turning lead into gold

Well, at least the Wright Group/McGraw Hill, publisher of Everyday Math, is attempting to clean up the mess they've created. On the same day the National Math Advisory Panel was busy making their report available to the public, Wright Group was introducing Pinpoint Math.

CHICAGO, March 13 /PRNewswire/ -- Wright Group/McGraw-Hill (News) has published a new math intervention curriculum, Pinpoint Math. The supplemental program, with both online and print components, was designed for students in Grades 1-7 who are one to two grade levels behind in mathematics.Pinpoint Math can be used successfully with any basal mathematics program. It incorporates the three essential elements necessary for improvement of mathematics performance among struggling students:

-- Diagnostic Assessment: Identify areas of weakness for individual students.

-- Targeted Instruction: Provides content in an individual Student Action Plan that meets the needs of the student with both print and animated tutorials.

-- Progress Monitoring: For ongoing assessment of students' advancement on individual topics in both formal and informal formats.

Districts who buy the supplemental program better be ready to fork up some serious cash. Not very good news for cash strapped districts in just about every neighborhood.

On the bright side of things, piggybacking on Everyday Math sales is definitely good news for the Wright Group. After all, they have managed to worm their way into 175,000 classrooms and still counting. That's a whole lot of potential sales generated by a whole lot of students who will require a whole lot of remediation.

Conveniently, Pinpoint Math "can be used successfully with any basal mathematics program." That way, schools can help those struggling students "who are one to two grade levels behind in mathematics."

This is edu-business at its finest. First, you sell schools a math curriculum that results in a significant population of struggling students who end up one to two grade levels behind, and then you sell them a scaffolding tool to remediate the problem you created in the first place. Remember, it's all about the children.

Nice job Wright Group/McGraw-Hill. Way to keep the stockholders happy.



Cross posted at Kitchen Table Math: the sequel

Reading between the lines...

Any approach that continually revisits topics year after year without closure is to be avoided.

really means...

Everyday Math is to be avoided.

National Math Panel works hard

I sure hope all those Everyday Mathematics books are recyclable because they won't do well on the re-sale market and no developing country is going to want them either.

The National Math Advisory Panel has issued the report they've been working on since 2006 having reviewed over 16,000 research studies in the process. Considering the findings of the panel, I would be worried if I were the Wright Group because if the report is any indication, Everyday Math's approach to teaching math to over 2.8 million students, is anything but right.

Math courses must be streamlined, focusing on "a well-defined set of the most critical topics".

Anyone familiar with Everyday Math knows that this curriculum is anything but. The approach would be best described as a "Jack of all trade, master of none" kind of thing. Students move through mountains of concepts at break-neck speed never slowing down to appreciate the scenery.

Michigan State University professor William Schmidt adds, "In the U.S., we're trying to teach first-graders 20-some topics." There is no call for mastery, because according to Everyday Math's take on the "spiral", the topics will be revisited again and again and again.

Despite the findings of the panel, the folks at Everyday Mathematics would have you believe the following:

Because very few people learn a new concept or skill the first time they experience it, the curriculum is structured to provide multiple exposures to topics, and frequent opportunities to review and practice skills. A concept or skill that is informally introduced in kindergarten, for example, will be revisited, developed and extended numerous times, and in a variety of contexts, throughout the year and into later grades. - About Everyday Mathematics

So, what happens to these children subjected to the Everyday Mathematics "spiral"? Dr. Larry Faulkner, president emeritus of UT Austin said, "There is a problem of kids not feeling like they're getting anywhere, that third-grade math is the same as fourth-grade math." I would add that it's more than just a feeling. They really aren't getting anywhere.

Any approach that continually revisits topics year after year without closure is to be avoided.


Everyday Mathematics does precisely that. In fact, they consider the it one of the program's most salient features. So, if you're the Wright Group and you've been pushing your "spiral" as the basis for your program, just how would you spin it?

In answer to the question of whether math should be all fun and games in order to be engaging and therefore effective (another feature promoted by the Everyday Math folks), the answer, as far as I can tell, is no. Foundational fluency leads to conceptual understanding-- you cannot have one without the other. Automatic recall of math facts is essential to that understanding. Even if you choose "games" to get there, fact mastery is serious business.

