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Monday, October 15, 2007

Math Conference

This article on a math conference was in today's Times. From the article,

"On Thursday, panelists from local companies talked about what kind of math skills they were looking for in job candidates." Unfortunately, the reporter didn't say what these panelists discussed beyond math being important.

Also:

"With the outside review as the basis, the Office of Superintendent of Public Instruction is working on revisions to state math standards, which will be presented to the Legislature by the end of January.

Math is the main thing on our radar screen," Bergeson said. "We have to make a course correction." And that means including more math basics, and making sure students know how to conceptualize math problems, as well as the basic algorithms and math facts to solve the equations.

The state and school districts also have to help parents understand what their children are learning in math, Bergeson said. Too often, children come home with math homework that parents don't recognize because it doesn't include standard algorithms for solving the problems.

"If parents can't help their kids with their homework, we're cooked," Bergeson said. "We have to build bridges to parents. We use all of our education babble, we use words that ... have deep meaning to us, but if a person doesn't understand the context, they won't have a clue what we are talking about."

No kidding.

41 comments:

Dan Dempsey said...

From: Dr. James Milgram of Stanford University
Date: Thu, 11 Oct 2007 09:04:29 -0700 (PDT)
Subject: Re: More info on House Science and Technology Committee's hearing held on Oct 1

As both one of the main designers of the focal points and one of the two main reviewers of the completed document for NCTM, let me assure you that anyone who suggests that the Focal Points support the use of crap programs like TERC is blowing smoke.

On the other hand, they are emphatically not a call for "return to basics" if, by that one means the math programs in the country from 50 years ago. What they actually are is an attempt to try to align instruction in this country with what is actually done in the high achieving countries. They focus on the key topics and develop them to great depth. They also require students to solve many, many increasingly more difficult problems in these Focus areas.

Absolutely none of the NSF funded curricula do this.

Jim


So Dr. Bergeson has been headed in the exact opposite direction for years and continues to still be headed in that direction despite the attempts from the legislature and the State Board of Education to alter these failing plans.

Seattle mindlessly follows Dr. Bergeson to the detriment of our children.

Will Ms. Santorno ever reduce the incredible number of topics covered in the Everyday Math pacing plan to something that can be effectively taught and learned?

Dan

Dan Dempsey said...

OSPI Actions Raise Conflict of Interest Concerns Regarding the Review of State Math Standards

Recent actions of the Office of the Superintendent of Public Instruction (OSPI) are undermining the intent of the Washington State Legislature to objectively review and revise math standards and curricula in Washington State. In September, OSPI announced that it had selected the Dana Center of Austin, Texas to revise Washington math standards. Unfortunately, the Dana Center has serious conflicts of interest and a history of promoting failed reform math approaches.


You can find the rest at:
http://www.wheresthemath.com/blog/

Dan Dempsey said...

Is Bellevue doing any better?

For Black and Hispanic students NO!!

White students test scores are higher than Seattle's White Students but how does that occur?

For a partial explanation watch the video at:

http://www.wheresthemath.com/blog/video/

Anonymous said...

With CMP I haven't been able to help my kids with math homework for ages now.

We're not "cooked" but burnt toast.

Anonymous said...

No offense, Dan, but why don't you just start your own blog rather than monopolizing this one? As I math teacher for just as many years as you, and as a Stanford grad, I totally disagree with your comments and Dr. Milgram's.

If you have never taught the TERC Investigations curriculum, you can have no idea of the amazing conceptual development that occurs for children in the program. In order not to totally turn students off to math at a very young age, kids need to be able to explore and learn rather than memorize and recite.

I'm not at all against students developing speed and facility with math facts and algorithms. What I am against is assuming that methods used to teach math in the 40's will work well with our current students or that the math of the 40's is what today's students will need to solve problems that we have not even imagined yet. I want to develop a generation of learners who are interested in math and know what to do to figure out something that they don't immediately have the answer for.

