Why Is Algebra a Big Deal? - Gifted Issues Discussion Forum

Good article, I thought!

Quote

Why Is Algebra a Big Deal?
Algebra is the "gatekeeper" that lets people into rewarding careers and keeps others out. Here's how you can help your child succeed in this important class.
By Linda Strean, GreatSchools StaffIt is frequently called the "gatekeeper" subject. It is used by photographers, architects, upholsterers and just about everyone in a high-tech career. It is simply a civil right, says Robert Moses, a veteran of the civil rights movement.
Basic algebra is the first in a sequence of higher-level math classes that students need to succeed. Because many students fail to get a solid math foundation, an alarming number of them are graduating from high school unprepared for either college or work. Many are taking remedial math in college, which makes getting a degree a longer, costlier process than it is for their more prepared classmates. And it means they're less likely to complete a college-level math course. For middle school students and their parents, the message is clear: It's easier to learn the math now than to try to relearn it later.
What Makes Algebra So Important? The first year of algebra is the prerequisite for all higher level math: geometry, algebra II, trigonometry and calculus. According to a study by the ACT, students who take algebra I, geometry, algebra II and one additional high-level math course are much more likely to succeed in college math. (To read this PDF file, you need Adobe Acrobat Reader, which you can download for free here.)
Algebra is not just for the college-bound. Students headed straight from high school to the work force will need the same math skills as college freshmen, the ACT found. This ACT study looked at occupations that don't require a college degree but pay wages high enough to support a family of four. Researchers found that math and reading skill levels required to work as an electrician, plumber or upholsterer were comparable to those needed to succeed in college.
Algebra is, in short, the gateway to success in the 21st century.
What's more, your child develops abstract reasoning when he makes the transition from concrete arithmetic to the symbolic language of algebra. That helps him become an abstract thinker, a benefit that will carry over into his study of other subjects.
When Should Your Child Take Algebra? Students typically take algebra in the eighth or ninth grade. The benefit of starting the sequence of high-level math classes in eighth grade is that if your child takes the PSAT as a high school sophomore, she will have completed geometry. By the time she's ready to take the SAT or ACT as a high school junior, she will have completed a second year of algebra. Both of these college admissions tests have questions based on algebra II.
There's a growing movement to have students take algebra in seventh grade. That may work well for students who are motivated, mature and prepared to tackle it. But many seventh-graders aren't, math educators say.
"Some kids get turned off of math because they start math too early," says Francis "Skip" Fennell, president of the National Council of Teachers of Mathematics, the nation's leading organization of math teachers.
Parents, he said, need to "make sure you ask yourself, 'Is this move for you or for your child?'"
Fennell recommends talking to your child's current teacher to help you assess her readiness to advance. The goal is for your child to learn algebra well and keep her engaged in math, not push her through the curriculum as quickly as possible.
How to Evaluate Your Child's Math Program The National Council of Teachers of Mathematics has spelled out three math "focal points" for children in each grade, from kindergarten through eighth. Fennell said the council developed this short list because state standards vary widely and some of them include more than a hundred objectives for each grade. While the NCTM wrote these focal points for teachers and other educators, the list also offer parents a way to understand what their children should be focusing on.
"If my child is in Grade 6, I know a focus will be fractions," says Fennell. "That will take up more time than, say, adding whole numbers, which he should know how to do by now."
W. Stephen Wilson is a Johns Hopkins math professor who teaches freshman calculus and is a former senior advisor for mathematics in the U.S. Department of Education's Office of Elementary and Secondary Education. He also reviewed the states' K-12 math standards for the Thomas B. Fordham Foundation, and he has strong opinions about which offer the best guidance. He called California's math standards "the gold standard." Wilson recommends that parents who want to make sure their students are getting prepared for high school and college compare the topics in their students' textbooks to the California standards.
"Odds are, if you can't do that easily then there is something very wrong," he says.
Look for Homework Clues Wilson offers this advice to parents trying to evaluate their students' math instruction:
"If a student isn't bringing home work that requires lots of manipulation and lots of word problems, then there is probably a problem."
Fennell suggests talking to your child and the math teacher about how homework is used. You may learn a lot from the answers if you ask:
� Are homework assignments corrected and returned in a timely way?
� Is homework reviewed in class so students can learn from their mistakes?
� Does the teacher change the pace or direction of his instruction, based on the feedback he gets in homework?
You don't need to be a mathematician to ask good questions about the content of your child's class, Fennell says. "Ask the teacher 'What is the math? Is it a repeat of math that should have already been mastered? When my child finishes this year, will he be ready for high school math?'"
Bill Moore directs the Transition Mathematics Project in Washington state, which is working to better prepare students for the transition to college math. He summed up what middle school students need to get out of math this way:
"Students need to have a very solid foundation of basic procedural skills that really make problem-solving more fluid. There's a fundamental set of stuff that just has to be memorized, and there there's a sense of numbers, a sense of what's a reasonable answer. That's particularly important with the use of calculators. In some cases, in the elementary grades, they've been used as a crutch. Students go straight to the calculator and if the calculator says it's right, then it must be right."
Look at How Calculators Are Used Talk to your child's math teacher about how calculators are used in the classroom. Debate has raged for years over whether students are relying too much on calculators and failing to learn the standard algorithms - addition, subtraction, multiplication and division.
But there does seem to be general agreement with the view expressed by Fennell: "The calculator is an instructional tool. It should support but not supplant anything. You don't use it for 6 x 7."
October 2006
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More on GreatSchools.net
� How to Help Your Middle and High School Student With Math
� Study Survival Skills for Middle School and Beyond
� How Much Should I Help With Homework?
� Is Your Child Ready for College Math?
Related Links
� The National Council of Teachers of Mathematics' "focal points" detail the three most important math topics for each grade level, from K-8.
� Civil rights activist Robert Moses founded the Algebra Project with the goal of instructing more children in higher level math.
� The American Diploma Project includes 22 states working to prepare every high school graduate for college or work. The project breaks down college readiness skills into four: number sense and numerical operations; algebra; geometry; and data interpretation, statistics and probability, with examples of each.
� Math.com offers a quick refresher for parents who want to help their students with math.

