Saturday, June 7, 2008
20 comments:
- Tricia said...
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What we know from current research is that experience, not age, is what allows students to move on to more sophisticated concepts. They simply must be exposed to the ideas, and the earlier the better.
We may not call it algebra in first grade, but those missing addend problems require algebraic thinking. The empty box in the problem stands in for the more traditional variable ("x"). It's not as abstract, but no different in approach. We solve by subtracting, just as we do when we isolate the variable. - June 7, 2008 at 3:57 PM
- Tricia said...
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Sorry, I must add a post script to my last comment, particularly after reading all the comments about this issue.
I work with a grant funded program that provides five week of intensive summer study to urban middle school kids in an effort to prepare them for algebra and earth science in grade 8. Putting them on this "accelerated" track is the only way to prepare them for A.P. classes in high school, particularly if we want them to consider studying math and science once they get to college.
There is simply no reason for postponing algebra instruction until high school, and for kids with college aspirations, it's simply a bad idea. - June 7, 2008 at 4:22 PM
- ChrisA said...
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Well I don't know whether to laugh or cry, but I am glad I took my blood pressure pill!
I would like to point out that there are similar idiots over in the UK that want to stop teaching academic subjects that are "middle class".
http://joannejacobs.com/2008/06/06/unsustainable-schooling/
You just can't make this stuff up. Speaking of making stuff up, this is slightly off topic but still illuminating...
http://rightontheleftcoast.blogspot.com/2008/06/id-have-canceled-play.html
Is there a way to make these links show up as "clickable"? - June 7, 2008 at 5:01 PM
- Instructivist said...
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[I would like to point out that there are similar idiots over in the UK that want to stop teaching academic subjects that are "middle class".]
This prof who is advising the government doens't want any academic subjects taught. Why the government would hire this clown to advise them is a mystery.
Link here:
Brain-dead education now
Read the comment from soneone from "Teacher Leaders Network." This leader thinks the ignorance-peddling prof is a visionary. She uses Schopenhauer to make her case. Hilarious! - June 7, 2008 at 6:10 PM
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Mathematics is a continuum!
I think we'll wake up one day to find that lumpkin school oganization is the greatest crime of the 21st century.
Each kid should be delivered individualized instruction that empowers him or her to go at her own pace, wherever it goes. We were able to do it in the 19th century. In the 20th century we blew the model up. In the 21st we have technology to help us get back to that model but we only use it to make more lumps. - June 8, 2008 at 3:19 AM
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One aspect of algebra that is entirely missing in this and other threads is the importance of algebraic notation. It's also entirely absent in Investigations and most of CMP (parts come into play in grade 8).
I've always understood math as a language. It has its vocabulary and spelling (arithmetic), sentences (equations), and composition (problem solutions). Early algebra should focus on the syntax that is the notation used to communicate a solution. I'd be happy if any algebra course spent more time on this. I don't see teachers that know how to do proper notation in pursuit of a solution and it certainly isn't in texts (they don't have real text anyway).
This results in solutions that are unreadable mush. Not surprisingly kids struggle with the 'math' in algebra when they don't have the composition tools. The lack of tools imposes a lack of organization, death in higher mathematics.
This is a fundamental skill that is not taught unless you luck out and get a teacher that is passionate about it. - June 8, 2008 at 3:36 AM
- SteveH said...
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The greatest crime is low expectations.
"We were able to do it in the 19th century."
Really? Everywhere?
"In the 21st we have technology to help us get back to that model but we only use it to make more lumps."
I guess I don't have the same optimism that you have about technology. Lumps don't bother me. The problem is that K-8 schools are eliminating lumps and redefining education.
A main theme in many of the comments to the article is that schools get to decide what constitutes a proper education, not parents. Schools don't even want to allow (internal) choice in K-8. Will technology change this mindset?
I've commented before that this might happen under the guise of providing all students with an IEP. If schools (like ours) are big into differentiated instruction and teachers as guides on the side, then perhaps they would allow parents to select an individualized, computerized learning path that meets the needs of the child and the goals of the parents.