Let's face it. One of the reasons that most parents say they can't help their students with the math homework is because they didn't develop good problem solving skills themselves. It's also been viewed as OK for parents to say "I was never very good at math" which they would never say about reading, thus communicating to their own children, so get it, some don't.

Give it a rest, Dan.

Dan Dempsey said...

Liping Ma,
author of Knowing and Teaching Elementary Mathematics,

said.....
that Chinese students find algebra to be very easy, because they have had such a solid foundation in arithmetic.

The OSPI and SPS idea is clearly not to follow Liping Ma.

Perhaps that is why we find 50% of recent high school graduates at Seattle Central Community College unable to start above the High School Math 1 level.

Washington State ranks as #49 in the nation in State University attendance and #5 in community college attendance.

Dan Dempsey said...

Anon Stanford grad at 2:07 PM said:

What I am against is assuming that methods used to teach math in the 40's will work well with our current students or that the math of the 40's is what today's students will need to solve problems that we have not even imagined yet.

I am also vehemently against that.
Given Multiple choice of:
a) Traditional Math
b) New math from 1960s
c) Reform math like TERC CMP IMP
d) International Standards

I pick "d"

Interesting that Milgram says the NCTM Focal points are:
...emphatically not a call for "return to basics" if, by that one means the math programs in the country from 50 years ago.


Now that we have established that the traditional math should be gone, perhaps more people should pick up a Singapore book and find out why our mathematical tails are being kicked.

Available from:
www.singaporemath.com

Take some time to read "What is Important in School Mathematics?" from the NSF funded Mathematics Standards Study Group (2004). It is only 8 pages.

Read the State Board of Education funded consultant's Review and Recommendations for the State Math Standards.

Since 9/11 it has become increasingly difficult for technically talented foreign students to come to US Colleges and more importantly graduate schools. It is also more difficult to remain in the USA after graduation. Is that new Microsoft campus in Surrey or Abbotsford BC?

Check out the following:
http://www.crosscut.com/mossback/7919/

The Scientific Dark Age of George Bush by Ed Lazowska

----...Obviously, there is a huge pipeline issue. Eighty-five percent of our undergraduates in UW computer science and engineering are from Washington state, and they are mind-blowingly good. But that's only about 150 students a year. Kids, by and large, don't come out of K-12 prepared or inspired to pursue careers in science and engineering.

With the advanced thinking of TERC and CMP supporters it appears likely we can fall further out of international competition.

Roy Smith said...

dan dempsey said ... Kids, by and large, don't come out of K-12 prepared or inspired to pursue careers in science and engineering.

With the advanced thinking of TERC and CMP supporters it appears likely we can fall further out of international competition.


I suspect that this has little or nothing to do with the math curriculum, and much more to do with the fact that much more prestige, money, and power accrues to business school graduates than to engineers and scientists. In Japan and Germany, engineers get more respect than managers. The reverse is true here.

No offense, Dan, but why don't you just start your own blog rather than monopolizing this one?

Or at least stop replying to yourself. It gets rather old to read 4 comments in a row by "dan dempsey". If you've got multiple things to say, why not condense them into one comment?

It's also been viewed as OK for parents to say "I was never very good at math" which they would never say about reading, thus communicating to their own children, some get it, some don't.

This attitude (which I have seen plenty of) also communicates to kids that math isn't important.

Anonymous said...

This whole math thing really isn't that hard, but when you toss in all the philosophical and ideological baggage, you get the mess we're in now.

First, let me be completely clear that there is valid content in TERC Investigations. About 5% of the subject matter. The rest is garbage - busywork, art projects, and writing assignments. If you are a mathematically inclined teacher, one could turn this lemon into something sweet, but why bother.

CMP2 is much better. It has about 15-20% of the subject matter which is grade-appropriate and mathematically rich. In this fine textbook series, we spend many of our glossy color pages describing how to operate a TI calculator, or including pages from a world atlas. The district should save their money.

Keep it simple. Look at the 3 pillars of education: teachers, curricula, and family support. In the perfect scenario, we would have teachers with strong content knowledge in their subject areas, concise, relevant, and accurate teaching resources, and active family support in the classroom and at home. We don't always have that wonderful combination, so we owe it to our students to constantly improve all three pillars to the best of our ability.

