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I've talked about how our high school's math expectations drove out CMP in 7th and 8th grades. There was a curriculum gap for those kids who wanted to move into geometry in high school. The problem was clear and parents complained. I suppose our school could have put the top kids onto a pre-algebra/algebra track and left the lower kids in CMP, but they decided to use the same books and go at different speeds. This was probably for practical purposes, since the school only has one math teacher for 7th and 8th grades.
However, that's where everything stops. K-6 is driven by Everyday Math and the state's low requirements. The school looks at the number of kids who get to algebra in 8th grade and thinks that is perfectly normal. It's probably about the same number who made the top track in high school math as in the old "traditional math" days. (Is there any data on this?) The lower schools only focus on improving the relative scores of the state math test. It doesn't help that the scores at all of the other schools in the state stink. They only see a relative problem, not an absolute one. Everyday Math spirals along and assumes that kids will develop the necessary skills at their own speed. When 6th grade comes along and it doesn't happen, it's too late, so I assume they just point to the kids who did well. Of course, they never ask the parents of the good students what happens at home.
Do lower schools ever try to track kids longitudinally to see if any one particular teacher is a problem? Do they ever check to see if kids really do achieve a balance of understanding and skills; that they really are developing up to their potential? You would think that if they studied these problems, they would use teachers who were certified in math starting in first grade. Does anyone know of schools that send K-6 kids to a separate room/teacher for math? What math curriculum do they use? Do they separate kids by ability?
It seems to me that many of the problems kids have in math are caused by gaps and gaps are caused by "trusting the spiral". These problems can happen for both understandings and skills. Schools don't want to take the responsibility for ensuring anything but some state minimum on a statistical basis.
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The public school my son went to for K-3 and the private school he went to for 4-6 both had kids go to different classrooms for math.
The private school had the math levels established by placement tests, independent of the grade level for the other subjects. Everyone in the school taught math at the same time, with the more mathematically sophisticated teachers teaching in the higher level classes. For a while they used the Singapore books, but they have since switched to a different (to my mind less mathematically and pedagogically sophisticated) series.
Too many questions for one blog post, Steve.
But first, the problems aren't caused by "trusting the spiral". The problem is bigger and harder than that. The non spiral textbooks are just as awful, though at different things. (Only Singapore's Primary Math is good.) In most states, standards are too low and incoherent. Even when there are decent assessments, no one even thinks about closing the loop--they don't know how. But all of these pale in comparison to the primary problem: the teachers of K-6 do not know enough math to teach their required material to mastery, and they are given no guidance on how to do that.
All they get for support in teaching the math content is what their textbooks provide--which is garbage. In small districts or private schools, curricula are centered around textbooks, and teachers don't know the difference between curricula, standards, and texts. (In big districts, some people know, but not all.) Their pedagogical background doesn't help them with their lack of math content. They simply do not know what mastery looks like--*because no one ever taught them*.
The few teachers in K-6 who like math and are good at math may still not know how to build up to mastery because they aren't used to bridging the conceptual and procedural. If you're good at the procedural, you may overlook that your procedurally strong students don't understand why they do what they do, and you may struggle to teach the ones who lack the procedural fluency, too, because you simply can't go back far enough to correct their problems--and this is true even if you have a nonspiral curriculum.
I've never heard of a public school where a separate math teacher was brought in prior to 4th grade.
My MIL is a retired 3rd grade teacher and while she's a wonderfully warm and patient teacher, I've noticed that her math knowledge and skills are very weak. Primary grade teaching seems to attract folks like my MIL who are great on the touchy-feely aspects and not-so-great on the academics.
"Do lower schools ever try to track kids longitudinally to see if any one particular teacher is a problem? "
re: K-6: In some of the schools I'm working with, the *individual teachers* are quite aware who the problem teachers are when it comes to math, but since these teachers are teaching *every subject*, the administrators may not act on it anyway--and what's the alternative?
