Math Question--In what grade do you teach Algebra I?

[Mrs Twain]

We are a math/science family with mathy kids. Dh and brothers have engineering degrees. We are interested in an advanced math track for our kids.

 

When dh and I were in school, the advanced math program was to take Algebra I in 8th grade, and follow the sequence to BC Calculus in 12th grade. This worked well for dh and I and others in the math/science field.

 

Recently, I have heard that there is a lot of emphasis in our local community/middle schools to encourage advanced math students to take Algebra I in 7th grade, while students who are average at math would be encouraged to take Algebra I in 8th grade.

 

Dh and I have talked to multiple people, including one of his engineer brothers about reasons why a student would need to take Algebra I in 7th grade. We are not against doing Algebra I in 7th, but we would like to have a good academic reason for teaching it that early. If there is no academic adavantage or other reason to take it in 7th, we would probably favor doing Algebra I in 8th because the 8th grade brain is more developed for abstract thinking. The 7th grade brain may not understand the concepts as thoroughly, and thus a student taking Algebra I this early could potentially (in our view) be at a disadvantage down the road with an inadequate foundation in math.

 

There are only two reasons we can come up with for teaching our kids Algebra I in 7th:

--The kid is so bored that he needs a challenge.

--We want to get our kid in a special math/science program which requires Algebra I in 7th.

 

Dh and engineer brother doubt that an engineering school would accept credit for any high school math class higher than BC Calculus, so what is the point of taking math classes beyond that in high school?

 

Please share any thoughts or advice about when to plan for Algebra I for an advanced math student. Thanks!

[RootAnn]

DH & I both have engineering degrees. I'm a registered Professional Engineer. (That's my 'street cred.')

 

I will teach Algebra I to my kids when each of them is ready for it. I don't care if that is when they are 10 or 15. I'm not particularly worried about what grade that turns out to be.

 

There is something to be said for a wide & deep math foundation, not shooting straight to Calculus & calling it a day. (I think AoPS has some articles on this. This might be it.) Think of a tree with a good set of roots (solid arithmetic base) branching out into many strong limbs (probability, number theory, discrete math topics, etc.).

 

I don't think of "beyond" as much as having time to expand their skills to a variety of interesting problem sets. So, if they are "mathy" and get to Algebra "early," I know I have things that will keep them challenged and help them expand their thinking in more complex ways.

 

If they get to Algebra "right on track" (in 8th or 9th grade), there is still plenty for them to explore.

 

So, I guess my point is, :chillpill: keep in mind what you are shooting for here.

[Sunshine State Sue]

I didn't plan it, but ds hit Algebra 1 in 7th grade. Unfortunately, so did puberty. :ack2: We used an easier program in 7th (MUS) and repeated with a challenging program in 8th (Foerster). With 20/20 hindsight, I would have used Patty Paper Geometry in 7th as well for an intro to geometry. We squeezed it in in 8th instead.

 

FWIW, I have a degree in math. I took Algebra in 9th grade and completed AP Calculus in 12th after having Pre-Calc in summer school after 11th grade. That was back when dinosaurs roamed the earth. ;)

Edited January 14, 2012 by Sue in St Pete

[wapiti]

Recently, I have heard that there is a lot of emphasis in our local community/middle schools to encourage advanced math students to take Algebra I in 7th grade, while students who are average at math would be encouraged to take Algebra I in 8th grade.

 

This is my understanding as well. It will be interesting to see what happens when this crop of kids gets to the end of high school, what their transcripts will usually look like - it may be that they'll take BC junior year of high school, and then something else senior year, so that the AP score will be available at the time of college application. I keep in the back of my mind that these kids will be the same ones competing for spots at highly selective schools.

 

Taking it early also allows extra time if it turns out that extra time is needed.

 

If your kids are advanced, you might ask this question on the accelerated board.

 

I will teach Algebra I to my kids when each of them is ready for it.

 

This.

 

It might also be true that some of the fun "extra" stuff is best attempted after one has Algebra I under one's belt (e.g. the AoPS Counting and Probability, or Number Theory books), a way to put off calc for kids who take algebra early (I'm trying to put dd off until 7th, but one of my boys will likely end up taking it in 6th).

 

Kathy in Richmond may have lots of ideas for the young algebra-takers can do for more math before and/or after they take calc. Here is her post of what her kids did.

[MyLittleBears]

:bigear:

[boscopup]

I agree with RootAnn. My kids will take it when they're ready for it, regardless of age. My oldest will likely be in 5th. I intend for him to take calculus in 11th or 12th, and if it's in 11th, he can take calc3 and diff.eq. at the local university via dual enrollment. That's the "really advanced" track for public schools here anyway (I believe in my class of 550, 3 students did that... And 2 ended up at MIT).