However, when the district chooses curriculum materials which weaken the other two pillars (familes & teachers), that is unconscionable, yet it happens regularly. CMP2 is so obtuse with its pseudo-mathematical open-ended questions that parents are helplessly lost. Teachers with poor math content knowledge (=most in elementary school & many in middle school) are immediately placed at a disadvantage to effectively deliver the content. As a result, we follow our expensive purchase of bloated textbooks with more money for the publishers to come and "train" our teachers.

You don't need to be a gourmet cook to bake from a well-defined recipe. A mathematically sound program (Singapore, Saxon, Harcourt Math, etc. but NOT TERC, Everyday Math, CMP2, etc.) is that recipe which helps instructors and parents shape and develop their students' math expertise.

It's not that hard. There are lots of people who make money by making this issue harder then it is. Look for and apply the simple answer and the kids and district budget will both benefit!

Anonymous said...

Let me say that I am NOT a math teacher, and not a math expert in any way, so I'm not defending or supporting CMP or any other math curriculum. What I want to say is that I have two children that attended SPS. My oldest went to an alternative school and though I was concerned about math being less than rigorous, I stuck it out. I was never really sure how much he was learning or if he mastered what he learned. I do know that he was able to do a lot of complex math in his head. He used a lot of reasoning, rather than pen and paper. This year (7th grade) in a different district that uses a much more traditional approach to math, he was assessed and it was determined that he was well above grade level. They bumped my 7th grader up to 8th grade honors math and he is doing well. This tells me that there was some merit and value in the math instruction that he received all of those years. Even our little, sometimes less than rigorous, alternative school.

Anonymous said...

Anon Stanford grad at 2:07 PM

I'm in my fourth year of teaching math in schools with > 35% non english home languages and > 40% free and reduced lunch.

I've tried to be open to the new stuff, as I thought there were definitely problems with how I was taught math 30+ years ago. I really like a lot of the problems in the CMP booklettes.

Over 75% of the kids I've taught have little to ZERO chance to compete with the affluent kids of lexington or newton ma., palo alto CA., ... never mind our 'affluent' enclaves out here in the northwest.

here are 2 math facts for you.

1. kids without basics can't do your cmp fuzzy stuff.

2. the credentialed crowd that has waved its magic powerpoint wands to prove that group work and cooperative learning and hetergenous classes ... solve all problems, well, except for the incompetent teachers, has failed miserably, other than staying employed to screw things up.

how any of you could look in the eyes of my struggling and stymied with basics high school kids, and sleep at nights, is a testament to ...

mastering doublethink?

anon at 4:44

Dan Dempsey said...

Roy,

The opening statement that you attribute to me is from Ed Lazowska of UW Computer Science a distingushed professor.

It was said: why don't you just start your own blog rather than monopolizing this one?

From Wikipedia:

A monopoly (from Greek monos, one + polein, to sell) is defined as a persistent market situation where there is only one provider of a product or service, in other words a firm that has no competitors in its industry. Monopolies are characterized by a lack of economic competition for the good or service that they provide and a lack of viable substitute goods.

I have labeled all my comments with my name so you are free to easily skip reading them.

I appears that there is plenty of time and space for others to use -- So hardly a monopoly.

Roy said: If you've got multiple things to say, why not condense them into one comment?

Each posting contained separate content that I thought would be best posted separately.

Anonymous said...

Get your own blog, Dan. You repeat what you say over and over and over and over again. It really is TIRING

Dan Dempsey said...

Anon at 5:05,

Rather than advocating for suppression of speech --- stop reading. I am not disguising anything under a different name, how difficult is it for you not to read my postings?

Anonymous said...

Spent the evening trying to solve 4th grade Everyday Math homework.

The problem told the student to "use the strategy Mrs XX used..."
OK, so what was that strategy? Looked in both books, no strategy to be found. Invented our own, which meant he had to do long division, which he has not been taught yet.
Pulled out the calculator.
Parent problem solving at its finest.

