Does Any One Else Think That it's a Little Odd That...*math ramble*

[mom2bee]

The way the education system is set up to handle math, you spend anywhere from 6~8 years learning and applying arithmetic and then are expected to learn all of your basic Algebra in essentially just 2 years? Those years being Algebra 1 and Algebra 2. That has always struck me as a little odd. Even when I was a kid. To this day I have no idea why Geometry is often put between the two? Can some one please shed some insight on this for me if they know why this is?

 

Arithemetic is a lot more straight forward, in a sense, than Algebra for the most part, its using just those four operations on numbers in base 10 (which includes decimals). I know that the elementary math education also tends to include lessons on applying arithmetic to fractions, money, time, measurement, graphs and some geometry. Later on they include some basics statistics. But why do they do it this way? Does anyone know? Older text books didn't always include the 'superfluous' topics, so what were kids doing

 

The parts of arithmetic that help you to understand algebra most directly seem to be glossed over a lot of the time at various points between 5-7th grade and never made "The Star" of the show. (factoring, bases, powers, the properties of real numbers and how to use them to your advantage, equations, graphing equations, integers). Why does it seem like every single text book for grades 5-8 begins with "Operations on Whole Numbers" and then Integers, etc...

 

I know that I am missing something and that this isn't just 'arbitrary' but it seems this way to me. I was talking a little while ago with some friends and even the math majors and math education majors have no idea. They haven't read anything yet that explains this. I have searched my schools and public library shelves for books but haven't found anything that address this topic, so if you know of one, please let me know.

 

Does anyone know when this current scope/sequence of "Basic Math and Applications for 8years" became popular? Does know one else think that it's odd? I know that many say that little kids can't do algebra/aren't ready for it cognitively so do they 'spread out' basic mathematics on purpose--just to give the kids time to 'age'? Is that the only reason why they spread "basic math" out so long?

 

Would it be better to design a scope and sequence that helps to better prepare kids for algebra earlier? Perhaps a curriculum that blatantly draws the parallel and guides kids toward algebra from 5th-8th grade? It seems a little unfair that kids are expected to learn all of Basic Algebra in just 2-3 years, if it is so complex, while Arithmetic is drawn on and on for all of their childhood.

 

Anyway, these are just my thoughts this morning. I spent most of the night fumbling through a problem set and I was reminded of this thought strain that I entertain from time to time.

 

It just seems that as the math gets 'harder' and more and more abstract, we're expected to learn and master it at a faster and faster rate and on the surface it seems more than a little unfair.

 

Arithmetic and Applications are studied in math K-8, for many kids, so thats 9 years.

Basics of Algebra and its Application and Introduction to Geometry (in 2-3 years)

Calculus in 2-2.5 years (assuming that kids take it in highschool they get Calc I and II for a year and then Calc 3 at university for one semester. If you only take Calc in college then you only have a year and a half at most (3 semesters--Fall, Spring, Fall or Spring, Summer, Fall) to study/learn it.

 

Am I just slow? Why do I struggle to learn and retain math so much from semester to semester?

Why are we expected to master the basics of various branches of "higher level" math in just 15/16 weeks during college?

I have taken college courses in algebra, statistics, calculus, linear algebra, differential equations, discrete mathematics, proof writing and am currently taking a course in Numerical Analysis. I enjoy it and this is probably the best math teacher I have had since I transferred, but I am not an encyclopedia. I don't memorize the definitions of theorems verbatim and am constantly having to look things up, go back and refresh.

 

I enjoy the math courses--that's why I take them. But I can't say that I have "mastered" the material from these basic classes.

I have a strong grip on Algebra and Calculus I, and can do some calculus II, but the others? It depends on the alignment of the stars whether or not I can recall/utilize that knowledge on the fly. I know that it makes no sense to generalize my experience to everyone else. But I do wonder if any one else feels that our math education system is a little...off? Or if its just me.

[msjones]

There are curricula that begin algebra, geometry, probability, etc in the early grades.

 

You could find many threads on this site about how much many parents energetically hate those programs.

 

Everyday Math and TERC Investigations are the two I have used.

 

 

[regentrude]

 

The way the education system is set up to handle math, you spend anywhere from 6~8 years learning and applying arithmetic and then are expected to learn all of your basic Algebra in essentially just 2 years? Those years being Algebra 1 and Algebra 2. That has always struck me as a little odd. Even when I was a kid. To this day I have no idea why Geometry is often put between the two? Can some one please shed some insight on this for me if they know why this is?