 

With AoPS books, there is plenty of math inbetween Algebra 1 and Calculus. :)

[8filltheheart]

Our approach is to simply teach the kids when they are ready.

 

My kids that have been ready for alg early have not had any problems w/the abstract thinking, nor have they ever slowed down as they progressed. For our most accelerated student, we did slow him down as much as we could by going broader w/non-traditional courses via AoPS.

 

All of our kids have taken alg 1 twice. Like Sue, they completed an easier alg 1 course (MUS) followed by a more challenging course. (Foerster) If I had known about AoPS when our ds was younger, I would have put him in AoPS sooner b/c it is more challenging than Foerster. It develops a greater understanding of the processes by having the students prove via discovery.

 

As far as what engineering schools will accept, it depends on the school. Our oldest dual enrolled in a local university and his courses transferred easily to another instate uni. Top-tier schools typically will not accept transfer credits like that. However, they also do not typically make students repeat material that they have obviously mastered. The unis that our younger ds has spoken to have stated that students may begin their course work where they place into, but that they require the same number of credits in that subject. I think I understood Kathy in Richmond to say that Stanford does accept EPGY's credits. They offer the following courses beyond BC:

M51A Linear Algebra

M52A Multivariable Differential Calculus

M52B Multivariable Integral Calculus

M53A Differential Equations

M106 Complex Analysis

M109 Modern Algebra

M115 Real Analysis

M131 Partial Differential Equations

M146 Point-Set Topology

M152 Number Theory

M157 Introduction to Logic

 

FWIW, I personally don't "accelerate" students. They work where they are. Our ds would have been incredibly unhappy if he had had to follow a typical math sequence.

[Samiam]

My DS did Algebra in 7th. He excels in Math, and is generally a grade ahead. When I shopped around Pre-Algebra curriculums, I realized it was a parking lot. About half was 7th grade math, and half was a gentle introduction to Algebra. He'd just finished a 7th grade math course, and flew through it. No reason to spend another half-year doing it again. Why not just get into Algebra and take it slow, if needed.

 

So that is what we did. 7th grade did a full year of Algebra. He did wonderfully. But that being said, I don't feel a need to rush him, so now in 8th, he's doing Algebra again, although we are using Life of Fred, so it's a really different way of looking at it. It's not that he needed to do another year, but what's the rush, might as well get a firm base in Algebra and look at it from every aspect possible.

 

My DS has a math brain. I would love to see him go into Engineering on some level. We'll see.

[Riverland]

nm

[rocketgirl]

Our goal was Algebra I in 7th or at least 8th. From what I've read, it would help to complete Algebra I by the end of 8th, and complete Geometry by the end of 9th to be prepared to take the SAT in 10th.

 

p.s. they put me in honors Algebra I as an 8th grader because I was "designated" an honors student. I might have been in Language Arts, but I was anything but, in Math. Imagine a path from Algebra I to Geometry (just 2 classes, right?) taking me 5 years to complete. Definitely not proud, but it is what it is. They put me in Algebra I, I had to drop. They put me back in, I had to drop, They put me back in, I had to Audit. At some point, I passed. Needless to say I was one of 2 seniors in a Frosh/soph geometry class. Too bad they didn't just leave me alone in 8th so that I could "get" what I needed. While we have grade level goals for ours (like being in Algebra by 8th), it really doesn't matter if they are in the class if they aren't ready...

Edited January 14, 2012 by rocketgirl

[zenjenn]

When they are ready. In schools, Algebra is typically grade 8 or 9 for college-bound students, 10 for maybe someone who will go to CC or arts college after high school, and any later is for those who may not go to college immediately or at all. Earlier is a bonus. I could see it happening in 6th or 5th for a really mathy, bright/gifted kid, but not much earlier unless extraordinarily gifted.

 

So quite a range. ;)

[dereksurfs]

I agree with RootAnn. My kids will take it when they're ready for it, regardless of age. My oldest will likely be in 5th. I intend for him to take calculus in 11th or 12th, and if it's in 11th, he can take calc3 and diff.eq. at the local university via dual enrollment. That's the "really advanced" track for public schools here anyway (I believe in my class of 550, 3 students did that... And 2 ended up at MIT).

 

With AoPS books, there is plenty of math inbetween Algebra 1 and Calculus. :)

 

Yes, I can see the advantage to this only *if* the child is ready by the 7th grade. All three of ours are beyond grade level moving individually at their own pace. Secondary math, specifically Algebra, can be harder for some than others regardless of whether they are 12, 15 or <fill in the blank>. So having some extra time available to really dig in and understand it can be a nice luxury. If a child needs two years to really get it, then they can spend the extra time to do so.

