The following is a spreadsheet I created to analyze MEAP proficiencies in math in the Ann Arbor public school district and Lakeshore public schools (the district in which I live). Both districts use Everyday Math.

You will need to click on the image to enlarge. I apologize for the poor graphics. I’m sure I could make it more eye-friendly, but I just don’t have time.

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Michael Paul Goldenberg

said:Let’s see: math ‘achievement’ (as measured by what, exactly?) declines from elementary to middle school. Moreover, there seems to be a link between literacy levels (as measured, again, by what?) such that we could conclude: 1) lower levels of math achievement cause lower levels of literacy; 2) lower levels of literacy cause lower levels of math achievement; 3) there appears to be a correlation between literacy levels and math achievement; 4) there may be one or more variables not being considered that would contribute significantly to test results.

So let’s go with the last option (because that’s what anyone attempting to do meaningful research would do: propagandists have a different approach that I try hard to eschew. What could some conflating variables be? Well, we know your hypothesis: the TEXTBOOKS are to blame. To test this, of course, you would need to set up an expensive and difficult to control experiment. I wish you good luck with that. Remember, of course, that there is a world of difference between cherry-picking already existing data to support a foregone conclusion (i.e., EM is bad; find schools and data that appear to support that belief; ignore conflicting results; add rhetoric; stir well; publish as if it were an actual research study). A past-master at that particular method is Professor Wayne Bishop of Cal State-LA. If you don’t already know him well, further pursuit of your vendetta against EM would no doubt bring you into contact with him. He can help guide you towards mastery.

Another hypothesis: check the socioeconomic levels of the schools. Oddly enough, there are communities in which residents do not live in a random distribution of income levels, but tend to congregate with those who have similarly high, medium, or low levels of income. And by some bizarre coincidence, neighborhood schools comprise students from surrounding neighborhood homes! So just maybe the schools with the lower levels of literacy and math scores happen to be the ones with the lower income levels. . . it could happen. Wacky idea, I know, but maybe we should check before drawing too many conclusions about math textbooks.

cindy0803

said:Michael,

I did not attempt to do an in depth study of Everyday Math across the State of Michigan. I clearly stated that this was an analysis of Ann Arbor and Lakeshore school districts; two districts that utilize Everyday Math. I didn’t even draw any conclusions myself (on my blog). I just put out the information.

I am happy to consider other criteria that you think is relevant which I did not highlight. But are you willing to consider the possibility that where Everyday Math might appear to be working could actually be due in large part to the blood, sweat, tears, and dollars that the parents put into math education outside of school?

Do you know of any school districts in Michigan using Singapore or Saxon Math? I would love to take a look at them. The problem is that many (most?) school districts do not publish on their websites what math curriculum they use (I think this is on purpose). It was not until recently that Lakeshore published (albeit off-handedly) that they use Everyday Math.

I am not a propagandist. I am not trying to lead to a conclusion. I looked at the data, and I posted the results. I was not surprised by the observed trends because I have seen first hand the results of “new” math in my own school district.

To address your additional hypothesis that schools serving richer neighborhoods might have higher scores while those in poorer neighborhoods might have lower scores, I believe I can tell you where in Ann Arbor those schools are just by looking at the math and reading scores. But I don’t think it weakens my personal conclusions about Everyday Math. In fact, I think it just adds more evidence to the conclusion that Everyday Math only works for the wealthy and for those in families of the highly educated. That is not a good program for public education. In my opinion, of course.

If you want to really test the effectiveness of Everyday Math, use it with NO requirement that parents get involved at all. As a matter of fact, use Everyday Math in one classroom, Singapore in another, and just letting the teacher use whatever book, workbook, technology, app, or program that works best in his or her opinion in the other; again, with no expectation of parents helping. Then see which one prepares students for proficiency under those constraints. That will be the one which is best for public education.

Michael Paul Goldenberg

said:Oh, and while I’m at it: how do the numbers relate to numbers elsewhere? Part of a larger trend, perhaps, that might have little or nothing to do with which textbooks are being used? Or is everything down to EM vs., say, Singapore Math, and no similar trends appear in districts where SM is the text of choice? You’d need to look at more than two districts, of course. Unless you’ve already reached your groundbreaking conclusions with n = 2.

One of the problems with ‘research’ conducted by propagandists is that we really don’t need to look at their data, because we know in advance what the conclusion is going to be. So it’s a safe bet that the data will be selected so as to go along with the desired outcome.

It’s nearly reached the point where I am inclined to give little attention to research (even non-research research) in the social sciences unless I see the words, “Much to our surprise. . . “; that is, some indication that something truly unexpected shows up in the data. In that case, there is the chance that something noteworthy has gone on or that the researchers actually are capable of seeing beyond their desired outcomes. The day self-appointed Math Warriors write something with those words, meant sincerely, I’ll start being more concerned about the results they claim to have discovered.

cindy0803

said:Michael,

What research into Everyday Math being the “best” curriculum to use in public schools would you trust?

What do you have to say about the fact that Ann Arbor is considering a supplemental math program to Everyday Math because the evidence is starting to mount that it leaves Middle Schoolers unprepared for Algebra?