Good article. I'll have to show this to my son. He could do easy algebra equations when he was around seven but I think the ability to answer word problems using algebra was what he needed practice on and he is doing more of that this year, just with the little bit of easy algebra in his 8th grade workbook.

I told him that I want him to practice mental math and work on speed before he moves on to algebra. He complains about it and says things like "Mom, just because I walked out in the rain this morning does not make me Rain Man." But he does get faster with practice and he knows it and he feels good about it when he is timed on aaamath.com and he sees that he answered more questions in a certain amount of time than he did the last time he tried it.

I also told him that I became calculator dependent at an early age and I always admired people who were good at quick mental math. My mother was very good at this before she became ill and she didn't use calculators when she was in school.

I do let him use a calculator for some of his work now and I like that he tries to at least estimate the answer mentally before he uses the calculator. I think it helps him avoid mistakes.

I think things are slowly changing (a little at least) and it's less unusual to take algebra before 8th grade now than a few yrs ago. I never understood why the schools would let kids advance to pre-algebra, then wait wait wait. One DS was ready in 2nd grade but had to wait. Even in 5th the teacher asked the district and they said No, so we did online course at home. It made the world of difference. I still get angry thinking about the waiting.

This is a little OT, but since I saw the thread I'm curious. Is there something different about the type of thinking required for Algebra vs. regular math? I am NOT a mathy person (OK, so I'm not BAD at math but I'm a perfectionist and therefore never saw myself as GOOD at math! And on a board like this I would certainly not be considered strong--period!). I was MG and in advanced classes but always felt like math was my weaker area. UNTIL I took Algebra. I actually got the math award (for highest math average) the year I took Algebra 1 with a 99 average. And I REALLY liked it. It wasn't the teacher either. I taught myself using the textbook and never, ever spoke a word in class. I just sat at the back and did the homework and read and taught myself the lesson.