 

While on the other hand if the child is naturally gifted and really enjoys learning more advanced topics he/she is free to move ahead. And yes, dual credits from college can be obtained before graduation. Its not that uncommon for top math students to do this nowadays. Here is one track I found interesting from a bright young man who is in college now (Carnegie Mellon):

 

7th--Videotext Algebra (1st half) plus Singapore NEM 1

8th--Videotext Algebra (2nd half) plus Singapore NEM 2

9th--Videotext Geometry (through Module D) plus Singapore NEM 3

10th--EPGY Honors Precalculus, plus half of Singapore NEM 4

11th--EPGY AP Calculus A, B and C

12th--EPGY Multivariable Differential Calculus

 

EPGY is a program offered through Stanford for just such a student.

See the thread here for more info: http://www.welltrainedmind.com/forums/showthread.php?t=263276&highlight=videotext

 

I think you can see the advantage for him if you read the post. He was quite happy to have had that opportunity. Is this track best for every student? Obviously not. But on the other hand why hold a child back if ready for such an endeavor? Many have proven they can understand abstract reasoning sooner than the average US junior high student. Other higher performing countries such as Singapore, Russia, etc... introduce these topics earlier than the US and have for many years.

 

BTW, I was just talking with a friend of mine at work today about this. His 7th grade son is bright and going to public school. His wife wanted to 'hold him back' in pre-algebra this year when the school told them he was ready for either at his level/ability. Now he is getting A's in PA and bored he told his dad. Its too easy for him and so he's bored. His dad now wishes he would have challenged him more.

Edited January 14, 2012 by dereksurfs

[mom31257]

For my dd who can do math, but loathes it, she started this year in 9th. 4 math credits are required in our state to include Alg 1, Geometry, Alg 2, and one higher (Stat or Trig/Precalculus).

 

Ds is more of a math lover and about half a grade ahead now, but could be further if I put the time in. My goal is for him to do it in 8th if he keeps progressing and is ready.

 

I have a math degree and didn't take Algebra 1 until 9th grade.

[Mrs Twain]

Thank you, thank you, thank you for all of the replies. I haven't had time to look into the links yet, but I am very interested in reading those. Dh will also be reading this over the weekend.

 

That is an interesting idea to teach Algebra I over two years, particularly over 7th-8th. I could see us doing that.

 

DD1: In public school, Honors Algebra 1 in 8th grade. She did okay, but it wasn't easy. She *was* a very mathy kid with standardized scores in high 90's, but I think the highly conceptual math in her elementary gifted program really hurt her. She is now a freshman in college struggling with calculus.

 

DS: [...}

He also benefited from the switch in curriculum in the elementary gifted math; they added some traditional math.

 

 

Heather in PNW, could you please elaborate on this? I use a traditional math program as our main one, but I add in a fair amount of Singapore supplements because of all of the math threads I have read on this forum. From what I have read, many people here feel the more conceptual programs are better for creating a good math foundation. I am curious to hear more about your experiences.

[regentrude]

My DD did algebra 1 in 7th grade. She skipped 8th grade, did geometry the following year, algebra 2 and precalculus now in 10th, and will do calculus over the summer.

DS did algebra1 in 6th grade, did one semester of algebra2 in 7th and is finishing 7th with a semester on probability before resuming algebra 2 in the fall; we need a few months break for maturity.

 

Dh and engineer brother doubt that an engineering school would accept credit for any high school math class higher than BC Calculus, so what is the point of taking math classes beyond that in high school?

There are several points.

Studying math in high school and than studying the same math at a more in-depth level in college will lead to a much deeper understanding than a one-time course. Many things are only appreciated the second (or third) time through. I would not let my STEM interested student test out of calculus 1 at the university even if she had the AP score; this course is too valuable (but will be a lot easier if the student had prior calculus in high school.)

Also, having time to take extra math in high school beyond the absolute requirement means time to pursue math topics that are not part of the traditional sequence and that may not be required for their degree - discrete math, for example, or fractal geometry.

[Sahamamama]

My husband is also the mathy type, which is a relief to me, LOL! :D He studied Algebra I in 8th grade, then opted to do Geometry in summer school -- he was THAT interested in math! :001_huh: His 9th grade year was Algebra II, 10th was Advanced Mathematics (Trig/Pre-Calc), AB Calculus in 11th, and he signed up for a college calculus course in 12th. Alas, his car died, and he had no transportation to the college, so he was done with math -- the high school had maxed out its courses for him.

 

I asked him what he thought about studying Algebra I in 7th. His answer: Why not? If the student understands pre-algebra concepts in 6th, and it ready to launch into algebra by 7th, then why wait? HTH.

[boscopup]

I would not let my STEM interested student test out of calculus 1 at the university even if she had the AP score; this course is too valuable (but will be a lot easier if the student had prior calculus in high school.)