Anonymous said...

Interesting, because we have a 4th grader at Bryant. His homework tonight was three digit subtraction, the old fashioned way.

509
-299

I must say that it seems like this group of very bright kids could be doing much higher level math, but I must say that I am very happy to see a traditional approach.

Anonymous said...

My 4th grader is (at this moment) freaking out over rounding numbers to get a ballpark estimate. She insists on rounding to the closest ten (even for large numbers) and insists that is what she is supposed to do. There is no definition of "ball park" anywhere in sight. She doesn't believe us when we tell her 'ballpark' can vary with scale. She is having no trouble whatsoever with the fairly traditional three digit subtraction of the base problem, but believes she has to do the 'ballpark estimate' in her head (even if it is 5610-2720) because it is an estimate.

sigh

Anonymous said...

Anonymous at 738 here again...

Yes, our child had to estimate the answer too. He said he was told to do the math in his head, and make his best guess. He did very well. No frustration, he felt it was like a game, or a fun challenge.

Angeline the Baker said...

Now that we have Everyday Math, my second grader wants to know why she has to do this baby 1-digit addition homework when at the end of last year she was beginning multiplication.

She has also had difficulty with the ballpark estimating, when the actual correct answer is obvious to her.

Anonymous said...

Yes, I feel as though we have taken a HUGE step back. We were doing much more advanced work last year in third grade. My child (now a fourth grader) had homework a couple of weeks ago that asked him to identify numbers around our house. Yup you heard it right. I hope it gets better than this, and quickly.

Anonymous said...

If you think this elementary school math is bad, please take a look at the IMP series for high school. The table of contents occurs by Day. No mastery required, just another sunrise and sunset and it's time for another lesson. The amount of white space is at least as great as the white space surrounding this blog page on my screen. There are very few number anywhere; no variables either.

Anonymous said...

To the writers who've lamented here the level at which their children's Everyday Math is being presented - I went to a Math Night for parents put on by Olympic View and Daniel Bagley last week that was pretty useful to understanding the approach a little better.

(Please no dan dempsey diatribes, or screeds from people telling me why Everyday Math is an abomination - you may be right, but at this point, I just don't care - it's been adopted, my children are being taught that way, and I'm going to help them.)

In any case, I heard both the Olympic View math coach and the 5th grade teacher whose classroom I attended say that the curriculum, particularly in the "Math Boxes", incorporates review of past concepts as well as preview of future concepts, including ones the children may have no formula or approach for solving.

Again, I have no way of knowing whether this approach is appropriate, but right or wrong, I wish the district would put some information out there to enable the family involvement that is now vaunted as so critical - to inform parents and set expectations about how and what the curriculum is expected to deliver.

It's possible to put the Student Reference book (which explains the concepts) on the internet, and families are supposed to be getting letters at the beginning of each unit to describe what's going on.

Rosalind Wise, Carla Santorno, Bridget Chandler, Dr Goodloe-Johnson - are you there? I want to support you and this curriculum.

Anonymous said...

I second anon @ 2:07 - dan dempsey, please get your own blog.

Anonymous said...

Ultimate Fan, and other supportive parents,

Kudos to you. Your students will do fine, since you will provide the safety net for your kids. I'm in the same boat where nightly, my daughter and I cover the math content that is not provided by the CMP2 program. Duly explained, we then try to link that content to the textbook lessons and classwork which seems completely unrelated, but is actually connected by a thin, mathematical thread that the students are expected to discover.

Ultimate Fan stated:
I wish the district would put some information out there to enable the family involvement that is now vaunted as so critical - to inform parents and set expectations about how and what the curriculum is expected to deliver.

In reality, Everyday Math and programs like it perpetuate the achievement gap. Consider that parents need to to get involved to understand the program, help at home, come to Math Night, etc. Is this reasonable to expect disadvantaged students to have the same level of (necessary) family support. Those who can support their students will do so. those who cannot, will see their kids slip beneath the achievement gap.

Simple idea: Teach the content in the classrooms, so the parents don't have to do it at home.

If you have concerns about the current math programs, let the district know. Tell Rosalind Wise, Carla Santorno, and the School Board. They need to hear it.

Anonymous said...

It used to be that concepts were taught at school, and homework (when given) reinforced what was learned at school. It seem that today, we are teaching our children the concepts at home, instead of reinforcing them. Why is this? Why did we learn so much more when we were in school, without our parents as teachers, and with substantially LESS homework? What is going on? Where is the instruction?

Melissa Westbrook said...

Well, this goes to the whole homework issue. I barely had homework in elementary school, just projects and occasional worksheets. My take is that schools KNOW that they are assigning work that children can't do on their own (or the kids are told to ask their parents)and so, with a flourish, you get parental involvement. Kids get pride from being able to do work on their own and this constant looking over their shoulder isn't right.

I think it is wonderful that so many parents can sit down and work with their children. But we all know that is not the case and, as someone pointed out, it widens the achievement gap. Not every kid has a parent at home who can or has the time to help.

Dan Dempsey said...

The instruction is in "d"

but the district picked "c"

a) Traditional Math
b) New math from 1960s
c) Reform math like TERC CMP IMP
d) International Standards

If you wish to help your children, go to www.singaporemath.com

Download placement tests for free.
You click on placement in the second line of the green near the top of the page.

Figure out what your child knows and buy appropriate Singapore Math books.

You might also consider having the district actually define the necessary skills required at each grade level and ask them to teach those. Currently all teachers are required to follow the pacing guide provided by the publishers.

If you would like some instruction, put some pressure on the district to re-examine their flawed definition of mathematics:
Mathematics is the language and science of patterns and connections. Doing mathematics is an active process of constructing meaning through exploration and inquiry.

Now you know the reason that North Beach is continuing with Saxon and Schmidtz Park is using 100% Singapore no Everyday Math in either of those schools.

Dr. Bergeson (by stacking the selected oversight members and choosing for the Math Standards re-write a firm that agrees with her) is currently hi-jacking any hope of improvement in mathematics, as she has the supporters of these flawed materials in one of the largest conflicts of interests ever rewriting OSPI's flawed standards with little change expected by many. This OSPI action is done in defiance of the recommendations of the State Board of Education's consultants report.

If you do not like Everyday Math, just wait until every school in the state is picking from one of three of Dr. Bergeson's selections at each grade level.

Dr. Bergeson has an undergraduate degree in English. She fits right in with SPS Math leadership.

She has a Ph.D. thesis on some form of creating equity in Mathematics. That must explain the widening achievement gap for children of color in the districts that adopt this nonsense (ie. Bellevue and Seattle).

If you have the interest write your legislator. You can keep up to date at www.wheresthemath.com

Dan

Anonymous said...

When my elementary age child comes home with homework that he does not understand, I have been directing him back to his teacher for clarification. If he seem to "get it" but is just stuck on a particular problem, then of course, I am happy to help him out. I do not like the parent over the shoulder approach to homework. It makes kids dependent, and it is never harmonious.

For my middle school kid, I tell him to ask any and all questions of his teacher after class, or after school. There are also tutors that are in the school library after school for children to sit down with. I have taught him that it is his responsibility to understand his homework BEFORE he brings it home. In middle school it is hard to simply direct a child back to the teacher for clarification because then the homework will be late, and he does not get credit for him.

Anonymous said...

anon 9:21 - I agree and do the same with my elementary schoolers because I want them to feel they have the right to ask teachers for help, and, like you, to know that with rights they have responsibilities - in this case to understand what's expected.

Re others with concerns about the achievement gap, isn't it more about the quality of the instruction (and backing up a step, the quality of principal leadership in the building) and very small class sizes for high poverty children?

Can't we let the district focus on those, harangue them on those counts, and let this dead-horse, sunk-cost issue of elementary math curriculum go - or do we really think they're going to suddenly drop a x.x million expenditure because dan dempsey and a bunch of parents are frustrated and angry about it?

Eric said...