 

This is an idiosynchrasy of the US school system. the compartmentalization of math into "algebra" and "geometry" leads to a delay in math instruction because educators wait until students are ready to be taught advanced algebra concepts- instead of teaching simple algebra concepts as soon as students are done with arithmetic.

One can easily finish arithmetic with positive integers by the end of 4th grade, spend 5th grade on fractions, and begin with algebraic expressions in 6th grade as is done elsewhere in the world. Instead, educational philosophy in the US seems to assume that middle schoolers can not be taught any new material and that they must simply be parked and supervised for grades 5 through 8 until they are ready fro new stuff. It does NOT take 3-4 years to teach fractions!

Also, the splitting of geometry is specific to the US; an integrated math where geometrical topics are interspersed is much better IMO.

 

 

I know that many say that little kids can't do algebra/aren't ready for it cognitively so do they 'spread out' basic mathematics on purpose--just to give the kids time to 'age'? Is that the only reason why they spread "basic math" out so long?

 

That is what US educators assume. I am baffled, because I see no reason to assume that American students are less intelligent than, or developmentally behind, students from Russia or Singapore or Germany, where they are expected to be ready for algebra in 6th or 7th grade.

 

 

Would it be better to design a scope and sequence that helps to better prepare kids for algebra earlier? Perhaps a curriculum that blatantly draws the parallel and guides kids toward algebra from 5th-8th grade? It seems a little unfair that kids are expected to learn all of Basic Algebra in just 2-3 years, if it is so complex, while Arithmetic is drawn on and on for all of their childhood.

 

Sure. Look at how math is taught elsewhere. In my home country, much of triangle geometry, congruency, proofs is done in 6th grade, along with simplifying algebraic equations. Linear equations are taught in 7th. Quadratics later. geometry and some statistics are taught all alongside.

 

 

Calculus in 2-2.5 years (assuming that kids take it in highschool they get Calc I and II for a year and then Calc 3 at university for one semester. If you only take Calc in college then you only have a year and a half at most (3 semesters--Fall, Spring, Fall or Spring, Summer, Fall) to study/learn it.

 

There really is not THAT much to calculus. There are two basic ideas and a bunch of tricks; one year is entirely sufficient for single variable calculus. Multi-variable is a bit trickier, and I am pretty sure most students do not really understand vector calculus unless they apply it in theoretical physics where they need to have an understanding of curl and gradient. But I still think one semester suffices for that.

Our college math instruction was at a faster pace: we did vector calculus at the beginning of the second semester and spent the remainder of our five semester math sequence on functional analysis, probability and statistics, ordinary and partial differential equations, complex analysis.

[mom2bee]

Algebra isn't just two years now; it's only two years for the top students.  The 8th graders here who had their parents pull strings to get them into 8th algebra have this course sequence: Alg 1, Geo, Remedial, Alg2, Remedial..then off to College Algebra if they go to college.   Top students: Alg 1, Geo and A2, College Alg & Trig, Calc 1&2, senior year their choice (stats, Calc 3 & diffeq, discrete math, linear A, proofs).

Wow, is this more common in public schools also? I was homeschooled but none of my friends took this sequence in school. I have asked several of my classmates about their various math sequences and I have to say that this sequence is new to me. Why are the kids taking each algebra class twice? (One normal, one remedial?)

[Ellie]

It's why I like R&S arithmetic so much: The first three years are spent learning and mastering basic arithmetic; by fourth grade, children have that down pat and are ready for math.

[kiana]

Wow, is this more common in public schools also? I was homeschooled but none of my friends took this sequence in school. I have asked several of my classmates about their various math sequences and I have to say that this sequence is new to me. Why are the kids taking each algebra class twice? (One normal, one remedial?)

 

Because they didn't do well the first time around, but didn't fail. I would much rather see someone who got a C in algebra 1 and geometry taking a transitional course than just jumping into algebra 2. However, they probably don't need to retake algebra 1 and geometry fully.

 

Here's an example of a textbook used for that kind of course.

[Plink]

Huh. I thought kids were already moving toward learning algebra earlier.

