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Elementary math textbook adoption: Reactions to Wed. night meeting
Original post made
by Concerned Parent, Another Palo Alto neighborhood,
on Feb 25, 2009
The debate on what math textbook program Palo Alto schools should adopt continues with differing viewpoints on last night's Information Meeting. The school board is scheduled to make a decision on April 14.
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Posted by Mandy Lowell
a resident of Crescent Park
on Mar 2, 2009 at 11:01 am
Division-EDM does not give kids a good grasp of numbers, which is why by fourth grade, some students, have to do several steps to see that there are 3 12's in 38 or 8 7's in 57. See examples below. And rather than suggesting that students should do more problems to become nimble with numbers, EDM advises that "The student would reach the answer in three steps rather than two. One way is not better than another."
The actual layout cannot be reproduced here, but just examine the books and lessons yourself to make your own judgment.
In dividing 7/127, after subtracting 70, 57 is left; EDM appropriately offers the next step is to find the number of 7's in 57. EDM gives "two ways to do this." One is just to use the "fact family" that 8x7 is 56; the other is to use "easy numbers, " "are there at least 10[7's] in 57? No….Are there at least 5[7's]? Yes" then put the partial quotient 5 to the side, "subtract 35 from 57" leaving 22, in which there are 3 [7's], so put the third partial quotient of 3 to the side; then add the partial quotients 10+5+3 to get 18. (EDM p. 414.)
Were this just an example using easier numbers to handle, building up to understanding of division, there would be little concern. That, however, is not what EDM says. In a similar division lesson, when the student is using the partial products algorithm to divide 158 by 12, and encounters 38, EDM advises that the student can ask " how many [12's] are in the remaining 38?" The manual explains that "some students might know the answer right away (since 3[12's] are 36.)" EDM then gives an example the 4th grader tries 2x12, puts a 2 partial quotient to the left, then tries another 1x12, then adds the two partial products, etc. EDM tells the teacher that "the student would reach the final answer in three steps rather than two. One way is not better than another." As a way to understand how to break larger divisions into smaller ones, this type of example is not bad, but the concern is that EDM does not aim to move students to more efficient handling of numbers.
EDM lauds partial quotients because "students can use numbers that are easy for them." (EDM 4th grade, Teacher's Ed. P. 394.) Much of EDM is based on the notion that kids should work with the easy multiples2, 5, 10 and powers of ten of these. Warning teachers to watch for students who use only multiples of ten, EDM advises teachers to "suggest [they] first compile a list of easy multiples of the divisor as appropriate." This is for 5th graders :for a problem of 6/1010, the students would "make the following list: 200x6 =1200: 100x6=600; 50x6=300; 20x6=120; 10x6=60; and 5x6=30." "remind students that listing the easy multiples in advance allows them to focus on solving the division problems, rather than looking for multiples." (See 5th grade TE 250-52). The 5th grade Math Master has a sample charts for 5th graders to list multiples of 1000, 100, 50, 20, 10, and 5.
Again, if this were a bridge to demonstrate to students underlying concepts of how division of larger numbers works, and then to condense several steps into one step with a more efficient procedure, there would be little clamor. EDM validly wants students to learn the California standard of "when and how to break a problem into smaller parts." But breaking into 2's, 5's and 10's problems that are otherwise relatively simple math manipulations if one knows 3x12=36 hardly lays a solid foundation of working with numbers.
The California Math Frameworks notes that by 5th grade "students should know all the basic facts and be able to recall them instantly." (CDE CA p. 157.) While Everyday Math claims to teach basic facts, the problems offered in 4th and 5th grade, imply that the EDM either does not succeed or does not consider it sufficiently important for students to have mastered the essential multiples.
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Posted by Mandy Lowell
a resident of Crescent Park
on Mar 9, 2009 at 10:04 pm
Some people have asked what Everyday Math Spiral means. Isn't that "review?" Not exactly. IN maninstream programs teachers work to get students to master a concept or skill, through teaching and solving problems, assess to see whether the student can apply the concept to solve problems, reteach and practice more if necessary. One may later quickly review the already learned material, perhaps implicitly. For example, using a mainstream text, in reducing 7/21 to 1/3 or 6/42 to 1/7, a student is reinforcing multiplication facts and the concept of division being related to multiplication.