 

That's an interesting thought... I tested out of Calc 1 and 2 (AP test) and jumped right into Calc 3 at a university and had no problem. I always found the math in my engineering courses quite easy. I understood it well. Was I missing something valuable? I don't really think so, since I never had any struggles with the engineering topics or higher math (also did Diff. Eq. and Linear Algebra... not sure if I did anything else... those years are getting fuzzy now :tongue_smilie:).

 

I'd be interested to hear this fleshed out. I think it's a good point, but at the same time, I don't think I missed anything important by not taking calc 1 and 2 in a university (though maybe it helps that my AP teacher was married to a math professor at the local university, and she was a really good teacher in general - My favorite math teacher ever :D).

 

And of course, there is also the difference in materials and teachers. If you use an "easy" get 'er done self-taught homeschool calculus course, you're certainly not going to get as much out of that as if you use a college level text or an online class with a calculus teacher that really knows math (AoPS Calculus online with Richard Ruscyzk would probably be incredibly meaty, right?).

[abbeyej]

Well, my oldest was more than ready for algebra 1 in 6th grade (and a young 6th grader at that). It was the right choice for him and he did well and has continued to do well since then (through geometry and algebra 2 so far). ... My daughter will not be ready for algebra in 6th grade and probably not in 7th either, so she will likely do it in 8th -- but I'll make the final decision later on.

 

Maybe because it was so *not* the case for my oldest, I don't quite understand the "abstract thinking" argument. Maybe in general it's true? It wasn't at all the case for ds. For dd, I don't think it's a matter of abstract thinking, but her general facility with arithmetic that concerns me. Her abstract thinking skills seem adequate -- her ability to work with basic facts, not so much. ;)

[babysparkler]

Our approach is to simply teach the kids when they are ready.

 

 

This is my approach as well. My son has always been a mathy kid, and ended up ready for Alg I by 4th grade. We did Alg I in 4th-5th Grade, at a pace that he could really dig into it and gain a solid foundation. My other kids won't be ready until a later age... it is very dependent on the child.

[Crimson Wife]

I want my children to be competitive for admission to an Ivy League school if they can handle the work (the oldest I'm confident most likely will be, the other two are still too young to tell). So since the new norm for the honors track is Algbebra 1 in 7th, that is the goal in our HS.

 

My DD is going to be starting pre-algebra this month. The plan is to spread pre-algebra out over 2 years using a combo of Horizons and Singapore Discovering Math 1. That would put her starting Algebra 1 in 2nd semester of 6th. If she's not ready at that point, I might spend that semester working through some middle school math competition prep books like the one from Art of Problem Solving.

[regentrude]

That's an interesting thought... I tested out of Calc 1 and 2 (AP test) and jumped right into Calc 3 at a university and had no problem. I always found the math in my engineering courses quite easy. I understood it well. Was I missing something valuable? I don't really think so, since I never had any struggles with the engineering topics or higher math (also did Diff. Eq. and Linear Algebra... not sure if I did anything else... those years are getting fuzzy now :tongue_smilie:).

 

 

I am not talking about struggles or not understanding. I am talking about the possibility to develop deeper insights into math which come with more exposure, which will allow not only standard problem solving, but creative uses of math.

 

As a student, I had calculus based physics and the theoretical physics - and twenty years later I began teaching calculus based physics, and I must honestly say: despite graduating with A's from college, it was only when I started teaching that I really, fully understood many things. Repeated exposure to more abstract concepts, after the initial one, does provide deeper insight.

 

My DH essentially taught himself all the university math before going to college, and he found retaking the courses immensely beneficial. He got a lot more out of it that we other students who were taking them the first time. When you take a course for the first time, you stumble on problems and difficulties that will pose no obstacles the second time around, which will make it then possible to ponder other connections and concepts.

 

I see this in my students as well: the ones who are taking physics for the first time have to wrestle with certain questions and details and do not have their head free to see the big picture and to ask interesting questions; the ones who had taken a solid physics course and are now retaking it at the university do not have to focus on the elementary details and can think about the meaning, the concepts in a degree a first-time student simply can not.

[MeganW]

I have a very mathy dad, and had a strong math base in elementary school. Aced 6th & 7th grade math. Never struggled with word problems. I *got* it. Completely. I never understood why other kids thought math was hard. Partitioning numbers & figuring out ways around so you don't have to memorize anything was something I figured out on my own.

 

I was enrolled in Algebra I in 8th grade. I was young for my grade (end of summer baby that just made the cutoff). It was a complete and total disaster. I just was not developmentally ready. I ended up having to drop it and take another boring year of arithmetic that I already knew backward & forward.

 

I tried Algebra I again in 9th grade, and it was so intuitive and easy. At the time, I couldn't understand why I had thought it was so hard the first time around. And the teacher was much better in 8th grade, so it wasn't teacher-related. I don't think I ever got another grade below a 95 in math.

