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.