I came across this article about Common Core mathematics tonight. It's wonkish but well worth the effort of reading in its entirety. A quote:




These are just bits and pieces. The author has a lot to say about how to teach math in a more meaningful way and deficiencies in teacher education in mathematics. I don't agree with everything he wrote, but the article is very thought-provoking and encouraging about the Common Core.

Here are some newer follow ups:

This one is by the author of the article quoted above.

A math ed. blogger

Thanks for the link. Very insightful. About halfway through, and the big point seems to be there is a common misunderstanding of the word understand. Existing, pre common core, textbooks have drifted away from teaching "understanding" of math to training in math techniques. If schools+parents+teachers+curriculum writers continue to misunderstand "understand", then the potential of common core would be lost.

I was blown away by his explanation of the distributive property proving that a negative times a negative equals a positive. I don't think that was taught in the seventies. Now I really want to make sure DS has that understanding (weekend mission, if sewing costumes leaves any time for it.)

i.e. you can't train thinking

Right.
(-1)x=-x
is not an axiom. It has to be deduced from the axioms.

I agree; good read. Thanks for sharing that. I'm just trying to really figure out what elementary math really is so I can figure out what DD needs.

Thanks so much for this link, Val.

Interesting - thanks for posting it. I read the entire article as well as the first follow up. They make some valid points. I also have no doubt that Professor Wu's assessment is correct for a subset of the schools in this country as well as for a subset of elementary teachers. However, many of his observations have not been my experience or my children's experiences over different decades. Many of the textbooks are definitely lacking. However, in our school district, the math textbook is not the only source of the math curriculum or math assessments. The distirct office develops curriculum and assesments to use with the textbooks and the gt classes in particular have utilized curriculum developed by well-known gt education experts. For example, the way of teaching fractions over several years that Professor Wu recommends is the way that I learned fraction at my school and the way that my three children have been taught in their school. That is one of the reasons that the elementary curriculum spirals because the ideas are presented with increasing complexity over the years. His criticism regarding the misfocus on "variable" rather than "symbol" in algebra was interesting. I do believe that one of the reasons why elementary schools started teaching "elementary algebra" was to emphasize/develop the symbolic aspect. That is why in first grade, the curriculum introduces 7 + ? = 9.

Based on our limited samples, I must also disagree with his thinking that university mathematics is not sufficient to provide capable elementary math teachers. All the competent math teachers that my children have had over the years were trained in higher mathematics and it appeared to me that was the reason why they taught elementary math so well. The incompetent teachers were ones who did not have the advance math background. Again, obviously Professor Wu had a large sample of his own students from his training camps with which to draw conclusions so surely there is some validity to his conclusions. However, I do posit that his sample may not have been entirely representative.

I agree with Quantum2003- my kids would be hard-pressed to tell you which textbooks their school uses (as would I!) because much of the curriculum is developed by the district/teachers themselves. They use textbooks, but only as one of many resources.

FYI for all, this document lays out Professor Wu's ideas about how to teach fractions. I'm about to go over the third grade stuff with my DD, having just written up 6 pages of lessons. To me the differences between what see coming home from school and his stuff are subtle, yet profound. Wu's stuff builds a foundation of knowledge about how everything fits together, whereas the stuff I've seen from my kids' schools doesn't. The kids can manipulate stuff very well, but they aren't shown all (or most, really) of the connections.

Quantum2003 and cricket3, did you and/or your kids learn Wu's ideas?

Thanks again, Val. These are great links.

Yes, Val, his examples are exactly how those topics were covered. The fraction examples in particular could have been straight from their materials.

I do think our school is an outlier, though. I still don't really understand why, but they began common core implementation much earlier than other NY schools, it seems. The kids were ready for the new assessments, and overall did quite well (tiny brag- both my kids, while good at math but not math-lovers, got perfect scores). But the real news, in my opinion, is that many of the kids seem to be learning it and learning it well.

Disclaimer- one big downside, (which I assume is related to the common core implementation, though not sure) is that the district does not accelerate or skip, until 8th grade. The "accelerated" class my 8th grader has been waiting for years for, a high-school credit regents class which supposedly covers about 2 years of material, is still agonizingly slow for her (and almost half the students are in this accelerated class). And she has an A+ average without studying, etc.- a real disappointment; we are hoping but not optimistic that by the time DS gets there things may change.

Wow, cricket3, that's really great about how they're teaching. Not so great about the anti-acceleration policy, though.

Val, all my kids and I learn fraction the way Professor Wu recommended. The LCM approach was taught after the foundation was already laid and understanding secured. I was taught by an ancient (expert) 5th grade teacher and a brilliant 6th grade teacher (engineering degree/experience) who were masters at in-class differentiation.

