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I'm collecting data about the efficacy of math curricula. What I'd like is to get some statistical evidence that shows the effect of various mathematics curricula on student outcomes. Any other data--I'm thinking covariates that might affect the delivery of the mathematics instruction--would be appreciated.
So, for an example, how many students score proficient (or whatever) on the NAEP who use Saxon math? And the same for Everyday Math, Connected Math, etc.
Thanks.
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I don't know the answer to your question but I am curious how you think it would be possible to measure "student outcomes" in an ideal world?
My view is that it's very difficult to design a test that's not biased in favor a particular curriculum. For example, one curriculum might spend a lot of time on pie charts or Venn Diagrams, etc. whereas another one might not. So if those topics were on a test, a student who had never studied them might do worse than one who had studied those topics but, despite the worse score, actually have a better understanding of mathematics.
As an example, I never heard of "stem and leaf" plots until recently even though I had a career in computational math. However, whatever they are seems to be all the rage nowadays.
The NAEP doesn't break out the scores by specific curriculum, but it does break out scores by other curriculum factors. For instance...
The most telling factor is when you break out 4th grade math scores by whether schools "Address communicating math ideas" which we all know is code for "fuzzy math".
Here are the average scores for each answer.
A lot 226 ( 1.5)
Some 221 ( 1.8)
A little 228 ( 1.8)
None 237 ( 5.5)
I guess we should be suspicious of any program that emphasizes "math communication".
Conversely, the programs that emphasized "math facts and operations" scored better than those that didn't.
I did think of one answer. You should definitely watch this video if you haven't seen it before. (This was posted on KTM sometime back.)
http://www.youtube.com/watch?v=ymvSFunUjx0
It correlates the decline in college math scores at the University of Washington with the use of different curricula.
Hi Jenny!
Boy, good luck.
We've been looking for this data forever (using "we" loosely, of course).
I'm trying to think....I believe that the state of CA actually has some fairly solid data, which led to the parent-professor revolt.
Hang on; let me see what I can rustle up on my hard drive.
oh - yes; Susan J's source should be pretty useful, and Stephen Wilson has similar data from Johns Hopkins calculus courses.
This is "data-mining" type data, but that's the best there is at the moment (I think).
This post has a link to one of the Bishop & Hook papers:
http://kitchentablemath.blogspot.com/2007/02/to-read.html
Here's the abstract:
http://springerlink.metapress.com/content/013302t20rg73018/?p=9530da74639a4395b19960eff94cb5c7&pi=0
This one is great - I don't think it's been peer-reviewed or published; not sure whether they've been submitting for publication. (Wayne Bishop has had a terrible accident and is now paralyzed, though he's still at it -- !)
http://www.nychold.com/report-wbwh-040619.pdf
"Are Our Students Better Now?"
W. Stephen Wilson
http://www.math.jhu.edu/~wsw/89/study89.pdf
Wilson's paper doesn't look at specific curricula.
One of the ktm commenters thought Wilson's data may be affected by an increase in students placing out of freshman calculus via AP calculus.
Most (or all) of us have relied on comparisons between and amongst scope and sequence for different curricula.
When you put the end-of-5th-grade Trailblazers topics side-by-side with end-of-5th-grade Saxon, there's a fairly large difference favoring Saxon.
At the end of 5th grade Trailblazers kids haven't learned how to divide a fraction by a fraction; nor have the learned the traditional algorithm for long division.
Both topics receive extensive coverage and opportunities for practice in Saxon by that point.
It's also worth taking a look at Tom Loveless's report on NAEP, which apparently has been removing fractions from its tests.
A lot 226 ( 1.5)
Some 221 ( 1.8)
A little 228 ( 1.8)
None 237 ( 5.5)
Susan, how about we take stanadardized tests from several states and use those, and then show which districts use which curricula and got which scores. That would be fine.
To others: One of the problems using high school outcome data, or any data that involves evaluating end of HS/beginning of college math is that most students take courses through HS that are not part of Everyday Math, or some other curricula. Everday Math goes to sixth grade. What happens after that could erase or augment skills learned in EVeryday Math, thus HS performance doesn't necessarily say much about Everyday Math. The only way to know for sure is if we could control for all instructional programs that followed everyday math.
I have lately had an idea about why there is so much variation in math curricula and student performance, etc. I'm still collecting data, though.
What do you make of the report from IES's What Works Clearinghouse that looked at five curricula and found positive and significant effects for Everday Math but not Saxon Math?
http://www.whatworks.ed.gov/Topic.asp?tid=04&ReturnPage=default.asp
"What do you make of the report from IES's What Works Clearinghouse that looked at five curricula and found positive and significant effects for Everday Math but not Saxon Math?"
AAAAAAARRRRRRRRGGGGGGHHHHH!
Rewind tape.
WWC evaluates research. It does not perform research. It can make comments about research, but it does not have enough information to make comments about curricula. Unfortunately, they, and many others, seem to mix up the two.
At her site, JennyD inquires and discovers that SM spirals as does EM. She then wonders why SM is held in high regard and EM condemned by many if both spiral.
Not all spirals are the same.
A reader called Eric left a comment that makes an important distinction between additive and repetitive spirals:
Singapore's Framework is an Additive Spiral that Builds Topic Content Grade-by-Grade; NCTM's Framework Is a Repetitive Spiral Approach that Covers Similar Topics Across Grade Bands
Singapore
Spiral approach by content strand (additive)
Specific for each grade (K-6)
Clear, specific topics
Mathematically logical sequence
NCTM
Spiral approach by content strand (repetitive)
Within broad grade bands (K-2, 3-5, 6-8 )
Imprecise topics
Absence of boundaries and inclusive
That makes a lot of sense.
Not all spirals are the same.
Exactly. Which is why the word has become an irritant for many of us.
Saxon "spirals" via its own mixed reviews at the end of every chapter, so the student cannot get away from a previously taught concept.
It also helps a teacher better track which skills are being mastered and which are not. If little Johnny keeps missing the one or two percent questions thrown into the mixed review then it stands to reason that little Johnny is unclear on the concept.
The term "spiraling" with reform math appears to be about coming back to a concept the next year after an introduction to it the previous year. The idea is that some kids will get it and some won't, but when they spiral back around those other kids will get it.
What appears to be wrong with this idea is that the foundation set forth is one of shifting sand. Returning to a concept that you never mastered is like starting from square one.
Unfortunately, mastery and fluency do not seem to play a part in these curriculums. Teachers seem almost obsessed with "thinking skills" and "problem solving" and less interested in teaching the foundational skills one needs to accomplish such tasks.
And I do think you can look hard at the grade school math curriculum if the high school student's problems lie in basic arithmetic. This is just common sense. If mastery and fluency were not achieved then (or remediated for in middle school) then the big "wall" is coming.
Many other courses besides math become major obstacles for kids with math gaps. The chemistry teacher doesn't have time to go back and teach 5th grade math.
This isn't directly related to your inquiry, but it's related so I thought you might be interested.
The Education Consumers Foundation (disclosure: a client of mine) does a lot of work with value-added data, which as you may know gives insight into school effectiveness. They had someone visit several of the most effective schools in the state to identify common practices; the initial findings can be found at http://www.education-consumers.com/Bruce%20executive%20summary.pdf.
Again, it's not math specifically, but it's very interesting to see how many practices are shared by the highest-achieving schools.
"She then wonders why SM is held in high regard and EM condemned by many if both spiral."
Open the two books and look at them side-by-side. If you cannot tell, then go learn some more math. The main complaint at schools seem to be NOT that TERC or EM are better than SM. It is that SM would be too difficult except for the best students. It is best used for less "diverse" populations. Once again, the blame is placed on external causes, and at best, it indicates a goal of only meeting low expectations.
Everyday Math is repeated partial learning. It is NOT mastery followed by repeated practice or mastery followed by repeated use in more complex problems. EM states that the goal is not mastery at any specific point in time. This is specifically used to appeal to those schools that implement full-inclusion. They hope that with enough (completely out-of-context) Math Boxes that all students will master the basics eventually. It doesn't happen except for those who are smart enough to figure it out the first time.
