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I recently had a fantastic discussion with an administrator at my local public middle school. This person is new to the Town and school. My impression is that she is less pedagogically dogmatic than most I have met. She does not have an direct involvement with EM. In Middle School she see the pre-algebra and algebra math of 7th and 8th grade. She hears from many other teachers and administrators that EM is fantastic and wonderful and perfect for our school. However, she, and most other educators in town notice that this "wonderful" elementary math program isn't connecting well to middle school and high school. Kids aren't doing all that great on those high school courses.
The reigning wisdom has been that the problem can't be EM. It must be the middle school math program (with are traditional pre-algebra and algebra courses).
There is a failure to analyze their underlying assumptions. Nobody is willing to consider that EM might not be the best preparation for advancing in math.
But this administrator has shown an interest. I gave her my opinion on the matter at a forum a couple weeks ago and she was interested in what I had to say. I advised that she put EM and Singapore Math side by side and compare to cut through all the rhetoric. She could make up her own mind about it. I finished by saying if there was one thing I could convince this district to do, it would be to teach bar models as a means of problem solving.
She had just read an article about bar models. She wants to know more.
So here is your chance, everyone. If you had limited time available with an interested administrator, and you had 1st through 6th grade Singapore and Everyday Math at your disposal -- where would you start? What pages, links, sections would you highlight or focus on?
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53 comments:
Great move Lynn. Singapore truly speaks volumes.
One of my favorites is EM's coverage of multiplication of decimals in 4th grade. Just have an administrator look it up in the EM Student Reference book for 4th grade.
The only entries you find are how to multiply decimals using a calculator.
In contrast, Singapore 4B covers the four operations of decimals including multiplication of decimals WITHOUT A CALCULATOR.
My son is in a second grade EM classroom but is working on Singapore 2A/2B at home. It's like math on two different galaxies. 2A presuposes mastery of addition and proceeds to work on mastering multiplication and division. Everyday Math hasn't even come close to teaching multiplication and division to that degree. Most children in his class are still working on mastering addition and subtraction facts.
Good for you Lynn!
I spent more than a little time last year with the curriculum director at my son's previous private school. I tried a number of angles and none of them worked. She was predisposed to like EM.
Graduates of the school do well in the high schools they go to. I asked her what doing well means and whether they do well because of or in spite of EM. She was very nice and quite open to input, but she knew ed school rhetoric, not math.
I mentioned that the 5th grade teacher had to form an after-school study group to make sure that many kids knew their basic math facts. This didn't work either. She saw this as a problem with implementation, not the curriculum itself. She said (in so many words) that since some kids do quite well, the issue really isn't with EM. I told her that I supplemented with Singapore Math at home. What it all came down to in the end was that Singapore Math was just too difficult for the mix of students she had to consider.
Like my son's current (public) school, that school uses reasonable 7th and 8th grade pre-algebra and algebra textbooks. The big jump is from 6th to 7th grades. Many kids don't make the transition and are put on the slow road to checkbook math. By then, however, most schools blame poor results on the student. They point to the kids who are doing well. Do they ask those parents what they are doing at home? Nope! All we get are questions about whether we (parents) feel comfortable with helping our kids with subjects at home. The answer is yes, but are they asking because they can't figure out how to do it?
So, the reaction I got with the comparison was that Singapore Math was too difficult. I had loaned her my Singapore Math books and talked about a number of issues.
My overall reaction was that she didn't have enough math background to understand the issues that were being raised. She just looked at test scores and relative changes. She was completely unable to judge whether they could be doing a whole lot better. I was talking about absolute, and she was only able to understand relative.
I have yet to come across anyone who claims that Singapore Math is worse. At best, all they can say is that it is inappropriate and then walk away from the discussion.
I have to say that at this point, I am just hoping she is not humoring me.
I think the middle school is seeing the disconnect between EM and High School better than anyone -- they are going to take the blame when kids pass the state CMT test in 6th grade, but we see the High School results tanking on the CAPT and the SAT.
Our CAPT scores dropped almost 7% in math last year. CAPT is a ridiculously easy algebra and geometry test. Our pass rate was around 65%.