Anyway, I know this is a little OT, but are really verbal kids better at algebra? Or was it that I was not good at rote memorization but my thinking skills were stronger? I've always been curious. BTW, this strength did not carry over through all the rest of my math career. I was not as strong in trig, geometry, and calculus (although I did fine in math and got an "A" in Calc 2 in college), but I did LOVE algebra. It always made sense to me, and other math didn't.

I have read (in Right Brained Children in a Left Brained World, I think) that arithmetic and algebra are very left brained dependent while geometry (and higher?) relies more on the right brain. The point was to make sure you got your right-brained kid through algebra so they can discover the math that is better suited to their strengths.

I hope others can answer your question.

I like the math sequence at my daughter�s school. I would think that the entire freshman class there took algebra in 8th grade, but only 1 of 100 tested into their advanced geometry course. The rest of the top math quartile, including dd, take advanced algebra I. The remaining students are repeating algebra I.

The advanced algebra I includes more reasoning problems than her previous class and also covers the first half of algebra II. Advanced geometry is next, followed by the second half on algebra II with trig. Even though she is taking algebra I as a freshman, she will still have AP calculus as a senior. This is ideal for her. The repetition of the first semester was valuable reinforcement with more depth, ideal grouping and speed.

Of course, this would not be ideal for our ds and many kids here.

mom2boys - I read somewhere (I'll see if I can find a link) that kids that are high in VCI (verbal comprehension) do better in Algebra whereas kids that are higher in PRI do better in geometry. Now it didn't mention numbers and of course all is relative but it made sense to me at the time I read it lol.

My DS who is VCI>>PRI is great at critical thinking and intro to algebra concepts but is not quick on the rote memorization. Although I've spent 3days playing just games for division facts/factors/multi facts and he's getting faster already! He thrives on the competition aspect of the game and by playing them often (4games in a row) he's already showing progress!

When I first took Algebra I solved problems two ways - by substituting numbers until I got the right values then converting them back to symbols - and the normal way.

From what I have read, the very best mathematicians, like Von Neumann, are also verbally gifted and are able to use all parts of their brains to attack a problem.

Purely anecdotal, but here's my experience:

My strengths are definitely verbal, but I am a visual-verbal person. I didn't realize this until I started reading up about learning styles for my children at the same time as I was writing a novel. I realized that when I write, I see the events and characters in my head very plainly, and then my task is to describe what I see as accurately and descriptively as I can.

In school, I was good at both geometry and algebra, but I enjoyed geometry a lot more because I adored proofs! They were like logic puzzles, and were both visual and verbal!

I'm mostly posting to note that we shouldn't assume verbal kids will prefer algebra. (Not that anyone was...) They certainly might prefer algebra, but then again, not all verbal kids are auditory-sequential learners. There are shades and tones to kids with strong verbal skills.

I consider myself to be a pretty visual-spatial learner, and yet oddly enough I much preferred algebra to geometry. (though maybe it was because my pathetic school hired a bad geometry teacher who had just been fired from another school; a friend and I taught ourselves the entire course the weekend before the regents exam. not that I could be bothered to do so before that...) Algebra in 8th grade was the only time anyone really gave me any special accommodations in school, ever, and it was a chore for my mom - I guess advocating once is better than not at all.

My nephew will take algebra next year in 7th grade, but it's oddly broken up into two courses, so he takes more of it in 8th grade anyway (i.e. I'm not sure whether he ends up a year ahead of the way we did it years ago). However, I was so happy to hear him admiring another middle school kid who gets to go to the high school for math; at least his school sounds flexible.

Tell me what you guys think of this: it appears that in order to do more advanced math class (algebra I in 7th gr) in our local very large and well respected public middle school, one has to gain acceptance to the gifted program for middle school. It appears that a person can apply only for math or only for language or for both, but applying involves testing (cogat), etc. and even writing about what one would contribute to such a class. (I have long hated questions like that - I think they're dumb. How does one even contribute to the experience of others in a math class in the first place.) I suppose it could be that kids are coming from so many different elementary schools (and they start at the middle school in either 6th or 7th grade). But I don't see why a form from the 6th grade math teacher isnt' enough. I can't see an on-line curriculum so I don't know whether there's another option for 7th (or 8th) grade algebra outside of the gifted program, though I'm not sure why there would need to be more than one version of the same course in the same grade. Applying just sounds like a huge unnecessary pain in the neck, i.e. I'm so lazy. Or do you think it sounds like a positive arrangement? Keep out the kids who might slow it down? I guess I'm just not familiar with the idea of a middle school gifted program.