On top of it all, we have discussed at KTM the fact that EM has way too much (unnecessary) material in it. It can't be done. Teachers either fly trhough the material with very little regard for mastery or understanding, or they go more slowly and don't get to very important material. My son's fifth grade EM class didn't finish a large portion of the second Student Math Journal. The teacher thought it was fine because all of the kids were developing critical thinking skills. It made me sick to my stomach.
It should be obvious that any method that looks at external or global statistics on curricula will fail miserably. You cannot separate all of the variables. You can't treat it as a black box. You will learn a lot more by studying the details of lots of individual students over many years. You have to account for home-based or outside tutoring. You have to account for that one bad teacher who screwed everything up. Education should not be about statistics. It should be about individual educational opportunities. You find those answers by looking at individuals.
But you don't have to know the answer. There is a certain amount of conceit in the idea that the goal is to find the "best" curriculum. The way it usually works is that schools pick their pet curriculum based on opinion, and then expect anyone else to prove(!) that there is something better. It won't happen.
There is, of course, a very simple solution. Offer a choice of curricula starting in the earliest grades. Let the parents choose. This is not a fluff issue or one based on religious or racial differences. This argument has been going on for years. It is an academic difference of opinion. It is a difference of expectations. It is much more important to allow parents to select the best opportunities for their individual kids than schools to select the "best" choice for the lowest common denominator.
If public schools cannot provide choice and input from parents, then the monopoly has to go away. Parents don't have to prove anything; schools do.
Thanks Brett. This looks remarkable like some research done by MSU profs 20 years ago. With some adjustments for today's issues.
These schools have obviously implemented these items. And that's where the devil is in the details. This is easy to say; hard to do. Especially if you a weak teaching staff, or some other major obstacle.
Which brings me to my theory about math curricula. I posted it on my website.
"This applies to Everyday Math because it is a difficult curriculum to teach. Teachers need a lot of training and support to do it well. However, when teachers are skilled enough to use the curriculum, Everyday Math is very rich and can improve student achievement tremendously."
".. improve student acheivement..."
Compared to what? The goal is not relative improvement. The goal is algebra in 8th grade. Just because your kids seemed to turn out fine, it doesn't mean that EM is fine for other students. My son has had EM for a few years now. He is an A+ EM student. He is not fine. I have to supplement with Singapore Math. He would probably do fine without my help, but I'm not taking that chance.
"Is it possible the Saxon Math is the SFA of math curricula?"
Saxon Math definitely makes it more difficult for teachers to screw things up. That is not a new point. But Saxon Math is much more than that. It also doesn't mean that EM would be fine if the TEACHERS understood it better. In spite of the fact that it's much easier to screw up EM, it's much more than that. You can't look at bright kids who do well and assume that the curriculum is taught well. You can't assume that if kids do poorly that the curriculum is taught badly. You can't come to that conclusion. I could teach EM well, but I could teach Singapore Math better.
After watching my son for a few years with EM, I see that he picks up on everything very quickly. He is a model EM student. But what about the other kids? Blame it on the teachers and not the curriculum? How can you do that?
The problem with EM is structural. They don't believe in mastery followed by practice. If you are not smart enough to master the material right away, the hope is that it will happen eventually, but there is no mechanism to make sure that happens.
If you train teachers enough, they could use almost any crappy curriculum. That's not the goal.
But STeve, how can you tell a curriculum is better if it is implemented differently?
Here's the problem: your claim that Saxon math is better comes with no evidence except your assertion that mastery and practice as outlined in curriculum materials is better than something else.
You offer anecdotes (as I do about EM) as evidence it is better. But anecdotes don't tell me anything about how the curriculum works in schools and multiple classrooms, with diverse groups of students. (By diverse I mean children with different math backgrounds.) Saying that a math program works well for one kid, or works well when a parent teachers one child isn't really ringing endorsement of its efficacy for use in schools.
"But STeve, how can you tell a curriculum is better if it is implemented differently?"
There is more to a curriculum than how it's implemented. There is a content and mastery path from point A (counting numbers in Kindergarten) to point B (algebra in 8th grade). Schools can screw up any curriculum, but that's not the point.
Besides, it's not my job to prove anything. I'm not forcing curricula on kids without any proper research or proof. I'm not forcing my opinion, assumptions, and expectations on anyone else. In fact, I'm pushing choice.
"Saying that a math program works well for one kid, or works well when a parent teachers one child isn't really ringing endorsement of its efficacy for use in schools."
I'm not saying any such thing. I'm making the argument that there is more to the difference between Everyday Math and Singapore Math (or Saxon Math) than teacher preparation or teacher friendliness. I'm making the argument that Everyday Math is structurally flawed because it tries to cover way too much unnecessary material and does not enforce mastery. I'm saying that Singapore Math covers more important math in depth and requires more mastery.
Again, it's not my job to prove anything. At best, all we parents have to show is a certain amount of demand for a different curriculum. It's the school's job to meet that demand. Time will provide the answer and everyone should be happy.
Why should I demand a different curriculum if my EM taught kids do as well your kids in math?
How do I know that Saxon math is "Singapore" math? If American teachers use it, how do I know they teach and also use the collaborative aspects of it they way teachers do in Singapore?
Learning math is not like learning to speak another language or learning to play the violin.
Yes my granddaughter may never get rid of the trace of American accent she's gotten from my son despite her mother's having spoken her native language to her from the day she was born.
Yes someone who picks up bad habits when they first learn to play the violin may have a great deal of trouble overcoming them.
Math's not like that. It doesn't have an accent or require using your body correctly. It's there for anyone to understand. That's not to say you aren't better off if the curriculum you use gets you to understanding and facility faster and easier and with a more positive attitude.
I haven't read the whole thread (I wil1!) but - Jenny - if you're thinking about taking on a fairly large project, you should probably contact the KIPP folks.
They seem to use Saxon often; they've also combined Everyday Math and Saxon in D.C. (I believe); there's also a Jay Mathews column about a TFA teacher at KIPP using.... hmmm.
I can't remember now whether she was using a constructivist approach per se (of her own devising) or EM.
She may have created her own curriculum.
I can find it for you if you want the link.
Let's see....there's something else I'm remembering.
hmmm....
Oh!
Right.
The school profiled in Linda Perlstein's new book, TESTED, uses Saxon Math & the kids' scores rise like crazy.
Then the teacher is pretty much told the district is going to remove Saxon from her class....
So far, it's a fantastic book.
I cried at the end of the first chapter.
Again, I haven't read the thread, but when it comes to math curricula there just isn't a lot of data, and the data we do have probably isn't the data we need.
I've been using "Bayesian" data (I think it's Bayesian--)....
The members of Beyond TERC will pose questions like, "Where are all the parent websites trying to get TERC into schools?"
Possibly the main question I would ask, in terms of trying to figure out how effective a curricula is without having peer-reviewed studies with control groups & sound implementation, is: "How often do we see low-performing schools implementing a reform math curriculum in order to raise math scores?"
I think the answer to that is "seldom to never," although I don't know.
I should have finished.
If the answer is "seldom to never," I believe that Bayesian statistics probably tell you such an answer is meaningful.
I hope I'm not using the notion of Bayesian statistics incorrectly.
My point is simply that the absence of "frequentist" studies & research does not mean that you have an absence of evidence.
btw, years ago, before I had the faintest idea what Bayesian statistics were, an autism dad explained to me how you could tell which one(s) of the "miracle cures" for autism actually work or work to some degree & are worth pursuing.
He said all you have to do is cruise the internet & find out how many people are talking about & doing a particular treatment.
The effective treatments will be the ones that attract (and I assume hole) MANY parents.
That was a revelation to me.
He was right.
Of course, with the constructivist curricula every school in the country is adopting them & every school of ed approves of them....
However, as the Beyond TERC person pointed out, you can find zillions of parent-run web sites trying to get rid of constructivist math, and virtually no such web sites arguing for constructivist math.
(Actually, I do remember one such web site now. The author kept himself anonymous, which also tells you something in the Bayesian sense of "tells you something.")
For the record, I personally like EM, although I find some of it strange and unfamiliar. I always assume those things are not useful to teaching math, but I could be entirely wrong.
I find parts of Saxon math enormously dull, but not all of it. And then again, in the hands of a skilled teacher it might entirely absorbing.