Grand Rapids East uses Think Math and they have very high math scores. Kentwood switched to Math in Focus (Singapore Math based) in 2012. I will take a look at their scores and get back with you.

The bottom line is that many (most?) parents, whose help and input are a necessity for Everyday Math’s success, don’t like it. Nope. If enough parents do not like something, and it is not something ridiculous like book banning/burning, shouldn’t school districts, administrators and teachers be willing to try something different?

I always hear about the cost of these books being so great that schools couldn’t switch curriculum easily as it would be cost prohibitive. But math workbooks can be purchased from Amazon for under $15. Back in the 70s, I used to have to put down a $5 book deposit which was forfeited if I didn’t turn in my book in good condition. Now there are no books in a lot of classrooms, just teachers copying workbook pages. So, where is the cost?

Michael Paul Goldenberg

said:Cindy, where have I ever said or hinted at the idea that EM or ANY books are ‘the best’?

My concern is that there are perfectly sound mathematical ideas being used to attack books in their entirety. If someone has specific gripes with any book that make sense to me, regardless of the overall flavor of the book(s) in question, I’m always interested in considering the issues. But one repeated attack that has arisen in the context of the Common Core (which, I’ll remind you and any readers you have) I’ve opposed from the outset and continue to oppose), hinges on the teaching/investigation/discussion of alternative algorithms. A specific one that always gets raised is lattice multiplication. I have gone to great lengths in various places over the last decade trying to unpack how lattice multiplication, the standard algorithm, and at least two other models are intimately connected, grounded in the same basic issues of place value, and fundamentally sound. I’ve yet to see anyone refute that soundness, so instead, typically, the attack is on “efficiency” and/or “too much space needed.” But since my goal isn’t to get kids to switch from using other approaches to using lattice, but rather to see through a couple of lenses what makes multiplication algorithms work (which, I would think, would secure a student’s understanding of multiplication AND other aspects of arithmetic (and, later, algebra), those “refutations” are besides the point. If some kids, having had the chance to use both lattice and the standard approach decide in the end to go with lattice, I hardly think that’s tragic. My opponents seem to believe otherwise. So be it.

In any event, your opening question seems to ignore my entire previous post. I’ve grown very suspicious of most educational research. I would be shocked to see anything that convinced me that any textbook series is a panacea or, as you put it, “the best.” I doubt such books exist. So why are you trying to get me to take a position on something I don’t think to be true or possible?

cindy0803

said:Michael,

You have suggested a number of times that EM is a sound math curriculum. You have pointed to Ann Arbor in support of this claim. You asked at one point if people believed that Ann Arbor, with its focus on academics and surrounded by the University of Michigan influence, would choose a math curriculum that wasn’t good. While that may be a reasonable question, it is not scientific. We can all probably provide dozens of examples where people who should know better make poor decisions even when faced with overwhelming evidence pointing to a different course of action.

OK, so you don’t think EM is the best (or maybe you do, but don’t want to commit), but I am asking for evidence to support that it is the best or even a good math curriculum. I am trying to use logic here. What school district chooses a curriculum that they don’t think is the best? Surely the Powers-That-Be in Ann Arbor, at the time they decided to switch to Everyday Math, thought it was the best curriculum. Again, you have suggested as much.

I’m asking for you to provide educational research that supports the conclusion that EM is effective in public schools. You are attacking me because I have little other than my personal experience and the long list of High School and College math teachers who have observed a steady decrease in math ability in their students. The overall consensus, based on my reading, is that the weakness appears to be the shift from proficiency in a math skill before introducing new math concepts which is counter to math curriculum like Everyday Math.

Here is a list of links where smart people voice concern regarding EM:

http://pamath2009.files.wordpress.com/2009/04/carlsson-letter.pdf

http://seattletimes.com/html/opinion/2011097718_bruce17.html?prmid=op_ed

http://www.lit.net/orschools/critique5_too.pdf

http://www.csun.edu/~vcmth00m/riley.html

http://www.city-journal.org/html/eon_3_7_03mc.html

http://michellemalkin.com/2007/11/28/fuzzy-math-a-nationwide-epidemic/

https://tfteacher.edublogs.org/category/everyday-math/

http://eklhad.net/chimath.html

http://www.city-journal.org/2009/eon1113ss.html

http://greenwichmath.blogspot.com/2012/03/is-everyday-math-threat-to-our-students.html

http://www.math.jhu.edu/~wsw/ED/devclue.pdf

http://www.educationnews.org/k-12-schools/do-the-math-wars-really-exist/

http://www.math.jhu.edu/~wsw/ED/list

This is just a drop in the bucket. And it does not even represent the multitude of parents who do not like Everyday Math.

Still waiting to hear your take on Ann Arbor decision to supplement Everyday Math.

Michael Paul Goldenberg

said:Cindy, I tried to post a reply to your last comment more than a week ago, but it vanished in a puff of cyber-smoke and I was just too frustrated to try to rewrite it.

Rather than that, here are a couple of questions and comments.