 

My crew learned their math facts as groups (3+2=5 2+3=5 5-3=2 5-2=3) so converting an addition problem with a missing addend into a subtraction problem was never a big deal. They learned it when learning how to check their own work. My Ker is already solving for x in a very basic way. Each year they learn a bit more about the why behind the operations. It seems like an easier way to learn.

 

The year of geometry in between algebra does have me baffled. It seems it would make more sense to group learn all of the operations of algebra before moving on to geometry, trig. and calculus.

[madteaparty]

It is not clear to me what we mean when we say algebra, but don't programs like Singapore introduce algebraic concepts in 4A and 4B? For example, my son, who is not accelerated or gifted in math can build a simple equation of 2x +x-24=84 (instead of using the bar method) so he can solve a word problem.

Or are we talking about public school in general? if the later, I know the school I pulled him from recently adopted a new Pearson program that seems singapore-like (Not sure of the name. it is only a couple of years old).

[Sherry in OH]

The inserting geometry between algebra one and two happened within the last twenty years.  My understanding is that it was done because basic knowledge of geometry is necessary for decent SAT scores.  When the typical high school sequence was Algebra I, Algebra II, Geometry, Trigonometry, most students would just be starting geometry in the fall of their junior year. Traditionally, students took the SAT that same fall (giving time to repeat the test if necessary).   Inserting geometry between Algebra I and II means that most students have taken it prior to taking SAT exams.  

 

Other reasons I've heard are - It was an attempt to lessen the perceived unfair advantage to students who started the high school sequence early.   And that when public schools stopped requiring four years of math to graduate, administrators wanted to be sure that all students had reached geometry.  

 

Several math programs teach algebra earlier. Basic algebra and geometry are included in the first years of MEP. 

[kiana]

The inserting geometry between algebra one and two happened within the last twenty years.  My understanding is that it was done because basic knowledge of geometry is necessary for decent SAT scores.  When the typical high school sequence was Algebra I, Algebra II, Geometry, Trigonometry, most students would just be starting geometry in the fall of their junior year. Traditionally, students took the SAT that same fall (giving time to repeat the test if necessary).   Inserting geometry between Algebra I and II means that most students have taken it prior to taking SAT exams.  

 

Other reasons I've heard are - It was an attempt to lessen the perceived unfair advantage to students who started the high school sequence early.   And that when public schools stopped requiring four years of math to graduate, administrators wanted to be sure that all students had reached geometry. 

Both my parents took Alg 1, Geom, Alg 2. This was in the late sixties. Before that, it was not at all uncommon that college-bound students would only have one year of algebra and one year of geometry at graduation. Many of my college textbooks on 'college algebra' or 'analytic geometry' from the '60s or earlier expressly say they are designed for college freshmen who had one year of algebra and one year of geometry. I have friends who graduated (with a general diploma) in the '70s or earlier, and some of them didn't get as far as algebra. I don't really know what you mean by "stopped requiring four years of math to graduate" -- the move to requiring four years of math just for graduation (as well as not counting pre-algebra, general math, et cetera) is a more recent innovation.

[Tracy]

I think one of the biggest reasons that math is compartmentalized is the American need for box-checking.  It is easier to show what is taught, even if it is not learned as well.  It is all about showing it on a transcript.  My kids are very young yet, so I have a lot of time to think about this, but I really want to do a more integrated higher level math.  But then when she wants to take college classes in high school, how do I show them what they have already done?  

[kbutton]

I think we spend so much time on math because we fail to teach it properly in the early years, and we fail to teach conceptually, so the advanced math is harder to understand. I do agree that some kids will not be ready for algebra by jr. high, but I think that should be the exception. The school district I attended taught algebra 1 to 8th graders, so they didn't insert geometry between the two algebra courses. They taught them consecutively. I attended both private and public school, and I never learned math conceptually. In school, I was always missing something but didn't know what--it was the conceptual stuff (and I was an honors student). I could DO math, but it always seemed like a bunch of arbitrary rules with a few that made sense once in a while. When I took trig based physics in high school, math started to make so much more sense because it was connected to concepts. Unfortunately, that was a bit late, and my physics teacher couldn't repair my gap in knowledge enough for me to do anything with math past high school.

 

My next door neighbor teaches HS calculus. She is convinced that past 2nd or 3rd grade, we should have MATH teachers teach elementary math (I think it needs to be earlier). I believe we have (largely) math phobic teachers with a general elementary certification glossing over conceptual math and relying on algorithms and memorized math facts. I realize this may be changing, and I'm not trying to say bad things about all elementary teachers (I know some wonderful ones), so bear with me until I get to the examples. Just a hunch, but I'll bet that's not how the mathy countries teach math.