"Do they ever check to see if kids really do achieve a balance of understanding and skills; that they really are developing up to their potential?"
These are separate questions. First, again, in the schools I'm working with, the 6th and 7th grade teachers are quite aware of which kids are understanding little, and of course, those kids have poor skills. No one is checking on *anything* for kids who aren't in desperately bad shape.
No one in the schools I'm working with has *any idea whatsoever* what "developing up to their potential" in mathematics would look like. They have no horizon point of what a top student could really achieve (though they have some top students who they know could move ahead), and they have no yardstick. And more, they really have so little understanding of math themselves that they do not recognize gaps in understanding in kids who are procedurally fluent. At best, they have a test like the Stanford-10 or the ITBS which tells them how great or poorly their kids are doing, but that's like taking the NAEP--you know that the questions are so much lower than they should be, but I don't think most school admins have any idea how much lower they really are. So kids hit the ceiling without knowing schools being able to assess how competent they are, and kids who aren't high scoring are seen as okay when they shouldn't be.
"You would think that if they studied these problems, they would use teachers who were certified in math starting in first grade. "
Well...if pigs had wings....
In my state (and in most), practically, there is no way to hire a math-certified teacher for first grade.
Here, there are two certs for first grade: you can either be certified for "early childhood ed", which covers from 6 weeks to grade 3, or you can be certified for "elementary ed", which covers grades K through 5 or 6 (can't remember which.) There is no special math cert available, and procedurally, what's required to get those certs is formidable in terms of time and breadth of requirements, if not in terms of content. The math requirements for those certs are abysmal, as you might guess (I can post the details later, but suffice to say, at the U of MN, they don't have to take more than college algebra, 1 stat course, and 1 "math methods" course which as far as I can tell, is a course whose content is 100% dependent on the teacher and may have no math whatsoever.)
to be "math certified" for junior high/middle school or high school, you need an entirely different cert with different course requirements--years of coursework differences. And even then, the coursework required doesn't teach the math content *that the teachers will be teaching*.
Apparently, the idea of teachers of just-math in grades 4 and up IS coming into vogue here and nationally, but until the requirements of math content are changed, it won't help much.
As far as kids prior to 6th grade changing teachers for math, yes, it's done here starting in 3rd. They also regroup for reading. Subject acceleration in math is also relatively routine (more or less a kid every other year at this school, around 1/100). The school has a math specialist who primarily does pull-outs with the kids who need more help than they can get from just the regrouping.
Math is pretty much taught at the same time district-wide,from 3rd up through algebra classes at the middle school, so that math acceleration can work. (Some kids are bussed to the middle school for pre-algebra and algebra.) Not a huge district, about 7000 students, sounds like it might be larger than yours though.
"The problem is bigger and harder than that."
I know, but I'm trying to find out if there is a path to get there or whether the change requires a discontinuity, so to speak. CMP disappeared from our schools based on driving expectations down from the high school, and it seems that there are some places where something is being driven down into the lower grades. Having certified teachers might not mean too much, but perhaps that will reduce the cases where kids lose a year. It might also allow for more acceleration in schools. It would be interesting to know how schools which offer early acceleration evolved.
It would be really nice if undergrad ES programs (whatever they are called, including liberal studies etc.) required real, specific coursework - not just in math but in English grammar & composition, geography, sciences and history. Such courses should be taught by the academic departments and reflect the necessity of serious grounding in those fields. You can't teach what you don't know. I agree with the above comment that lots of ES teachers love kids and the artsy/crafty, touchy-feely stuff but are much less interested in, knowledgeable about academics. It just isn't their area of interest or expertise and they don't see the necessity for serious foundations from kindergarten.
The course work required for my dd to become an elementary teacher with certification in teaching gifted students requires her to take one math class. Now wouldn't many of the gifted kids be very good in math? Kids in our district enter middle school in 6th and change teachers but our school has gone to online ALEKS and I don't think the teachers are actually doing anything in math class but tabulating grades.