First, if your goal is to PROVE (to me, to your imagined or real audience, to “God,” or to the mathematicians’ hall of fame) that there are people who dislike EM (or at least have been convinced that they should hate it, based on very little evidence or a great deal of evidence, or somewhere in between), relax. I knew that at least 15 years ago or so. And the fact that I’ve written in opposition to many COMMENTS that I found unreasonable or inaccurate or downright dishonest attacking EM and several other math programs doesn’t mean: 1) that I get paid to do so (because I’ve NEVER been paid in any way whatsoever, directly or indirectly, for reviewing or writing about math education, books, products, materials, methods, etc. (unless we count free review copies which on some occasions I’ve been sent; and no, I have never sold those); 2) that I think that, on the whole, EM or similar programs are “the best” or “my preference” as THE SOLE RESOURCES for teaching/learning K-5 or 6-8 or 9-12 mathematics. I have long advocated that teachers do not use any textbook as a bible, but rather that texts are resources. Some of the best teachers I’ve seen draw materials from a variety of sources, not only from textbooks. The day of textbooks as the primary resource for teaching/learning K-12 subjects is likely over. Doesn’t mean books are obsolete, but there are other important means of teaching and learning most school subjects. And in case you aren’t aware (though you probably are), all the publishers these days offer tons of supplementary resources online and/or on dvd: the more the merrier, it seems. Doesn’t matter whether it’s a traditional program or something I would call progressive: multi-media is a clear presence with textbooks, and teachers and administrators and kids and parents expect it, more and more. Is that good? Sometimes. But that’s another conversation.

So please, Cindy: stop trying to put me in a corner. If you need to feel that you “win” something, just declare victory and ignore me. In the circles in which you travel, you won against me and those like me long ago, because YOUR friends and allies don’t read people like me, and if they do, they react with mockery, rage, and so forth. And that’s regardless of which particular rhetorical voice I choose to use: I can be sarcastic or plain-speaking, angry or calm, conciliatory or inflammatory. It doesn’t matter. If someone has already decided that they know what’s best in math education, and if some of what fuels that belief is grounded in the sorts of things that, for example, are quite common on your blog and on the blogs and discussion pages of many like-minded people – filled with religious, “patriotic,” and other sorts of content that are, well, quite different from what I’m interested in when it comes to mathematics education, then I’m undoubtedly the last person on the planet that individual is going to listen to.

So here is my final comment to you: unless you are actually interested in an exchange of ideas, please stop wasting your time and mine. You seem set on ignoring some pretty serious points I’ve tried to make about very specific mathematical ideas particular to teaching and understanding arithmetic. I would have thought you’d be eager to discuss such things, but instead, you keep harping on EM. And I really am not very interested in EM per se. If a good idea is in EM, I’m interested in that idea. If it’s in another book, I’m still interested in that idea. If something shows up in a book, or in someone’s blog post, or a magazine article that I think is confusing (maybe to me, mathematically, but more often likely to be confusing to K-5 kids and teachers), I comment on it. I ask QUESTIONS. And unless there’s a reason to do so, I try to keep the questions free of barbs and traps and gotchas. Which can be difficult after 20+ years of Math Wars, frankly.

I have sent specific criticisms about problems to authors of textbooks, including the folks who write EM. I have gotten feedback and thanks from them, and on occasion seen a change in the next edition as a result of my writing. That’s the way the world is supposed to work, at least as I see it. But I don’t think that’s of interest to you. I think you want me to say either “EM is the best book ever and if I’m wrong you may shoot me in the head,” or “EM is horrible, has nothing in it of value, and should be burned, along with its authors, editors, and anyone affiliated with the project.”

Well, neither of those will ever happen. Sorry. So if that’s what you need from me, give up.

On the other hand, if you want to have an intelligent, friendly conversation about various ways of thinking about arithmetic, as I think I suggested to you before, that would be just lovely. If you want to have a calm, reasonable discussion about how to improve mathematics teaching and learning so that we “lift the quality of math education across the board,” that could be useful (though maybe too big of a task to take on at once. Better, I suspect, is looking at small, specific ideas). But no more Math Wars-style stuff. I don’t have the interest or energy.

As for supplementing EM or any textbook series or other resource, what I’ve already written here should make it obvious to you what I think on that score, but I wanted to be sure you didn’t miss it. I was intrigued a number of years ago when I heard that Seattle Public Schools intended to blend EM and Singapore math in K-5, using the latter two days a week to supplement EM. Seemed like a reasonable idea. Don’t know how they made out with it. I hope it went well. I doubt that was a magic pill, but then I don’t know of any magic pills for teaching math or anything else. What I look for are ways to improve what we’re still a very long way from “perfecting” in the teaching and learning of math. Shouldn’t that be the goal? To reach more kids more effectively in ways that help them take pleasure from and find real, meaningful intellectual satisfaction in learning and doing mathematics and other subjects? If not, I guess the corporal punishment, hickory-stick, paddle, “no pain, no gain” crowd has it right, and we can openly turn our schools into prisons: seems like we’ve been heading in that direction – particularly in urban poor communities – for a long time.

cindy0803

said:Michael,

I have no wish to even be a part of the Math Wars. I have no agenda. I feel like I was sucked into this whole thing because I was looking for answers to problems I observed. I didn’t even have a name for those problems. My initial brick wall in public education did not begin with math but with Whole Language; a term I did not know existed until I started inputting symptoms and the name for the disease was revealed. I am a product of public education, and until my daughter entered it, I thought it was great. I was totally blindsided by the fact that I might not be happy with it. I guess you can either believe that or not.