 

Two days ago a college student studying elementary education told me he loved to teach reading and math. I commented on how unusual I thought it was to like teaching such unrelated topics equally. He told me that he's not very mathy, but elementary math is so easy that it doesn't really matter that it's not his thing. I would probably have thought that was a reasonable mindset until my older son started struggling to memorize the steps for subtracting with borrowing/regrouping because the teacher didn't explain the conceptual basis. I started to see that there is NOTHING simple about elementary math unless you think it's all about memorizing facts and following procedures (like how to complete an algorithm). Incidentally, my son immediately understood HOW to do the problem once I explained WHY the process worked. He didn't understand why the teacher hadn't explained it that way in the first place. I thought I understood place value until I thought about the algorithm for multiplying or dividing large numbers. Then, I realized that not once in my education did anyone actually ask me to connect place value to these algorithms in any meaningful way. I did figure out how it worked, and then when I later looked for homeschool curriculum, one of my qualifiers was that it taught kids to understand a concept before handing students an algorithm. 

 

If we're talking about literacy, we have benchmarks, levels, strategies, an understanding of how the brain attaches symbols and sounds, and methods to reach all kinds of learners to see where the literacy train could possibly depart from the tracks to derail learning. I've read articles that talk about how effective it is to develop and use a model for math that parallels what successful schools do with literacy, but actual practice falls very short of this. My son had excellent mental math strategies and number sense in first grade until timed tests came along. Then he started counting on his fingers so that he could finish the problems "on time." Then the teachers complained he didn't know math (He was getting A's and asking for harder math at home--he could add 5 or 6 four digit numbers together and borrow from zero to subtract 4 digit numbers. He also understood and enjoyed multiplication). Then they taught poor strategies for telling time. I pointed out to the teachers that he was confused about telling time. They told me it didn't matter because he'd learn it again next year--but I was warned again about the stupid math facts. I taught my preschooler how to tell time last year (using the MUS method), and he got the concept in a couple of days. If he forgets part of the idea, he can talk through the information with me and be on the right track again immediately.

[wapiti]

The inserting geometry between algebra one and two happened within the last twenty years.

 

I don't know when it started, but FWIW I think it was much earlier than the last 20 yrs.  That was my sequence:  I took algebra 1 in NYS in 8th grade around 1981-2, followed by geometry in 9th grade and then "algebra 2 and trig" in 10th (precalc in 11th, AP calc AB in 12th).

[vonfirmath]

The inserting geometry between algebra one and two happened within the last twenty years.  My understanding is that it was done because basic knowledge of geometry is necessary for decent SAT scores.  When the typical high school sequence was Algebra I, Algebra II, Geometry, Trigonometry, most students would just be starting geometry in the fall of their junior year. Traditionally, students took the SAT that same fall (giving time to repeat the test if necessary).   Inserting geometry between Algebra I and II means that most students have taken it prior to taking SAT exams.  

 

Other reasons I've heard are - It was an attempt to lessen the perceived unfair advantage to students who started the high school sequence early.   And that when public schools stopped requiring four years of math to graduate, administrators wanted to be sure that all students had reached geometry.  

 

Several math programs teach algebra earlier. Basic algebra and geometry are included in the first years of MEP. 

 

Longer ago than 20 years. I'm 22 years out of high school and the progression when I was 9th-10th-11th was Alg 1, Geometry, Alg 2

[kiana]

 

My next door neighbor teaches HS calculus. She is convinced that past 2nd or 3rd grade, we should have MATH teachers teach elementary math (I think it needs to be earlier). I believe we have (largely) math phobic teachers with a general elementary certification glossing over conceptual math and relying on algorithms and memorized math facts. I realize this may be changing, and I'm not trying to say bad things about all elementary teachers (I know some wonderful ones), so bear with me until I get to the examples. Just a hunch, but I'll bet that's not how the mathy countries teach math.

 

 

 

 

I agree with pretty much everything in your long post. We have reading specialists. Why not math specialists?