My children went to a school on the other side of the country from where I grew up and were seven years apart. Basic fractions were introduced in second grade math. Fraction manipulations were taught step by step in 3rd grade GT math (3rd and 4th grade math combined) along the lines of Professor Wu's approach. Then more complicated fraction manipulations like division were presented in 4th grade GT math (5th grade math). By 5th grade GT math (6th grade math), the students were expected to use the LCM approach and cross reduction efficiently. Based on the discussions and assessments prior to DS' acceleration into Pre-algebra at the beginning of 4th grade, our district predicates acceleration into Pre-algebra on mastery of fractions.

Cricket3, I also believe that Common Core will make it more difficult for students to accelerate in our elementary schools as well. The plan is to make GT math more rigorous by including more higher level math beyond the current one year acceleration plus enrichment. I am glad that DS was just ahead of that wave and is allowed to study algebra as a 5th grader this year. Interestingly, the Common Core inspired changes to the GT math curriculum would have benefited his less mathy twin sister, who refused acceleration, but completed Aleks 6th grade math the summer after 3rd grade when I had DS complete Aleks pre-algebra to decide on the advisability of another acceleration.

I've heard that too, that it will be harder to accelerate kids in math with the Common Core.
Currently my son, our in local public school gifted program, would take 7th grade Algebra I, 8th grade Geometry, 9th grade Algebra II (I think that's what that it), 10th grade Pre-Calculus, 11th grade AP AB Calculus, 12th grade AP BC Calculus. Plus they have AP statistics too.

Well, it definitely makes acceleration harder in the elementary years, at least that's my impression. Perhaps when they have taught this curriculum for a while things will change (though now that I think back, my daughter's third grade math class was already doing this, it was not new then, and that was 5 years ago...). However, they are still coming up with benchmark assessments and stuff like that, so even figuring out where a kid should be (if advancing, I mean) is not clear. Like Quantum2003 mentioned, there is a lot of spiraling and building on complexity; the repetition that our kids really don't need but which seems to be key for many kids. The school has done a relatively good job with enrichment/deeper material at times which has been great for our kids, but it is not built into the curriculum and therefore teacher-dependent. However, this curriculum seems to lend itself more easily to those kind of detours, I think. But the multi-year acceleration thing is not happening here- we know families who left the district over this issue. (There are too many positives outweighing this for us to leave, though it is frustrating).

Jack's mom, our advanced sequence of math also ends at calculus BC, with the option of AP stats. I think the topics now are arranged differently than they traditionally were, and there is more compaction- I don't think we have a "pre-calculus" course, for example (though it has been a while since I checked the course catalog).

Cricket3 is right. Here's a piece by Hung-Hsi Wu on acceleration
To Accelerate, or Not
Unfortunately, Common Core will make acceleration even more difficult for many students.

Well, that was depressing. I would expect better logic than this from a mathematician :


Talk about two different things! There doesn't seem to be any room for learning faster and learning thoroughly.

[speechless]

Okay, this is serious. Who is this guy Hung-Hsi Wu?

He was one of the people who wrote the Common Core Math standards. He's the guy whose work I've been quoting all over this thread.

Which is what makes his blog post so incredibly depressing.

The ending of the article was really sad and insulting:

"We should not allow a sideshow about acceleration to overshadow our nation's drive to achieve excellence in mathematics education."

Incredibly sad to call the need for acceleration for the brightest children a "sideshow". I guess he made his attitude toward the gifted crystal clear.

Wu is one of the good guys in the math education war. I do not think he was talking about the gifted kids at all. There has been a general association between acceleration and rigor, which is not necessarily true. Also school math is very algebra and calculus centric. I believe some mathematicians believe that the end goal being finishing calculus in high school is not necessarily all that. There're other subjects such as discrete math are very useful and lend it self to differentiation that are not covered in school math.

Anyway, Wu is talking about accelerating half of the class as we have seen in some school district and differentiating the truly gifted kids.

of course everyone should learn the basic principles etc thoroughly. But some people need 2 repetitions and some need 200. That is not skimming, that is learning quicker. I would agree that going quickly for the sake of going quickly is wrong but that is more hothousing than slowing a HG+ kid to do their thing.

Do kids who aren't gifted really get accelerated that often?? I would think the majority of accelerated kids would be gifted, so if he's talking about some accelerated minority, he should make that clear, and if he's talking about gifted kids then he's nuts.

I don't have statistics, but this page of the public school system thread has information about gifted programs and non-gifted kids.