I have a child who has just started in SPS (we recently moved here from China), and as a result, i have been spending a lot of time on this blog, trying to navigate the confusing straits of US education.

There are several points that have been made by readers that merit response:
1) Homework: I find it absolutely shocking that anyone would suggest that because homework could contribute to the achievement gap, that we should consider reducing, changing, or eliminating homework requirements. We should concentrate our efforts on bringing underperforming groups UP, not finding ways to put a cap on the achievement of high-performing groups.
2) reading curriculum: the Everyday Math curriculum concerns me-- the critiques of the method make intuitive sense, and the results seem poor. On the other hand, it is the chosen curriculum of the district, and I would like to work constructively to help children achieve as much as possible given the drawbacks to the system. I assume that the CAO, in choosing the curriculum, did a detailed study of the program, and understood its pros and cons. I would love to see a communication strategy by the district that
a) explains their choice of the curriculum
b) acknowledges the critiques of the methodology
c) explains steps taken to mitigate the perceived deficiencies of the system
AND d) shows a series of metrics (beyond WASL pass rates) that will be used to gauge the overall effectiveness of the program, and also success in combating the perceived deficiencies of the methodology

3) Dan and his contributions: as someone new to Seattle and SPS, i find his information valuable. It is repetitive, but I don't have to read all of his posts

to everyone on this blog: thank you for your time and passion. You have made our entrance into SPS much smoother

Anonymous said...

Did you really learn a lot more? It appears to me that most parents today view their children as doing well in math if their kids know their facts and can do computation with ease. Those same kids may totally panic when presented with a challenging problem in which computation is not the key to finding the answer and they have to actually reason and think to figure out the answer rather than recall a formula or procedure.

And to Dan, your contributions to the blog run the gamut - much like your public testimony at board meetings. If your message is not getting the impact you want, you might consider changing your approach. Personally after watching you blast the math adoption again and again, I got tired of seeing you and your charts.

I did not support the adoption of Everyday Math. I would have much preferred the new version of the Investigations program which addressed the computation concerns people had with the first edition. Many, many teachers and schools in Seattle were embracing this program which children enjoyed and which has very solid math concepts.

We need to develop thinkers and problem solvers. This starts in the primary grades where math needs to be a lot more than addition, subtraction, multiplication and division.

I agree that high school students who have not experienced this type of approach before high school may struggle - they are conditioned to think of math as just one problem set after another and what they are comfortable with is the teacher showing them how to solve one and then practicing it 25 times.

Anonymous said...

The CAO said early in the adoption process that she wanted Everyday Math. They were using it in Denver.

Anonymous said...

Dan and the other Math teachers on the thread,

Can you explain the relationship between the International Curriculum and New Math as it was taught in the 1960's and 1970's? I had New Math, and the short descriptions I've seen of the International Curriculum sound a lot like what I was taught.

Thank you.

Dan Dempsey said...

Dear 98112,

From Dr. Wiiliam Hook of Univ. of Victoria BC:

The “international” faction curriculum is derived from research and practice in the Soviet Union in the 1930’s and 1940’s. These ideas first spread to Poland and Israel, and eventually to parts of Europe and to Asia, including Singapore, Japan, Korea, etc. It features a greatly reduced number of topics taught in each grade, the integration of algebra with arithmetic starting in the 1st grade, early memorization of the multiplication tables aided by algebra methods, traditional algorithms for multi-digit operations, and lots of drill. Also fairly sophisticated algebraic concepts introduced starting in the 4th grade, demanding topics taught by the 6th grade, mostly direct instruction by the teacher, and no calculators (Schmidt et al. 2002). This is now the dominant curriculum of the six leading TIMSS countries. California is the only state incorporating an international curriculum into their math standards (Hook et al. 2007).

The "New Math" from the 60s was developed by University Mathematicians. National Science Foundation founded in 1952. The New Math from Yale University Press called SMSG [School Mathematics Study Group] made its debut in 1958. It was widely used in the 1960s and disappeared during the 70s.