 

 

 

When I read Liping Ma's Knowing and Teaching Elementary Mathematics, there were teachers in rural schools who taught all subjects who were interviewed for the book. The biggest difference I saw in attitude was that the teachers did not treat their college education as the be-all and end-all. In other words, they did not treat knowledge of elementary math as something that was finite. They continued actively working to improve their knowledge, and not just attending workshops to tick boxes for continuing education hours.

 

 

 

Are there teachers who do that here? Yes. But there are also a fair number of math-phobic procedural box-checkers.

[EKS]

It is not clear to me what we mean when we say algebra, but don't programs like Singapore introduce algebraic concepts in 4A and 4B?

 

This is correct.  Many (or maybe all) of the problems done with bar diagrams are algebra problems in disguise.  I just did all of the problems in CWP 3, and there were several where you had to use the bar diagram equivalent of simultaneous equations to solve them.  And that's third grade.

[Sherry in OH]

I don't know when it started, but FWIW I think it was much earlier than the last 20 yrs.  That was my sequence:  I took algebra 1 in NYS in 8th grade around 1981-2, followed by geometry in 9th grade and then "algebra 2 and trig" in 10th (precalc in 11th, AP calc AB in 12th).

 

It may be state specific.  I graduated in the 1980s.  Four years of math were required.  Academic track students took Algebra II, Geometry, Trig, Calculus or Algebra I, Algebra II, Geometry, Trig, depending on their eighth grade math course.  There were alternate math courses for those business and general ed  students deemed unable to handle the regular sequence.  

 

My parents graduated in the 1960s.  They followed the same sequence.  

[mom2bee]

I think one of the biggest reasons that math is compartmentalized is the American need for box-checking.  It is easier to show what is taught, even if it is not learned as well.  It is all about showing it on a transcript.  My kids are very young yet, so I have a lot of time to think about this, but I really want to do a more integrated higher level math.  But then when she wants to take college classes in high school, how do I show them what they have already done?  

 

Placement tests usually. As far as I know, if you want to take college classes as a highschool student you have to have passed a test--SAT, ACT, or sometimes just the schools placement test.

 

[kiana]

I think one of the biggest reasons that math is compartmentalized is the American need for box-checking.  It is easier to show what is taught, even if it is not learned as well.  It is all about showing it on a transcript.  My kids are very young yet, so I have a lot of time to think about this, but I really want to do a more integrated higher level math.  But then when she wants to take college classes in high school, how do I show them what they have already done?  

Usually she will have to take a placement test regardless of what she has had in high school. Very many students have precalculus or higher in high school and still place into developmental math, so placement tests are required for all. Some schools have a specific placement test, such as COMPASS, others use SAT/ACT scores for placement.

 

The biggest worry about using integrated math is if the student needs to re-enter school halfway through and the school does not have an integrated track, s/he may have to repeat courses. This is especially problematic if part of geometry has been covered. If you complete the full college-prep track for whatever integrated curriculum you choose, I don't think there will be a problem.

[GailV]

The inserting geometry between algebra one and two happened within the last twenty years. 

 

I graduated in the 70s, and the sequence at our school was Algebra 1, Geometry, Algebra 2.  During senior year some kids took trig/pre-calc., but most students didn't take four years of math.

 

Most kids around here take Algebra 1 in 8th grade.  My own children were surprised to meet some students from a different area who don't start algebra until high school

 

RightStart introduces algebraic concepts reasonably early.  It has geometry scattered throughout.  Montessori math has a big emphasis on geometry at every level.  It also has the uber-cool binomial and trinomial cubes so you can introduce preschoolers to those particular concepts (I love math manipulatives, and those two are my absolute favorites).  As others have said, other curricula also introduce the concepts early.

 

I think there's a lot more variety of math experience in the U.S. than we sometimes realize.

[Spy Car]

For what its worth, the PS students in CA are getting exposure to basic algebra in 4th Grade (and before). Same with some basic geometry.

 

Bill

[Down_the_Rabbit_Hole]

The curriculum I use has Algebra introduced early on, basic Algebra but still Algebra. And it presents it as Algebra so the word Algebra does not sent chills when they encounter it as a whole class later on.

[My3girls]

I took Pre-algebra in 7th and 8th grade because Algebra was not offered to 8th graders. Then A1, A2, Geometry, and Trig. Calculus was not offered at the high school either. I graduated in TN in '91.

 

Now, here in GA 8th graders take A1. 4 years of math is required to get into every college we have looked at. I really haven't checked on high school graduation requirements since that really isn't a goal for us.