Faulkner said that the panel “buys the notion from cognitive science that kids have to know the facts.”

“In the language of cognitive science, working memory needs to be predominately dedicated to new material in order to have a learning progression, and previously addressed material needs to be in long-term memory,” he said.

The panel also determined that "Americans should look at prowess in math less as a talent than as the result of sheer hard work." Furthermore, "Effort counts. Students who believe that working hard will make them smarter in math actually do achieve better."

“Experimental studies have demonstrated that changing children’s beliefs from a focus on ability to a focus on effort increases their engagement in mathematics learning, which in turn improves mathematics outcomes,” the report says.

“When children believe that their efforts to learn make them ‘smarter,’ they show greater persistence in mathematics learning.”

Clearly, Barbie had it all wrong.

As my daughter says, "Math isn't hard, it's just hard work."

Indeed.

A solution to how to teach math: Subtract
By Greg Toppo, USA TODAY
March 13, 2008

Panel Proposes Streamlining Math
By TAMAR LEWIN, New York Times
Published: March 13, 2008

Panel Finds Faults in America's Math System
By Maria Glod Washington Post Staff Writer
Thursday, March 13, 2008

National Math Panel Releases Final Report

Kindergarten Math

My kindergartener received her report card yesterday. So, what do they grade a five year old on in math these days?

Just take a look at the expectation for January:

Applies Understanding of Number Concepts and Basic Operations
Uses one to one correspondence to count objects
Identifies numerals 0-20
Writes numeral 0-20
Counts 0-70
Counts backward 10-0

Applies Mathematical Thinking and Reasoning
Sorts and classifies objects
Recognizes, reproduces and extends patterns
Understands estimation
Performs data collection and creates simple graphs

This is NOT the expectation for January:

• Counts 0-115
• Counts backward 20-0
• Understands the meaning of addition
• Understand the meaning of subtraction
• Recognizes penny, nickel, dime and quarter
• Tells time to the hour

Students aren't expected to know that until June.

This is life in the world of Everyday Math. It's like another plane of reality where it's more important for a five year old to learn how to estimate, collect data, and create graphs than it is to learn how to add, subtract, count coins, tell time or count backward.

Then they wonder why parents get upset.

Another Everyday Math debacle

I fail to understand why districts keep adopting Everyday Math despite everything we know about it and regardless of its very many shortcomings. A district in New Hampshire recently signed on with Everyday Math and it seems they're a bit worried about it.

They should be very worried.

Curriculum Coordinator Heather Cummings said that the Everyday Math curriculum, introduced this year, is still being worked in by teachers, and that there would be a learning curve before teachers could feel comfortable with it.

"It is a language-based program, so for those students who might struggle with that, we are working with teachers to deal with the issues," she said.

Just wondering...

Since when did math become "language-based" and more importantly, why? The fact that math is NOT language based is what so many children love about math. When I say language based, I'm NOT referring to word problems. Word problems are good. Word problems are math. By language-based I'm talking short answer response and essays about math. Why?

What happens to the children of Everyday Math while their teachers struggle with this "learning curve" anyway? In the meantime, they don't get through all the modules so that material is not covered at all and the children lose mathematics skills along the way. How is this acceptable? Apparently the plan is to plug the gaping holes left in sixth grade when the children get to seventh grade. Are you kidding me?

In the face of all we know about Everyday Mathematics, the human brain, and the results of those students who have gone through the program only to need remediation, why oh why do districts keep adopting Everyday Math? When will the madness end?

In the meantime, what happens to these children who don't even know what they're missing? What they are missing is rigorous mathematics that makes sense.

Source: The Citizen of Laconia, Math technology showcased at Belmont Shaker meeting

"Overlearning" Overrated?

Science Daily had an interesting article out this week discussing the value of overlearning. Recent research has found that studying material beyond mastery may be a waste of time in the long run.