(We have some time before we have to worry about middle school but I'm afraid it's going to creep up faster than I'm prepared for. I had been hoping to do private middle school but with our sixth child on the way, I don't think that's in the cards.)

The real world is ALL WORD PROBLEMS!!

If I had one piece of advice to give it is that most math is not number crunching. Its talking to someone about their issue, gathering information, choosing a method, setting up the problems, making sure conditions are met, then finally running the numbers, then convincing others you are right.

I usually get a phone call or an email, go to lunch, listen to a tale of woe, then get to dig in, fix the issue, write up the issue, then discuss it with the person, provide further background if they have another audience to communicate with. Sometimes I go with a much simpler approach that is wrong in some respects, but which is more easily grasped and used.

Just being good at math is not enough!! You have to be able to talk about it.

I think most intelligent people have an intuitive grasp for math, they just do not know how to communicate in mathematical terms nor do they know how to BE SURE they are right.

Our Middle schools have had a very unique approach to math. There is an advanced math program called GEM (Great Explorations in Math) which children can start in the 6th grade. The GEM program is separte from the gifted program. Not all gifted kids get in and quite a few children who are not gifted get in. They are looking for very high scores on our states standardized math test and they also need to have a passable reading score. In 6th grade they take Pre-Algebra, In 7th grade, they take High School Honors Algebra I, and in 8th grade, they take High School Honors Geometry II. In 9th Grade when they start High School, they have 2 high school credits in math and then move on to Algebra II. I believe most kids stay with the Honors math classes as well as through High School. The school district however has decided that this year would be the last year they would let 6th graders into the program. The children in the program will be allowed to continue on the same pass as before, however in the future new children will not start until their 7th grade year keeping them only one math grade ahead of the majority of the children versus two years previously.

Yes Kriston, I think it more depends on the teacher and the DC interest. But I can see if a person is not very visual, manipulating shapes in space might be more difficult.

Where Algebra came to me easily, I had to "work at" geometry and some of the Calculus problems that involved rotating on an axis. When I teach my students, I try to remember how this feels since I am fortunate enough to usually understand most of this fairly fast.
I worked at picturing where and how a shape would end up if changed and it took some time and effort - just like the distributive property did for my students.
Derivatives and such, I absolutely loved.

I think that Algebra is the first course where you can really distinguish which kids understand math and which were merely memorizing up to this point. In our charter school you are tested into an appropriate math class.
Taking algebra early will not make one a good mathematician. Starting to problem solve early will. My 8th grader is in pre-calc righ now but it is not helping him be good in math competitions. In fact none of the competitions up to USAMO (included) require any calculus knowledge. Yes, you might solve certain problems faster if you know calculus, but speed is not a problem once you reach AIME

I am probably beginning to sound like a broken record on this board, but I will repeat it again. So what that so and so has started in algebra early? Proves nothing! If your kids are interested in math forget about fighting the school about curriculm and begin problem solving journey with them. Involve them in mathcounts, math olympiad, american math competition etc.
Charging ahead in math curriculum is not going to make your kid learn faster and be less bored. Chances are he/she will still end up in the class of regular kids, no math geniuses, and no matter what the class is, it will still be too slow for your kid.
Yes, you have to take matters into your own hands most of the time, but you will love the results...

Ania, I hope this doesn�t come across as hero worship, but I am very grateful for the information that you post, specifically regarding math. As a direct result of info you have provided in the past, my son has taken an AoPS algebra course and has been participating in a math circle at a nearby U since the beginning of the school year. As a result of a conversation I had with a YSer parent I met at math circle, ds will likely start with a local summer/after school math program (number theory/counting and probability, ect.) designed just for gifted middle school kids. I will keep looking for the opportunity for math team competitions-No, I�m not qualified to lead one.
Thanks!