[regentrude]

I often watch the "homework help" show in the afternoon.  It's basically a local public access thing where kids can call in with questions.  So a caller called in with some math questions.  DH was not in the room when the caller said their grade.  But then he saw the math questions.  I asked him what grade he thought the questions were from.  He said 5th.  The caller was in 8th.  DH was shocked.  He doesn't seem to believe me that the math education is so radically different here than where he came from. 

 

Coming from the same country as your DH, I would not have believed it either, had my kids not attended middle school. What a sad eye opener that was.

[mathmarm]

I often watch the "homework help" show in the afternoon.  It's basically a local public access thing where kids can call in with questions.  So a caller called in with some math questions.  DH was not in the room when the caller said their grade.  But then he saw the math questions.  I asked him what grade he thought the questions were from.  He said 5th.  The caller was in 8th.  DH was shocked.  He doesn't seem to believe me that the math education is so radically different here than where he came from. 

 

I don't know what country your husband comes from, but sadly, I can believe it! Many of the school math texts I've seen weren't much better than...I honestly can't think of anything that is a just comparison. I was a HS math teacher many moons ago and it was...painful, sometimes to watch what the kids struggled with. If you have to count--on your fingers, and double check--to add a single digit and a double digit number, then clearly, something, somewhere has gone very, very wrong.

[Korrale]

I think algebra or algebraic thinking is taught much earlier than many realise. Solving ? For basic sentences like 5+?=7 or 5+2=3+? are covered in 1st grade in quite a few math curriculums I know. I think the focus in lower grades is to teach kids to have strong number sense and real world math before introducing more formal algebra.

 

I grew up with intergrated maths in Australia. I want the same kind of program for my son. Frankly I am not really sure where all the different mathematical disciplines differentiate. For years I thought I never studied trigonometry or calculus, but I did. It was just called Maths. In highschool we had Maths A, B or C. Maths A was just easier level, every day Maths. Maths C was more advanced and essential for students going into a field that needed Maths. Most students opted for. Maths B.

 

I did read some reasearch recently about how students that study intergrated math do better than what is commonly used in the US.

[kiwik]

I think algebra or algebraic thinking is taught much earlier than many realise. Solving ? For basic sentences like 5+?=7 or 5+2=3+? are covered in 1st grade in quite a few math curriculums I know. I think the focus in lower grades is to teach kids to have strong number sense and real world math before introducing more formal algebra.

 

I grew up with intergrated maths in Australia. I want the same kind of program for my son. Frankly I am not really sure where all the different mathematical disciplines differentiate. For years I thought I never studied trigonometry or calculus, but I did. It was just called Maths. In highschool we had Maths A, B or C. Maths A was just easier level, every day Maths. Maths C was more advanced and essential for students going into a field that needed Maths. Most students opted for. Maths B.

 

I did read some reasearch recently about how students that study intergrated math do better than what is commonly used in the US.

It is a US thing. In New Zealand like Australia it is integrated but in the very last year it is split into calculus and statistics and students choose one or both (assuming they take maths at all which lots don't). We mostly do the same with science except the last two years.

[DarlaS]

I grew up with intergrated maths in Australia. I want the same kind of program for my son.

There is actually something in the CC standards about this. Maybe we'll see some new programs out soon.

 

For now there is the NEM series from Singapore that begins in 7th grade (or is it called something else now?). There is another starting at the middle school level as well by the same publisher as Everyday Math. I think the first in the series is called Transition Math or something like that (Okay, that program's not integrated after that book. :-/).

[Lakeside]

This is an idiosynchrasy of the US school system. the compartmentalization of math into "algebra" and "geometry" leads to a delay in math instruction because educators wait until students are ready to be taught advanced algebra concepts- instead of teaching simple algebra concepts as soon as students are done with arithmetic.

One can easily finish arithmetic with positive integers by the end of 4th grade, spend 5th grade on fractions, and begin with algebraic expressions in 6th grade as is done elsewhere in the world. Instead, educational philosophy in the US seems to assume that middle schoolers can not be taught any new material and that they must simply be parked and supervised for grades 5 through 8 until they are ready fro new stuff. It does NOT take 3-4 years to teach fractions!

Also, the splitting of geometry is specific to the US; an integrated math where geometrical topics are interspersed is much better IMO.