 

I just truly think my brain was not developmentally ready in 8th grade for algebra, and by 9th grade I was there. I would have just turned 13 years old when I started 8th grade, and just turned 14 years when I started over in 9th grade.

 

I have come to think that algebra, reading & potty training are the same thing. Once the basic knowledge (be it foundational arithmetic, phonics, or the steps to using the potty) is provided, the best thing to do is wait until developmentally they are there. You CAN teach it before that, but it is going to be a lot of frustrating repetitious hard work, when it doesn't have to be that way if taught at a more appropriate time in that particular child's development.

Edited January 14, 2012 by MeganW

[boscopup]

I am not talking about struggles or not understanding. I am talking about the possibility to develop deeper insights into math which come with more exposure, which will allow not only standard problem solving, but creative uses of math.

 

As a student, I had calculus based physics and the theoretical physics - and twenty years later I began teaching calculus based physics, and I must honestly say: despite graduating with A's from college, it was only when I started teaching that I really, fully understood many things. Repeated exposure to more abstract concepts, after the initial one, does provide deeper insight.

 

My DH essentially taught himself all the university math before going to college, and he found retaking the courses immensely beneficial. He got a lot more out of it that we other students who were taking them the first time. When you take a course for the first time, you stumble on problems and difficulties that will pose no obstacles the second time around, which will make it then possible to ponder other connections and concepts.

 

I see this in my students as well: the ones who are taking physics for the first time have to wrestle with certain questions and details and do not have their head free to see the big picture and to ask interesting questions; the ones who had taken a solid physics course and are now retaking it at the university do not have to focus on the elementary details and can think about the meaning, the concepts in a degree a first-time student simply can not.

 

Thank you for that explanation! That makes complete sense, and I do agree... the things I'm learning for a second time do help me go deeper (and teaching especially helps you go deeper!).

[boscopup]

I have come to think that that reading & potty training are the same thing. Once the basic knowledge (be it foundational arithmetic, phonics, or the steps to using the potty) is provided, the best thing to do is wait until developmentally they are there. You CAN teach it before that, but it is going to be a lot of frustrating repetitious hard work, when it doesn't have to be that way if taught at a more appropriate time in that particular child's development.

 

And the nice thing about homeschooling is that you can quickly see if your child isn't developmentally ready or if they are just fine to start early. Some kids truly are developmentally ready to potty train at 18 months, and some truly are developmentally ready to read at age 3 (those usually teach themselves).

 

Your comment fits with what's going on at my house, btw. I don't normally even try potty training until 3 years old. At that age, my boys are usually trained very easily in less than a week (oldest was 4 days!). Middle child wasn't even quite ready at 3, but he was ready 4 months later and trained easily. My youngest... I was going to wait until 3, but he decided he wanted to potty train now at 2.5. I think he's basically ready. His communication is better than that of his brothers at this age. He understands the process well. We gotta stop peeing in dribbles every 15 minutes, but I think that will come as he gets better at it (while typing this, I had to go take him to the potty, and he's gone 30 minutes between decent pees this morning - woohoo! Progress!). He has stayed dry on outings this week so far, so we're running with it! Likewise, my oldest is a math geek and an abstract thinker. He tends to figure out a lot of math on his own. The supposed boogey men of math (fractions, long division, decimals, etc.) have not been a problem at all for him. He just gets math. I will not be surprised if he is truly ready for algebra in 5th grade. The only reason he wouldn't be ready now (besides not having finished elementary math yet) would be his inability to sit and work on a problem. But 2 years from now, that may have changed. I've already seen a change in that in the last year. I don't think he'll be ready for AoPS Algebra in 5th grade, but a lighter traditional text will probably be fine (and he may surprise me by being ready for AoPS, but I'm not counting on it ;) ). If he struggles even at a slow pace and just clearly isn't ready yet, we'll go sideways for a bit until he's ready. No biggie. That's why we homeschool - so he can go at his pace.

[kiana]

I have come to think that that reading & potty training are the same thing. Once the basic knowledge (be it foundational arithmetic, phonics, or the steps to using the potty) is provided, the best thing to do is wait until developmentally they are there. You CAN teach it before that, but it is going to be a lot of frustrating repetitious hard work, when it doesn't have to be that way if taught at a more appropriate time in that particular child's development.

 

Yes, absolutely! I don't think people would advocate continuing in Algebra 1 with a 7th grader who was seriously struggling, but dropping back and hopefully doing some sort of applied arithmetic for the rest of the year, and continuing again next year.

 

But that doesn't mean, imo, that you shouldn't *try* with a student who appears to have mastered arithmetic. Just like if your 4yo has mastered letter sounds, there's nothing wrong with trying to teach reading, but if they just.don't.get.it... you put the book back on the shelf and continue readalouds.