So what is Everyday Math's spiral? See how their materials explain it.
Here are excerpts from EDM handouts that the district distributed at the Math Committee meeting:
copyright 2001 Education Development Center, Inc.
This has been difficult for teachers, because they are accustomed to pedagogic
procedures in which you bring up something, then teach and test to "mastery," all
within a fairly short time. What we want teachers to do is to bring it up, drop it,
bring it up again, let it go, bring it up again, let it go, and then at some point, aim
for mastery. That's built into essentially every part of our program. Teachers have
to be aware that they will seldom push something on to mastery the first or second
time the kids see it. It's one of the things about Everyday Mathematics that is
strange and difficult for both teachers and parents. But it does work well and will
remain a feature of our program. . . .
The spiral curriculum is one of the hardest things for teachers to adjust to. When
I work with teachers, I tell them, "You need to have the faith that the children are
going to see it again. Don't be afraid to leave a concept, don't expect mastery right
away." I think the teacher at the outset has to talk to her class or his class and
explain to the children that, "We don't expect you to learn everything the first time we teach it. You're going to see things over and over again and you might not
understand it the first time, and that's okay." For your high-achieving students,
that can be very difficult. They've always been able to pick something up the first
time they've been taught, and all of a sudden some of the high-achieving students
are not the high-achieving students, and that's very, very hard. We have to constantly
remind the kids that it's okay not to have complete comfort with this: "Don't
worry, you're going to see it again."
. . . .
With the spiral curriculum, when a child is just not understanding a concept, we
don't spend day after day after day on that same concept with the child feeling
worse and worse and worse every day because they're just not understanding it. If
a teacher is explaining to a child, "We're going to see this again. Don't worry about
it and let's move on," that's comforting to a lot of kids. If they hear, "I don't have
to know this right now. I'm going to see it againthe teacher's not worried that I
don't know it right now," and then move into something that the child can be successful
at, then the child's attitude towards math becomes much more positive. On
the other hand, one of the weaknesses of the spiral that I seeand this is related
to its strengthsis that we're constantly changing topics, and that sometimes is frustrating for children and teachers." End of excerpt
Here is a typical district's instruction to teachers about mastery in Everyday Math:
"Please review the Management Guide in the Teacher's Reference Manual for assistance. Remember, Everyday Mathematics is a spiraling curriculum with repeated exposure to objectives throughout the year. If teachers are struggling with the pace, they may be trying to teach to mastery instead of "trusting the spiral". "
Resume comment--In evaluating whether Everyday Math is good for your student, you should consider whether your student enjoys repeating material in successive years, and whether if your student would be better off revisiting partially learned material in the following year, or as in a more mainstream text, would benefit from teaching, practice and reteaching until mastery. I do not know PAUSD teachers that just "move on" after one lesson, so this is not saying that mastery is expected in the first lesson. but in a mainstream text there is a sense of assessing to see if the concept can be applied, and not just moving on whether or not the child seems to have learned. Mainstream texts view math as more sequential, later material building on earlier learned material. In history, one can understand US History without learning about Greece and Rome; with math, it is harder to learn Algebra if you have not mastered the Distributive property. Also, students can have gaps that go undetected.
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Posted by Ze'ev Wurman
a resident of Palo Verde
on Mar 12, 2009 at 1:53 pm
Warning: Long post.
Yesterday superintendent Skelly asked for a straw poll about the math textbooks, which eventually never took place. Today I want to provide Mr. Skelly with what would have been my vote on that poll and, because the medium allows it, with some of my key reasons for it.
A fist: Everyday Mathematics. (EDM)
Why? The program has three major issues.
(a) It spirals, never teaching to mastery. It does not provide sufficient practice, and it assumes mastery will mostly happen through osmosis. The belief in spiraling forces EDM to have a fractured and incoherent flow of topics day by day and week by week. The National Math Panel clearly said that this doesn't work, and recommended a "focused, coherent progression of mathematic learning, with an emphasis on proficiency on key topics" and that "[a]ny approach that continually revisits topics year after year without closure is to be avoided." Everyday Mathematics is anything but.