The problem is that one of the major goals of our school is socialization and working together in child-centered, mixed-ability groups. This is not impossible with individualized IEPs and computerized curricula, but many educators will just dismiss this model. They have different goals and they get to decide.
Then there is the issue of technology replacing the role of a good teacher and direct instructon. Is there any technology that can do that? I'll buy that software. Actually, there are a lot of good printed books and training material, but what is the educational overhead required per student? Technology can reduce that overhead, but how much educational burden does it place on a child without parental support? Schools will still be sink or swim models of education. Kids will be allowed to go at their own speed, but it will be really, really slow.
Technology is not going to change their assumptions, expectations, and desire for control. - June 8, 2008 at 5:17 AM
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The quote below is from the article "Why the Best Math Curriculum Won't Be a Textbook"
http://www.edweek.org/ew/articles/2008/05/07/36patton.h27.html?tmp=1040308925
"Given the action agenda set forth by the National Mathematics Advisory Panel, the time is now right to consider alternatives to the traditional publishing model. In an unchanged publishing environment, and with the same pressures to meet the needs of 50 states in a one-size-fits-all book, we should expect the same outcome: bloated, incoherent texts. Only by going digital can we integrate what Singapore does best—maintaining a tightly engineered, coherent core curriculum—with what America does best—inventing adaptations that better cultivate the mathematical genius of a large, diverse population."
There are some other VERY interesting points in the article with GREAT potential (imho) for improving mathematics education.
Correcting our failed "delivery system" in a transparent and non-profit way could provide many more opportunities for our children. - June 8, 2008 at 6:16 AM
- Maddy said...
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This the crux for me -
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Pushing the regular kids into advanced math is just as bad as keeping the advanced kids in regular math.
Why can't we just teach them what they are ready for? (because we don't have the time or money to teach individuals in our school system)"
That at the irony that 'the richest country in the world can't afford it,' I always love that one.
Best wishes - June 8, 2008 at 6:46 AM
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Maybe I was being too obtuse with my previous post. When I referred to lumps I was not refering to kids. I was refering to the lumps caused by arbitrary placement models. The lump is a group of 30 kids with a huge standard deviation put in an environment where a single teacher is assumed to have the superhuman ability to get to ALL of them ALL the time.
When I refer to technology I am not proposing some kind of robotic teacher. I am proposing tools that allow a single teacher to grasp where each kid is at, in real time, while at the same time having a means to present, over and over if necessary, professionally prepared 'lessons' on an individaulized basis.
The teacher's job is to uncover misconceptions, devise alternative representations, and perform the ongoing analysis to maximize the time kids spend in their own ZPD instead of the ZPD that was created for the median child who is not in the class.
The 19th century model that worked is the one room school house. Kids were moved along at their own pace. There were no arbitrary grade groupings. The older kids helped the younger ones (a fantastic learning paradigm). Most kids went just through grade 8 and I would bet large sums of money that most would blow away today's high school students in the three Rs. - June 8, 2008 at 8:39 AM
- Ari-free said...
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High school math in America used to involve proofs. That part of math has also been watered down. It doesn't seem that even Singapore cares either. American math today is not so good but maybe we need to dig up our own old textbooks.
- June 8, 2008 at 10:39 AM
- Barry Garelick said...
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Gee, maybe somebody can ask Jerry Weast, the Superintendent of Montgomery County why they dropped the piloting of Singapore Math in that County. (See here. )
As for the elimination of proofs, you would think that the clamor for critical thinking would increase the demand for the teachng of proofs, but like everything else in edu-land, it's "critical thinking appreciation" rather than the real thing. As for using older textbooks, see here.
While there is some objection to the older texts as also having problems and being poorly written
they at least had some content, and time on task for basic skills and concepts by the way--not merely rote. Where they were lacking, they could be repaired, filled in, by a good teacher, even by the student himself if he was willing to think. Many of today's
books--even the traditional ones, not just the NSF-EHR grant-fed atrocities--force ignorance, on the teacher and student alike. - June 8, 2008 at 11:15 AM
- Ari-free said...