Anecdotally, my eldest's school put about a third of his class into geometry in 8th grade. It was definitely a watered-down course. But then, it was following a watered-down but state-approved textbook, so it wasn't necessarily that acceleration was the cause of making it too easy.

At the school my other two attend, finishing algebra in the 8th grade is considered to be the regular track and finishing geometry at the same time is the accelerated track. I know that a fair number of kids (e.g. way more than 2% of the class) take geometry. My own DD's 5th grade class has 7 out of 12 kids in a very accelerated group (they're doing pre-algebra mixed with 5th grade math). I'm not really sure what to think about that. More than half of a class is a lot of kids doing algebra 2 way ahead of schedule.

When I was in school, algebra in 8th grade was considered accelerated, while taking it in 9th grade was above average. Taking it in 10th grade and going through algebra 2 was more "regular."

Actually, I do have some statistics. Entire states have pushed for algebra-for-all in 8th grade (e.g. Minnesota and California, but it's been abandoned here). Here's an piece about this trend. Also, here's a paper about algebra for all in 8th grade in a district in North Carolina. It didn't work out so well there.

So, yes, there are a lot of students being accelerated when they shouldn't be accelerated. It's possible that Wu was referring to this group and wasn't thinking about gifties. In that case, he was right, but he was still wrong to paint everyone with the same brush.

I don't know when non-US students take algebra and geometry. I know that some countries teach them at the same time, but I don't know when.

No. It's not possible that he meant that. What he is saying is quite clear. He is saying that with the new standards, acceleration will not be needed, by anyone, ever, period.

My daughter is in accelerated math where they complete 3 years of math in 2 years. In 5th grade they will be in pre-algebra a 2 year program. 7th grade is algebra and 8th is geometry. There are 72 4th graders and the accelerated class has 7 students.

Good thing my youngest is in 4th grade and only has 5th grade before we homeschool for middle school and we will cross high school bridge when we get there and figure that out.

I agree.


^ THIS is what he's talking about.


Honestly, part of the culprit is the WAY in which math is taught now (or was, prior to CCSS) really seems to produce poor understanding of some concepts. Even in the brightest of students, such as those whose parents post here.

I know that we have certainly had to backtrack and remediate material that our DD seemed to have learned at the time, but apparently learned incorrectly vis a vis her math curriculum in grades 4-6. It really showed up in geometry and algebra II, quite frankly.

I also think that he's talking about Tiger cubs. We're such small demographic that I don't think he's referring to kids who are accelerated in order to meet their individual needs as learners.

He's definitely talking about the "you HAVE to finish calculus in high school" track as representing "rigor" and some kind of badge of smartness/worthiness in high school students. That's not at all the same thing as a student who legitimately takes a very rigorous approach to mathematics but simply does it FASTER than most learners can. Those students are somewhat rare. That's what he's getting at; undermining the prestige of "advanced in mathematics" for its own sake, and a return to rigorous learning-- for ITS own sake.

I still think that most of OUR kids are going to be just fine under CCSS. DD was pretty thrilled to learn some set theory in helping a CC-Course 3 student the other night. The teacher advisor sent them to my DD because she knows that my DD could learn the material and explain it in just a few minutes, and would ENJOY doing so. So yeah-- HG+ kids are different, and teachers who know them will still 'get' it.

Unfortunately, as long as advanced learners do actually exist, there will be parents willing to do whatever it takes to make their own kids look like that which they are not. If I had a nickel for every casual acquaintance who has said something along the lines of "Oh, yeah-- we COULD HAVE done that with little Timmy/Janey, too... but __________" (meaning a 3y acceleration and advanced coursework and-and-and, presumably). It always has this faint whiff of sour grapes about it, and I just cringe for their kids, who are often already whipped to perform. I'd love to tell just one of them once that it's really obvious that this is not true, and that I wonder why they can't just accept the wonderful child(ren) that they HAVE. But anyway. That's what fuels the practices that Wu is decrying. IMO.

Enh. I just read the blog and can't tell whether he's simply saying that pushing kids through the material without ensuring they truly get it is the issue or whether he is truly saying endless repetition is needed by all. I think he's talking to the former. It really doesn't appear to be aimed at truly gifted kids to me, but then again, I didn't think it said all that much, which seems to be the case with so many Huffpost articles.

What's funny, is that I think my radical acceleration in math is what saved me from learning stuff wrong. I puttered along in school, taking Algebra I in 8th grade, then did Algebra II, Trig, Geometry, and Analytical Geometry that summer at a camp for gifted kids, and took Calculus in the fall. (Actually, I didn't take Geometry, I just tested out of it. They didn't teach Geometry, and the test was really, really hard. I pestered the head of the program to let me take the test, which was in two parts. She agreed to give me part one, and told me that part two would depend on how I did on part one. I'm sure she expected me to bomb it and then she could tell me she told me so. Instead I got 100%, and a 96% on part two, so they had to support me in not taking it.)