They know there is a problem, but no one wants to believe it could start as early as the elementary grades.
ConcernedCTParent: Is there a math journal in the 2nd grade? My 2nd grader never brings anything home and I sort of thought maybe there wasn't any journal in those grades. But you are 100% correct, in 2nd grade there is a huge gap in multiplication between Singapore and Everyday Math.
I'll definitely bring up such an early and obvious gap.
In the 6th grade, what strikes me is the lack of story/word problems in EM. I don't know if I can find any that require two steps to reach the conclusion. Singapore works in complicated multi-step word problems in every section.
SM covers rate, ratio, and pre-algebra. I don't see any of those topics in EM. Well, EM does some pre-algebra concepts. I'll have to look more closely at how this is covered in EM compared to SM.
My second grader says there is a math journal. Of course, it never comes home. The only thing we ever see is the Homelinks.
I purchased the student reference book myself because I really try to be an informed "critic". It is a first/second reference book and my school and the district don't even own a copy.
My son's class was actually without EM material until sometime in October.
As for word problems, clearly EM can't even touch SM with a ten foot pole. Talk about real world!
The word problems in SM are superb and a upper elementary student fed a steady diet of EM would struggle to answer even some of the third grade SM word problems and would likely find those at SM grade level almost impossible.
I pulled out my son's second grade HomeLinks workbook. Apparently, there is some coverage of multiplication and division and word problems for each:
Everyday Math
11.3 Multiplication Number Stories
Use counters or draw pictures or arrays to help you.
1. The store has 6 cans of tennis balls. There are 3 balls in each can. How many tennis balls are there in all?
Answer: ___ tennis balls.
Number model: ___ x ___ = _____
11.4 Division Number Stories
1. Our group needs 18 pens. There are 3 pens in each package. How many packages must we buy?
Singapore 2B
Review 3
11. The tigers in a zoo are fed 6 kg of meat a day. How many kilograms of meat are needed to feed the tigers for 4 days?
Exercise 54
2. Lauren poured 16 qt of orange juice equally into 8 jugs. How many quarts of orange juice were there in each jug?
There is a huge difference between the two sets of word problems that you wouldn't know from comparing the above. In EM these types of word problems were covered in lesson 11.3 and 11.4, most likely in two days. One day on multiplication story problems and one day on division story problems. The next day, in 11.5, they're on to Mulitiplication Facts (Show someone at home how you can use arrays to find products. Use .s. dots)
In SM, by contrast, these types of word problems can be found throughout.
You would never find something like this in Everyday Math second grade:
A tank contains 17 gal of water. 25 more gallons of water are needed to fill it. What is the capacity of the tank?
Singapore 2B, Review 8, #18
The difference is vast and the results are as well.
"Well, EM does some pre-algebra concepts. I'll have to look more closely at how this is covered in EM compared to SM."
I went through the new version of 6th grade EM with my son last summer to prepare him to skip to 7th grade Glencoe Pre-Algebra this year.
Sixth grade EM has a number of topics that are in my son's 7th grade Pre-Algebra book. However, it's the usual EM approach of throwing new topics or skills at the students before they are ready. In their approach to spiraling, they think nothing of giving a quick exposure to advanced topics and then jumping to another topic. I think that part of the motivation is that reviewers will open the workbook and see these topics.
What reviewers won't see (unless they spend some time with the books) is that the coverage is superficial and there is no continuity or development of the material. It pales in comparison to my son's current (traditional)pre-algebra textbook.
Sixth grade EM is in a mad rush to fix all of the problems they created in the previous years. For each new topic/unit, half the pages are math box reviews of earlier topics/skills, even from years ago. At some point mastery matters, and they are struggling to make that happen. They can't do it. How can you fix problems that are years old while learning new material?
And why is it that a spiraling, don't worry about mastery, approach is fine for K-6, and then completely thrown out the window for 7th grade? My son doesn't hear his math teacher telling them that it's OK not to understand how to do the homework.
I suppose that if you can get them to compare EM with Singapore Math side-by-side, then you will at least force them to argue about real things, not philosophy or some vague traditional math.