Oh yeah, one more thing: New York City schools implemented Everday Math districtwide in 2004. They continue to use it. In the school year 2005-2006 the percentage of NYC students grades 3-8 who rated proficient in math rose by 8 percentage points, with the greates improvement among 6th and 7th graders.
http://www.nytimes.com/2007/06/12/education/12cnd-math.html?ex=1339300800&en=f9a56adcac4aad97&ei=5088&partner=rssnyt&emc=rss
Maybe it's all about whether teachers know how to use the curriculum. Clearly disadvanged and minority kids can improve math achievement when taught Everyday Math.
So again, how do I know that any math curriculum is intrinsically better than another? and I mean, beyond some "Because I said so" evidence.
"Why should I demand a different curriculum if my EM taught kids do as well your kids in math?"
I didn't say that. If you and your kids are happy, good for you. But there are lots of kids and parents who are not happy at all and they have no choice. That's what this is all about.
"How do I know that Saxon math is "Singapore" math?"
?????
You mean Singapore Math is "Singapore" Math?
How do you know Everyday Math is "Everyday Math"? That is a meaningless comment.
There is no magic curriculum, but there are better curricula and poorer ones and we can discuss the reasons without claiming that it's meaningless by bringing up all sorts of other variables. I'm sure that Singapore Math could be taught very poorly. So what?
Actually, I think it's much more likely to prove that what gets taught for Everyday Math is not "Everyday Math". This follows your comment that it requires teachers who are trained more in its use. In spite of those concerns, one can still argue curricula differences in content and mastery.
There is a goal and not just a process.
["How often do we see low-performing schools implementing a reform math curriculum in order to raise math scores?"]
Here in Chicago fuzzy math (and constructivist science)are imposed on failing schools from above.
http://www.cmsi.cps.k12.il.us/
The choice of curricula often is not not guided by effectiveness but by ideological commitments.
Steve, my mistake. I thought earlier you had said Saxon and Singapore math were the same thing more or less.
BTW, when I talk about teacher preparation I definitely don't mean friendliness. I mean content knowledge and also pedagogical content knowledge. Both are essential to good teaching.
You're right in that it's possible that Saxon math might have more fidelity to the design interms of implementation because it is easier to teach. That means, it is designed to be successful when used by a teacher with weak content knowledge or weak pedagogical content knowledge. It's possible that EM is designed to be successful only when implemented by strong, well-prepared teachers.
Again, it might be less about the curriculum and more about the implementation. But there is no evidence of this, just my hypothesis. Likewise, there is no evidence that my hypothesis is wrong.
Meanwhile, thanks to all for this lively conversation. Thanks catherine for many comments. It is so useful and important to have these discussions. I learn a lot.
"Clearly disadvanged and minority kids can improve math achievement when taught Everyday Math."
RELATIVE! This is not the goal. This is low expectations. How do you know that many of these kids could not do a whole lot better? You're just happy that some statistics improve. I want the opportunity, the choice, to allow all kids to reach their highest potential.
"So again, how do I know that any math curriculum is intrinsically better than another? and I mean, beyond some "Because I said so" evidence."
If you don't know the answer to this, then you have no alternative than to let the parents decide. It's not our job to provide you with proof. That's your job. We already know what we want and we shouldn't have to prove it to anyone.
This is angels dancing on the head of a pin.
Why not look at the results of an international test like TIMSS, and then look at the methods used by the countries that score the highest?
This really isn't rocket science. The vast majority of math-savvy people will tell you that Saxon and Singapore Math do a good job. Can Saxon be dull? Yes, repetition is dull, but it teaches you the stuff. Doing page after page of binomial expansions by hand is deadly dull, but I don't know of a better way. This is what Catherine calls "teaching to mastery". When you come out on the other side, you can estimate the answers to questions in your head with a fair degree of certainty.
Saxon often appears dull to me. This is partly because it doesn't treat the subject like it's rocket science. It's extrememly clear and coherent. It is not enrichment, although there are conceptual exercises and experiments throughout. Enrichment is enrichment.
As far as state testing, I always take those with a grain of salt. I believe NY is one of the states that lowered its standards and then cheered when more people passed. I'm not sure what year.
It also appears as though the authors of the math portion of these tests and the creators of the new reform curriculums are the same people. In fact, it's clear that school districts are attracted to them largely because they are looking to improve their test scores and older curriculums don't have a whole lot on stem and leaf plots or histogram analysis.
When test time rolls, teachers have their hands full trying, not only to teach basic arithmetic, but also how to answers the questions in the elaborate way the tests want answered.
An example was when my son had to draw a big elaborate chart for a problem even though he could solve the problem mathematically. The teachers spent a couple of weeks teaching them how to answer the questions as if they were two years behind since they would get it wrong otherwise.
Teachers also have to spend time in math class teaching them how to write paragraphs about math concepts. Again, to answer it mathematically would be wrong.
So, the teachers do what they have to do and some even like it. But ask the middle school teachers what they think about having to teach long division and fractions due to all of the time spent in grade school drawing charts.
One more thing about state tests: My son is accelerated 2/3 years beyond most of his classmates, yet when the state scores come in some of his classmates score higher. He is in his second year of algebra while many of these students haven't had pre-algebra yet. I think it's clear that he forgot how to forget what he knew to make a higher score.
"I think it's clear that he forgot how to forget what he knew to make a higher score."
Very nicely put.
I have real trouble taking this kind of ed-school navel-gazing seriously. In a poorer country perhaps people would have less time for this kind of foolishness.
One can always hope :-)
"It's possible that EM is designed to be successful only when implemented by strong, well-prepared teachers."
Let's assume for a moment that this statement is true. Let's assume even more: that if you could magically compare the outcomes of different math curricula only when they were each implemented by strong, well-prepared teachers, that EM would give the best results.
[Just so there's no confusion, I do not believe that this is what you'd find.]
This would be useless information in the United States. There is nothing we are doing that has any chance of increasing the number of strong, well-prepared teachers.
You can't make a silk purse out of a sow's ear. No matter how hard we try to improve teacher preparation, there are not very many strong, smart, talented people even going into the profession and we aren't retaining those few who do.
It would certainly be an interesting coincidence if there had been a sudden drop in teacher quality just as EM was first adopted but I haven't seen any data to suggest this.
There was a chat today on The State of Math Standards that I missed.
But I can read the transcript:
http://www.edweek.org/chat/
Guests:
Francis M. "Skip" Fennell, the president of the National Council of Teachers of Mathematics; Tom Loveless, a senior scholar at the Brookings Institution; and Sean Cavanagh, a staff writer for Education Week.
Wow, Susan. I'm glad I don't think the way you do about improving teacher quality. If I did i would leave the US immediately because what you suggest guarantees the end of the US as we have enjoyed it.
Plus, I think that's pretty defeatist and maybe not particularly insightful. People said the same thing about medical education in 1900.
I am pretty discouraged.
I went to "Ed School" and earned an M.A.T. [from a new program specifically intended to improve teacher quality] in 1963 and taught public school for four years. I've been been following education pretty closely ever since then.
If you knew me, I'd hope you wouldn't call me defeatist. Even though I'm retired, I've worked full-time for the last 6 years as a volunteer on a project with the goal of improving math education for students who are braille users.
I'm a scientist and I think facts are important. I'm not saying we can't do better; I'm saying I haven't seen anything yet that makes me hopeful that we are going to do better.
I'd be delighted for you to prove me wrong and point me to some projects that are succeeding in improving teacher quality.
"Where are all the parent websites trying to get TERC into schools?"
It's often instructive to observe which direction the refugees are going.
Jenny D said:
"Here's the problem: your claim that Saxon math is better comes with no evidence..."
..."anecdotes don't tell me anything about how the curriculum works in schools and multiple classrooms, with diverse groups of students. (By diverse I mean children with different math backgrounds."
**********
Jenny,
These papers by Wayne Bishop and William Hook are based on data from TIMMS. Their findings seem to illustrate that there are significant results obtained using Saxon Math.
copy and Paste these links into your brouser.
http://www.nychold.com/report-wbwh-040619.pdf
http://www.nychold.com/talk-hook-040404.pdf
Scroll through both papers to view the charts and see the year over year growth in test scores for both economically disadvantaged students and those students who hail from more prosperous communities. The reports even show what happens when a school changed from Saxon to Everyday math.