Anon,
The U of MN reqs are for "real, specific coursework"--in fact, so many courses in such a broad range that none of us specialists can even *enter* the master's programs to become teachers, because we would need two YEARS of ugrad coursework to hit their core minimums.
I've attached the list below. It's for the PREREQs to even enter their master's program, not counting the coursework in one's major or in the master's. The problem is not the lack of requirements, but the breadth of them and lack of depth: there's 2 1/2 years of coursework not counting one's major's requirements, and nearly all of it at the introductory level (that's what 1000s are at U Mn.) It's survey courses in everything. That's not helping someone develop knowledge, nor skill. But you can't possibly take all of these subjects to a deeper level in an undergrad progam, so this is what remains.
From http://www.cehd.umn.edu/CI/Programs/college/ILP/Elementary/content.html
I. Preadmission core requirements for grades K-6 elementary education licensure
Students must complete all of the following preadmission core requirements:
A. Basic requirements
Intro to psychology: PSY 1001 or PSTL 1281
Literature: Any course that meets CLE literature requirement
B. Mathematics
College algebra: MATH 1031 or PSTL 1006
Math for elementary teachers I: MTHE 3101 or MATH 3113
Math for elementary teachers II: MTHE 3102 or MATH 3118
C. Sciences
Biological science (biology, biochemistry, botany, or ecology)w/ lab: BIOL 1001 or PSTL 1131
Earth science w/ lab: AST 1001 or GEO 1001 or PSTL 1171 or SOIL 1125
Physical science w/ lab: PHYS 3071W or PSTL 1163
D. Social studies
History: Any course that meets CLE requirements for HP Social science electives
Human geography: GEOG 1301W or GEOG 3381W
Social science elective (not psychology): PSTL 1204
E. Communication arts and literature
Linguistics: LING 3001 or ENGL 3601
Foundations of Reading: CI 5413
Practicum: Working with developing readers: CI 4413
Children’s literature: CI 3401
F. Arts
Performing arts: PSTL 1312 or MUED 5011
Visual arts: CI 3001
G. Kinesiology
Teaching physical education: KIN 3327
This is such a timely post. I was having this same connversation with my husband the other day - he felt that math specific knowledge wasn't critically necessary (although nice to have) at the K-5 level as the math is relativly simple (to his engineering point of view).
I understand that high performing countries use teachers trained in math in their elementary programs but WHY?... what do we lose by having the dunderheads teaching math to 2nd graders?
What higher level connections need to made- or do the certified teachers not know the very basics of multiplication , division and basic fractions?
Many thanks
Dee
"...do the certified teachers not know the very basics of multiplication , division and basic fractions?"
Yes.
The K-5 teachers in general can teach the mechanical parts of K-5 math (e.g. invert-and-multiply as a technique for dividing fractions). But they do not (as a rule) understand *WHY* the algorithms work [NOTE: The vast majority of non-teachers in the US also don't know why the algorithms they know work the way they do].
The book "Knowing and Teaching Elementary Mathematics" by Liping Ma elaborates on this.
-Mark Roulo
Also, the K-5 teachers don't know WHY students really need to know fractions well or why it is useful to know the standard algorithms. Since they don't see where the basic math is going, they are easily convinced that curriculum like Everyday Math are better than the traditional curriculum that they remember being bored by.
There is also the problem that Glen's talked about -- since many elementary school teachers didn't like math, they aren't enthusiastic about teaching it, and spend as little time on it as they can get away with.
What do we lose by having the dunderheads teaching math to 2nd graders?
What higher level connections need to made- or do the certified teachers not know the very basics of multiplication , division and basic fractions? In 2nd, some of the teachers probably are shaky even on the basics. They can work through the types of exercises that they are used to but may not be able to deal with some questions. I'd guess that they probably don't see the root of some students' misunderstandings. They may also be unable to provide any type of extension for the kids who are ahead, and may confuse those kids with incorrect information.