The "Reform Math" is more a product of University Math Educators than mathematicians. The NSF has about $100 million into development of this stuff, not counting the NSF grants to Universities like the UW to push this stuff (train and guide teachers in the correct implementation of these materials).

Seattle adopted Everyday Math at a non-videoed school board meeting. An adoption document as a .pdf was briefly posted on the SPS website. It was taken down. Thanks to the Freedom of Information Act, I now have a copy of it. Drop me an email at dempsey_dan@yahoo.com if you would like a copy.

You can get a quick look at Singapore Math if the district ever makes it available as a supplement, which was promised during the adoption in late May.

Singapore Math in the grades 1 through 6 consists of 2 books and 2 workbooks per grade level. First semester and second semester. These run about $8 each retail from www.singaporemath.com

There are a number of other supplements available at each grade level. Intensive Practice, Challenging Word Problems, etc.

The difference between Connected Math used at 6th grade in SPS and Singapore grade 6 is absolutely staggering; as is the difference between Everyday Math grade 5 and Singapore grade 5.

India is currently working with Singapore to further improve Singapore Math.

These are books that have been thoughtfully developed over many years. Fine tuning what works.

The Everyday Math - Connected Math combination is used in both Denver and the Colorado Springs area with poor results.

This combination is most aligned with Washington's OSPI created "F" rated math standards. These standards coupled with OSPI's flawed definition of math are the causes of the State Wide Math failure announced in August of 2006.

Everyday Math is far and away the most used elementary school math text series in the US. This a great testament to the power of McGraw Hill's marketing and the willingness of school district administrators to make decisions with little individual independent investigation.

Dan

Anonymous said...

Maybe the biggest problem we have with Math is that too few Math teachers at the middle school level have real expertise in teaching Math and are basically just following whatever textbook is put in front of them. They can check whether answers follow the algorithms from the book (in traditional math curricula) or the grading rubric in the reform curricula but they don't have a more fundamental understanding.

The middle school years require a big transition from arithmetic, which largely involves executing algorithms (requiring lots of practice) into dealing with abstraction. Arithmetic and abstract math involve different kinds of thinking and even different parts of the brain (see e.g. Keith Devlin's The Math Gene). One good aspect of the reform elementary school curriculum is that it introduces simple forms of thinking about abstract math much earlier so this transition is not so sudden.

Different kids cope with this transition at different rates and it seems to me that a lot of what is being done in middle school math is to introduce a variety of topics in a bit of a holding pattern hoping that more and more students will catch on.

My kids did CMP in both public and private Seattle middle schools. On an individual basis, the books are very good and I think that they were particularly good at the 6th grade level as students are making that transition to abstract thinking. The problem that I see is that within the CMP system there is too much freedom in selecting which books to use at a given grade level. It is possible to choose a pretty incoherent subset of the books and to choose too many of the books that are at too low a level. A couple of the CMP books that were 6th grade at the private school were 7th grade books at the public school even in the Honors Math sequence.

If students get a good middle school sequence that has them comfortable with abstraction then there is lots of flexibility at the high school level to provide challenging material for students.

On a separate note:
I grew up with the old New Math curriculum which had elementary school teachers who had no clue about math trying to teach abstract math definitions as early as 4th grade. A lot of it was silly. However, there was a pre-algebra piece of it that began in 3rd or 4th grade that was intuitive and a really good transition to algebra that seems to have been eliminated from school curricula along with the silliness. The simplest were the 'Fill in the blank box" problems. These would begin with something simple like "Fill in the box so that 2+Blank=5" and would slowly get more difficult. The later replacement of blank boxes by x when starting algebra was a very easy adjustment. I don't know why this has largely disappeared.

Anonymous said...

Paul,
I couldn't agree with you more. I am a math teacher who has taught many different curricula. I also have a degree in mathematics. I would add that often in America, elementary school teachers are ill-prepared to teach math. What proponents of programs like Singapore math seem to neglect is that in countries like Singapore and China elementary and middle school math teacher are specialists. They are far better trained in the subject than their American counterparts. Thus, no matter what curriculum they use, they have more math content knowledge. In America, I see this as a systemic problem that must be changed by addressing our teacher preparation programs. I am not bashing Seattle or American elementary math teachers. What I am saying is that our teacher preparation programs are very different.