My school gave me credit for all of them, but only after I slogged through every homework assignment and test. My calculus teacher very kindly agreed to grade it all (which I bet he regretted when I didn't do much of it until after the Calculus AP exam, and then I started blowing through multiple chapter tests and homework per day). Thirty years later, I still vividly remember fretting all night because I knew I had fudged a step in a proof when I couldn't figure out a way to do it rigorously, and him marking it correct without even noticing.

But it all meant that all my teaching before calculus was from math graduate students who knew exactly how to do the math right and didn't know anything about pedagogical reasons for dumbing it down. It was awesome.

All of these recent comments are true, but the problem is that his blog post didn't distinguish between gifted learners and tiger cubs. Unfortunately, his post may make things even harder for MG+ kids. Yes, the standards that I've seen are good, but their value is diminished if MG+ kids are still stuck listening to the same lesson again and again while they wait for the rest of the class to get it.

I've been going through his Common Core fractions with my daughter. The differences between CC fractions and bog standard math textbooks are subtle. They're really important, but so far they're nothing that would take a year for her to learn.

This seems to be what he is talking about here, The Common Core Mathematics Standards Implications for Administrators :


But in his Huffington Post blog, he links to this article Common Core Math in North Carolina Would Keep Elementary Students From Taking Middle School Courses which specifically mentions gifted students.


Whether he means to include gifted students or is just talking about tiger cubs, I believe that many (if not most) school administrators interpret the shift to Common Core as eliminating the need for acceleration.

This is a charitable interpretation, but I take his article
http://www.huffingtonpost.com/hunghsi-wu/math-education_b_1901299.html
at face value. I am sure he is highly articulate and capable of clearly expressing what he wants to say, so if he had meant to say something different he surely would have done so. The article is unambiguously vehemently anti-acceleration. Based on this article I certainly don't see him as one of the good guys. I also question the ability of someone who thinks this way to construct a good set of standards. His reasoning is so totally non-sensical.

I disagree; I've started going through his stuff and he seems to really get it as far as the curriculum is concerned. Read the document I posted earlier in ths thread and you'll see what I mean. Remember, this guy is a professor emeritus of mathematics at UC Berkeley. I looked through the titles of his his non-education papers and they seemed like serious stuff.

I agree that the blog post comes across as being essentially clueless about HG+ students and is lumping them in with the tiger cubs. It's possible that he really has no idea about giftedness and levels thereof. Many of us here are HG+ and didn't understand the topic before we had kids and/or arrived here. Not knowing something is okay, but what I don't like is that he made sweeping pronouncements without examining the problem thoroughly. Someone in his position should know better than to do that. Especially someone who has put so much effort into fixing mistaken assumptions about math education.

Agreed.

Can I just say that ElizabethN's post up there made me SMILE a mile wide?? I love that anecdote.


Well THAT is clearly nonsense. But then again, this is school administrators talking-- not necessarily those who "get" what gifted can mean... and honestly, I place Dr. Wu in that category as well.


Good point. But that's not to say that the architects intended such a thing-- but that they are tired of TigerParents push-push-pushing kids who really can't master material at rapid rates or young ages, and eventually need remediation in post-secondary. Some of those kids probably COULD become competent in STEM, but by the time they get their math deficiencies sorted, they're a couple of years into college. Bummer.

I think that Wu would probably maintain that districts need to stop "vanity-identification" of kids who are in fact candidates for acceleration in subjects like mathematics, and resist pressure to accelerate when it IS NOT appropriate. Not that they should move all kids in lockstep with the mean.

I think that Sho Yano's quote is pretty apt here ( not directly related to Maths but does hit the nail on the head wrt holding back or accelerating )


See story here:-

NBC coverage

To Val's point I had no clue of how quickly true gifties grok things until DD came along even though it seems normal until it became obvious that it wasn't. I think that Dr Wu is talking about skipping in terms of leaping over parts of a curriculum without having had experience of kids with such a prodigious appetite that n whole year's curricula can be consumed within a given year.

From Wu's article:

The word "correct" is used often above. What does it mean? Were 5th grade students previously not taught to multiply fractions using the formula

a/b * c/d = (a*c)/(b*d) ?

My 8yo is learning to do this in EPGY 5th grade math.

Many scientists, engineers, and economists will use calculus and other math as a tool. I wonder how much rigor they need. I don't see how a year of geometry with proofs helped me in my academic or working career. A benefit of acceleration through calculus is that it enables you to study physics, statistics, economics, and other subjects at a higher level.