Many of the K-3 teachers (and higher grades, even) do not understand place value because they have never been taught. They do not know why the standard algorithms for addition and subtraction work. They can't motivate it to their students, they can't catch misunderstandings.
They wouldn't know what to teach about regrouping of sums and differences that would help make the standard algorithms clear.
I would add that people who are quite natural at place value may overlook just how expert they are at it, and how much it isn't obvious to children. Similarly, someone for whom fraction manipulation is easy may not understand why it matters to teach reasoning behind the algorithm for multiplication or division, but assuredly, most K-5 teacher do not know the reasoning themselves. They know "of means multiply", which is not teaching how to reason about math.
For some reading on what's so sophisticated about elementary math, here is Prof. H. Wu on the subject:
http://www.msmi-mn.org/home/documents/sophisticatedelementarymath.pdf?attredirects=0
For a look at what elementary teachers get for training and development in Singapore, read this:
http://www.msmi-mn.org/home/documents/BeyondSingapore%27sTextbooks.pdf?attredirects=0
As to why it matters whether teachers know math well in K-5, short answer:
success in college depends on success in 5th grade math.
You won't get there if you didn't get competent grounding in K-3 math. K-3 math needs to be both procedural and intuitive: you need to know math facts and you need to have number sense. You can't master fractions, decimals, pre algebra or above if you haven't mastered place value.
Middle school math is extremely important because it's the bridge to algebra 1. Success at algebra means successfully grasping abstractions--no longer are you answering a question about the product of these two numbers, you're answering about relationships in general.
Fractions (including decimals, percent, rates, etc.) are the first abstractions, and provide the first opportunity for students to move beyond what they can do on the fingers or with manipulatives.
American curricula artificially dumb down the teaching of this material in grades 4-7 so that students are grossly unprepared for the onset of real abstraction in grade 8.
Worse, most math is taught incoherently, so that students don't understand that the rules they were taught for arithmetic continue to apply to these new things like rational numbers. Connections aren't made for them, because their teachers have never made those connections. When math seems incoherent, you stop bothering to learn the rules--what's the point if it's all just seemingly arbitrary. Likewise, this material is taught without precision, so students are denied the ability to work with definitions and learn how to make statements that are true in general. If you never are taught that math makes sense, that it is coherent and precise, you will probably hate math. You certainly won't be able to be good at it.
-- what do we lose by having the dunderheads teaching math to 2nd graders?
For the record, characterizing elementary teachers as "dunderheads" for not understanding math concepts when in all likelihood, no one ever taught them any, is unhelpful at best, and slander at worst. It helps to stick to the issue at hand: what are teachers lacking in knowledge, and how can we provide it to them? how can we educate the bulk of our children without doing so for our teachers?
"...since many elementary school teachers didn't like math, they aren't enthusiastic about teaching it, and spend as little time on it as they can get away with."
And Everyday Math lets them get away with that. You could do more with EM, but their web site specifically tells teachers not to push mastery "at any one point in time"; just keep moving through the material and "trust the spiral". Of course, when you get to 6th grade and run out of "Math Boxes", then what do you do? Filter and blame the kids. There is no feedback other than low expectation state tests where the goal is only to raise the numbers by any small amount each year.
The main issue I raised is how do we get there. What do schools go through when they decide to have specialists teach math in K-6 and offer real acceleration? Why do some schools decide to use Singapore Math? What causes that? It seems like it is not a smooth continuous change; that it all depends on a few key people. Does it mostly happen from within, or are there examples of parents pushing for change?
In our schools, CMP was pushed out due to parental pressure, but I don't see any way to change the full-inclusion, spiraling mentality in K-6. That seems to be a fundamental roadblock, especially when enough parents do the work at home and bail them out.