I found the information contained in the Bishop and Hook papers dramatic and it is what propelled me to order the Saxon books for my son. Nathan is now at the top of his class in private school. His best friend who attends public school (Everyday math) is woefully behind and has a tutor 2 days a week.
Jo Anne C
Jenny D said:
"Plus, I think that's pretty defeatist and maybe not particularly insightful."
You're misssing Susan J's point and responding only to its tone. Her point is that you have to teach with what you have, not with some imaginary dream teaching squad. You seem to grasp at anything to show that your pedagogically favorite curriculum is workable. You show this by being happy about small relative increases in test scores in NYC.
But Everyday Math is flawed, and you can't blame it only on teacher preparation. The biggest problems are too much unnecessary material and no enforcement of mastery. Everyday Math can't have it both ways. They can't throw in everything but the kitchen sink, include lots of slow-moving development of material, and then expect teachers to get to all of the important material in the book. My son's fifth grade EM class just stopped when the school year ended. They were at least 30 percent from the end. The teacher declared victory.
When you open up the workbooks at any location, it looks like math, and it doesn't look too bad. But then you look forwards and backwards a few pages and see the content jump all over the place. The Math Boxes are the worst. Many teachers skip a lot of them. Where does that leave students who are still struggling to master that old material? If you do the Math Boxes, you're wasting the time of kids who already know the material. It's nice to review, but not constantly, and not right in the middle of lessons.
Then you look at the toal number of pages in the reference manual, the Student Math Journal, and the Home Links. For a simple analysis, divide the number of pages by the 180 days in the school year. Teachers have to move really fast, without much concern for mastery, or else they have to pick and choose over units. Then they want teachers to let the kids do the work on their own or in gourps in class. This guarantees that it's impossible to cover all of the material, and then you want to blame teacers for EM's failures.
EM can't load down the curriculum to make them look good to review committees and then do a "wink, wink", "nudge, nudge" to the schools and teachers, or complain that all they need is better teacher preparation. This is a copout.
It's obvious that those in the education field have an extraordinary bias and will grasp at any relative improvment or excuse to support their pet curricula. When challenged, they avoid details, talk about any small improvement they can find, and then require others to provide proof.
Thanks Steve!
Here;s the truth, I am quite open to the idea that EM is flawed. But no one here is even remotely open to the idea that Saxon math isn't nearly perfect. So I'm trying to figure out what's so great about it. As far as I can tell, there are other curricula that are similar, and then some not. There's not good data to show it is better and by how much. But there are people who are utterly certain it is the best thing. I just wanted to know why.
I do think teacher prep matters. I do think teacher prep can be improved.
Saxon is pretty vanilla, non-reform math. Whether it's better or worse than EM depends on the teacher; certainly EM offers more opportunities for an outstanding teacher to shine; but apparently kids in Pittsburgh would have been better off with Saxon.
The real issue is equaling Singapore. And it might be more cost effective to train a teacher who can do that than it is to train a teacher who can leverage EM.
"I do think teacher prep matters. I do think teacher prep can be improved."
And what makes you think that Ed schools can improve teaching? They have brought K-12 to its knees, ably assisted by the unions and the administrators.
How much actual teaching has your dean done? A year in elementary school? What makes her better qualified to teach a beginning teacher than a teacher who, over many years in a classroom, has shown that he can do a great job?
If Singapore and the other high-scoring countries can do without Ed school theory, I imagine the U.S can too.
This is an excellent article (and quick read) to get a perspective of what is underlying this discussion:
http://math.berkeley.edu/~wu/C50.pdf
What I think Steve (and perhaps others) is (are) saying is that Saxon is structurally better than EM. I don't see that his argument needs to rely on achievement data in any way.
This is the way I look at curricula as well, because I still operate under the assumption that books don't teach kids, teachers do.
Well, I'm familiar with around 4 years of Saxon math, including the fifth grade text. No, it is not perfect. I'm not sure what that would be exactly.
I will say that whether you are a gifted math teacher or very weak, you can lean on Saxon to get you through. The gifted teacher could wander away from it easily if he/she felt that the material was learned. The weaker teacher could just work with it more closely.
The biggest difference I see between Saxon and Singapore is that with Singapore there isn't much teacher help. You need to know your math and how to teach it, in my opinion. Also, Singapore appears to be more challenging at times. I have several of those books, but used them more as a supplement.
I had very little memory of math in school so I used Saxon as a script for my special ed middle schooler, who was literally regressing before my eyes. No one would respond to me at the school, so I decided to just take the reins and go for it.
I followed it to the letter and I was amazed at the results. So were his teachers who informed me that he "suddenly" seemed to be able to do some algebra. (I taught him the Saxon 6/5 book every night for 1/2 to 1 hour for exactly one year. He did all of the exercises, most of the mental math and drills and most of the "investigations." Now he is into 7/6. We had worked from earlier texts before, so I'm familiar with them, but this was the first time I followed it to the letter.)
I have taken Saxon myself (all of the 8/7 text and around half of the Algebra 1.)
What I learned from this is that Saxon sets the student up to succeed. It primes the student for the next chapter in a way that opened my eyes. Yes, it looks like a typical, boring traditional math text, but after actually doing it myself I realized that there was more to it.
Saxon is careful about its use of language. My son has serious LD issues in language and while he isn't borderline IQ, there are days when he operates around that area. However, it was clear that he understood the text when it was read to him. In fact, it was when I started speaking off the cuff to him to reinforce that his eyes would glaze over. It was too much.
I learned a lot about how appropriate vocabulary for struggling kids is critical. I imagine it's just as critical for disadvantaged children. Teachers shooting off relating to their bright ones will lose the others, but it doesn't necessarily mean those children can't learn the material. That was the eye-opener for me.
Anyway, that's my personal take on it. It has more going on than you realize. Catherine can expand on that, also, since she has taken a few of the courses herself.
Jenny D. said (about Saxon):
"There's not good data to show it is better and by how much."
*******************
Your claim about a lack of evidence reminds me of the response to Project Follow Through which indicated Direct Instruction was superior to other teaching methods. FT results have largely been ignored by educators.
I'm afraid that even if a major study existed which showed Saxon math to be superior to all other math programs, Saxon would continue to be ignored by the education establishment.
Saxon works, it has all the necessary ingredients, repetitive practice spread throughout the year, and it teaches the subject to mastery, rather than to exposure. Are there areas to be improved? Perhaps, but making changes to address my pet peeves might spoil the program for other students.
For my son the most important features of Saxon (home school version) have been the timed math fact sheets and the mental math warm ups. Other programs do not have these features built into the daily lesson. My son used his fingers to count up or down until we began using Saxon at home. Other programs we have seen (CA Houghton Mifflin, CA Harcourt, Everyday math) do not provide fact practice similar to Saxon's. Now my son is at the top of his class and one of the fastest at recalling his facts.
If a child does not have the facts memorized (cold) this will be the gate that keeps him (her) from entering the halls of success.
I am a very satisfied customer of Saxon Math and Singapore challenging word problems. No matter which program the school chooses to employ I will continue using Singapore and Saxon at home. It is unfortunate but school administrators will take full credit for my son's math success and attribute it to their less productive math programs.
"But no one here is even remotely open to the idea that Saxon math isn't nearly perfect."
Strawman.
"So I'm trying to figure out what's so great about it."
Mastery, mastery, and mastery. And it doesn't take a dream team of teachers to make it work. Mastery means understanding, not just speed. Ed schools are bound and determined to unlink the two. You can't have understanding without mastery. This has to be done from the bottom up, not the top down. You cannot spiral mastery.
"There's not good data to show it is better and by how much."
There you go again. The onus is on you to prove that Everyday Math (chosen without proof) is better. Businesses don't tell customers to "prove it".
"But there are people who are utterly certain it is the best thing. I just wanted to know why."
Mastery. Mastery. Mastery.
If you don't believe in this, then we can't agree on any basis for "proof". If there is no basis for proof, then please get out of the way.
"But no one here is even remotely open to the idea that Saxon math isn't nearly perfect."