University of South Florida psychologist Doug Rohrer decided to explore this question scientifically. Working with Hal Pashler of the University of California, San Diego, he had two groups of students study new vocabulary in different ways. One group ran through the list five times; these students got a perfect score no more than once. The others kept drilling, for a total of ten trials; with this extra effort, the students had at least three perfect run-throughs. Then the psychologists tested all the students, some one week later and others four weeks later.

The results were interesting. For students who took the test a week later, those who had done the extra drilling performed better. But this benefit of overlearning completely disappeared by four weeks. In other words, if students are interested in learning that lasts, that extra effort is really a waste. They should instead spend this time looking at material from last week or last month or even last year.

Researchers concluded that once mastery was achieved it was better to leave that subject alone for a while and return to it later. They actually found that an optimal "study break" of about a month resulted in long-term learning-- something they refer to as the "spacing effect".

Is this "spacing effect" an argument for the spiral approach? Perhaps so, yet it does seem to be a well executed spiral in which the content is first studied to mastery and then revisted for reinforcement later. This is certainly not the haphazard "spiral" I've witnessed my children being subjected to with Everyday Math and seems to be more in keeping with Saxon's idea of a spiral curriclum and to a more limited degree with Singapore Math's "spiral".

Just to be clear, it has absolutely no resemblance to the Everyday Math "spiral".

I hope they keep looking into this subject. Children have such precious little time to learn so many important things. Imagine all that could be accomplished if we implemented teaching and study skills that were actually efficient.

That would be a nice change.

Source: Back to School: Cramming Doesn't Work In The Long Term


ABSTRACT—Because people forget much of what they learn, students could benefit from learning strategies that yield long-lasting knowledge. Yet surprisingly little is known about how long-term retention is most efficiently achieved. Here we examine how retention is affected by two variables: the duration of a study session and the temporal distribution of study time across multiple sessions. Our results suggest that a single session devoted to the study of some material should continue long enough to ensure that mastery is achieved but that immediate further study of the same material is an inefficient use of time. Our data also show that the benefit of distributing a fixed amount of study time across two study sessions—the spacing effect—depends jointly on the interval between study sessions and the interval between study and test. We discuss the practical implications of both findings, especially in regard to mathematics learning.

Increasing Retention Without Increasing Study Time

cross posted at Kitchen Table Math

Does this sound eerily familiar?

Today’s 4th Grade Everyday Mathematics “chapter review”

This final unit (Chapter 12) has the students learning about rates: dollars per hour, miles per hour, and calories per serving, for example. Understanding them will certainly be of value as consumers. Sounds practical, and in theory I have no argument with that.

Having said that, the questions on the review (and this week’s homework) point out yet another thing that drives me crazy (in a bad way) about EM:

1) The correct answer requires a written explanation of at least a couple of sentences when a simple numerical equation could have clearly demonstrated understanding or lack thereof. Half the problems on this chapter review ended with “explain,” “explain your strategy,” “explain your answer.”
2) Some of the “word problems” (generous description) require multiplication using decimals. This isn’t a problem per se and especially important when we’re talking about money, right? However, in fourth grade Everyday Mathematics, students are only taught to multiply decimals using a calculator. In fact, a quick search of the index of the Student Reference Book (4th Grade) would provide you with three entries (p. 37, 161, 180) and every single one involves using a calculator to multiply decimals. Don’t even bother looking up division of decimals because it’s not even in the index at all. Yes, really!
3) Some of the questions are so subjective that the possibility of answers is not limited to one that would teach the lesson of rates, but could be virtually unlimited if you take into account the author’s explanation. In the “Family Letter” they state “Other factors to consider include quality, the need for the product, and perhaps, the product’s effect on the environment.”

Here’s one example from this study guide:

5. Use the sign below to solve the problems. Explain how you found your answers.
DOUGHNUTS
60 cents each
6 for $3.40
$6.80 for a dozen

b. Pretend that your mother sent you to buy 11 doughnuts. If you had enough money, would you buy a dozen doughnuts instead? Explain.

I’m guessing here, but since we’re supposed to be talking about rates, and the student is supposed to understand unit price and be a wise consumer doing comparison shopping, the objective is supposed to be to choose the lowest price per unit-- the "best buy".

It seems to me that they never asked which is the best buy. Or did I miss something? Fuzzy, fuzzy, fuzzy!

Indulge me for a moment, but...

• What if I always listen to my mother? Shouldn’t I buy only eleven even if I am going to save a few coins by buying the extra doughnut?
  
• What if we only need 11 doughnuts and mommy doesn’t want to be tempted by the 12th one because she’s on a diet?
  
• What if they only have 11 doughnuts in the flavor that I want to buy. If I buy that 12th doughnut, no one is going to eat it and I will have wasted my money.
  
• What if Mom said I could keep the change and I’m saving up for something really cool? (Remember she’s only expecting eleven doughnuts).

I think you get my drift…

Are any of these answers acceptable? If they were, did it really teach me about rates as a mathematical concept? If they are not, then what is the point of asking such an "open ended" question?

I guess this is one of those "consumer" questions that's supposed to make me a better shopper. (From the "Family Letter": "Is an item on sale necessarily a better buy than a similar product that is not on sale?" Well that depends....

Oh boy, am I glad this is the last chapter. Can’t take much more of this fuzzy logic. I need a break (so do my kids!)

CBS "Reform Math" Story

I was watching the CBS story about "Reform Math" that aired on Saturday, May 26th. On the one hand, I'm encouraged that the controversy with reform math programs like Everyday Mathematics made the network news and found its way into living rooms across America. On the other hand, I dissapointed that the story wasn't more balanced.

http://www.cbsnews.com/stories/2007/05/26/eveningnews/main2855775.shtml?source=RSSattr=HOME_2855775

CBS highlighted interviews with a parent who is supplementing with traditional math at home and one of the authors of Everyday Mathematics. However, there were no interviews with mathematicians or scientists or leaders of the many grassroots parents groups that oppose reform math, there was no data about the decline of our nation on international standards assessments like TIMSS (Trends for International Math and Science Study), they didn't even mention the National Mathematics Advisory Panel that is in the process attempting to sort out the state of math education in our schools. And so, for the most part, the story was unbalanced. But hey, it was a two minute piece and at least it got a few people thinking about this issue that might not have otherwise.

So, what bothered me most about this story? It was something that Amy Dillard, one of Everyday Mathematics authors, said:

"We're preparing kids now for jobs that we don't even know are going to exist, and we can't be teaching them the same mathematics that we did years and years ago, we really have to prepare them for the workforce that they'll be headed to,”
says Amy Dillard, author of “Everyday Mathematics,” a reform math textbook.

Message to Amy Dillard: How could you possibly know how to prepare someone for a job that you don't even know is going to exist? How are you so certain that students should rely on the "spiral" to get them to where they need to be in the future if you admitedly have no idea what that future holds for them? Are you even aware that there's an entire world that is producing generations of mathematicians and scientists using methods of teaching mathematics that continue to respect the value of traditional algorithms? These high performing nations aren't teaching reform math, that is for certain.

"Asian countries are setting the pace in advanced science and math."
-Ina Mullis, codirector of the International Study Center at Boston College that manages the TIMSS.

And guess what, Ms. Dillard, you won't find Asian countries touching reform math with a ten foot pole. In fact, they must be thanking you for increasing their competitive advantage.

Everyday Mathematics: When Comedy Becomes Reality

Experiment:
I showed my kids a couple of comedy gags from the 50's about math without telling them what they were about and refrained from making any comments to gauge their reaction.

Sample Data:
If you haven't watched Abbott and Costello or Ma and Pa Kettle "do math", you might want to do that now:

Abbott and Costello Math

and

Ma and Pa Kettle Math


Reaction:
My fourth grade daughter said, "Hey mom, that's just like Everyday Math! They're using invented algorithms" as she giggled uncontrollably. My first grade son said, "Mom, those answers are wrong." He then proceeded to tell me the right answer for each equation and asked if he was correct. (Which he was) but being new to the mysteries of Everyday Math, he seemed somewhat perplexed.

From the mouths of babes.