What makes a school go to Singapore Math? Parents can do it in some places by starting a school. Teachers are probably the driver in others. Certainly without buy in from the teachers, it would be very difficult. I have no idea how you would ever get a big district to change anything.
I know of one public K-5 school in Minneapolis where the teachers were very professional with several years of experience for each of them and a great administrator. They were forced by Mpls district to go to TERC. They came in to their principal BEGGING for something else, anything else, because their fourth graders were still doing 2 + 5. The principal told me he had teachers in his office literally crying in frustration over it. He responded by finding Singapore Math for them, and ignoring the district telling him he couuldn't. I don't know how he had the money to buy the books or do prof dev. We'll see what happens in a couple years when he and his vp both retire at the same time.
I know of a private school where the teachers on their own went to a Singapore prof dev event, and loved it. They are now asking for some outside people to come in and help educate the rest of the school about it. For them, though, there's another BIG reason: the best charter school here has a lottery of over 200 people for 20 some slots in K, and one of the big reasons in Singapore Math and ability grouping. So this private school knows it needs to compete with that if it's going to stay alive.
I know another school where the teachers recently went to Saxon and are very unhappy with it. They had never seen Singapore. When someone came in with the books and a lot a experience with Singapore, even a tiny little explanation of how the ideas are presented was enough to get them interested.
We need to turn the spiral into a mobius loop.
Teaching elementary math the Asian way has been surprisingly challenging for me, and I'm a Stanford grad who got A's up through calculus and >700 on both the math portions of the (pre-recentered) SAT and the GRE.
Before I began homeschooling, I could've quickly calculated the correct answer but would have been clueless had I been asked to explain why the algorithms worked. I had the procedural knowledge down pat from the traditional math instruction I had received growing up but the conceptual knowledge was *VERY* shaky.
This is the biggest stumbling block I believe in the widespread adoption of Asian-based math in the U.S.- teachers will need extensive training (or self-education) in order to get themselves up to speed on it.
I'd like to see all ed colleges require their elementary ed candidates to take the Singapore training. Even if the teachers wind up in a school using a different curriculum, the conceptual understanding will help them be better math teachers.
One of the effects of having the same teacher teach all subjects is that the teacher often gets to choose how much of each subject to teach. Without a math specialist, who would require a scheduled math time, math can end up just another ingredient in the subject soup prepared by each teacher every day according to her personal tastes.
So what suits the taste of most elementary teachers? Like all of us, they like things that make them look competent and dislike things that make them look incompetent. They'll tend to teach more of what they're good at and less of what they're not good at.
Competence at people management is a brutal challenge for any teacher, but a lot of academic competence (relative to their kids) comes naturally from just living twenty years longer in the same society.
By consuming an extra twenty years of popular media, you can build "language arts" skills that seem impressive to kids. You'll know far more about your favorite "social studies" topics, after years of Oprah and magazine articles, than the kids will. And now that science is mostly environmentalism, you can get your science training from movie stars.
As long as teachers aren't required to teach more than they can learn from long-term popular media exposure, they'll all be competent. As long as there is no sentence diagramming, or historical details, or real science required anymore, they'll feel fine about teaching those subjects.
But math is so...alien to popular culture. You don't just pick it up; you have to make a special effort to study it. It's hard to get right, yet easy for kids to spot when you're wrong. You can't hide behind your superior verbal skills if challenged. And Cosmo, Oprah, NPR, talk radio--they won't help you.
This is why whoever is responsible for teaching math needs to be rigorously trained and tested for competence in math specifically. It can't be assumed. Those who are confident in their math will teach more of it, teach it better, and demand better curricula.
"..the best charter school here has a lottery of over 200 people for 20 some slots in K, and one of the big reasons in Singapore Math and ability grouping. So this private school knows it needs to compete with that if it's going to stay alive."