At the risk of “wasting more of your time”, let me give you a little background about me, because I think you have erroneously put me in a box. You refer to MY friends and religion and minds being already made up, etc. This is not a religious blog. I started this blog not to be famous or get followers. Seriously, I could care less. That is why I chuckle at your words, “real or perceived audience”. See, I realize you are insulting me with these words. Either you think I’m stupid and believe it is over my head, or you can’t help yourself, or perhaps you don’t even realize it. I doubt the latter, but I would like to think that you are not a complete ass. Why? Because you work with kids.

People get away with being mean for no good reason other than the cheap thrill of it. Why? Because others allow it. This infuriates me. Most people don’t point out bad behavior because they dislike confrontation or they are trying to be polite or they don’t want to be bothered or they are afraid. This is the reason I started this blog and the whole reason you and I ever started conversing in the first place; because I took offense to how you were treating other people in a conversation about education (for no apparent reason other than you could). I was happy to just follow along and see what people were saying, but you were not happy just to make your point; you had to be cutting, surly, snarky and disrespectful. We all get frustrated and lash out, but I think you go beyond that. Perhaps you disagree.

Anyway, back to a little background about this blog, which you so aptly and rudely observe that not many people read. It was a way for me to try and stop being angry and maybe not feel like I was alone in the world in my disgust. I was mad at the way the last election cycle was going. Because I am a Christian, I got to see how many “Christians” (not all) justify their bigotry and lack of respect for the President, Democrats, or any Republican who strays from the party line. I was fed up. Politics and religion have no place together, and yes, I’ve made my mind up about that one, and I do not believe anyone will be able to change it. I make no apologies.

So, perhaps your experience with homeschool parents leads you to believe that I am the type of person who wants to just control what my daughter experiences socially, and therefore, you feel justified in dismissing me and insulting me about academics. That is not why I chose to homeschool, though I am not going to judge those parents who do, because I can tell you that the things I started to see even in elementary school were troubling. I dreaded the thought of Middle School. The elementary school counselor gave me a copy of “Queen Bees and Wannabees” to read. It was supposed to be a parent’s playbook for helping their child navigate Middle School and beyond, but I just found it disgusting. Anyway, I initially pulled my daughter out of school for purely academic reasons. The school was not meeting her needs. She is bright and should have been doing better (that means more than average). There were plenty of other children who fell in the same boat. I had the means to teach my child at home, and so I did and I do.

Education made its way onto the blog, not because I was homeschooling, but because after President Obama endorsed the Common Core, I began to see the same political misuse of education that I had seen other issues misused in the 2012 election cycle, and I felt education had no business being political. Whatever your position is on EM or Common Core (and by you, I mean YOU as in all of us), it should at least be rooted in a pinch of facts. I observed the religious right once again warping the truth to turn people away from the Common Core because they hate President Obama, just as I saw people on the left doing the same thing but for different reasons (you know what those are). And it’s not just the Common Core, it is education in general. Everyone seems to have a vested interest in maintaining the status quo. I don’t. My vested interest is my child. At some point, the rest of the world can go to hell in a handbasket, because my ultimate priority is to take care of my child. I am not going to apologize for that either.

I’m not a “professional” teacher, but I am intelligent (I know the jury is out on that as far as you are concerned). Furthermore, I have been a student and I try my very best to understand the breakdown between teaching and learning. I look for solutions. I am single-minded in my determination to uncover the whys and the hows. If not for my own personal experience at my daughter’s school, I may have very well found myself in the camp of anti-Common Core and anti-education reform. I would have been reacting strictly from my personal experience with public schools which was a good experience for me.

However, I go where the evidence leads me. You saw the math results for my school district which are significantly different than yours. You also know how Michigan fares overall in education, and it is not pretty. It is not acceptable. I weighed how much my daughter was learning at school, how effective the curriculum was or I perceived it to be, and how much she needed the kind of socialization she received at school against the kind of results I saw elsewhere, I decided public education in my district and in my state, in general, is substandard. Sure, there are pockets of acceptable teaching and learning, but that doesn’t mean there are not plenty of rotten apples. Even so, I still care about public education, and I hate to see it divided into black and white, because that ultimately hurts the kids who MUST use it. This is why I venture into the fray.

So, I agree with you that teachers should use whatever works. Wholeheartedly. What I didn’t see happening was anyone doing that. Lesson plans are made, workbooks are chosen, and the plan is followed for the duration. If there ARE changes, they are introduced in the following year. Well, that is too late. Most of the education politics and policies are top down driven. No one places enough emphasis on elementary education except to heap more work on it with more and more children in individual classrooms. It never seems to be about quality or support of any kind, especially the money.