These are excellent points.
6th grade EM feels like an octopus. We are jumping topics around trying to cover a lot of ground. Plus there is so much time lost on reviewing graphs, mean, median, range, and mode (AGAIN!!!). If only they spent as much time on decimals, fractions, and percent (without resorting to a calculator). Maybe that's what I need to emphasis.
And I guess a reference to the 6th grade "focal points" wouldn't hurt.
6th grade focal point #1: multiplication and division of fractions and decimals (including multi-step problem solving).
#2: multiple and divide to solve ratio and rate problems
#3: pre-algebraic expressions and equations with variables.
You can't look at EM and believe that it focuses on these 3 main objectives in the 6th grade. The volume of problems addressing these topics is superficial, as Steve points out.
Still, NCTM is far from an ideal benchmark, but would it carry weight with administrators?
Does she have Sybilla Beckmann's article?
Let me get the link (I'll email to you as well.)
Solving Algebra and Other Story Problems with Simple Diagrams: a Method Demonstrated in Grade 4-6 Texts Used in Singapore by Sybilla Beckmann
concernedCTparent - Can't agree with you more about the word problems in SM. We're actually switching to Math Mammoth and the Key to...Series for math for my 9 year old (budget considerations - I already have all the MM and Key to stuff whereas I'd have to buy SM) in our homeschooling but I've still ordered the word problems books from SM.
John Hoven and I wrote an article about Singapore Math which appeared in the November 2007 issue of Educational Leadership. That may have been the article your administrator read since it focused on bar modeling.
I'll try to do an embedded link. Here goes:
The article has been posted at NYCHOLD.
(If that didn't work, the link is:
http://www.nychold.com/art-hoven-el-0711.pdf)
Many of the math reformers glom on to the bar modeling of SM and not much else, not realizing that bar modeling is only a means to an end and not the whole show. This quote is from the article:
"It would be a mistake to think that the bar model approach to solving problems could be lifted out of Singapore Math and used by itself. Although bar modeling provides a powerful tool to represent and solve complex word problems, it also serves to explain and reinforce such concepts as addition and subtraction, multiplication and division, and fractions, decimals, percents, and ratios. If not linked to the concepts embedded in the lessons, the bar model would not necessarily be meaningful. The bar model and the basic skills embedded in the mathematical problems bootstrap each other."
Sybilla Beckman makes a similar point in her article; that bar modeling is a way to get to algebra and should be taught that way. Some reformers are starting to make a quick buck by selling books and programs on how to use bar modeling to solve problems. This is like teaching a course in bicycling with training wheels. They're missing the point! Ironically, these books and programs take a "rote" and "algorithmic" approach to bar modeling which gets away from the linkage between math concepts and problem solving which SM does so well.
Your administrator is free to contact John Hoven or myself. Our emails are included in the article.
"Ironically, these books and programs take a "rote" and "algorithmic" approach to bar modeling which gets away from the linkage between math concepts and problem solving which SM does so well."
Very well said.
As I've always said, we give them way too much credit.
The key point is that they are in charge and they want to keep it that way. When challenged, they talk about balance, but they get to decide on what balance means. When shown bar models, they decide how it's to be done, and it's not by using Singapore Math.
They get to select any curriculum based on any methods and criteria they want, but they demand research-based proof before any change is accepted from anyone else.
Large school districts could provide a choice of at least 2 math curricula. They won't do that because they are in charge, it wasn't their idea, they don't want more work, and they don't want proof that they are wrong about the curriculum they are using.
The problem is not that we have to convince them that Singapore Math is better. We have to convince them that all students can do Singapore Math. We have to get them to set higher expectations for themselves. The problem is not with the kids, it's with the school.
I'll bet she was referring to Barry's article. Thanks for providing the link.
I can see how bar models alone would appeal to math curriculum directors -- they look like they could be a quick fix and everyone likes easy tinkering without having to look closely at the basic assumptions.
Still, even a mediocre version of bar model solutions would be preferable to doing guess and check. Eek.
Lynn,
another great article to include is from the Mathematical Association of America:
What is Important in School Mathematics
http://www.maa.org/pmet/resources/MSSG_important.html
The value of a mathematical education and the power of Mathematics in the modern world arise from the cumulative nature of mathematics knowledge. A small collection of simple facts combined with appropriate theory is used to build layer upon layer upon layer of ever more sophisticated mathematical knowledge. The essence of mathematical learning is the process of understanding each new layer of knowledge and thoroughly mastering that knowledge in order to be able to understand the next layer.
Thanks, ConcernedCTParent.
This is a great find. I know it is preaching to the choir around here.
Does everyone agree that lifting the bar models out of Singapore Math without adopting the programs can't help at all?
I'm inclined to think that bar models are better than nothing but I don't know and couldn't argue the point well (or even at all....)
This reminds me of Steve's point, in another thread, that drawing a picture is preferable to relying on charts....
If nothing else, bar models are a means of drawing a picture.
I guess I'll add that as I've been teaching myself math I've "instinctively" been drawn to the idea of drawing-a-picture -- and have often found I couldn't do it.
Motion problems (two trains leave a station) eluded me completely until I learned Saxon's mode of representing them visually.
I didn't spend a lot of time trying to work out a visual model; I might have come up with something if I had.
But nothing came to me quickly.
Sixth grade EM is in a mad rush to fix all of the problems they created in the previous years. For each new topic/unit, half the pages are math box reviews of earlier topics/skills, even from years ago. At some point mastery matters, and they are struggling to make that happen. They can't do it. How can you fix problems that are years old while learning new material?
I'm starting to think math can't be taught in our public schools as they are currently structured, period.
Maybe Saxon Math can do it, but that's the only curriculum I can imagine working. (I'll get a post up about this -- it's based on the fact that C. has a very good math teacher this year - 2 very good math teachers, in fact. The 8th grade has math 5 days a week and math lab 3 days a week.)
Does everyone agree that lifting the bar models out of Singapore Math without adopting the programs can't help at all?
It can help, sure, but using it by itself without integrating it into everything SM does is getting only half the story. You yourself said you finally understood what subtraction is about thanks to the bar modeling. It's more than a problem solving heuristic, it's also a means to integrate the concepts SM talks about (part/whole, etc). Bar modeling should also be used as the entree to algebra, rather than teaching kids how to use bar modeling to solve even more complex problems. After a while, bar modeling is extremely inefficient, and there are some problems that just can't be solved using the technique. Sybilla Beckman makes this point and advocates in her article that SM should introduce algebra in 6th grade. I agree. By 6th grade, some of the problems in SM are so complex that you spend a lot more time using bar modeling to solve them than you would if the natural transition to algebra were made. At that point, it's learning the fine points of training wheels, rather than learning to ride a bicycle without the training wheels. Or putting wheels on crutches.
But is it better than guess and check? No argument.
Barry says it all. "wheels on crutches"
"This reminds me of Steve's point, in another thread, that drawing a picture is preferable to relying on charts....
If nothing else, bar models are a means of drawing a picture."
I'm going to quibble a little bit. Charts and bar models might allow you to see things graphically for certain problems, but they are no substitute for algebra. The goal is not charting or bar modeling in 8th grade. Some reformists might grab onto bar modeling because their goal seems to be anything but algebra; i.e. concrete understanding, not abstract understatding.
When I talk about pictures, I mean that they should be used to help create the equations. I would prefer that bar models and charts be used to define the equations, not avoid them. After a while, students will go straight to writing down equations.
When I talk about pictures, I mean that they should be used to help create the equations. I would prefer that bar models and charts be used to define the equations, not avoid them.
That's how I was (attempting to) use them.
Lately I'm thinking that teaching math to oneself is different enough from being taught math by a good teacher that my experience isn't always relevant. This is just an impression at the moment.
In any case, I've had multiple experiences of trying to figure out how to solve a word problem, by which I mean set up an equation, pretty much on my own. No one ever taught me how to do it and I've either skipped ahead in the book, skipped to another book altogether, or found some problem online I've gotten hooked on (STILL HAVE NOT ATTEMPTED BARRY'S TENNIS BALL PROBLEM!!!).