Anonymous said...

My kids are still too small to be in school, so I can't comment directly on the quality of math instructions in Seattle Public Schools.

I can say, however, that the more a learn about math instruction, the more troubled I am.

Interestingly, it's not math critics, like Dan Dempsey (whose posts I welcome on this blog), or parents who have had bad experiences that make me concerned.

The more alarming information comes from the publishers of the Everyday Math curriculum and by folks involved in providing professional development and training.

Here are a couple of examples I thought might interest folks.

Annenberg/CPB has some instructional videos for teachers that I found illuminating.

They cover both teaching kids to
read and teaching kids math. You are required to create a login to view these, but it's worth it. I especially recommend comparing the videos set in 1st grade classes.

I thought it was notable that the reading instruction shown in the videos looked *great*. I'd be extremely happy to have my child in any of these classrooms. The math instruction, by contrast, was abysmal (and these are supposed to be model classrooms.)

What are the main differerences between the reading and math instruction?

The reading instruction shows a lot of careful assessment students' abilities and is carefully differentiated, so students are challenged at just the right level. Students also receive both a great deal of practice in the process of reading as well as great deal of direct instruction on ways to approach reading problems. Teachers use a variety of means to get concepts across and students are directly taught a tool box of methods to help them decode text.

The math instruction, by contrast, does not generally show careful assessments or differentiation of instruction. Kids are not always given much practice working with numbers or mathematical reasoning. Sometimes there is very little math content in the lesson. Little direct instruction is shown. Also commentary in the instructional videos is often not about math instruction, but fuzzy qualities like whether students are excited and having fun.

It's staggering how different the approaches are to these two subjects, but it certainly helps explain the gap between reading and math achievment.

Also interesting, I found some newsletters to teachers written by the Everyday Math publishers. I found them also troubling, particularly the newsletter related to how to deal with parent criticism of the program

Here's a link

Dan Dempsey said...

I regard to Paul's comment about Singapore and teacher preparation.

In many of the High Achieving nations once out of grade 2 your math teacher is a math specialist.

That person can devote great energy to mathematics. Seattle is spending $4.2 on academic coaches for teachers. A large portion of that focuses on Elementary teachers.

In most of the US, children get a math specialist after grade 5, who may or may not know math well enough to be a great teacher.

Singapore books have fewer topics per grade level and require much greater understanding of those topics, than the mile wide inch deep Everyday Math curriculum.

For the teacher however Singapore can be much easier to teach, because the teacher will learn mathematics through teaching this program because it is carefully structured and coherent.

Dan

Anonymous said...

Hmmm. And what are those "High Achieving" nations?. Singapore, the mono-cultural city. Perhaps, the big "China"? That's where knowing 1500 written words is considered literate. That's about 2nd grade here in the US. Or is it India? Have you ever been there to see who is actually educated? and more importantly who is NOT. I believe they educate 1 or 2% of their population well.. so maybe your refering to the Indian 1 or 2%.

Do you have any model for a great achievement gap reducer for any city of 1/2 a million to a million here in the good old USA? And I don't mean 1 school that did well with "direct instruction" or any other marketing literature. Do you have a model in mind?

Anonymous said...

Maybe he's considering Japan as a high achiever. Another country that is famous for the education of a few percentages, but not very good for anyone else. They don't really mind since people accept their rigid place in society.

Roy Smith said...

Another country that is famous for the education of a few percentages, but not very good for anyone else.

This is an important point that is lost in most discussions comparing academic achievement in the United States vs. other countries. The U.S. is one of very few (or perhaps the only) industrialized countries that doesn't divide students into academic vs. vocational tracks fairly early (usually by high school, at the latest). Comparisons of school children are usually made between typical high schools (in the U.S.) vs. typical academic high schools (anywhere else). The comparisons are usually not apples to apples.