"Better than the available alternatives" is very different than (to/from) "nearly perfect". If you have specific suggestions of how one might change Saxon to make it more useful, I don't think anyone would be averse to listening. But you'll have to make a real case that there is a problem and that your suggestion will probably result in a correction.
You've made no such attempt so far, following instead the common path of asking questions, demanding proof of anything that might contradict your preferred position, and then ignoring any response. While it's possible that you are attempting to argue in good faith, I'm finding that increasingly difficult to credit.
I hope I'm misreading the situation.
"While it's possible that you are attempting to argue in good faith, I'm finding that increasingly difficult to credit."
I agree. She has been around this argument for quite some time but acts like it's all new to her. I was really surprised at her original post to KTM. It was almost as if she just didn't "get it". I can fully accept that she has a different opinion, but she seems incapable of understanding the issues raised at KTM. She is always looking for loopholes rather than arguments.
"I agree. She has been around this argument for quite some time but acts like it's all new to her."
Her modus operandi as far as I can discern is that everything is a tabula rasa. But thankfully we have ed schools coming to the rescue to do original research in the vast wastes of ground zero. When you are at ground zero any research will be original and hugely important.
Oh dear. I hardly want to be the enemy.
First, my dean was a classroom teacher for 15 years. She is pretty blunt that teacher education needs major improvements. She gave exactly that speech at the American Educational Research Association last March. You can certainly criticize her for things, but being blind to the serious problems of ed schools and teacher prep isn't one of them.
Second, I'm not naive, just trying to understand. You know, the term fuzzy math is a strawman too, a vague but perjorative way to describe a math program so you don't have to learn more about it. Drill and kill is another term that people use to dismiss a program and not learn more about it.
I always have more to learn, and I'm not concerned about sounding like I don't know things. No shame in learning.
I really like that Saxon pays attention to language. One thing we struggle with at the Ed School is how to use appropriate and accurate language to represent mathematics to young children. We need to use words that get them to understand, while making sure to use the proper language too. It's an interesting problem.
I also agree that it might be more expensive at this point to train teachers to be expert at teaching EM.
Also, I know in my school teachers believed they needed to supplement EM with a dab of drill and kill, and that worked really well.
So...I've actually learned a lot about Saxon math and Singapore math from all this. Which will help me with my task force to work on my local schools. And will help me work on the Ed School.
I would like elementary school teachers to stop using the phrase "drill and kill" in the pejorative and replace it with "drill for skill."
"You know, the term fuzzy math is a strawman too, a vague but perjorative way to describe a math program so you don't have to learn more about it."
We use the term "fuzzy math", but we know lots about those curricula. It's an appropriate term because many things are never defined, like "critical thinking", and they don't explain how mastery is achieved. Most seem to think it isn't necessary.
"Drill and kill is another term that people use to dismiss a program and not learn more about it."
This has to do with what you think needs to be done. Is drill bad because it's boring and dull, or because it's unnecessary? Do you think that mastery can be accomplished without drill? Have you found some magical way to achieve mastery without taking a lot of time while keeping kids happy? You can always exchange a slow pace and low expectations for easier and happier learning. Drill and kill implies that there is something else to take its place or that mastery is not necessary. If there is something else to take it's place, then that is another reason for calling them "fuzzy". That something else can't be found.
"I also agree that it might be more expensive at this point to train teachers to be expert at teaching EM."
It's not just money, as if Everyday Math would be the best solution if you could only pay for it. I've tried to explain that it is not the best curriculum on many levels.
"Also, I know in my school teachers believed they needed to supplement EM with a dab of drill and kill, and that worked really well."
"Dab"? Everyday Math is only workable if schools trim the enormous fat carefully and add lots of mastery the first time kids are introduced to new material. You need much more than a "dab". You need a commitment to ensuring mastery before kids move on to the next grade. This might make EM workable, but it's like trying to change EM into something it's not.
The goal is not to see what you can do to save EM. The goal is to explain why another curriculum is not adopted. This is not a matter of making a little change here or there. It has to do with fundamental assumptions, like how much mastery is needed and what exactly are the grade-level expectations.
"So...I've actually learned a lot about Saxon math and Singapore math from all this. Which will help me with my task force to work on my local schools. And will help me work on the Ed School."
This is like the response I got from the curriculum head at my son's previous school. "Thanks for the input. I'll take it from here." She was bound and determined to make Everyday Math workable. She made reference to WWC and talked about different learning styles, not all kids are math brains, and the coup de grace, that some kids do quite well.
That last one always works. Of course, these might be the math brains, get help at home or with tutoring, or could survive any crappy curriculum.
The fundamental basis of Everyday Math is mastery over time; over years! This is a structural flaw and a "dab" of change is not going to fix it.
Steve, you cannot seem to have a reasonable conversation. I am sorry. This is not some kind of war.
"Steve, you cannot seem to have a reasonable conversation. I am sorry. This is not some kind of war."
What exactly, is unreasonable about my comments; the fact that you don't like them?
Up above, you say that the devil is in the details. I've been trying to discuss the details over and over.
You say that you want to understand why people like Saxon Math and Singapore Math so much. We try to tell you. Mastery.
Then you tell us that :
"... they needed to supplement EM with a dab of drill and kill, and that worked really well."
How do you know that? What does really well mean? This kind of vague talk is extremely exasperating.
These issues about math are not new. They have been going on for many years. There are obviously large differences in opinion that aren't going to be solved with a "dab" here or there. It would be one thing if I could pick or choose schools or curricula, but the schools seem to think they are the sole arbiters of what constitutes a proper education. So get used to the criticism!
Steve, I'm on your side concerning math, but when you say things like "there you go again" that's inflammatory and a little demeaning.
Please let's treat those with whom we disagree with respect.
I am feeling this strong need to defende Steve, but I must fix dinner first!
We just finished dinner so I'll defend Steve. He's tried extraordinarily hard to be reasonable in an extraordinarily frustrating situation.
The person who made the original request for information is currently going for an advanced degree in Education (per her own blog). She's likely going to have the opportunity to do something about the very situation that is the concern of the people who've taken the time to post the many informative responses to her request. However, it doesn't seem that any of us have been able to get her to think outside the box.
It's not surprising when we let our feelings show. This is an issue we've all invested a lot of time in and that we all care about enormously.
"the schools seem to think they are the sole arbiters of what constitutes a proper education."
You might consider befriending a state legislator. They like making educators more accountable. You might possibly slip something past the ed schools' legislative liasons. You might check how your state's administrative rules for ensuring local control compare with Ohio's. Not that we've mastered how to ensure administrators have the skills to "listen to and appropriately respond to stakeholder concerns." But at least the rule is on the books.
In any case, Jenny is looking for data, and, like FDA studies, somehow high quality studies of the "walk-on" treatments don't get done. Nothing is gained by intemperance, especially given her dean is on the National Math Advisory Panel.
I do share your concern that we're seeing (a dab!) too much mathiness and not enough math. But we've bigger fish to fry--like folks who misrepresent their intentions to Congress or SCOTUS.
"... but when you say things like "there you go again" that's inflammatory and a little demeaning."
It's not inflammatory or demeaning. It's a statement of fact. She is repeating her position that it is up to others to prove that there is a better curriculum, and by how much. Speaking of demeaning or patronizing, you need to go back and read the original thread that started all of this.
"There's not good data to show it is better and by how much."
I'm tired of this position. I saw it from my son's previous school. Schools get to select the curriculum based on whatever opinion they might have. When challenged, they talk in generalities and expect others to provide proof. They don't have the answers, but they are in charge and it's going to remain that way because this is their turf.
This is important because it's a perfect reflection of what's going on.
"However, it doesn't seem that any of us have been able to get her to think outside the box."
Thank you Susan J.
After all of the messages, she still comes out with:
"I know in my school teachers believed they needed to supplement EM with a dab of drill and kill, and that worked really well."
She can't even call it practice, let alone mastery, and she doesn't address any of the detailed issues that were raised about the curriculum. If it were me, I would be very interested to learn why others value mastery so much and how their expectations of mastery differ so much from mine. Being on the other side of the issue, I struggle to figure out what, exactly, is meant by "understanding" and "critical thinking" in reform math. Nobody can explain what understanding without mastery means.