(b) It avoids teaching standard algorithms. The California version is essentially identical to the national version, with few additional pages slapped on in student reference book, to satisfy Calif. demand for teaching standard algorithms. The teacher edition focuses exclusively on EDMs idiosyncratic algorithms, never addressing the standard algorithms except through a sidebar "balloon" mentioning only that they exist, and that "Some students may prefer to use this method [standard algorithms]." Teaching the four arithmetic operations is a major topic in elementary mathematics, and EDM will need major supplementation if selected.
(c) It has no real student textbook that can be used to help students and parents at home. What is has is a disjoint collection of topics, which the publisher himself calls a "Student Reference" rather than a textbook. It may help with extra practice, but it doesn't really help a parent to understand what is going on in the classroom, what has been taught last week, or what will be taught next. The need for a textbook that allows parents to help their children came up strongly in yesterday's meeting.
Two fingers: envision Math (EVM)
Why? The program is quite decent, but it is not great. It has an OK mathematical progression, even if not too cohesive, and it has a much better practice. The major reason it gets at least two fingers is because it represents what we already have and perfected over the last 6-7 years. So we know we can handle it without major disasters, even if our mathematics achievement in elementary schools could be much better, particularly for children from challenging background.
Five fingers: Singapore Mathematics (SGM)
Why? It is unquestionably mathematically the strongest and the most cohesive program, with effectiveness proven in variety of situations: rich schools and districts, private schools, demographically diverse schools and districts, and even home schools. It is praised by traditionalists and reformers alike, and both sides agree that it develops skills as well as exceedingly strong conceptual understanding and problems solving.
If this is the case, it may help to consider why SGM was not considered as one of the top contenders in Palo Alto. From my discussions I believe the concerns turned around (a) "only one style of teaching," lack of opportunities for differentiation, and lack of support for English Language Learners (ELLs), and (b) requires stronger math preparation of elementary teachers.
(a) SGM is a program that works well for a broad spectrum of abilities in the classroom. With SGM the teacher typically does not need to worry about bright kids being bored, or about weak kids being left behind. Consequently, it does not need the abundance of tips and suggestions that average US textbook offers to teachers to deal with "struggling kids", "kinesthetic learners" or "high achievers." Most of those tips are generic and worthless in any case, but many teachers came to expect them and interpret their absence (incorrectly) as lack of differentiation, or lack of support. Similarly, lack of SGM support for ELLs is sometimes cited, but SGM is much less language-based and more mathematics based, and it does not need special "ELL interventions." I happened to follow piloting of SGM in two schools in DC over the last two years. One was a majority Hispanic minority black school, the other was a Spanish immersion school, and the issue never rose. On the contrary, the teachers were complimentary about how accessible the program was for kids with limited language skills.
(b) SGM is made up of longer topical units than is customary with typical US textbook. In SGM the topics are bundled into cohesive units that take few days to few weeks to teach. This promotes focus and cohesion as recommended by the National Math Panel, and is in stark contrast to other textbooks that jump from topic to topic. However, this is often misinterpreted by many teachers that are used to the jumpy style as "boring" and "one way of teaching."
SGM does require stronger mathematics understanding from teachers. With SGM the focus is on mathematics, and teachers are expected to prepare much more of the lesson plans than they are with regular textbooks. This turns off some teachers that expect predigested plans for every day. What they often miss is that preparing the lesson plans causes teachers to understand in-depth the material they are teaching, and become ready for any question they may face in the class. This does not happen when the lesson plans are predigested. I also don't think this concern should apply to Palo Alto anyway, as we always have been proud that we hire above average teachers. If teachers in Los Angeles or D.C. can handle this knowledge, surely our teachers can too.
In summary, I think that the committee may have been turned off by the unfamiliar look of the Singapore program. I believe that if we were to seriously pilot it for few monthsideally at one elementary school for a full yearwe would all become convinced of its advantages, and the math issue would finally be gone from Palo Alto.
Turns out that we do not have to adopt this yearbecause of the budget crunch, the state just allowed anyone to extend the adoption for another two years. So now we have a chance to adopt the best program around that is praised by all sides of the issue, and save ourselves a chunk of money in the process by delaying the adoption for two years. Sounds like a win-win to me.