Yes, sometimes faster is the best available, but that doesn't mean it's the best. It's good to be reminded that sometimes these kids really need different--in the form of problem-solving and critical thinking when it comes to math.

I third the thanks, Ania!

Hm.
My dad taught me some light algebra before I took the sat when I was in 7th or 8th grade, I think I picked it up ok. I am very strong verbally and visually although pretty sketchy with actual computation. (At least one of our apples did not fall far from this tree.)
When I got to 9th grade to take it (again) it was soooo boring, it was one of the few classes I really hated. Geometry I have very much enjoyed and did well in calc.

OT, but on the 'manipulating shapes in space' thing, one real 'aha!' moment for me in school was in college chemistry class; the spectography just really clicked for me. I found myself raising my hand with 'wild' guesses about 'what molecule this is' and getting a lot right. Very bizarre.

I am currently taking gemotry right now. I jumped out of algebra in the middle of the year. I think that algebra shouldn't be a full semester class because as soon as you know one thing in algebra you know them all. The only reason I got out of algebra so late is because the school didn't want me going ahead.

First why can't all Algebra be named the same so as not to confuse those of us who are already confused?

Could someone please share more about the AoPS textbooks mentioned?

My DD9 is working on ALEKS LV6 using yourteacher.com pre-algebra to make sure she gets a little more on each topic. The school district said that based on testing from the beginning of the school year she would be in 7th or 8th grade math by their "standards" from that point in time. She has moved forward exponentially from then. It doesn't help much because standards are so varied.

We are looking for suggestion and ideas when deciding a path from here. We are looking at the PLATO Algebra I which would be a pre-algebra or middle school algebra. Some of the examples look like review but it would be a start. She would then be able to take their Algebra II and then Geometry.

"PLATO� Algebra I, Part 1 is a pre-algebra curriculum that teaches students the foundation skills they need to understand and apply basic algebraic concepts. In Part II, students work with sets and numbers, polynomials and factoring, and equations and inequalities."

Would the AoPS textbooks be a good companion to this plan? Are their other suggestions or curriculum? We have considered other classes from the online virtual school but PLATO would allow her to move at her pace. I was also looking at the AoPS online classes. I'm sure I remember someone using them as well, please share?

I'm interested in hearing comments about algebra options as well.

I did just buy "Painless Algebra" by Lynette Long, whose praise I often sing for her "Painless Geometry" that I used with DS7 last year. It was cheap-cheap at the Scholastic Books Warehouse sale going on now for teachers and homeschoolers at warehouses all over the country, and I actually squealed aloud when I spotted it.

But that's just a place to start next year (or maybe even this summer if he wants math this summer). It's not going to be sufficient.

Watching with interest...

Kriston,

Our Scholastic Books Warehouse sale doesn't start until the 29th. I will surely be going there to pick up some books!

Is "Painless Geometry" written for younger kids?

I have the Painless Geometry. Agree that it is good.
For Algebra reading, DS8 loves Real World Algebra by Edward Zaccaro.

I do NOT think AoPS Algebra is a companion to the PRE-algebra course. AoPS has divided into 2 courses so Algebra 1 should be companion to Algebra 1. AoPS also has number theory and counting/probability.

It's not specifically written for younger kids, Cindi, but it is simplified without being "dumbed down," if that makes sense. The books are geared to ND middle school/early high school kids, I believe, which has been just about right for DS6-7 the past 2 years. The material is still very highly conceptual, but is written more clearly than most that I've seen and doesn't require tons of practice. That helped keep my son's interest. It also seems to break complex concepts down into bite-sized pieces that worked better with my young child. To speed up, you simply do more of the "bites" at one time. To me, it seemed tailor-made to meet an HG+ young child's needs, FWIW.

I haven't done anything more than thumb through Long's algebra book yet. I didn't even know there was one until I saw it on the shelf. Oh, happy surprise!

But since I bought $350 worth of books at the sale (!!!), I haven't had time to sit down and really look at it. On first blush, it looks every bit as good for introducing DS7 to algebra as the geometry one was for introducing "real" geometry to him.

But I know I will want him to have a complete course ala AoPS and/or PLATO eventually. We're just at the starting gate!