This gives me a little bit of hope. I know that our K-8 public schools are sensitive to loss of kids to private and charter schools, although most of those schools use Everyday Math. It seems as though once one school goes to Singapore Math, the discussion becomes much more concrete and the demand will be a big warning to other schools. I hope.
Our state will never allow a charter school for K-8 that sets high expectations or allows acceleration and ability grouping. The charters that are allowed have to be more thematic and the theme can't be higher expectations or more rigor. That's because the regular public schools do not want to lose their best students. Our schools claim that since they meet all (minimum) state test expectations, none of the kids in our town should be allowed to go to any charter school. They claim that those kids take money away from them when they are doing a good job. Actually, it's a separate line item in the town's budget.
"Without a math specialist, who would require a scheduled math time, math can end up just another ingredient in the subject soup prepared by each teacher every day according to her personal tastes."
There is also the push to include math in all other subjects. I remember my son having a part of the day where they looked at the clock and discussed the month, day, and time. (first grade?) They would track the day of the year and ask kids to come up with number statements that equal the day number. OK, for school day 102, a student might say that 50+50+2 = 102. This is all fine, but only a couple of kids would do it each day. This was counted as part of math time for all. They go through the motions, but they have no day-to-day interest in results.
Having specialists and specific times of the day for math would help. It would be nice to think that these teachers would then be more open to better curricula. This would be difficult in our public schools because full-inclusion is such a fundamental assumption. They assume that differentiated instruction will work. They know it doesn't, especially for the most able students. I got them to allow my son to skip a grade in math, but that only allows them to think that they have a workable solution. In fact, many other kids could do the same thing, but Everyday Math never gets them close.
My child was accepted to one of the most rigorous charter schools in the state of Arizona for 5th grade. This school is a 5th-12th school. For the 5th grade this year, 205 students applied for 130 spots. The waiting list for 2011-2012 is about 80 deep.
As a charter schools, there is no entrance exam, but we have already taken exams and received results that allow us to gauge our child's performance against the incoming class and past classes. The school then offers sessions to give parents guidance on how to prepare their children for the school year in areas where they may be lacking.
Incoming 5th graders are assigned to one of two tracks. The standard track is Saxon 8/7 (yes a text intended for 7/8th graders). 4 of the 5 sections will do Saxon. In this track students typically take AP Calculus in 9th or 10th grade.
The other track is Algebra 1. The Algebra 1 track leads to students taking AP Calculus AB or BC in 8th grade.
You can see the math sequence chart here...
http://www.basisschools.org/bsi/index.php?option=com_content&view=article&id=94&Itemid=111
Is anyone else amazed that it takes our schools 7 or 8 years (k-7) to essentially teach our students addition, subtraction, multiplication, division, decimals, and fractions?
Anon, I looked at the link for the math sequences -- no real detail. What will kids who take calculus in 8th grade do later? Are they making subject or curricular plans? Do they have teachers who can teach beyond calculus?
bky,
They offer classes in...
AP Statistics
Differential Equations
Game Theory
Category Theory
As far as if they have staff capable of teaching it, most of the staff have area specific degrees and not teaching degree of Masters in Ed.
Students are offered the option to graduate after 11th grade.
I remember talking to a student from Bangladesh who told me that students in the math/science track there take calculus in grade 8.
I also had a 15-yo neighbor who moved here from Colombia. He was forced to take the lowest level freshman math class offered by the school. He recently decided to go back to Colombia (after about 1-2 of trying out the US schools).
Is anyone else amazed? People should be outraged.
"I remember talking to a student from Bangladesh who told me that students in the math/science track there take calculus in grade 8."
I would not conclude very much from this without a lot of confirmation.
I work with a *TON* of Indians (um ... India Indians, not native American Indians). On balance they are *very* well educated in math and science (and a large percentage are IIT graduates). India does not get to Calculus in 8th grade. Not even, as a rule, for the super-high-performing IIT bound kids.