I'll speak to economics. All that's really needed to cover graduate material is the first year university series of calculus and linear algebra for math majors, with some second year stats to cover econometrics. To get published in AER or Econometrica, it's helpfully to have more econometrics.

I studied in Canada. My profs who had taught at Harvard and Princeton used their graduate textbooks for my upper year classes because, apparently, those universities' students didn't have the requisite math background to do the graduate work yet.

My husband stopped his studies in physics and math in high school. Had he had more rigorous treatment of math before university, he says would have gone into physics and not law/finance.

My DD is no Maths prodigy but she had all arithmetic operations on vulgar fraction 'down' by 7 just from talking about it with me from the back seat while we drove to places.

Why should she have to wait for everyone else?

I had no intention of 'accelerating' her Maths but just kept giving her stuff and she just seemed to effortlessly get it so we kept going.

I was reading about the uptick in hip displasia in infants being attributed to an uptick in the practice of swaddling. Apparently, the joint needs full mobility in the legs to develop properly.

What would we be doing to our kids' minds in 'swaddling' them by unnaturally restricting their natural learning abilities?

Wu's point is that students are made to memorize an algorithm, rather than being taught why it works and how it fits into the bigger picture. He's right about that. EPGY may very well be different, but the vast majority of today's textbooks present algorithms with minimal or no explanation about the ideas behind them.

Regarding "correct," he means that a lot of teachers don't understand this stuff, either, and so they don't see how standard algorithms fit into the bigger picture of mathematics. This problem makes them susceptible to the flawed reasoning behind goofy algorithms like partial products and guess-and-check.

This stuff is the bigger picture of the problem with the Dolciani algebra textbooks blog post that you posted.

Well, speaking to chemistry there, it was of NO use to come into chemistry (as a major) having already gone through a calculus sequence in high school, because most major's tracks have you taking general physics as a sophomore undergraduate, anyway, and you only need VERY good algebraic skills and the rigor taught by the study of geometric proofs (IMO and my DH's) in order to really learn gen-chem well.

HOWEVER-- those students who do NOT have good geometry backgrounds often find themselves at sea when it comes to molecular geometry (and all that comes with it), and truthfully, that "sense" of spatial intuition comes only with a great mastery of the subject. It's part of what makes chemists-- chemists, and not biologists, statisticians or pharmacologists. This makes organic chemistry in particular a NIGHTMARE for those students, many of whom change majors to either biology or physics at that point. (It also makes instrumental analysis, molecular spectroscopy, and inorganic chemistry far, far more difficult than they should be.)

So while I respect that most people feel that they have "never used" the geometry that they learned so arduously, I disagree. That deeply embedded understanding, and the diligent practice of logic applied to proofs is unmistakably preparation of the very best sort for some STEM fields.

Also true that as a chemist, having advanced skills in mathematics isn't really very useful (beyond calculus) until you get into distinctly graduate level topics. Stat Mech, instrumentation design, etc. Better to have had Statistics early and well, IMO, than calculus in high school (where it is often taught very BADLY-- by people who don't really understand it well conceptually).

So I think that what the university professors in mathematics are really saying is two-fold, but the second part of it is mumbled a bit so as not to offend those that they hope will go along with CCSSM:

a) students are NOT really "advantaged" significantly by taking very high-level mathematics topics earlier and earlier, and some of them may be "rushed" if this is encouraged; and

b) most high school teachers have no business teaching anything past trigonometry anyway, so they should leave the advanced math topics to those who DO understand them.

ITA with Val's post, by the way.

Honestly, the "allows study of more advanced topics" thing makes no sense to me unless one assumes that there is a finite shelf-life to learning math and science topics. As far as I can tell, there isn't.

Acceleration allows students to reach advanced topics EARLIER. The question is whether or not that is a good goal. I'd say that as a side-effect of natural learning and meeting an individual's needs and interests, it's fine-- but probably not a good thing to have as a primary GOAL, so much.

But that's me.

EMPHATICALLY agree.

My opinion is that this only highlights a major oversight in education, though, because except for Geometry proofs, and some conversations about the scientific method, high school students are not introduced to the basics of logic. Even college students mostly manage to avoid the topic, since it's mostly presented in a philosophy course which is elective for most students, and considered a to-be-avoided one at that. As a result, most people think they know what "logic" means, and then go about proving how they don't.

Logic is only the basic building block of scientific, mathematical, and philosophical thought, so how important could it be?

Yes, exactly. It all fits together in one big meshy intertwined whole.

... or 'mushy intertwined hole.'



As the case may be, I mean.



DH and I were discussing the learning process for him, me, and our DD this morning...

for him and her both, it's as though their "mastery" is an enormous floating dock of boxes... and "learning" is a process via which there is "capture" and then there is "placement" within that larger scaffold. Simply TYING a captured idea (or seagull) to the scaffold and letting it continue to fly in circles isn't mastery to either of them-- they have to be able to reel it in and place it within the larger scaffold in order to "own" it (mastery).

It BUGS them when it is assumed that just tethering more seagulls = "learning" because to them, it seems pointless and arbitrary. But without an expert teacher to respond to questions about where things fit within the scaffold, and whether there are ties to other parts of it... well, it just doesn't STICK for either one of them.

Me, I'm a trivia Goddess, so I can roll with the tethering of more and more seagulls. To a point.

But for learners like my DH and DD, having actual subject expertise in a teacher isn't just a nice bonus-- they in all probability CANNOT really learn much or very deeply from anyone else. DH is a pretty impressive autodidact now (as am I), but this was definitely not true at our DD's age. We both suspect that learners like us often HAVE to have a certain maturity and level of mastery (broadly) before we CAN function effectively as autodidacts. Our position of learning is dependent upon the strength and extent of the seagull-stuffed scaffold under us.

Like a Borg ship. Metaphorically.

Definitely a point of view I've had. Along with a range of meta- skills from research design, skepticism, logic (and fallacies), and set theory to heuristic development, mnemonics, mind-mapping, introspection, learning theory, and more... I'd have all that taught directly when kids are ready for it. Not accidentally and unmeasurably fluffed under other topics like literature or speech or geometry, etc.

I see the need for acceleration as being most important for polymaths who have multiple future avenues of study. Per Bostonian's point, if a student is potentially interested in a field that requires higher level math to access more than a conceptually basic understanding of the subject (e.g. finance, economics) then I do think math acceleration is warranted. Granted, most of our children will see the need for the math in their field(s) of interest and be intrinsically motivated to learn it, too, so the acceleration will be needs-driven.

Really, in many fields, you have to be at least at the senior undergraduate level in the topic before you have a realistic understanding of your interest in, and willingness to continue in, studying the topic.

I think all students would benefit from the topics Dude and Zen Scanner mention. Ideally, elementary math courses would incorporate proofs and logic as early as possible. To be an effective critical thinker requires a deep meta knowledge, and I think that is largely lacking in modern math instruction. (It's also why I'm keen on the idea of AOPS.)

And I agree with your critical seagull scaffold hypothesis for autodidacts to take flight. (Terrible pun!)

LOL-- so glad that our stream-of-consciousness seagulls-and-Borg analogy made sense to someone else.

This is often the sort of thinking that makes other people decide that we're freaks.

Zen Scanner, I love that idea. Do you think that all people have the innate capacity to learn those things as children? I wonder, given what I've seen of the ability of adults to absorb and utilize those meta-skills. It's really aggravating sometimes.

Frankly, those that needed to memorize the algorithm never understood the two arithmetic operations of multiplication and division properly - it has nothing to do with fractions per se.

I agree with Dr Wu IFF all he IS saying is that at each stage, a solid conceptual understanding needs to be there before the next stage is introduced and acceleration for its own sake should not be considered without proof that that understanding is there. That is real rigor and I fully support THAT.

However, has anyone here actually corresponded with Dr Wu to confirm that that is what he means?

From the little that have read from links posted here his words could be interpreted either way and most of us know how many school administrators will interpret them...

That's not the point he's making. It's not that kids need to memorize an algorithm, it's that they don't have a choice in the current teaching system. He's saying that 1) yes, it is all interconnected and 2) the background stuff demonstrates stuff in point 1. If you read the materials I linked to, you'll see that.


Again, read that document in the first message in this thread for your answer. Here's another link to it.


I wrote to him about the acceleration piece two days ago. No reply yet.

All is a tricky word, and I have to own up to a bit Pollyanna-ism... I've a knack of making other people feel smart (I know, lol) because I anticipate it. I don't know, really, but if it is treated as bread and butter as the alphabet and addition? It's actually research I wish I had followed through with in college.

The first syllogism is likely: Cry when hungry, I'm hungry, therefore cry. It is pretty primary to how we work. Piaget talked about the concrete operational phase covering around age seven through to maybe eleven or twelve. That's the time when that sort of meta groundwork could be set.

I know there are studies showing strong impact of chess instruction for kids, which is basically positioned closer to direct instruction on metacognition. Gonna skim related research.

So, still no reply (yet)?

Nope. I'm not really expecting one at this point. Oh well.