Michael, I have tried to treat you as if you had an agenda other than insults and sarcasm. I think if we sat down across from each other where civility is more expected, we might discover that we have some things in common. But you seem to have nothing but contempt for me. You say you have asked me a lot of questions which I have not answered, but I reread your comments and only found one question mark (there were two, but one was a restatement of a question I asked you). I have asked you several times for you to summarize these questions I have avoided, yet I do not believe you have done so.

In the end, I am still unconvinced that EM is a good math program regardless of whether it has some good parts. Most teachers do not teach the parts, they teach the whole. Few supplement the whole or the parts. To the extent supplementation occurs, it occurs through the parents. I’m not certain if you disagree with me or not. You seem to want to just be a cog in the wheel by stating that the lattice method is not the anti-Christ of math. It is not just about lattice or partial products or any “one” tool of the whole. It is the whole I object to. It is the results I object to. If educators can find a way to implement EM or its likeminded brethren and produce results without a lot of extra effort on the part of parents, I will have no beef. I think other parents would have no beef either. It really is not that complicated.

P.S. I did not delete your comments that disappeared.

Michael Paul Goldenberg

said:Thanks for the response, Cindy. I will not have time to go through it line by line in reply, so forgive what will likely be many omissions or oversights on my part in what follows.

(In no particular order of importance): I wasn’t meaning to suggest you deleted anything. What happened was simply that when I hit send, something went amiss: the lengthy reply didn’t get sent and I couldn’t recover it. My son said, “Didn’t you copy it before you hit “Send”? Well, unfortunately, no, I didn’t. Sometimes I remember to do that, but not that time. 😦

And in what I hope is a conciliatory tone: I do NOT think you are stupid. Not at all. I think we have some fundamental differences in world view that I WISH I knew how to reconcile sufficiently that we were able to have comfortable disagreements and relaxed conversations. Maybe that is possible, maybe it isn’t. But to be fair, I will admit to have been less than cordial with you at times, as well as judgmental in ways that were off-putting. Part of that is a result of 20+ years of the Math Wars. Whether you WANT to be part of those or not, when anyone starts arguing math education issues online, chances are s/he will get the opportunity to participate. I can’t undo the huge investment of time, thought, and energy I’ve put into such debates, fights, arguments, and conversations. I’ve been badly-treated and have treated people as I thought they deserved, and after so long, I admittedly jump to conclusions about what any given person is bringing to the table. That’s unfair, but then you should recognize that much of what you say is familiar to me and comes with associations to a lot of other exchanges. I would have to be superhuman not to include a lot of those connections, but that isn’t your fault. I merely ask you to try to empathize a bit.

So if I’ve assumed specific things about you that are false, I apologize. I’ll try to avoid that in the future. Better than that I can’t do.

The unanswered questions remain, for me, SPECIFIC conversations about math teaching and learning. But you close your lengthy comment with something that makes it sound like you still see this as fundamentally a conversation about EM and “like-minded brethren”: I don’t think that way. The specifics are what matters to me and historically, attacks on progressive math teaching seem to hinge on throwing out examples of alternate ways of teaching and thinking about basic math and heaping mockery upon them. That’s going on all over the place now in the Common Core version of the Math Wars. I don’t want to have to repeat arguments I’ve made to you before about why it’s crucial to have conversations about THE MATH and to stop making this about EM or any single program. Just as you seem to want me to defend EM as a whole (and I’ve made clear that I have no intention of doing that for lots of reasons), I could try to make you “defend” Singapore or Saxon or Khan Academy, but it would be pointless (from my perspective). Those are textbooks, video lectures, etc., with some good and some bad in them. If you have found one or a combination that works for you, great. I don’t believe it’s that simple. And I think that each of those misses some very crucial elements of what mathematics is about, thus making it unlikely that any one of them or even a combination of their best elements will accomplish what I think needs to happen in K-5 math for many or most of our kids to really have a legitimate shot at serious mathematics at any meaningful level.

I wrote extensively yesterday about some of these issues yesterday on the Crazy Crawfish blog. Allow me to copy those comments here and see if any of it makes some sense to you. If so, I’d be interested in your thoughts. But no more on Everyday Math, Cindy. You can write about it all you like, but leave me out of that conversation, please.

==============================

“But if folks on all sides of these issues could stand back for a second, I think most people responding here are serious and reasonable (with some exceptions, of course). And what I see based on 20+ years of Math Wars debates is this: an on-going problem in the US with what it means to know and do mathematics, and how knowing and doing mathematics should inform teaching and learning mathematics in K-12. Most Americans see basic math as indistinguishable from calculation/computation. From that perspective, the idea is to get kids to be quick, accurate number crunchers. And maybe at some point in our history, that made sense, but it doesn’t any more and hasn’t for a very long time. Mathematics is a way of thinking about the world that involves numbers, true, but much more than numbers. And it isn’t strictly a matter of “Here’s some bunch of numbers, letters, and symbols on the left, an equals sign, and your job is to write the correct number to the right of that equals sign.”