When I can't see how to set up an equation I'll see whether I can draw some kind of model (any kind, not just a bar model) that will help.
I fairly often find that if I can't think how to set up an equation I also can't think how to draw a picture....but I'll have to pay attention to this in the future & see if my impression is right.
Lately I've been thinking I'm going to have to take an actual math course pretty soon here.
You yourself said you finally understood what subtraction is about thanks to the bar modeling. It's more than a problem solving heuristic, it's also a means to integrate the concepts SM talks about (part/whole, etc).
yes
absolutely
I also saw, probably for the first time, that when you have, for example, a ratio of 3:4, a whole of 7 is implied.
Gosh I wish I could remember the Comment someone wrote about doing a bar model problem with her daughter, I think it was -- was it Lynn???
Or Tex?
heck
Whatever it was she described was another moment of revelation for me....which I have either assimilated or forgotten...
In their approach to spiraling, they think nothing of giving a quick exposure to advanced topics and then jumping to another topic.
This is a chronic strategy amongst weak curricula and weak math teachers everywhere, I think.
All we get are questions about whether we (parents) feel comfortable with helping our kids with subjects at home.
You get that question, too?
I'm pretty sure that is a standard part of the Tri-State Consortium parent survey form that gets sent out in preparation for visits from the Tri-State folks. (At least, I believe the surveys are sent out in preparation for visits...)
I'm hoping most parents here answered "absolutely not" to that question.
That was my answer.
One of the things that bugged me about the Tri-State survey was that it asks whether you've hired a tutor but doesn't ask whether you are reteaching courses at home.
I find that irresponsible wording in the case of Math Trailblazers, a K-5 curriculum.
I think many or most parents here can reteach K-5 math at home without having to hire a tutor.
Ed spent C's entire 4th grade year reteaching math at night when C. tried to do his homework and had no idea how to proceed. He never mentioned this to the school, just accepted that this was his job as parent.
His brother seems to have re-taught math to both his kids (now in college) throughout their entire school careers.
They attended a public high school that has a high rate of acceptance to Ivy League colleges.
I'm close to certain he never mentioned this to the school, but saw it as a normal part of having kids in school.
[I also saw, probably for the first time, that when you have, for example, a ratio of 3:4, a whole of 7 is implied.]
A nice little ratio exercise is to make a figure with, say, 6 squares and to shade some of them, e.g. 4. Then ask the students to make as many ratios as possible from the figure. There are six possibilities. This should get the idea of the whole across.
Many things bug me about the Tri State Consortium.
The survey is virtually useless, costs a lot of money, and schools could have accessed the sample on line for FREE.
The visit is announced much too far in advance, the schedule for that day is completely altered to impress the "critical friends" visiting that day, and is, from what I have seen, very much different from an actual school day (they save the flashy stuff for that day).
Finally, the schools they are comparing themselves with are too similar to be of any constructive use at all.
We don't need to compare our schools to schools like our own, we need to compare our schools to schools that are better, different, and that challenge the existing belief system in our district, state and nation.
We need to compare our schools to top performing schools internationally.
It's time to think globally.
"Critical friends" are not global at all.
A nice little ratio exercise is to make a figure with, say, 6 squares and to shade some of them, e.g. 4. Then ask the students to make as many ratios as possible from the figure. There are six possibilities. This should get the idea of the whole across.
That's a great idea!
I could be the poster child for what an entirely procedural math education looks like -- both for what's bad about such an education and for what's good about a procedural education.
As I've said many times, I've always been able to use math to function in the day to day -- and when I needed to learn more math I could do it.
Not only do it, but teach it to myself (with some success, I think).
"Critical friends" are not global at all.
I still remember the first time I heard the "critical friends" line.
How much does it cost to do this???
I had the impression it wasn't a paid-for undertaking --
In colleges people do this kind of thing for free. (I'll check with Ed, but I'm pretty sure evaluating other people's professors &, at times, programs is considered part of one's professional responsibilities.)