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The philosophy of today's reformists is that everyone should be the same. There must be no competition. The higher skills are watered down so that *everyone* would have a claim to them and even parents of students with higher math ability are on board because they think they are getting a modern 21st century math education. The strategy of equalization works when you can even fool the best and brightest to give up their advantage.
- June 8, 2008 at 1:24 PM
- ElizabethB said...
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"Its amazing that people are able to make statements like these without reference to actual living, breathing, math-learning (or not), flesh and blood children."
I always joke about really poorly designed education products--that they must have been designed by someone who never even saw an actual child, let alone taught one.
Most of the best phonics programs were designed by people who had been working with ACUTAL CHILDREN and teaching them for years, observing what worked and what didn't and changing their program to reflect this.
Blend Phonics: free online at Don Potter's webpage, designed by a lady who taught for many years and was forced to come up with a good phonics method that would work in large (40+) classrooms.
Phonics Pathways: reasonably priced, designed by a lady who has been tutoring reading for 30+ years.
Pollard's Synthetic Series: free online at Google books (linked from my webpage,) a really fun method with songs and great pictures and explicit instruction on how to use it, designed by a lady who taught for many years.
Right Track Reading: Developed by a lady who tutored for years, reasonably priced online.
We All Can Read: Uses nonsense words! Developed by a man who taught many remedial adults.
I also like to joke that my phonics lessons are on version 10.2.6. (I actually don't keep track, they're always changing based on new students and new ideas. I'm in the middle of another revision now.)
And, an ACTUAL CHILD did great with Webster's Speller, it does get amazing results. He must have seen an actual child sometime, and maybe even taught one, or at least watched others teach with his Speller. One of his later Spellers talks about a decision to go with syllable division that reflects pronunciation instead of common dictionary division in his spellers, a decision made to help children learn to read and spell easier although they would not get the exactly correct syllable division that way. - June 8, 2008 at 3:04 PM
- ElizabethB said...
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"Given that these educated people are parents, what are the chances that the average parent will be qualified to help their kids with math homework in the grades?"
"I know the answer to that one.
Slim to none."
The 3 most popular math programs for homeschoolers are Saxon, Singapore, and Math-U-See. Math-U-See has great DVDs to go along with the program. In the upper grades, most of the programs that are popular have some kind of DVD or CD-ROM.
I'd rather have a good program on DVD than a fuzzy math program taught by a real person who doesn't know much about math.
Although I'm qualified to teach up to Differential Equations (with a lot of brush-up) and worked as a statistician for 6 years, we're currently using Math-U-See with our daughter because it's working best for her. Next year we'll supplement Math-U-See with Singapore.
Note: we looked at our ACTUAL CHILD and selected a method that worked best FOR HER. If you had asked me when she was 2, I would have said, "we'll be using Saxon." (I hadn't seen Singapore Math then.)
I'm thinking Saxon/Singapore for our son, but he just turned 3. Right now, he likes to put the green units pieces from his sister's Math-U-See blocks on his fingertips and pretend he's a red-eyed tree frog. (Actually, she like to, too! It's quite funny, for some reason.) - June 8, 2008 at 3:40 PM
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In our district, the mathematically talented kids take algebra in 7th grade. This is about 14% of the population. The kids who are above average in ability take algebra in 8th grade. The below average students take it in 9th grade. I'm not sure about the kids who are right in the middle.
This seems to work well. Sometimes parents try to get their kids moved up or down a level, but most seem okay with this method of offering algebra. - June 9, 2008 at 6:57 AM
- Catherine Johnson said...
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We may not call it algebra in first grade, but those missing addend problems require algebraic thinking. The empty box in the problem stands in for the more traditional variable ("x"). It's not as abstract, but no different in approach. We solve by subtracting, just as we do when we isolate the variable.