All of this should never, ever be a problem. Parents, mathematicians, scientists, and engineers have been arguing for different curricula for years and years. It's not our job to provide proof when they can't do it. There is no excuse. Schools need to provide dual paths and let the parents decide.
"Nothing is gained by intemperance, especially given her dean is on the National Math Advisory Panel."
Nothing is gained any which way. Speaking of intemperance, very few TERC students (without outside help) will ever get accepted into the University of Michigan's School of Engineering. Perhaps they can apply to the Ed School. They are already pre-trained.
She's likely going to have the opportunity to do something about the very situation that is the concern...
Any you don't have an opportunity? The Math Advisory Panel has hearings in St Louis and Phoenix; looks like they take public input; Here's an example:
http://www.ed.gov/about/bdscomm/list/mathpanel/6th-meeting/presentations/killion-kevin.pdf
"...looks like they take public input;..."
These hearings have been discussed at KTM in the past. Many very good arguments have been made. If they can't change the direction of math education, nobody can.
I would only add that there is nothing stopping any school from providing choice. Except arrogance.
Susanj--
My thoughts exactly! We took our daughter to Kumon for 2 1/2 years, starting halfway through her third grade, and continuing through fifth grade. By that point, she had a solid foundation in the fundamentals, and also had an excellent 6th grade teacher, and we decided we could stop Kumon. She isn't a weak student, and while she is not a math brain, she gets math conceptually.
Our daughter's third grade teacher used the "dab of drill and kill" approach. It was our judgment, as parents, that Kumon was worth the time, energy and money to ensure that our daughter's future educational opportunities would not be at the mercy of what we considered to be a flawed math curricula.
Our decision paid off; she successfully completed Algebra this year (8th grade). In fact, she liked Algebra, even with the attendant and necessary nightly homework. On occasion, she would look up from her homework and say, "I like Algebra."
We were lucky in that we had both the educational background and the financial means to make sure our kid received a solid, fundamental arithmetic background. Other parents have figured this out a bit later in the game, and it has been painful. I should note that I have also been vocal on a local level as well, as have other parents, and some changes have been made for the better.
But the process was (and is) excruciating. The point that KTM readers make is that we either want genuine input into the curricula selection process, or we want the right to choose what we think is best for our child.
I also wanted to comment briefly about the statement that Steve is unable to have a reasonable conversation. I don't get that at all. When I put on my professional hat and ask for input about a topic, I want the unvarnished truth, the ruthless critic. I am looking for people who will find the holes, if any, in my argument or position If your opinion differs from mine, tell me why, and back it up with evidence. The more important the topic, the more that dissent is vital.
I often seek out my husband's opinions on many topics, because he is very analytical, has the ability to see the big picture, and also has the ability to look at things from different perspectives. He also seems to know how to ask the right questions and poke holes in what I thought was sound logic. He is also somewhat blunt and matter of fact when he his asked to give his opinion. I value that input, mostly, even when he disagrees with me, and yes, it sometimes makes me mad. However, when it is a matter of personal concern, such as a question of whether he thinks I have gained weight, I really don't want the unvarnished truth, and he has learned that the hard and painful way over the years.
This is what Steve does, I think. He cuts to the chase, articulates his opinions in a well-thought out manner, and pokes holes in what he sees as flawed logic. I have read his comments for long enough that I realize that he has "math chops." In short, he knows what he is talking about. And he's been on the front lines of teaching, in a college classroom, so he knows a few things about pedagogy.
One final note, if I may. I think this may be the point that Susanj made, but when we realized that JennyD was asking for input about math curricula, we hoped beyond hope that she would set aside any existing personal biases and preferences and try to really understand why so many intelligent, well-educated folks are so unhappy with the math education that their children are receiving.
In short, take off the kid gloves and try to figure it all out. Read the information available at Illinois Loop. org, and Mathematically Correct, and the multitude of other web sites, including Mindless Math Mutterings. Talk to parents, and listen with the purpose of understanding. Talk to high school math and science teachers; off the record, if need be. Talk to veteran elementary school teachers. And listen, really listen, without a preconceived bias for one program or another.
"...there is nothing stopping any school from providing choice..."
Better professional development for teachers; better arithmetic skills for teachers; perverse incentives (NSF SSI); more perverse incentives (ed schools); lack of clearly communicated expectations; confusion about how to craft instruction for reluctant learners; desire for alignment with standards-based high-stakes tests; ...
I'm unsure how mortal discernment can distinguish arrogance from all possible combinations of ignorance, fear, and bluffing!
Your state board of ed might want to take a look at Ohio's rules for education stakeholder input.
Hi Karena, you said what I meant a lot better than I did!
I love your specific examples of going "outside the box." The woman we are responding to says she was a reporter for 15 years; she ought to do a great job following your suggestions.
That fact that a doctoral candidate from a leading university is asking for data on the efficacy of various math curricula leads me to believe that such data either doesn't (or don't, if you prefer) exist, or is unreliable or hard to come by. The candidate would most likely already be familiar with such data if this weren't the case or would simply access the resources of a major reseach university and not ask.
I can see a slew of variables that would complicate any such research undertaking. You would have to account for innate student ability, teacher competence, parent involvemnet, tutoring, etc. It's not even clear what efficacy means since the goals of traditionalists and constructivists differ so widely.
However, all is not lost. There is no need to throw in the towel on quality curricula. One can always rely on one's power of observation, thinking ability and good sense to make a judgement. My sense tells me that a student who has access to good explanations and a coherent curriculum (either through a teacher, book or both) and practices a lot is likely to do better than a student who is asked to discover (reinvent the wheel) without these benefits. Such judgements based on observations, experience and good sense might be anecdotal but if you pile up enough anecdotes you might end up with statistics.
Also, if memory serves, this isn't new. JennyD has been asking the same questions for at least the last three years but hasn't grokked the answers.
"... leads me to believe that such data ... doesn't exist ..."
policy makers in search of expert guidance have often discovered that the research they needed did not exist or offered conflicting or indeterminate findings-or no findings whatsoever."
"... judgements based on observations, experience and good sense might be anecdotal ..."
Meaning data gathered around a kitchen table? Works for me! In addition, look at TIMSS (Singapore) and NAEP scores (thanks, Rory!).
What you've hit on is the "medical" versus "engineering" perspective. One diagnoses and prescribes an FDA-approved remedy. The other adapts better when standards of practice (and potential for litigation) are less clear.
Klahr has pointed out that ed researchers are employing the wrong metaphor, but mustn't abandon the scientific method altogether: "Indeed, it is surprising that science educators so often abandon one of the foundations of science--the operational definition--when they engage in heated debates about discovery, inquiry, hands-on, and the rest. No science can advance without clear, unambiguous, operationally defined procedures. Neither can education science."
Sound school governance--work by Robert Strauss and David Mathews--is also essential.
One might also reflect on the potential for federal intervention in education to disempower both parents and teachers. Once local teachers and board members start coming to you (because of your reputation as an honest broker), it might be time to take action at the state level.
For the record, if you search more closely at the comments my dean has made in the past you will see a couple of things:
she has disagreed strongly on occassion with the panel you all hate so much, but stays on it because she wants to make her voice heard;
she has called for a national math curriculum, and not advocated for EM, or any curriculum for that matter.
Really.
You guys are something else.
I'm ready to dig deep into the problems of EM and the potential power of Saxon both on this mastery aspect, and on the possibility that is easy for new teachers to implement well.
And you guys are here defending someone who like to throw around inflammatory statements.
If this is about math, let it be about math. If this is about debate, let's debate.
If this is about trashing those who disagree, or make alternative arguments, then you won't really contribute much to the search for even better math curricula.
Most Americans frown on experimenting on human subjects without informed consent. The preponderance of the evidence is that "discovery math" has been less effective than formerly-used curricula. We do not need to know why this is so nor to wait for new, better curricula (or better teacher training) to conclude that it is immoral to continue to use "discovery math" when we have the option of using available older curricula.
Research on dyslexia has led to a better understanding of how the normal brain handles the task of reading. It may be that research on dyscalculia will provide similar information and help us devise new, more effective math curricula.