[MeganW]

... my oldest is a math geek and an abstract thinker. He tends to figure out a lot of math on his own. The supposed boogey men of math (fractions, long division, decimals, etc.) have not been a problem at all for him. He just gets math. I will not be surprised if he is truly ready for algebra in 5th grade. The only reason he wouldn't be ready now (besides not having finished elementary math yet) would be his inability to sit and work on a problem. But 2 years from now, that may have changed. I've already seen a change in that in the last year. I don't think he'll be ready for AoPS Algebra in 5th grade, but a lighter traditional text will probably be fine (and he may surprise me by being ready for AoPS, but I'm not counting on it ;) ). If he struggles even at a slow pace and just clearly isn't ready yet, we'll go sideways for a bit until he's ready. No biggie. That's why we homeschool - so he can go at his pace.

 

 

My mom probably would have thought the same thing. But my brain was just NOT there! Your son should be thankful that he has you, to allow him to move laterally instead of forward if not ready! My mom just could not understand how her star math kid suddenly just could NOT even begin to comprehend the work. She really thought I just suddenly wasn't trying anymore, when I actually was making more of an effort than I ever had before. :(

[wapiti]

I am not talking about struggles or not understanding. I am talking about the possibility to develop deeper insights into math which come with more exposure, which will allow not only standard problem solving, but creative uses of math.

 

As a student, I had calculus based physics and the theoretical physics - and twenty years later I began teaching calculus based physics, and I must honestly say: despite graduating with A's from college, it was only when I started teaching that I really, fully understood many things. Repeated exposure to more abstract concepts, after the initial one, does provide deeper insight.

 

In light of these thoughts on repeated exposure, suppose, hypothetically, that you had a student who had done a good amount of prealgebra (including some but probably not all of AoPS Prealg). Suppose the student was headed to a school for 6th grade that used a fairly traditional math curriculum, not bad/not great. Without more info, and placement test results aside, would a deeper understanding in the long run more likely result from the student taking the more advanced/honors sort of prealgebra class or the "algebra lite" class? Either way, the student probably would take regular Algebra I the following year in 7th.

 

On the one hand, at least some of the prealgebra class might be repetitive. On the other hand, in this case, it might be confidence-building (shy student who lacks traditional classroom experience, and might well find the review useful).

[regentrude]

In light of these thoughts on repeated exposure, suppose, hypothetically, that you had a student who had done a good amount of prealgebra (including some but probably not all of AoPS Prealg). Suppose the student was headed to a school for 6th grade that used a fairly traditional math curriculum, not bad/not great. Without more info, and placement test results aside, would a deeper understanding in the long run more likely result from the student taking the more advanced/honors sort of prealgebra class or the "algebra lite" class? Either way, the student probably would take regular Algebra I the following year in 7th.

 

On the one hand, at least some of the prealgebra class might be repetitive. On the other hand, in this case, it might be confidence-building (shy student who lacks traditional classroom experience, and might well find the review useful).

 

Depends on the student and the curriculum used. If the school curriculum is less demanding than the prealgebra at home (which will very likely be the case if you use AoPS), I would not expect many deeper insights - because, after all, most pre-algebra courses are really just a regurgitation of arithmetic, and most schools do not teach a deep understanding; they are happy if the students can use the algorithm correctly (as in: the students can multiply fractions, but may not necessary understand why everything works the way it does). I would be very surprised if your student would get anything out of prealgebra at school after doing AoPS.

If confidence building is important for your student, go for it.

If, OTOH, your kid would be bored out of his mind, that would be a clear negative.

I see repeated exposure as particularly beneficial if the second time is slightly harder than the first time, not vice versa.

 

So, for a student who had homeschooled a rigorous pre-algebra using AoPS, I would consider neither a school prealgebra nor a school algebra lite the right way to proceed, but would prefer an actual algebra course. If that is not possible, I would choose "algebra lite" over prealgebra, because this might possibly introduce at least a small amount of new material.

[letsplaymath]

... Recently, I have heard that there is a lot of emphasis in our local community/middle schools to encourage advanced math students to take Algebra I in 7th grade, while students who are average at math would be encouraged to take Algebra I in 8th grade.

 

... There are only two reasons we can come up with for teaching our kids Algebra I in 7th:

--The kid is so bored that he needs a challenge.

--We want to get our kid in a special math/science program which requires Algebra I in 7th.

One big reason for the new schedule is that the newer textbooks are not as rigorous as the older books. One algebra 1 book I saw a few years back did not even get to quadratic equations (or perhaps mentioned them in the last chapter, I can't remember for sure -- but many classes never get to the last chapter of their books). If that is what the school is doing for "algebra 1", then of course they need to start earlier in order to cover all the standard high school math sequence.