I'm glad to get your opinion on this.
I've always thought those problems were a VERY good idea. I first saw them in Saxon Math (though I believe Math Trailblazers has them).
C. learned inverse operations from these problems. He also segued easily to the idea of a variable.
His pre-algebra course was a miserable experience, but that was because of problems on the school's side, not the kids'. - June 9, 2008 at 7:42 PM
- Ari-free said...
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Hi elizabeth. I've never heard of those programs before. I have just started using Zig Engelmann's "Teach Your Child to Read in 100 Easy Lessons" as it teaches everything involved in the reading process.
- June 11, 2008 at 5:30 PM
- ElizabethB said...
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Ari-
Teach Your Child to Read in 100 Easy lessons is good, one of the best conventional phonics programs out there, but it doesn't teach your child to read 3 and 4 syllable words like A Beka or Webster's Speller. (Webster's is free, the copyright has been expired for ages!)
My just turned 6 year old is now spelling at the 3rd grade level and reading out the KJV Bible after working through Webster's Speller this year, you can find out how to teach it here, it's really easy, 16 year olds taught it in the days of one-room schools:
http://www.thephonicspage.org/On%20Reading/webstersway.html
The Pollard series is from the late 1800's, most people haven't seen it! It's great, free online from Google books.
Blend Phonics was published in 1980 and is not commercially available, it is free online only, from Don Potter's Website, www.donpotter.org.
The rest of the programs are more recent, but most of them are not as well known as they should be, they're more effective than most phonics systems that cost far more. - June 11, 2008 at 8:24 PM
- Unknown said...
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- May 9, 2014 at 1:17 AM
Here we go again:
Its amazing that people are able to make statements like these without reference to actual living, breathing, math-learning (or not), flesh and blood children.
Supposing Piaget did say 8th graders can't learn algebra.....(did he?)....shouldn't we ask ourselves how it is exactly that 8th graders everywhere else on the planet are able to learn algebra while American kids are not?
How long ago was Piaget debunked, anyway?
News travels slow in the edu-world.
this one's fun:
and this one:
here we go, "freakshow stage parents" -- good one!
reading right along.... another Piaget comment from a physics teacher, no less. I'm not cutting and pasting any more from JP.
sigh
Piaget has a lot to answer for.
from France:
Here's the one Paula quoted:
Slowed to a crawl. Yup.
The help-with-homework issue rears its ugly head:
I know the answer to that one.
Slim to none.
Next:
Another Stop Manic Moms and Dads! sentiment:
This is a big one around here.
For years we were told that the accelerated math class was filled with "kids who don't belong" and got in thanks to "pushy parents" etc.
That particular meme went splat after the district clamped down on the pushy parents and required all the kids to test into the class. The first placement test was Top Secret; the middle school refused to show a copy to the 4-5 teachers in order to prevent them from prepping their students. The goal was to cut kids from the track, not help kids get into it, so the grade school teachers had to be kept in the dark.
Lo and behold, the kids who tested in fair and square also had a he** of a time of it.
C. was one of them.
Moving right along:
and:
That's sure my beef.
Next:
Things went downhill fast after the 1950s. See: The Race Between Education and Technology.
old chestnut:
There isn't any higher teen suicide rate in Japan.
There is a higher teen suicide rate here. (see: Stigler, The Learning Gap)
Pushy parents! Holy moly, life would be good without pushy parents, for sure.
Here's the full version of the pushy parent quote:
I for one am not remotely concerned that teachers will "submit." They won't. History tells us this is true.
Will they feel beaten down & survive from one paycheck to the next? Yes. Algebra in 8th grade will, like everything else in the edu-world, be implemented from the top down with teachers being handed heterogeneous groups of kids half of whom won't remotely be ready to learn algebra. It will be a miserable experience.
That's not because of pushy parents.
That's because of pushy administrators.
Pushy parents have even less control over the administrative practices of public schools than teachers do.
and, last word: