any algebra until every student is ready for the hard concepts.

 

I do not believe that US kids are developmentally behind kids from Russia or Germany - that would make no sense. If they are behind in math, the problem has to be math education, not developmental readiness. There is no biological reason why a German 6th grader's brain can be expected to understand geometric proofs while a US kid's brain is not considered ready until grade 10.

 

It's not as if the math organizations in the US haven't been trying to do this for years. For example, the NCTM published a yearbook in 1988 that advocated algebra throughout the curriculum, from grade K onward, at age-appropriate levels.

 

But I suspect it's not elementary school teachers who are reading that book & incorporating its advice into their (home or otherwise) schools. :glare: I wish BIG TIME that the US would go to a model of elementary school that allowed subject experts to do the teaching, especially in math.

[Crimson Wife]

And no one should feel pressured to take algebra early because it will somehow "affect college admissions" or "signal to colleges" that you aren't a good student.

 

You may not like it, but that's the reality of the situation today. The level of competition for college admissions these days is absolutely insane. My alma mater only accepted 5.8% of applicants this year, and even the local Cal State has gone from accepting 2/3 of applicants to rejecting 2/3. If I wait until 9th grade to start algebra 1 with my kids, then that would signal to colleges they are in the bottom 25% of their peers (because algebra 1 in 8th is the standard for the entire state).

 

Perhaps it would be better in general if schools backed off from algebra 1 in 7th/8th, but until that happens, homeschoolers need to be mindful of how their children will be seen vs. their competition.

[wapiti]

Wapiti, it's the less thoughtful school systems that rush their brightest kids through algebra early, only to spend the last three years of high school dragging out Calc AB, Calc BC,and AP Stats. IMO, this does math-talented kids an injustice. When I was planning high school at home, I found math department web sites like IMSA's(residential STEM public boarding school in IL) to be very interesting and useful. Many of my kids' college classmates who are majoring in math or computer science had such backgrounds in high school. Those who were not fortunate to be able to attend a school like IMSA instead did lots of advanced dual enrollment math courses at local universities or else did lots of EPGY or AoPS classes.

 

Of course, their non math- and CS- major classmates generally stopped at AP Calc BC in high school (including many of the engineering majors).

 

 

Thank you, Kathy! This is very, very helpful, as I look toward the possible future and then backwards to see what my kids would have to do to get there (and they should have the time, fortunately). I have your description of your kids' sequences saved someplace, but it really helps to know that their classmates have similar backgrounds. Who knows where they'll end up, but I'm trying to keep as many doors open as possible. Now if my kids would just listen to all my (I mean your :)) advice...

[crazyforlatin]

 

 

These are from the "top" high schools in my area.

http://www.paly.net/academics/math/mathPausdFlowChart.pdf

http://lynbrook.schoolloop.com/file/1346928306289/1226804937203/5186278870320010832.pdf

http://www.debratroxell.com/MathDept/images/MathScopeAndSequence.jpg

 

My school district is middle of the road and has dual enrollment arrangements with the community college near my home. So I don't know how that affects the accelerated math track.

 

 

I wonder if Paly students are allowed dual enrollment at Stanford, and if so, I suppose the student pays the cost of each class. Maybe some of them opt for Foothill instead, given the cost.

 

Okay, this is such a derailment....

 

 

[Kathy in Richmond]

I wonder if Paly students are allowed dual enrollment at Stanford, and if so, I suppose the student pays the cost of each class. Maybe some of them opt for Foothill instead, given the cost.

 

Okay, this is such a derailment....

 

 

My dd occasionally has Palo Alto High kids in her math and Latin classes at Stanford, but I have no idea who's paying for them. Very convenient; they just have to bike across the street.

[crazyforlatin]

 

 

My dd occasionally has Palo Alto High kids in her math and Latin classes at Stanford, but I have no idea who's paying for them. Very convenient; they just have to bike across the street.

 

The odd part is that Paly doesn't offer Latin or Greek, so those kids took Latin in middle school (and I don't think the district offers it, so possibly a private school route) or were homeschooled or.... I can't think of another reason (maybe the parents afterschooled Latin). I mean, it's Stanford so I would think taking a Latin class as a high school kid requires some sort of background. I'm just wondering what that standard would be, what a Stanford professor would look for. Anyway, must be great to be a high school kid, walk across the street and attend a Stanford class :).

[Kathy in Richmond]

The odd part is that Paly doesn't offer Latin or Greek, so those kids took Latin in middle school (and I don't think the district offers it, so possibly a private school route) or were homeschooled or.... I can't think of another reason (maybe the parents afterschooled Latin). I mean, it's Stanford so I would think taking a Latin class as a high school kid requires some sort of background. I'm just wondering what that standard would be, what a Stanford professor would look for. Anyway, must be great to be a high school kid, walk across the street and attend a Stanford class :).

 

Weird! Maybe the girl moved to Palo Alto from somewhere else. It was advanced Latin at Stanford & dd remarked that the high school girl was extremely sharp in class.

 

One of dd's college math friends went right from Paly to Stanford...when I met her, I asked her why she chose to (she'd had other good options) & she replied that it was just so comfortable; after all, she'd been crossing the street to take math at Stanford for the last couple of years and it felt like home to her. Ah, the good options some kids have!