It may be that we will discover some simple tests that will allow us to better match teachers to curricula and/or to individualize teacher training or the teaching of students.
I'm certainly not against research in this area and I don't think the other KTMers are either.
But meanwhile today's students can't wait.
she has disagreed strongly on occassion with the panel you all hate so much, but stays on it because she wants to make her voice heard;
I don't believe anyone ever said anything about hating the National Math Panel. In fact, I for one, highly respect the insightful anlysis of panel members such as H. Wu, as only one example. The panel is comprised of an interesting cross-section of minds involved and interested in questions crucial to the math debate. The panel members sacrifice their personal and professional time because they see the significance of improving math education in our country. There is certainly nothing to hate about this important process although I do admit to being anxious to hear what they have to say.
I hope you don't continue to see yourself as "the enemy", because if you do then all is lost from the outset. This shouldn't be about being right, it should be about doing the right thing. It's not about what one particular person believes, it's about putting all the information out in the open and analyzing it objectively and honestly with no strings attached.
It's a passionate subject particularly when you have a child in the crossfire so, yes, things can get a little heated. Most of us who have been vocal have had our share of heat in the kitchen too. But it's too important to get out of the kitchen and sometimes, I hear something that makes some sense if I keep listening. It is real, sometimes raw, but in the end crucial to making true progress for our children. If this isn't the point, then no amount of debate is worth my time and energy and I shouldn't be here either.
Jenny,
We've all been following the math panel. We post the transcipts when they come out and discuss them. I have no idea why you would think we hated them.
I'm fascinated by the various math panel member's comments. One of our commenters is actually a neighbor to one of them.
I appreciate you taking the time to respond to various people. I'm not agreeing with everything you say, but so what? We sometimes don't agree with each other.
We don't speak as one voice around here, but we are bonded as parents looking for something that works when the school system isn't quite measuring up. And we do share what we've heard or learned about. KTM is invaluable in that respect.
"... Most Americans frown on experimenting on human subjects without informed consent ..."
But trained professionals know how to finesse an Institutional Review Board. :-)
Earlier I mentioned Klahr and the effect of metaphor choice upon ed research. Now you've raised another good issue: are public schools government schools or local schools?
If we're operating government schools, then they ought to serve a compelling state interest to justify the loss of liberty schoolchildren suffer as a result of compulsory attendance. Curricular choices (experiments) would need rigorous evaluation to establish compatibility with the stated "compelling interest."
If we're operating local schools, then the compelling interest is for parents to provide an education for their children adequate for the child's future success. School governance and discipline would be justified via in loco parentis. Curricular choices would need parent approval. (Hence, local school district boards of education--LSD boards.) Now local schools don't have a budget to provide infinite choices, but they ought to comply with state governance standards that align with the high school civics curriculum. Administrators ought to be prepared for honest deliberation with parents regarding curricular (and other) choices.
However, by blurring the above distinction, educators can avoid explaining themselves to parents and simply appeal to mandatory compliance with "mandates" from above, or "research shows." Now, it might be there is no explanation: The "gods" of Mount Olympus more closely resemble a character from L. Frank Baum than from Edith Hamilton. As Lovely Billups explains, "The activities of these 'gods' often set off new fads in education which strike the professional lives of the school personnel below like bolts of lightening from the clouds."
So the underlying problem with ed fads is a governance and civics problem, not a math or education problem--well, possibly a civics education problem.
So if you're tired of being victimized by middle class welfare recipients who, uh, make unjustifiably bold statements to the US Congress and Supreme Court, you might want to hone your own civics skills. I'd recommend downloading David Mathew's greatest hits and buying his book.
Jenny:
I would like to continue the discussion and move away from pointing fingers at Steve undeservedly.
I am frustrated because as I understand it, educators mostly agree that children have different learning styles. Yet, when it comes to math NCTM discovery based programs seem to be the only offering, choice is virtually non existent. My son would never survive a constructivist math program. He requires direct instruction and must practice, practice, practice (throughout the year) until he masters the material. There is no other way for him.
If Saxon is *highly* effective for a student (which can be readily verified by evaluating student performance records) and a parent wants to use it, why on earth would any educator deny access to this program? Why can’t parents choose what they want for their children? I am happy for other parents to use the discovery approach, I would never think of denying them the right to choose what is best for their children.
I had the extreme discomfort of having to go toe to toe with a Director to remove my son from a poorly conceived grade 3 honors math class. This administrator (likely insulted) began by rubbing my nose in her 25 years of education experience inferring that she knew far better than I which math was best for my son. (Never mind that her 5th and 6th grade honors students are still counting on their fingers) She proceeded to tell me that I should stop using Saxon at home because I was likely *confusing* my son.
I was astonished by her arrogance; she had never met me or my son, and had no clue as to his abilities. I informed the director that what I did at home with my child was not in her jurisdiction and we would not speak further about it. It came to a point that I had to ask the director if she wanted me to remove my son from her (private) school, which took a moment to register with her. Only after the threat of loosing our tuition was I able to get my son placed in a grade level math class. For the record, my son is among the strongest students in math.
I believe that Steve made a very compelling point when he spoke of the arrogance of educators who refuse to accommodate those of us who only ask for a choice to use what works best for our children.
My fellow math activists I want to tell you that there is hope!
This fall my son will be allowed to use Saxon Math independently during his regular math class in the same private school if *I* determine that the 4th grade honors class will not be appropriate. I will get to make that call thanks to a very kind and level headed principal, who has chosen not to consult with the director regarding this matter.
After working at grade level in Saxon at home this past year, my son is still on equal footing with the honors students and perhaps more advanced in some areas. The honors math students worked with material one grade level ahead but were only taught to exposure in the classroom, not to mastery, it was up to the parents to provide the mastery at home.
"You guys are something else."
You still don't get it. This is not about you. It's about teaching math and dealing with the criticisms that have been raised over the years. By the way, if you have kept up with KTM, most of us are big supporters of many panel members. I bet you know which ones.
"I'm ready to dig deep into the problems of EM and the potential power of Saxon both on this mastery aspect, and on the possibility that is easy for new teachers to implement well."
No you aren't. You have failed to dig into the details of mastery versus understanding after all of these posts. From your first posting, you have avoided details.
"And you guys are here defending someone who like to throw around inflammatory statements."
You can't even address me directly? Please be specific about this accusation. I have raised many issues that you have avoided. By the way, you were the one suggesting that we don't have enough knowledge of teaching and, perhaps, too much math knowlegde to contribute to the solution.
"If this is about math, let it be about math. If this is about debate, let's debate."
That's what I have be trying so hard to do. The best you can say is that you require some sort of proof, but then think that Everyday Math might be pretty good with a "dab" more mastery; no, "drill and kill". I wrote long posts detailing, from first-hand experience, problems of Everyday Math. You did not respond to any of them. I tried to explain why Everyday Math is structurally flawed. You did not respond. This is not debate. You don't like how I respond? Perhaps it's because you have no response.
"If this is about trashing those who disagree, or make alternative arguments, then you won't really contribute much to the search for even better math curricula."
Here it is. I've heard this position before. "If I'm not part of (your) solution, then I am part of the problem". It can't work like this because the problem has to do with fundamental assumptions. We're on different busses going in different directions. The problem is that your bus goes to the schools and my bus goes home. You want me to get on your bus and have everyone work nicely towards one goal. The problem is that we're going in different directions and you can't see that. How can you talk about proof when there are different assumptions?
I'm sorry you don't like what I have to say. I'm not averse to barbs and satire, but I ALWAYS try to get to the heart of the problem. I have been struggling over the years to really understand what schools of education have against mastery and proper grade-level expectations. I have many theories and they all have to do with low expectations. (as in your comment about NYC making small gains using Everyday Math) Supporters of reform math claim that that curricula like Everyday Math and TERC provide better understanding and critical thinking skills. I don't see that at all.
Nobody can explain how that works, especially when the understandings have to bridge the gap from pictures of pies to a more abstract application of algebra. You can always trade slower coverage of material for more understanding, but that isn't the claim, is it?
I want to debate the details of content.
I want to debate the details of mastery.
I want to debate the details of grade-level expectations.
I want to debate the details of understanding and critical thinking.
Actually, KTM has done a whole lot of this. Where were you?