 

I think it may be something similar to grade inflation, but it's the title of the course that has been inflated.

[EKS]

My older son started algebra at age 10 using Jacobs Algebra at half speed. The first half of the book is essentially prealgebra. My 9yo son is covering the same material right now in Derek Owens' prealgebra class.

[AimeeM]

In light of these thoughts on repeated exposure, suppose, hypothetically, that you had a student who had done a good amount of prealgebra (including some but probably not all of AoPS Prealg). Suppose the student was headed to a school for 6th grade that used a fairly traditional math curriculum, not bad/not great. Without more info, and placement test results aside, would a deeper understanding in the long run more likely result from the student taking the more advanced/honors sort of prealgebra class or the "algebra lite" class? Either way, the student probably would take regular Algebra I the following year in 7th.

 

On the one hand, at least some of the prealgebra class might be repetitive. On the other hand, in this case, it might be confidence-building (shy student who lacks traditional classroom experience, and might well find the review useful).

I could have asked the same question. Math-y child is on track to complete Pre A concepts (using a mix of resources, supervised by ultra-math DH) this summer. Wants to enter traditional Catholic school next year (for sixth) that has no option to move ahead in one subject. In this school, she wouldn't even be slated to start Pre A until 7th or 8th grade (I believe it's 8th grade). I can see repeating Pre A once to get a better footing; but we're talking several years back tracking. I'm not sure. She is NOT the type of student who would fare well with 2-3 years of reviewing material she's known. She would get bored... and mischief would soon come to face.

[nmoira]

My older son started algebra at age 10 using Jacobs Algebra at half speed. The first half of the book is essentially prealgebra. My 9yo son is covering the same material right now in Derek Owens' prealgebra class.

After more than a year of throwing diversions her way, DD the Elder started this year, in 4th. There was little choice as I'd run out of diversions, and she can't go on in science without the equivalent of Algebra I. However, I see no need to progress straight through the standard US sequence. Thank goodness for AofPS. :D We'll also add in a rigorous course in statistics.

 

DD the Younger is on track to start Algebra in 7th or 8th (have I mentioned lately how impressed I am with MEP?).

[wapiti]

. 

 

[AimeeM]

Thanks for your thoughts - they make a lot of sense. I really appreciate your opinion. I didn't exactly plan this out, lol - we started AoPS as an experiment to see what happened, not expecting to finish in a timely manner (and originally not planning on school next year), and AoPS has lived up to expectations for really stretching her, but I think it may be pushing her a bit too hard, or too soon. Nonetheless the depth has been good for her development. Right now I have to make decisions about the rest of the school year - whether she "finishes prealgebra" depends entirely on pace, probably with some combination of AoPS and other choices (I have a ton of resources for this level :D; placement test is in May, and the school's prealgebra text publisher has on-line quizzes and exam available so that I know what she hasn't covered yet). I guess we ought to shoot to prepare her for Alg 1, and then see what she's able to accomplish.

 

 

 

Yes, that sounds like it would be a problem. In the Catholic school we're looking at, math placement is by test, fortunately - in fact, finding that out was what led to this sudden change of plans. 6th graders in Algebra 1 at this school are not common, but definitely not unheard of. We talked about the possibilities for after Algebra 1, which I'm satisfied with; I just don't know how dd will fare in a classroom, where there is no "pause button," compared to working at home.

From what I understand (we are going to the open house later this month) there may not even BE an Algebra 1 class at the school since it is K-8 only, and I think Pre A is the highest math offered. Lucky you! We were told there was a placement test - but it doesn't mean, for our school, apparently what it means for yours :glare:

[Pen]

I took Algebra I in 7-8th grade. It was fine. Either alone would have been fine, but I think 7th for algebra and then 8th or even 8-9th for geometry (more time for proofs and understanding how geometry worked in real life, like calculating distance of celestial objects etc., would have been better than extra time on solving for x.)

 

In 9th grade I moved to a new school which did not allow me to go on in math even though I'd already done algebra 1. Had to do it again. It was extremely boring. (And I ended up tutoring others without learning anything myself that year.)

 

But worse, when I then got to yet another high school and university, I was then behind for math needed for sciences, particularly for physics when I got there without Calculus under my belt, but even for other sciences. (For example to have a good base of geometry imo helps with chemistry, and geometry generally follows algebra...) It did not stop me from going to an Ivy League school, but it did make my college time much harder.

 

I also think there are other important math subjects-- often left out of schooling, such as statistics (and understanding their real use and manipulation in politics, science, law, advertising, news, etc.), and consumer and financial math applications that would be wise to add into a curriculum before college or work life as the case may be.

 

But of course, it depends on the child.