Annual Dues: $6,000
Visit Fee: 6,000
Follow Up Visit: 1,000
Consultancy Fee: 1,000
District Team Training: 150per
Regional Team Training: 400per
etc.
http://www.tristateconsortium.org/Intranet/Fees07.doc
Critical Friends are a bunch of people who consider themselves peers, think alike, and find some value in patting each other on the back.
Unbelievable.
I had just assumed this was a professional association & hence free.
What a load.
So our Critical Friends cost us $15,000.
And none of these Critical Friends is a college professor.
or a content specialist
calling Richard Elmore
The Brentwood School, in L.A., asked Ed to evaluate its history program.
I just asked him whether they paid him; he doesn't think so.
"If they did, it was a token fee."
Evaluating other programs is a professional responsibility.
I have to go look up "Critical Friends".
http://www.educationworld.com/a_admin/admin/admin136.shtml
http://www.nsrfharmony.org/faq.html#1
How is this related to accreditation?
Out here in the west, we have two levels of accreditation for private schools:
Western Association of Schools & Colleges (WASC)
http://www.wascweb.org/
The Western Association of Schools and Colleges (WASC) is one of six regional associations that accredit public and private schools, colleges, and universities in the United States.
Here's the URL for the criteria for accreditation
http://www.acswasc.org/about_criteria.htm
and the California Association of Independent Schools
CAIS
http://www.caisca.org/accred_overview.asp
The school I'm most familiar with was new, so had separate accreditation processes for WASC and CAIS. I think eventually you get on the same calendar.
Both WASC & CAIS charge membership fees, but I don't think they are as high....
And the "visiting teams" for accreditation are not compensated--it is part of your professional duty to serve on a team.
The Tri-State Consortium is a learning organization devoted to assisting its member public school districts in New York, Connecticut, and New Jersey in using student performance data to develop a rigorous framework for systemic planning, assessment, accreditation, and continuous improvement. As critical friends, we advance teaching and learning and share best practices among member districts through the application of the Tri-State assessment model.
This isn't related to accreditation. They consult with high SES public schools in the tri-state area.
http://www.tristateconsortium.org/index2.html
Liz, thanks for those links.
It looks like someone took the idea of a Critical Friends Group from the Anneberg School and found a way to make some money with it.
I know our district has been participating for at least a few years.
That adds up. But does it make a difference? I don't really see think so.
I was led to believe (by a parent, not an administrator or teacher) that it was a privilege to be allowed to join the TriState Consortium.
"Perhaps you've heard the buzz about CFGs! This week, Education World takes a close-up look at CFGs -- what they are and what they hope to accomplish."
(STILL HAVE NOT ATTEMPTED BARRY'S TENNIS BALL PROBLEM!!!).
Thanks for letting me know. I was going to send you a holiday greeting asking whether you've done it yet, but you've saved me the trouble!
I'm developing a phobia.
That probably means I should just go find the problem and do it.
Phobias are bad.
"A tennis ball can with radius r holds a certain number of tennis balls also with the same radius. The amount of space in the tennis ball can that is not occupied by the tennis balls equals at most the volume of one tennis ball. How many tennis balls does the can hold?"
OK, I'm off.
I couldn't resist a problem like that. The answer I get is two. I wonder if Barry can confirm. I don't totally trust my skills. Conceptual, procedural and computational errors tend to creep in.
drat
I keep getting 2 when I set it up as an equation, but it seems as if the answer ought to be 3 "logically."
oh wait!
I'm mixing things up
The 1/3 that's left over isn't 1/3 of a tennis ball. It's 1/3 of a cylinder with the same radius as the tennis ball.
The answer is 2. Correct.
If the can only held one tennis ball of radius r, the can would have a height of 2r since the can has same radius as the tennis ball.
We don't know how many balls it holds, so let x = number of balls.
Now you can solve for x by setting up equation as:
Volume of can of height 2r and radius r - x *volume of ball of radius r) = volume of ball of radius r.
Kudos to Catherine and Instructivist!
Happy new year to all.
Hi Barry!
I see I've wild-goose-chased it...
Where did you get this problem?? I've forgotten...
Also, I remember you telling me to look at a Dolciani section.
I'm going to look at my email queue.
That's the difference between instructivist & me.
I was able to resist this problem for months.
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