The rest of the world *does* seem to get to Algebra in around 7th grade (versus the historical US 9th grade), but Calculus in 8th grade as anything other than an outlier I find very unlikely.
-Mark Roulo
I hope you'll read my latest post, "The Birds and the Bees and Constructivist Math." Thanks!
The Birds and the Bees and Constructivist Math
I'm going to post about this up front soon, but I am highly skeptical of acceleration, because largely it is at the expense of depth.
To say "why does it take 8 years to teach the four major operations and fractions" is to miss just how sophisticated this material is. Place value should not be rushed--it should be taught both procedurally and conceptually, with time spent developing both in parallel on more and more extensive problem variations. Similarly, fractions should be taught in such a way that their abstract quality is clear, and students learn to use definitions to make sense of, and argue about how the operations on them work. Decimals, percent, rate problems are all sophisticated, and should be taught with that depth to allow as much understanding of mathematics as possible.
Should some bright children accelerate? Sure. But most should be given rich, content-filled coursework in these subjects instead of the dumbed down curricula they get, not just accelerate through the dumbed-down curricula faster.
@ Allison,
my daughter will be accelerated one perhaps two grades next year (she'll be in 3rd grade and will move up to 4th or 5th grade for math) using Math Expressions. Is this something I should be concerned about? We do Singapore Math(she will is in 3B) at home, but it is currently sporadic because of my other daughter's health needs.
"my daughter will be accelerated one perhaps two grades next year ..."
Accelerating in something like TERC or Everyday Math is not very meaningful. I don't know much about Math Expressions, however. Allison is right about the problems of acceleration, but if our K-6 schools officially offered it, I would have taken advantage of it earlier. It may not be too meaningful, but it could get you through the bad math faster. You just can't assume that you won't have to continue the good math at home until then.
Our son was allowed to skip 6th grade Everyday Math even though that wasn't normally done. Our goal was to go on to a real course in pre-algebra in 6th grade rather than 7th. However, since he was the only one, they didn't have any common procedures. In 6th grade, they put him in with the 7th graders, but that screwed up his schedule, and some teachers didn't like the exceptions made for him. Being a "baby" in with the big 7th graders wasn't fun either.
In 7th grade (algebra I), I decided to teach him at home rather than screw up his schedule or have him take some sort of online course at school. (the ones I looked at were lousy) So there are the practical aspects of the acceleration.
I never saw it as a race. I don't see much advantage to getting to calculus before your senior year. I would rather that he had better or more rigorous courses. So, here he is with a 98 average in algebra II as a freshman, but he thinks he only got 9 of the 25 questions on the AMC/10 test correct. That was with no practice, but the point is that you can accelerate all you want and get A's in math, but still be missing something. The AMC test might not be the best indicator of that, but my "A" son is still not being prepared in math as well as he could. Then, when his senior year comes, he has nothing to choose from to continue the calculus sequence. The school might claim that kids can go off and take a college course, but exactly how is that done? They offer little or no support.
--my daughter will be accelerated one perhaps two grades next year (she'll be in 3rd grade and will move up to 4th or 5th grade for math) using Math Expressions. Is this something I should be concerned about?
Math Expressions is reasonably good for K-3. After that, it's like all of the rest--very bad at teaching fractions, decimals, pre-algebra, etc. It's a shallow curriculum that leads to a big steep wall for algebra.
You should be concerned, yes. And if this is the only math your child is going to see, then your child may have a major problem, just as nearly every other child who only sees this stuff has major problems.
But my concern is not that your child will have a problem now, but that your child will have a problem later. That's the hard part to see, but lots of bright children, especially those who are very good at getting the procedural parts right hit a wall in high school or college because what they received wasn't meaty enough to make algebra or algebra 2 or even calc graspable. At some point, they start having to ask themselves why they are doing what they are doing--maybe they can't keep track of the procedures anymore, or maybe they mature enough to notice they don't know WHY they do anything they do in math. Bright kids can get stymied by that all of the sudden, and have nowhere to go afterwards, since their foundations have nothing to build off of. For kids who have never learned to study because it's always been easy, this can be a painful awful experience.