 

 

 

That is what US educators assume. I am baffled, because I see no reason to assume that American students are less intelligent than, or developmentally behind, students from Russia or Singapore or Germany, where they are expected to be ready for algebra in 6th or 7th grade.

 

 

 

Sure. Look at how math is taught elsewhere. In my home country, much of triangle geometry, congruency, proofs is done in 6th grade, along with simplifying algebraic equations. Linear equations are taught in 7th. Quadratics later. geometry and some statistics are taught all alongside.

 

 

 

There really is not THAT much to calculus. There are two basic ideas and a bunch of tricks; one year is entirely sufficient for single variable calculus. Multi-variable is a bit trickier, and I am pretty sure most students do not really understand vector calculus unless they apply it in theoretical physics where they need to have an understanding of curl and gradient. But I still think one semester suffices for that.

Our college math instruction was at a faster pace: we did vector calculus at the beginning of the second semester and spent the remainder of our five semester math sequence on functional analysis, probability and statistics, ordinary and partial differential equations, complex analysis.

Do you have any suggestions on a more integrated approach?  I have read a lot of your math posts and appreciate your perspective.  If you have already posted that information I'd love to read it. I seem have a hard time finding things on the search feature these days.  :o

TIA

[momto2Cs]

One of the things I enjoy about Life of Fred math is that it introduces algebraic and geometric ideas early on, so that by the time a student hits algebra, they aren't "shocked" by it. I also like that Stanley Schmidt recommends both Algebra I and II before Geometry. From his website:

 

First, advanced algebra is much more "mechanical" than geometry.  Like beginning algebra, much of it consists of learning procedures—such as how to factor trinomials.  Those who have had success in beginning algebra will continue on that same road.  Some of the items in advanced algebra ask that the students remember what they learned in the first course in algebra.  So taking advanced algebra right after beginning algebra will promote more success in advanced algebra than putting geometry in between them.

       Secondly, the proofs and the reasoning that are a real part of geometry require a more mature mind that the mechanical stuff of algebra.  There is not just a single way to do some of the proofs—more creativity is involved.  And older brains seems to do that kind of reasoning more easily than younger brains.

[Spy Car]

For now there is the NEM series from Singapore that begins in 7th grade (or is it called something else now?).

My (perhaps imperfect) understanding is that NEM has essentially been discontinued and that another similar (reputed to be slightly easier but far more user-friendly) series called Discovering Mathematics has essentially taken its place as the "integrated" Singapore program that is easily obtained here in the USA.

 

Bill

[DarlaS]

My (perhaps imperfect) understanding is that NEM has essentially been discontinued and that another similar (reputed to be slightly easier but far more user-friendly) series called Discovering Mathematics has essentially taken its place as the "integrated" Singapore program that is easily obtained here in the USA.

 

Bill

I think they offered both programs for a while. I knew I remembered something, but was too lazy to look it up. :-)

 

More user-friendly is a plus. Most drop Singapore after 6B because NEM is not for the faint of heart.

[a27mom]

I actually had integrated math in high school, in NY state. At the time I believe the entire public school system in the state used the same curriculum for regents (college prep) level. This was early 90's. We had Course 1, Course 2, Course 3, Advanced Math ( pre calc), then AP Calculus. The norm was to start course 1 in 9th grade. The advanced track started course 1 in 8th (that was the most advanced you could go in our school district). In addition to algebra, geometry, and trig the "courses" also included logic.

 

I now live I a different state, so I have no idea if NY still has this progression.

[Spy Car]

I think they offered both programs for a while. I knew I remembered something, but was too lazy to look it up. :-)

 

More user-friendly is a plus. Most drop Singapore after 6B because NEM is not for the faint of heart.

They definitely published both at one time. I'm pretty sure NEM was dropped by singaporemath[dot]com. I spoke with them years back (when NEM was still available) and they recommend Discovering Mathematics based on the additional teacher support. If my memory serves, NEM didn't even have soulution books?

 

Bill

[DarlaS]

They definitely published both at one time. I'm pretty sure NEM was dropped by singaporemath[dot]com. I spoke with them years back (when NEM was still available) and they recommend Discovering Mathematics based on the additional teacher support. If my memory serves, NEM didn't even have soulution books?

 

Bill

You remember correctly. No solution books. I've resisted the temptation to buy it based on that alone.

 

I may have a peek at DM soon though. It's been a LONG time since I've been to their site.