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Posted by Experienced Mom
a resident of Midtown
on Mar 17, 2009 at 6:43 am
Yes, Singapore Math and any of its "peers" usually teach one way, maybe two, to approach a problem. Yes there is little room for "explaining strategies". Yes, these programs DON'T spiral..on purpose.
There is a reason so many of the high end private schools and tutors use a regimented program such as Singapore Math. Math is learned and processsed in a different way from language based subjects. Except for the brightest, or the kids who are quite good in expressive language ( for example, elementary school girls), math that isn't taught in this way simply confuses them, and fails to mortar in the bricks needed for the foundation that LATER, around 7th or 8th grade, a kid can begin to build on for the language based expresssion of strategies, and the learning multiple paths to the same end, and the "connecting the dots" spiraling that are,indeed, critical to higher math. For example, about the time boys begin to develop their expressive language abilities and their "connecting the dots" abilities.
In the meantime, we have kids who are good at the numerical portion of math classes in elementary and 6th grade who are struggling because of the language-based requirements in homework and exams ( explain how you arrived at your conclusion? is different from "show your work mathematically"), not nailing down the basics of math basics, and developing an aversion to math since it is a constant struggle for non-high language skilled learners.
I suspect part of the problem is that we have highly skilled language based people ( teachers, volunteer moms ...sorry, not to be sexist, but women in general are much more verbal, and also do better as girls with these language based circular thinking math programs, PhDs in Education, Marketing, Attorneys etc)trying to make decisions based perhaps on what they wish they had had in school,or what makes sense to them, not based on statistical results, and not on what works for the future mathmeticians of the nation.
What is the goal of math teaching? Those who will not go past high school or past a year or so of math in college..need a strong basis in math for everyday functioning and good citizenry. So, making it to a solid micro-macro Economics class for example in high school would be a good outcome, and provide enough math for financial transactions, life planning, wise voting etc.
For those who catch on fire in math and want it to be an integral part of their careers, they need a great basis so that they can catch on fire before Junior year or so, so they can apply to the math based programs in Universities that can provide them the kind of math education they want.
In either case, circular, language based, strategic but non-"math fact" memorization, elementary school math programs do not serve either of these groups well, based on outcome measures, but if we really think our kids are different, why don't we find out?
Let's find out how many of our kids who successfully completed a Junior year Math AP had ONLY our elementary/middle school programs in math. If most of them did, then there is something about our programs that works. If most of them had tutors or went to a private school through 6th or 7th grade..well..that is good information to have.
As for "disrespected teachers"..I think that whoever is feeling "disrespected" is going to have to realize that this isn't about any teacher or group of teachers, and any sensitivities in that direction have to be re-directed toward what this is abouut.
This is about MATERIALS and consistency. This is about giving our kids the best tools possible to achieve their goals, and giving teachers the best tools possible to achieve their goal, which is presumably to give the kids the best tools possible to achieve THEIR goals.
This is about looking at outcome measures and applying logical thinking to a decision about which materials work best for the most kids.
This is about elementary school teachers, educated and perhaps even gifted in methods of education for the young person, listening to those who have become highly educated in math fields, such as engineers, mathmeticians, physicists, statisticians, physicians ( who aren't normally in the "math" group of professions, but who had to get through AT LEAST a year of college calculus to continue to med school, so I include them) and others who have gone much further than college algebra and know what our kids need to master in order to keep their choices open to them later in their lives.
We, as parents, have seen what happens with "laning" to the kids, and see how by 7th grade they are separated out, rightly so in my opinion, into the "higher" lane and the "lower lane"..so the basics for math must be acquired before 7th grade to keep our kids' doors open.
Obviously it isn't the end of the world to be in a "lower lane" math option, and obviously a kid could still conceivably catch on fire and "catch up" by Junior year so that his post-high school options open again, but it certainly makes it more difficult for a kid in the lower lane to end up becoming an astrophysicist if that is what he would have really been happy doing.
So please, don't get caught up in the defensive, turf-ishness of this stuff, keep focus on what we ALL want, which is OUTCOMES.