Steve is right to say that you can't move up and then assume you don't need to be homeschooling on the side still.
Singapore Math has the depth to make this material meaningful, and since you're already doing it,
I would concentrate on making Singapore Math your focus and finding a way to make that as regular as possible rather than whatever they do for her. If moving her ahead keeps her from being bored to tears at school, fine, as long as you know that somewhere she's getting the substance she really needs.
"Why do some schools decide to use Singapore Math? What causes that? ... Does it mostly happen from within, or are there examples of parents pushing for change?"
Steve:
It happens both ways. A school in a neighboring district took a look at their CSAP scores & realized that as classes aged through their school, they did worse each year. Determined to change that trend, they looked at 4 new curricula and chose Primary Mathematics over Math in Focus, Envisions, and Scott Forsman.
Another school, also in CO, but in a different district had, parents complaining incessantly about the Everyday Math curriculum. This prompted the principal to suggest a change at the school. Teachers were slightly put-off adopting a curriculum that the parents pushed for, because they felt like the parents were in charge, not the teachers, but... They switched to SM and are seeing the benefit this year.
The district in which we lived from 2006-2009 eliminated Singapore from consideration when it adopted a new math curriculum for the 2009-2010 school year because they claimed it would not be appropriate for English Language Learners. They chose Every Day Math instead :-(
about acceleration/depth etc:
My favorite book for general "how to deal with mathy kids" info is "Developing Math Talent" by Assouline and Lupkowsky-Shoplik. IIRC there is a nice list or two in there of good enrichment topics. I'm not so sure that you can really separate enrichment and acceleration myself, to me they go together. In practice, we've found it difficult to get problems with sufficient depth given, whether covering regular curricular topics or enrichment. I agree that schools sometimes accelerate at the cost of depth and understanding. My less mathy child (who is nonetheless accelerated in math) would have benefited more from classes taught with much greater rigor. In order to get her this, we have to go outside the school district. Ugh, I can tell you, it is painful to get her to work in this area at home.
@Genevieve
I have experience with almost exactly this situation. (DS8, accelerated 2 years in math, having had Math Expressions in school for 1st& 2nd grade.) I'm not sure our school uses Expressions so much for 5th grade though - at least, I see lots of stuff that is not directly from that curriculum. If your daughter is being accelerated in math, I assume that the school has tested her on the end-of-the-year tests to determine where she is in their specific curriculum. If not, this is a good thing to do. I find that the problem for my mathy kid is getting material that requires him to think for any time at all. Continuing to work with Singapore math is probably good, another good place to look is at the math contest problems books - such as for Math Olympiad. We've also used Zaccarro Challenging Math Problems. The good thing about the math contest problems is that the types of problems are varied, so one has to think more about what approach to take to solve the problem. Anyway, point is that a child that really needs the acceleration will also need enrichment beyond what happens in the regular classroom.
I think the policies in math in my district are driven by a strong personality in the math curriculum head position who has been there for a long time. Also, because TAG here is solely based on verbal (and is largely a popularity contest, TBH), resulting in some very smart kids not qualifying for any kind of enrichment.
Thanks to everyone for the advice. I had a feeling I would still be working with my daughter, but I was hoping it wouldn't be as important.
I know once she is past 5th grade math, there is a different teacher that comes in and teachs the accelerated math students, so hopefully that will be better (and that the position won't be cut).
Kcab, the acceleration plan is based on observations from her classroom teacher and her gifted and talented consultant. I don't know if they will test her before the final placement for next year. I am also not as familiar with Math Expressions, because it is new in our district. They adopted a math curriculum two years ago( I don't think they had and official curriculum before then) and kindergarten and 1st grade use TERC.
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