Inflammatory? Then get down to the details.
You know, this all started with your cross link about a vaguely-defined course for rising fifth graders. I think you thought we all would go ooooh and aaaah. When we raised specific questions about details, none came.
We parents get this ALL OF THE TIME. And then schools expect parents to work with them just like you expect us to work with you - on your terms. Just don't start talking about balance.
Excellent post, Steve.
"I have been struggling over the years to really understand what schools of education have against mastery and proper grade-level expectations."
What about "follow the money?"
Schools of education are in the business of making money just like other institutions of higher learning. They make money from tuition (or tuition subsidies), including that provided by their many students who do not have the grades or SAT scores or whatever to get into (or if they do get into, to succeed in) most non-Ed-school programs.
It's not to their advantage to turn down applicants or to have students flunk out which means thay really aren't in a position to make their courses more rigorous.
It's also not to their advantage to have their graduates stay in teaching longterm. The more teachers who drop out of teaching the more money the schools of education make by training new teachers.
"Supporters of reform math claim ... better understanding and critical thinking skills. I don't see that at all. ... I want to debate the details of content."
The NSF/NCTM based curricula have a greater emphasis on "data." If "data" were emphasized in other core subjects, there would be many more opportunities in the school day for "critical thinking skills." For example, social studies (and certainly science) could be much more quantitative. We see charts and graphs in newspapers; why not in English class?
"I want to debate the details of mastery."
Specifically, why make excuses for not including long division in EM? If the usual multiplication is mastered, the multiplication required in the division algorithm is mastered as well. Looks to me like dropping common algorithms is an attempt to hide lack of skill, not promote understanding through construction of alternatives algorithms!
"I want to debate the details of grade-level expectations."
A grade by grade mastery highlights guide would be valuable. Anyone know of one?
"We parents get this ALL OF THE TIME."
I don't think Jenny meant to throw salt in the wound. Personally, I moved my family out of Colorado rather than put up with the ed fads--so I don't really feel your pain. That said, you seem to have a "T" vs "F" thing going with Jenny, and you're not anticipating where she might be contextually bound (e.g. need for statistically significant data) and where she can be deliberative.
"Inflammatory? Then get down to the details."
I get the feeling that the details are inflammatory.
Generalities are much more soothing. Bromides go up in flames when looked at closely.
"...moved my family out of Colorado rather than put up with the ed fads..."
AAAACCCK Flachback! I remember ... CSMP ... daughter loses 10 IQ points ... AGHHH!!!!!
You guys are something else--apparently whiners who can't speak to the prompts. And before you "run away, run away" or say "help, help, I'm being repressed" by EM, ask yourself, "what would Rosa Parks do?" And be glad you never had a kid in CSMP:
"To this end, the content is presented as an extension of experiences children have encountered in their development, both at the real-life and fantasy levels. Using a 'pedagogy of situations,' students are led through sequences of problem-solving experiences presented in game-like and story settings. Powerful non-verbal 'languages,' such as strings, arrows, and the Papy Minicomputer, allow students immediate access to the mathematical ideas and methods necessary not only for solving these problems, but also for continually expanding their understanding of the mathematical concepts themselves."
"Looks to me like dropping common algorithms is an attempt to hide lack of skill, not promote understanding through construction of alternatives algorithms!"
They want math to be a pump and not a filter, but how can you do this when the hard work of mastery gets in the way? You pretend that it's not so important.
This is a classic comment from "Algorithms in Everyday Mathematics" by Andrew Isaacs:
"Reducing the emphasis on complicated paper-and-pencil computations does not mean that paper-and-pencil arithmetic should be eliminated from the school curriculum. Paper-and-pencil skills
are practical in certain situations, are not necessarily hard to acquire, and are widely expected as an outcome of elementary education. If taught properly, with understanding but without demands for 'mastery' by all students by some fixed time, paper-and-pencil algorithms can reinforce students’ understanding of our number system and of the operations themselves. Exploring
algorithms can also build estimation and mental arithmetic skills and help students see
mathematics as a meaningful and creative subject."
No mastery by some fixed time. "Exploring algorithms", instead of mastery. "... meaningful and creative subject." This sounds like math appreciation. It also sounds like low expectations. Clearly, they have a different mindset. As my old engineering school advisor says: "They've hijacked math."
"A grade by grade mastery highlights guide would be valuable. Anyone know of one?"
Most refer to the "Green Dot" California standards, but I don't think it sets any exact performance levels.
Susan, how about we take stanadardized tests from several states and use those, and then show which districts use which curricula and got which scores. That would be fine.
Oh yeah, one more thing: New York City schools implemented Everday Math districtwide in 2004. They continue to use it. In the school year 2005-2006 the percentage of NYC students grades 3-8 who rated proficient in math rose by 8 percentage points, with the greates improvement among 6th and 7th graders.
Every state using their own tests, and recent articles in the press have shown how some state tests are dumbed down to a great extent. States with good results on state tests don't necessarily have good results on the national test (NAEP). And NAEP isn't exactly challenging either.
Please see this article by Diane Ravitch about the unreliability of NY City and State's tests at http://nycpublicschoolparents.blogspot.com/2007/06/diance-ravitch-reflections-on-math.html.
One of the problems using high school outcome data, or any data that involves evaluating end of HS/beginning of college math is that most students take courses through HS that are not part of Everyday Math, or some other curricula. Everday Math goes to sixth grade. What happens after that could erase or augment skills learned in EVeryday Math, thus HS performance doesn't necessarily say much about Everyday Math. The only way to know for sure is if we could control for all instructional programs that followed everyday math.
Good point. Classes that students have after EM could help teach them what they were supposed to learn. If they do well in high school, it could be the result of intermediate steps. In my daughter's middle school (7th grade) the teacher as aghast at the results from her initial exam to see how much the students knew. She told all of the parents on back to school night how shocked she was at lack of mastery of basic skills. This teacher happened to be good, and made sure the students learned what needed to be learned. Everyday Math is used in a few of the schools that feed into the middle school. So now you have the situation you describe. Of course in Ann Arbor, you have a double whammy. You have Everyday Math in elementary and an equally bad if not worse program called Connected Math Program in middle school. If Ann Arbor high schools adopt Core Plus, there's no problem; they don't teach math in that program either, so kids can just sail through.
For another perspective on Everyday Math, please read the Op Ed by Elizabeth Carson, Executive Director of NYC HOLD, located at:
http://www.nychold.com/oped-nydn-carson-061016.html
Many parents are tired of being told to trust those who have been trained in education. Many parents are questioning the theories and methods that the school boards and school administrations are saying are good for the kids. Parents are tired of being told "You're the only one who's complained". Parents who happen to be mathematicians are tired of being told that mathematicians don't really know anything about teaching math. (The subject of "content" is studiously avoided in such dialogues.) Finally, Sadly, there are just as many parents who, having had bad experiences in math when they were kids, believe that what is being offered to their kids is an improvement.
In June 2005, the DC Public School Board voted to adopt Everyday Math and Connected Math for the DC schools. Protests from parent groups and advocacy groups like NYC HOLD were ignored. Testimony was given showing high test scores for the six schools that piloted EM in previous years--schools with high SES indicataors, and that have traditionally had high scores in math even before EM was implemented there.
The dialogue and actions of the DC board that evening were typical of most school boards in the U.S. and typical of the "I'm in education and you're not" attitude that prevails in this country. You may find my documentation of the events interesting. It is located at: http://www.thirdeducationgroup.org/Review/Essays/v2n6.htm.
This is the latest from her site:
"What the Dean Told the Reporters"
"She told them that the real work of teaching math goes on in classrooms, not in debates over curriculum. She said it's more important to have a well-educated (in math and teaching) teacher in a classroom than to have a particular curriculum in place."
Ooooh. Convincing reporters. That's really tough.
This is the easy way to solve the curriculum issue; claim that it isn't an issue. If you have good teachers (whatever that means), then issues of content, mastery, and expectations all magically go away. They argue with generalities to make people go away, then they can decide the details.
But, if curricula don't matter so much, then why are they so dead against Saxon math or Singapore Math. Why do they trumpet the advantages of reform math? Chameleon arguments. They hope that others won't see that the arguments are incompatible.
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