It all sounds very similar to the presentation at our school (in NZ) on the "modern learning environment". I think it is a flaw in their logic which appears to go like this:

All children benefit from high expectations (research seems to back that children who are expected to suceed do better than those expected to fail)

High expectations equals challenge.

Therefore no-one will need more as everyone will be challenged.

there is flaw big enough to drive a truck through but somehow they don't or won't see it.

Admitting it means that not everyone is equally able to begin with, though. Can't have that.

The corollary seems to be that few expect gifted children to succeed; Commonly the media refers to alleged criminal suspects as "gifted".

Rather than identifying innately gifted individuals and supporting their intellectual growth so it may continue in a positive trajectory, equipping these kids with new things to think about and a sense of trust in their fellow humanity... the world has developed a system predicated on recognizing wealth-driven achievement, hot-housing, and quotas... often excluding the very children we ostensibly set out to serve.

In schools, many gifted children receive only the "challenge" of waiting for other students, having their own thoughts and questions ignored, being sandbagged if their minds may wander, being used as free tutors for slower classmates. Many innately gifted pupils do not receive an academic challenge worthy of their intellect, but rather a steady flow of teacher admonitions, and choices to undertake higher level academic work in social isolation vs slogging through work they have already mastered while having some semblance of inclusion with the cohort.

While Common Core may help set a standard for a performance floor, it does not address removing the ceiling. The establishment of further testing, reporting, and regulatory systems designed to ensure conformity of educational outcomes among pupils of diverse capabilities may further harm the educational opportunities for innately gifted kids.

This topic seems strongly related to the recent threads "Number sense in infancy predicts math ability" and "How to Hothouse Your Kid".

Here are a couple of article I got from googling about Acceleration and Common Core.

http://math.dpi.wi.gov/files/cal/CCSSM-Talking-Points.pages_.pdf [5pg pdf]

http://www.doe.mass.edu/candi/commoncore/MakingDecisions.pdf [3pg pdf]

It seems that acceleration is certainly possible in Common Core, but it should be done with compacting rather than skipping, so states and districts have to design such a compaction plan properly (not so hard, just cover all the material, just faster). Many states and districts will use Common Core as an excuse to stop acceleration, but it seems it is not a legitimate excuse.

Thank you for sharing these links. Similarly, I also found information regarding serving gifted pupils, when reading ABOUT the Common Core, but not IN the Common Core.

While the Common Core is presented as State Standards, the information at these links shows that international sources also informed the creation of Common Core. In discussing this and other talking points presented, some excerpts and phrases which may raise questions include:
1) "Students who are truly prepared for an accelerated sequence should also have access to one." Because of how this is worded, some might wonder whether "truly prepared " indicates not only readiness and ability based upon mathematical mastery but also skill in writing, etc.
2) "Students who have demonstrated the ability to meet the full expectations of the standards quickly should, of course, be encouraged to do so." Some may ask whether all students meet the full expectations? In other words, does "full expectations" mean 100% mastery, or 80% to pass, or...? How quickly may children meet these expectations? May pupils and/or their parents request end-of-year tests at various intervals? May pupils work ahead, at their own comfortable pace, with support, and without admonishment?
3) "Data from international studies suggest that we are far behind the rest of world in bringing even our advantaged students to the highest levels of accomplishment." Might this have been presented as a chart or numerical comparison rather than a generalized statement without definition of "advantaged" or "highest levels of accomplishment"?
4) "There should also be a variety of ways and opportunities for students to advance to mathematics courses beyond those included in the 2011 Framework. Districts are encouraged to work with their mathematics leadership, teachers, and curriculum coordinators to design pathways that best meet the needs of their students." Curriculum compacting (three years of math condensed slightly to two years) and doubling-up enrollment in math classes are discussed. Neither of these options explored sound like they may meet the wishes often expressed by parents on gifted forums. Fortunately, the talking points do not state a prohibition to skipping.
5) "Common standards also allow the nation’s teacher preparation programs to be more focused on the mathematics teachers will be teaching, rather than on generic courses designed for a wide variety of state standards." Some may wonder whether a teacher less versed in mathematics beyond the prescribed standards for one's grade level may be less inclined to provide curriculum compacting or other acceleration support.

Honestly, I'm not seeing how this presents the schools with a different problem than the one they've been facing for decades. Schools have always had curriculum standards. Students who exceed those standards for their age level have always had a need for acceleration. And the new standards are not a radical departure from those faced by previous generations.

Ye, but schools resist acceleration like it was tantamount to feeding plutonium to students. The Common Core and the various writings about them claiming that acceleration isn't necessary just give the anti-acceleration and/or anti-gifted crowd more excuses.