People have written many books and articles on the above. I can’t possibly squeeze the excellent ideas that have been offered in them into a reasonable post here. But if you read the previous paragraph and thought to yourself: “Hey, that’s exactly what math is!” then I suggest you start with an article you can google and download free (it was later expanded into an even better book of the same name: A MATHEMATICIAN’S LAMENT by Paul Lockhart. Read the article. You might just start seeing a different and useful perspective on math and math education.

Otherwise, there will likely be mostly a lot of yelling past each other. I have been “accused” of being in agreement with crazycrawfish (by crazycrawfish) and I don’t disagree. But then, doesn’t that go both ways? And if so, where is the sense that most of us are on the same side, fighting for better teaching, better learning, and so forth? I’m not sure I feel that flowing toward the many things I’ve spent a lot of time trying to explain here (and other places, of course).

I understand the frustration Pi Lady expressed, and I understand why parents and teachers are firing shots that seem to be in opposition to that sort of viewpoint. Maybe that’s the sick genius of the folks behind the Common Core: they have a lot of us yelling at cross-purposes instead of listening more carefully for the many points of agreement.” [posted here http://bit.ly/1lYpwOl on Wed Jan 8, 2014]

cindy0803

said:Michael,

At the risk of sounding sappy, I am moved by your response. I did not expect it, which just goes to show you that we all prejudge.

I truly would like to see education, math included, focus on the individual. I think textbooks and workbooks should be the “extras” or resources, not necessarily the main tool for teaching. I think this is especially true for math. I do believe with all my heart, however, that students should have access to textbooks IN THEIR HANDS so they can look backward if they need to and can look ahead if they are capable.

Even among homeschoolers, many seek the magic bullet “text”. Texts for me are guides, even Singapore. I try to teach based on the feedback I get from the worksheets my daughter completes. My goal is to see improvement to the point where she is proficient up to my standards; which are high, I will admit. I also encourage application of higher order understanding at every opportunity and we celebrate when the connections are made, but I do NOT make them my focus at this stage of the game.

One homeschool mom, just recently out of public schools, looked at my daughter’s math workbook and said, “You are a tough grader.” I initially agreed with her but wished later that I had responded with, “I am a fair grader.” I think her reaction is indicative of many problems in education. First, grades are shunned, and second, parents cannot stand to see their child fail at anything…seriously, anything. I am not an ogre. I give my daughter the opportunity to redo a really poor outcome (if it is that poor, the fault is mine, not hers) and I always throw out the lowest grade, but she needs to have no delusions about her achievement. Achievement is not always about innate capabilities, it is also about effort and persistence. Effort and persistence are the very skills that are not happening in many schools because there are few drills. I have seen many with innate capabilities who do not put in the effort while those who work really hard run circles around them.

I will cop to using mockery for my distaste of many things, but I usually try to avoid that in education forums that are putting themselves out there as trying to solve education problems. But I have bad days, too, and sometimes my delivery carries more venom than is warranted. So I apologize for any past of future failures in this category.

I am intrigued by your statement, “Most Americans see basic math as indistinguishable from calculation/computation. From that perspective, the idea is to get kids to be quick, accurate number crunchers. And maybe at some point in our history, that made sense, but it doesn’t any more and hasn’t for a very long time. Mathematics is a way of thinking about the world that involves numbers, true, but much more than numbers. And it isn’t strictly a matter of “Here’s some bunch of numbers, letters, and symbols on the left, an equals sign, and your job is to write the correct number to the right of that equals sign.”

If I understand what you are saying, and I admit I might not, then we are in disagreement at a basic level. You see, I am in a business where number crunching is part of the process; I am a commercial real estate appraiser. I have had the opportunity to see appraisal work performed by appraisers who have no idea what the numbers they are putting on the paper mean and they make mistakes, even when using spreadsheets, because they understand neither the theory behind the math nor the calculation. These are people who have had theory as the cornerstone of their math education. I’ve seen children of family members and friends who can’t count back change, can’t reduce a recipe, and can’t figure out a percentage if their lives depended on it, but they can tell you what a rhombus is. Yes, there were plenty of people schooled the old way who were challenged in this area as well, but they WERE proficient in adding, subtracting, multiplying and dividing without a calculator. This is not the case with students today. It just isn’t working, in my opinion.

When I was in grade school, although I was considered “good” at math, I had a mind block when it came to telling time on an analog clock and with word problems. Perhaps if my teachers had employed some different teaching methods, I would have caught on quicker, but these deficiencies did not keep me from becoming proficient in the basics of math. In fact, because I could “do” math, it left me more time to focus on understanding the parts I was struggling with. There were many things that I did not understand in depth as I was being taught (not just math), but as I matured, the deeper understanding came. I could then use my drilled skills immediately and seamlessly on higher concepts. I understand that this is anecdotal, but it is a shared experience with my peers.

When I first started appraising, I was thrown into the deep end of the pool having to perform discounted cash flow analyses which required the computation of discount rates for each year of an income stream. My mentor was a no-nonsense, World War II veteran who graduated from Columbia after he came back from the war. He was not amused when I insisted that I wanted to compute the discount rates by hand. He felt it was a waste of time as I could do it quickly on the calculator. He was red-in-the-face, but he DID research the equation and presented it to me. Until I could compute the discount rate accurately by hand, I never used my calculator to do it. Did I understand all the nuances of discounting at that point? No, but I was able to recognize if a computer- or calculator-generated discount rate made sense. The deeper understanding came later.

So, when you say, “And it isn’t strictly a matter of ‘Here’s some bunch of numbers, letters, and symbols on the left, an equals sign, and your job is to write the correct number to the right of that equals sign,’” I tend to think that is exactly what math should be in elementary school, because that is primarily what children at that age are equipped to handle. Our understanding of the world through math came from the work of mathematicians throughout the ages. I doubt many of them were producing their greatest works at age nine or ten. Does that mean that some children are not able to understand more than just the basics? No, but I think the basics are most important and the deeper understanding should be introduced only as an adjunct at this age. Those who are ready to comprehend will and those who are not will possibly file it away until such time as it sticks, but it should not be “required” for proficiency.

It is possible that you agree because maybe your comments are aimed at Middle or High School. I’m not sure. This is the problem when we discuss education as K-12, because what perhaps makes sense in Middle or High School, say “group work”, backfires in elementary school. What I see at the elementary school level is equivalent to little girls and boys being forced to march around in their mother’s high heels and their father’s work boots. Forced. Once you get that picture in your mind, it just seems creepy.

When I read Lockhart’s piece, I am convinced that there are alternate universes at play in U.S. education. His frustration resonates with me, but I think – think – we are coming from different perspectives. Take this quote, for example: “A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”

Lockhart is trying to force the cloak of mathematician on elementary school students; at least I think he is. A mathematician, a painter, and a poet learn the basics first. So do musicians. Yes, some of it is boring. Maybe a lot of it is boring, but in everything we do, we take boring baby steps first.

My daughter wants to cut up onions with a knife before she learns how to use the knife or watches me do it, because that is FUN. There is no guarantee that if I turn her loose with the knife that she will automatically develop a deep love of cooking, although she might cut off a finger. And even if she doesn’t cut off a finger but merely survives with a couple of stitches, it doesn’t mean she will not get bored with the idea of cooking and decide she doesn’t much like “cooking” after all before she has even cooked. Instead of being schooled in the basics while anticipating the thrill of using her skills for the fancier culinary feats once the basics are mastered, her fire has been extinguished because she tried too much too soon. I guess she will eat out a lot when she moves out of our house.

I can understand that teachers want their students to have fun, and I don’t mean to belittle that desire, but parents don’t much care if their child likes to mop the floor or vacuum or clean a toilet. They think it is necessary that their children learn these skills and to learn them properly and efficiently. It is only by requiring them to DO them that they understand that mopping the floor BEFORE you clean the toilet might not be the best way to approach the task. Beautiful ideas are fine, but not every child has or is ready to have beautiful ideas about math regardless of how many Unifix cubes you place in their chubby little hands.

I am willing to agree with Lockhart that Calculus should probably be made more relevant (I still do not fully understand its usefulness after two semesters of university Calculus and another two of Differential Equations), but again, elementary math does not require such abstract thought. And although I hated with a passion High School Geometry, I do remember and use a number of its formulas.

I suppose at its most basic level, public education should be about what the public wants. I know that this will not sit well with a lot of – perhaps most – teachers, but it is the reality. If the public wants math taught as art and theory with little focus on paper and pencil skills, then that is what should happen in a democracy. But if the public wants their children to learn math skills to proficiency even if it means that higher understanding might not ever evolve, or might not evolve until much later, then that is what should happen in a democracy. If I was a teacher, and I believed my public school did not share my teaching philosophy, then I would choose to teach in a private school or another public school which did. And if I am a parent whose philosophy lies outside the mainstream, then I am the one who should choose an alternative route. Otherwise, everyone is miserable.

Michael Paul Goldenberg

said:I don’t think you sound sappy. Sounds like you took me at my word. I can’t ask for more than that.

My internet access is very limited these days, so I won’t be able to give your long reply the sort of response it deserves, at least not right now. But I would like to point you to a blog that I think might change your mind about what we could be doing – as educators and/or parents – with math teaching for all kids. I think we can go a lot further without having to abandon the kind of foundation you and others like you think is the whole story for K-5 math. There is a web page that I’ve only looked at briefly and which seems to be growing: http://talkingmathwithkids.com/

The blog is here: http://talkingmathwithkids.com/2014/01/13/more-patterns-on-the-multiplication-machine/ and I recommend that entry and the one that led to it as a good introduction to what Chris and his kids are up to. I briefly supervised him when he was doing his student teaching at U of M about 20 years ago. We reconnected about 2 years ago via his teaching blog which I also really like. We co-authored a piece that was critical of Sal Khan’s approach to lecturing that ran in the online Washington Post July before last

I really hope you’ll look at some of Chris’ writing on the Talking Math With Your Kids blog. It almost always makes me smile. And I believe it points to one approach that is generally missing from a majority of K-5 (and probably 6-12) math classrooms, regardless of what book is in use. Of course, it isn’t a trivial matter to scale what he’s doing to classrooms, particularly the really challenging, high-needs classrooms that SUPPOSEDLY are what the politicians and educational deformers are worried about (I frankly don’t believe most of their rhetoric, however). So much of what Chris does seems “obvious” once you read it, yet so little of that seems to go on. I worry a great deal more about how to make what he’s doing commonplace than I do about textbooks. Frankly, I’m sick of typical textbooks, more than you could possibly imagine.

Kat

said:Everyday Math is a good for children with “math sense”. If a child does not have “math sense” it only confuses them and leads to low self-esteem. I had a friend who loved “Everyday Math”. Her two boys excelled in math and she thought it was a terrific program. Couldn’t understand why I thought it was horrid. Until she had her daughter. She struggled in math, and then my friend finally got why I disliked the program so much.

My sister has two adult boys who grew up with “Everyday Math”. They were both A students in math and are planning on being accountants. When one of her sons took a math class in college, he struggled for the first time. They were studying material he had never had in high school. His friend (also an A math student in high school) had to get tutoring in college for math.

Mathnasium where we enrolled my daughter for a year and a half, had many, many middle school students enrolled. Those students struggled when they were no longer allowed to use the lattice method of doing multiplication. I did not allow my younger daughter to use that method during elementary school. My younger daughter has “math sense” and did fine with “Everyday Math”, but the state needs a program that is suitable for ALL students.

Michael Paul Goldenberg

said:First of all, I am very skeptical that any college professor would not let someone multiply using the lattice method unless that professor was Wayne Bishop or some similarly-minded “Math Warrior.” What reasonable person would care a fig for how someone arrived at the answer to multiplication problems (in college???) by hand, as long as the results were correct and the method used did not entail cheating (I’m assuming calculators weren’t allowed in this alleged classroom for some reason).

Second, you’re arguing against EM because those boys saw math they hadn’t seen in high school? Um, wouldn’t that have something to do with the high school program, rather than EM?

Third, you seem to be calling for a “math program that is suitable for all students.” Well, the Common Core gurus might well agree with you, but what program is suitable for ALL students, please? Particularly if there are in fact parents who are quite happy with a program that other parents dislike? How many pro-EM parents is enough to outweigh ONE anti-EM parent? Or vice versa?

The logical conclusion here is that there IS no one-size-fits-all approach to math education if you’re relying on a single text book or text book series (and not even if you only rely on text books!) We’re past the point where text books alone suffice or should be expected to. And there are good ideas in some books that don’t appear in others. Why shouldn’t teachers be allowed to use their professional judgment about marshaling as many available resources as they see fit based on the needs of the students they currently have to teach? Next year, that will change and the teachers should be prepared to change the mix of materials (text and non-text), and possibly find some new one(s).

But of course, if your goal is to eliminate the use of EM, or ensure that NO books or other resources are used that teach something you personally dislike (but can’t make a single valid mathematical argument against – like lattice multiplication), then no logical arguments of mine will persuade you to be more open minded or that you’ve made a call for some magic texts that frankly do not exist, never have, and never will. We’ve never been able to successfully educate ALL students in mathematics, not even in K-5 or K-6. The idea now is to do better, not return to some mythical era that never existed when “all” kids learning arithmetic well in this country. Considering that basic algebra was a COLLEGE class before the 1950s or so, it makes no sense to believe that we were churning out kids with really solid understanding of arithmetic on a routine basis, but those kids just couldn’t handle algebra, particularly given that the key to success in algebra is almost certainly a deep understanding of and facility with . . . arithmetic! My mom and aunt should have been whizzes at algebra – two very bright women who graduated high school in 1944 and 1937, respectively. Didn’t happen. Neither of them ever took it.

Stop fighting wars against textbooks and start looking at what it means to know and do mathematics in 2014, rather than, say, the imaginary Golden Era.

p.s.: I posted a reply to Cindy’s last comment here in which I recommended that she (and readers) look at two blogs by Christopher Danielson. Nothing to do with textbooks. One is called OVERTHINKING MY TEACHING. The other, probably more relevant one to her last comment is called TALKING MATH WITH YOUR KIDS. It’s brilliant and, in my opinion, goes far towards address some concerns raised here. Where that comment went I don’t know.

Michael Paul Goldenberg

said:Oh, I see that my comment about Chris Danielson is still awaiting moderation. Posted it on 1/17/14, a week ago today. Wonder why it’s still awaiting moderation. . .

cindy0803

said:Michael,

I will go check that now. I haven’t had a chance to jump on in several weeks. I don’t have my settings for moderation of replies, so I do not know why that would happen.

cindy0803

said:Michael,

The comment awaiting moderation was one that I saw, so the internet gods must be messing with me. I did approve the comment just now. Wonder if there will be two of them.

cindy0803

said:Michael,

I will look at the links. I’ve been swamped. This is the first chance I’ve had to jump on in a while.

Caduta dei capelli

said:I’m curious to find out what blog platform you have been working with?

I’m having some small security issues with my latest site and I’d like to find something

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