[wapiti]

. 

 

[Riverland]

Thank you, thank you, thank you for all of the replies. I haven't had time to look into the links yet, but I am very interested in reading those. Dh will also be reading this over the weekend.

 

That is an interesting idea to teach Algebra I over two years, particularly over 7th-8th. I could see us doing that.

 

 

 

Heather in PNW, could you please elaborate on this? I use a traditional math program as our main one, but I add in a fair amount of Singapore supplements because of all of the math threads I have read on this forum. From what I have read, many people here feel the more conceptual programs are better for creating a good math foundation. I am curious to hear more about your experiences.

 

Based on the experiences of my kids, I am a believer in a combination of conceptual and traditional. Any parent (or teacher) who understands math should be able to take a curriculum and supplement/tweak it to cover both. It sounds like that is what you are doing. My biggest mistake with DD1 was allowing an inept “gifted†math teacher to teach her and not supplementing at home.

My DD1 received almost no instruction in basic computational skills. The teacher focused 99% on concepts for grades 1-5. Most of the parents (mainly engineers and scientists) clamored for more computation, but the program had been using CSMP for years and was not interested in changing. I think the real problem was the teacher was not a math person herself, and was only comfortable with what she knew. She always pointed to the very high test scores of the students as proof that the program worked…completely dismissing the fact that the kids had to first have these scores to even be admitted into the program! My dad once visited the class as a guest instructor for science. He came home and said “That teacher has no business teaching gifted kids. They understand science better than she does.†A non-science/mathy teacher paired with a highly conceptual curriculum does not work.

I didn’t know it at the time, but wasn’t surprised when I learned that when these kids got to middle school the math teachers had to “catch-up†the gifted kids in how to perform basic calculations. They knew how to think about math, but not how to do math. My DD1 wondered why she was no longer good at math, and her confidence tanked. All through high school, and now in college, her math teachers have looked at her confusing, round about (and frequently) wrong ways of solving problems and said “where on earth did you learn this?†The answer: elementary school, all they learned was round about playing with numbers. I feel terrible about not stepping in and giving her more computational instruction at home, but my DD2 had significant medical issues & ld’s, so this slipped through the cracks. I also thought that *maybe* the teacher was right. Not.

With my DS, a new teacher had taken over the elementary gifted math program. Her second profession was a teacher, having been a banker before. Her husband was a scientist. She completely agreed with me (and other parents), and was able to pair concepts with traditional computation. She understood math and the skills required for advanced science & engineering careers. My son understands concepts and has the computational skills to solve the problem. This is crucial. It was still not perfect, but far better then what my daughter had.

[Mrs Twain]

Based on the experiences of my kids, I am a believer in a combination of conceptual and traditional. Any parent (or teacher) who understands math should be able to take a curriculum and supplement/tweak it to cover both. It sounds like that is what you are doing. My biggest mistake with DD1 was allowing an inept “gifted†math teacher to teach her and not supplementing at home.

 

 

My DD1 received almost no instruction in basic computational skills. The teacher focused 99% on concepts for grades 1-5. Most of the parents (mainly engineers and scientists) clamored for more computation, but the program had been using CSMP for years and was not interested in changing. I think the real problem was the teacher was not a math person herself, and was only comfortable with what she knew. She always pointed to the very high test scores of the students as proof that the program worked…completely dismissing the fact that the kids had to first have these scores to even be admitted into the program! My dad once visited the class as a guest instructor for science. He came home and said “That teacher has no business teaching gifted kids. They understand science better than she does.†A non-science/mathy teacher paired with a highly conceptual curriculum does not work.

 

 

I didn’t know it at the time, but wasn’t surprised when I learned that when these kids got to middle school the math teachers had to “catch-up†the gifted kids in how to perform basic calculations. They knew how to think about math, but not how to do math. My DD1 wondered why she was no longer good at math, and her confidence tanked. All through high school, and now in college, her math teachers have looked at her confusing, round about (and frequently) wrong ways of solving problems and said “where on earth did you learn this?†The answer: elementary school, all they learned was round about playing with numbers. I feel terrible about not stepping in and giving her more computational instruction at home, but my DD2 had significant medical issues & ld’s, so this slipped through the cracks. I also thought that *maybe* the teacher was right. Not.

 

 

With my DS, a new teacher had taken over the elementary gifted math program. Her second profession was a teacher, having been a banker before. Her husband was a scientist. She completely agreed with me (and other parents), and was able to pair concepts with traditional computation. She understood math and the skills required for advanced science & engineering careers. My son understands concepts and has the computational skills to solve the problem. This is crucial. It was still not perfect, but far better then what my daughter had.

 

 

 

I am sorry that happened to your dd1, but thank you for telling about your experiences. I appreciate hearing your perspective.