I just can't wait to hear what they have to say about Lisa Simpson's take on constructivist math ideology:
(The Simpsons on math)


It's a sad statement that what was a funny gag a half century ago and what is clearly satire in our generation is eerily similar to what's happening in constructivist classrooms today.

Comedy has become reality and I'm not amused.

Math as a Foreign Language

A violinist who still worries about fingering positions cannot hope to impress with the beauty of tone or the elegance of phrasing, and an opera singer without the requisite high notes would try in vain to stir our souls with searing passion. In good art as in good mathematics, technique and conception go hand in hand. –
Hung-Hsi Wu

I don’t know if I’ve ever spent as much time thinking about mathematics as I have lately. I am an interpreter by training and aside from the calculus, trigonometry and statistics I took in undergrad, and the business type math I took in grad school, my world is a world of language. I do know about learning language, teaching language, and speaking a foreign language, however, and it occurs to me that it is much like learning math.

Math starts out much like a foreign language, something unfamiliar with it’s own symbols, and meanings, and structures. It’s hard work at first and requires repetition, memorization, and practice. You’re not really comfortable with a new language until you use it over and over, consistently and successfully. There is no resting on your laurels, because fluidity depends on practice and vocabulary depends on exposure to rich sources of language.

You don’t discover the language on your own. You don’t invent the language. The language is already there for you to master, to seize, to make your own if you’re willing to work for it. It’s a beautiful thing to move seamlessly between two or more languages but it doesn’t magically appear by placing a dictionary under your pillow and wishing it so.

You learn language by listening to others speak, by looking words up in the dictionary, by learning the rules of grammar and then memorizing the “irregular” applications that break all those rules. Finally, you are able to communicate with others in this new language and the more often you do so, and the more challenging the conversations become, the more you grow in your ability to communicate.

You can always tell who had the benefit of a good foundation through formal instruction (grammar, syntax, pronunciation, vocabulary) and who just "picked it up" informally, on their own and without academic support. The latter tend to be more limited in the range and depth of communication in that foreign language. There is a limit to what they are able to accomplish with the "tools" in the "toolbox" so to speak. Those with the strong foundation move through their discipline with ease, with confidence and with mastery. I think the same applies to many other disciplines be it ballet, basketball, the violin or dare I say, mathematics?

Yes, learning math is much like learning a language. When you master the basics through diligence, perseverance, and the benefit of good instruction, one day without realizing it, you’ve opened the door to a whole new world.

Everyday Math: A Nimble Mind is a Terrible Thing to Waste

Okay, I think I’m going to be sick….

My first grader, who loves math and finds it quite easy, sat down to do his Primary Mathematics (Singapore) and Kumon work. This day's work involved word problems requiring subtraction of double digit numbers with regrouping. He said, “Mom, do we have a number chart?” I said, “A number chart? You haven’t used one of those since you were learning to count. Why do you need one now?” “Because” he said, “that’s how we’re subtracting at school.” “Well, you know how to subtract without one. Just set up your problem and then you can do the math!” It took him no more than five minutes to complete the entire exercise of world problems.

Why did he think he needed a number chart to subtract when he’s done this type of math before successfully? To think of him counting back to find the answer on some number chart for each question when he already knew a much more efficient way to do it is disconcerting. He finished and promptly asked if he could work ahead on the next exercise.

This is another reason to dislike Everyday Mathematics. I feel likes it's a constant fight to keep the efficient algorithms in play lest my children come under the false notion that the EDM way is actually better, cooler, or newer. The teacher is teaching it, their friends are using, so maybe it's better and mom hasn't caught on yet. I don't mind if he learns about them but doesn't EDM pride itself on letting students choose? I strongly believe that most every additional algorithm is a collosal waste of time and who has time to waste? (If you don't believe me, just check out this video on youtube http://www.youtube.com/watch?v=eKld7lQHKRg )

I find them to be inefficient, unnecessary. I also believe that dependence on manipulatives, charts and calcuators certainly does not allow children's minds to do all the amazing things they are capable of. These methods reinforce and even reward laziness and when they rely on these "crutches" children fail to exercise their brains and train them to work nimbly.