Well, I agree that they aren't profound. My DD9 needed about 30 minutes to learn the 3rd grade fraction standards, and an hour-ish for the fourth grade fraction standards. And I was teaching her the stuff that Wu teaches to the teachers (i.e. he does basic proofs using algebra). If I was just teaching her the stuff they teach students, we would have done 3rd through 5th grade CC fractions in a single session and she would have been feeling underchallenged by the end of it.

But the math standards are a significant departure from the usual memorize-and-move-on approach, and there are presumably a lot of teachers out there who are feeling uncomfortable around them. I've read through the fractions standards. They're arguably the most difficult of the K-6 stuff, yet also are extremely important. I can see that a teacher who had relied on rote teaching of algorithms from a book would feel stressed by these standards. TBH, unless schools start hiring math specialists for K-8 students, I'm dubious about the CC's chances for success.

I am, as well.

I'll also say that as long as spiraling is ubiquitous as a feature of coherent curriculum design (and it certainly still is, in spite of the shell game of moving things about and using the term "rigor" until I have a regrettable, cheeky impulse to ask my software to replace it with rigor mortis instead...);

well, as long as spiraling is happening in significant amounts, as much as I personally have a preference for supporting compacting over "skipping" to start with, I have to say that it really isn't suitable as an approach for accommodating highly able mastery learners.

Ask me how well compacting worked for my own HG+ daughter in mathematics. Go ahead. Ask me.

(Hint: it made both of us CRAZY-- and led to truly almost unfathomable hatred of the subject and refusal on her part.)

Wow, I'd like to know more. To me, compacting means, "go through the material at a faster rate with fewer repetitions." However, after reading your message, I'm questioning my idea. What happened?

Okay, going through the material at a faster rate is great-- and works just as intended...

provided that the curriculum itself doesn't keep looping back to repeat the same topics ad nauseum.

Currently, that is precisely what K-8 mathematics seems to be dead-set on doing.

Apparently spiraling is a highly effective tool for most average and below-average students in mathematics, because it reinforces skills and slowly builds upon previous learning (or fixes it as needed) in order to construct proficiency, say, with place value.

Or fractions.

Or multiplication.

{sigh}

The problem is that HG+ kids who are mastery-oriented learners (and so many of them are)-- they notice the holes in the explanations, and worry at them like terriers the FIRST time around, interrogating teachers until they GET all four years' worth of explanations out of them.

OR-- they can see that there is just so little there there (novelty to learn from) that they refuse to engage with it at all. {yawn}

We saw both things happen IN SPADES with my DD.

Now, some kids are more compliant about demonstrating skills that are three or four years in the rear view mirror, and there was a time (3-7yo, about) when my DD was, too.

Also-- that tends to build really negative socially prescribed perfectionism in those kids who are susceptible to it, because they eventually come to a place where they already KNOW what they are being offered-- all of it-- and therefore there is NO reward for learning, only punishment for not knowing/showing-- perfectly.

Does that make sense?

This is why my hypothesis is that with this type of learner, it's way better not to introduce topics that they don't have the skills/tools to REALLY dig into and master. Teach it like you're building a pyramid. Upside down.



But that's not how math curricula are intended or constructed. Singapore comes closest to that ideal, with the least spiraling/repeating and the lowest levels of drill-and-kill... but most N. American curricula at this point is fatally flawed for this kind of student, IMO.

Now that she's finally into traditional "college" mathematics, the repetition is virtually nonexistent, and she is rediscovering a passionate love for the subject.

I don't consider that a coincidence at all. But I do consider it to be rather ominous for other kids like her. Common Core (from what I've seen of the curricula designed around it, which, as noted elsewhere, has been limited to the middle grades and early high school math) doesn't seem to have fixed this underlying problem of relying upon extensive spiraling for efficacy.

Compacting is supposed to represent a mastery based approach to material. It is supposed to allow for skipping mastered material. Functionally different than accelerating through a curriculum which may be structured with intentional repeated material.

I like this quote from a seminar doc about compacting:
"Curriculum Compacting might best be thought of as organized common sense, because it simply recommends the natural pattern that teachers ordinarily would follow if they were individualizing instruction for each student. "

http://www.gifted.uconn.edu/sem/semart08.html

Val posted this elsewhere.
http://giftedissues.davidsongifted....eo_criticizing_Common_Co.html#Post175160

In my google search "common core acceleration" I came across this
http://commoncoretools.me/forums/topic/acceleration/
which is a forum thread with Bill McCallum responding to question about Common Core and acceleration.

Very interesting. Thanks for the link, 22b.