And a nimble mind is a terrible thing to waste.

Jimmy Neutron's Unofficial Take on Constructivism

"What's the point of being smart, if it just makes me miserable?"
- Jimmy Neutron

Methinks that the Boy Genius would detest “constructivist math” curricula like Everyday Mathematics, Connected Math and TERC. For that matter, so would Cindy Vortex!

Here is what I imagine James Isaac Neutron might have to say about Everyday Math:

• I don’t have time to waste discovering algorithms that were perfected ages ago. I think Euclid, Descartes, Pythagoras, and Pascal did a pretty good job.
  
• Thank goodness for long division. Polynomial long division (algebra), finding roots and asymptotes (pre-calculus), and integration of rational functions and Laplace transforms (calculus) wouldn’t be possible without it. Yep, gotta have long division!
  
• Sorry guys, there are no shortcuts to math mastery. You just gotta be computationally fluent in mathematics and be able to calculate quickly and accurately. Come on Sheen, I’ll help ‘ya with those times tables!
  
• Using a calculator is a cop out. My brain works faster and it never runs out of batteries! Carl, put that calculator away, you can multiply decimals without it.
  
• Partial products, partial quotients, lattices, and trading-first! Are you kidding me?
  

"Gotta blast!” –Jimmy Neutron

Tired of Everyday Math

I lose a lot of sleep over Everyday Mathematics and I’m very tired. My children are tired too. They give up much of their free time to do extra homework (supplementation with other material) that actually builds the foundation they will need to succeed without a calculator. The effort is certainly worth it, but that doesn't make it any less exhausting. I am beyond frustrated...similar to the process of mourning when you finally get to that acceptance that you must move forward. I'm tired of researching, writing letters, and becoming more and more angry. I'm tired of talking to administrators who either just don't get it or just don't care.

What bothers me most is that our children are inheriting some monumental problems--- global warming, terrorism, and massive national debt, for example. It will be the job of our children’s generation to find a way to make things better. To correct all the errors we made along the way. That takes knowledge, science, engineering, and a strong foundation in mathematics. Ironically, in our hour of greatest need our public schools aren’t giving our children the tools they need to succeed in this huge endeavor. For over two decades these constructivist math curricula have found their way into our classrooms and the damage they are causing has long term consequences for the future of our nation. It’s really that serious. It’s really that important. It's really that timely.

They call this debacle the “math wars” and sadly, a war is certainly what it has become. So much arguing on both sides of the debate, no one willing to admit that an experiment isn’t working out as planned while only the textbook publishers benefit from the bonanza of meaningless standardized testing and curricula that lacks content while our children keep waiting for us to figure the whole mess out. In the meantime, our children lose precious time, precious learning opportunities, and the precious gift of choice. They are robbed of the chance to fulfill dreams and change the world along the way. It is a war, and nobody wins.

Mostly, I am frustrated that curricula like Everyday Mathematics goes against what I teach my children. I’m not just referring to the importance of mastery, quick math fact recall, and agile mental math ability, I’m referring to something much bigger…. WORK ETHIC. Our children will need to work harder, smarter and better than their international peers to succeed in the global economy. What does Everyday Mathematics teach them? Don’t worry about long division or complicated multiplication, just use a calculator. In fact, we think calculators are so important that we’ll teach your kindergartner how to use one. Math should always be fun and games, we shouldn't submit them to ‘rote memorization’ (drill and kill). That’s too boring, that’s too traditional, that’s just a waste of creative time that could be used for discovery. Well, guess what? Sometimes work is fun, but sometimes work is work and you just have to bear down and do something until you get it right. Like learning to add, subtract, multiply and divide effortlessly, accurately, and efficiently.

In The World is Flat: A Brief History of the Twenty-First Century in a chapter entitled “The Quiet Crisis”, Thomas L. Friedman says it much better than I ever could:

I am not suggesting that we militarize education, but I am suggesting that we do more to push our young people to go beyond their comfort zones, to do things right, and to be ready to suffer some short-run pain for longer gain. --Thomas L. Friedman