What’s So Elementary About Kindergarten Math?

It was back during the latter days of the Clinton Administration when I was hired for my first position as an elementary level math coordinator. This came after teaching middle school mathematics for the previous 15 years as well as earning an M.S. in elementary mathematics education. The fact that I had not spent a lot of time working with kindergarten through 4th grade children did not seem to deter the hiring committee, perhaps because there were not a lot of people who had expertise working with young children in mathematics. After all, if you were interested in mathematics, why would you want to work with little kids?

Is this all we can expect from elementary school math?

After a few weeks visiting classrooms and observing children at work, I was quickly disabused of the notion that there was not a lot happening in these classrooms. The concepts the students were working on were very complex and, as I spent a considerable portion of my day working with them one on one, there was a lot more that could be done with them beyond counting and making simple patterns. As I worked alongside teachers, I pointed out ways that their mathematics lessons could be richer, more engaging and challenging, while still reaching its intended audience. What I realized is that my previous 15 years of middle and upper school mathematics teaching was not a liability, but an actual advantage: Not only did I know what mathematics students would encounter a year later, but I had the additional foresight to know what these same children would learn 5 – 10 years down the road.

During this period of revelation, I found myself on a car ride with a colleague who taught in the the school’s high school program. As we were driving along, this teacher candidly stated her opinion of my professional work: “I don’t know why we need a lower school math coordinator; after all, aren’t these kids only learning how to add and subtract?”

I held my breath for a few minutes, and then, releasing it slowly, I suppressed my best Dan Akroyd imitation.  I calmly explained to her that the children at our school would learn more about mathematics between the ages of 5 and 10 than the entirety of their lives thereafter. It reminded me of Hillel’s dictum about studying Torah: whatever is abhorrent to yourself, do not do unto others. Everything else is commentary…. 

Everything this man knows about mathematics he learned in kindergarten….

If you think about it, all of advanced math is essentially an elaboration of what a child will learn in elementary school. Algebra is a generalization of arithmetic, while trigonometry builds upon the concepts of ratio and proportion. If you’ve read Dr. Seuss’s “The Cat in the Hat Comes Back,” where Cats A through Z are half the size of each succeeding iteration, then you will understand that he is describing the concept of a limit, from which we get, yes, calculus. Children’s literature is filled with descriptions of advanced mathematics, whether it is the concept of exponential growth described in “One Grain of Rice,” to the “crypto-arithmetic” problems posed in “More Sideways Arithmetic From The Wayside School.”

At the same time, there was plenty that had to be accomplished during the elementary school years when it came to the essentials of reading and writing numbers, as well as solving simple addition and subtraction problems. This does not mean that I had to hold back on doing in-depth investigations that would demonstrate powerful analytic tools while developing important ideas.

All of which lead me to develop an exploration that I conduct with the kindergarten class at my school, which involves an in-depth look at the children’s game, “Crocodile Dentist.”

Can this children's game be a lesson on data, statistics? and patterns

Can this children’s game be a lesson on data, statistics and patterns?

If you are the owner of this game, you know it mixes both surprise and terror: players take turns pushing down one of the lower teeth on this plastic reptile, until the croc “bites” the player who has selected the “dangerous” tooth. The biting tooth changes location each time the game is played, so the surprise comes because the players never know which tooth will bring down the jaw, or whether it will be the first, second or even the last one selected.

The idea of randomization is a fertile ground for exploring mathematics with young children, who are always concerned with the notion of “fairness.” Do all the teeth have the same opportunity to “bite” or do some come up more often than others? Is there a way to predict which tooth will be more dangerous than another, or is the game entirely arbitrary?

I introduced the game by explaining that as someone who is interested in math, this game made me wonder whether a “strategy” could be developed to figure out if some teeth were “safer” to press than others. How would we find out if this was true? This led the class into the concept of “sampling.” It was not enough to play a few games to determine if certain teeth bit more often than others; we would need to play a lot of games, and keep track of which teeth did the biting.

Results of 10 games played by a group of four kindergarteners.

Results of 10 games played by a group of four kindergarteners.

For the next four math sessions, I took a small group of kindergarteners out to play 10 rounds of Crocodile Dentist and recorded the results as a table on a sheet of chart paper:

As we were recording our results, the students learned about some important techniques used in mathematics: we organized the data we collected into a table, and that table is read both vertically and horizontally. They learned about the different kinds of numbers that could be used to describe the game.  For example, ordinal numbers show the “order” of things, like the first through 10th game played, while cardinal numbers record the number of times a specific tooth bit us (for example, tooth #3 bit us 4 times.) The also learned that a number could be used to locate a position, which is called a “nominal number.” In this case, there were 10 teeth on the game, and each one specified a certain location in the crocodile’s mouth.

The entire kindergarten class helped crunch the data from 40 "crocodile dentist" games.

The entire kindergarten class helped crunch the data from 40 “crocodile dentist” games.

The students also learned how to look for patterns in the data they collected: they saw that the same tooth might bite two, three times or even four times in a row, while others may pop up less often or not at all. At the end of each session, each member of the investigating group had to come up with a statement to describe some aspect of the data table we had constructed.

After working with all four groups, we assembled our findings at a “summit” where the 4 posters were displayed, and the class analyzed the results from 40 different games. Looking at the data, the class uncovered specific patterns that could be used to optimize one’s certainty of escaping a bite. For example, tooth #3 came up consistently in all 4 sessions, to the point where in one set of games, it bit us 4 times out of 10 games played. Tooth #2 was even worse: not only did it show up in all 4 samples, but with one group it bit 4 times in a row, for a total of 6 games altogether. This finding developed the idea of a ratios and how they could be compared: tooth #2 was more dangerous than tooth #3, because it came up 6 times out of 10 compared to 4 times out of 10.

The students also found that certain teeth were “safer” than other teeth. For example, tooth #1 was the losing tooth in only 2 out of the 4 sessions, and in those groups, it only bit once each time. Tooth #8 was an even safer bet: it showed up in one of the 4 investigations, and it only bit us once in all 40 games played.

Finally, we saw that while the data could help us make good choices while playing this game, nothing was certain: after discussing our findings, we played a round of Crocodile Dentist using our findings. We avoided teeth like #2 and #3, choosing teeth #10 and #9, which didn’t come up as often in the past. Wouldn’t you know it, but the tooth that bit us during that game was #8, a tooth which had been considered “extremely safe.” 

This investigation models what many would consider “good mathematics,” in that it develops powerful ideas in a context that is provocative and relatable. It motivates children to think analytically about something they might otherwise ignore, and, most of all, it’s just a lot of fun. For a kindergartner, “fun’ is the most important attribute to learning about mathematics (and shouldn’t it be for us all?)

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Have charter schools become a “meme”?

I had to wait a few weeks to post this, because the whole situation made my blood boil, but now that the dog days of August are upon us, and my ire has had a chance to mutate to annoyance, I have reached a conclusion: you know something is wrong with the concept of charter schools when they have become “memes.”

Truthfully, I don’t really know what a “meme”  is, except that they seem to have something to do with the internet and are cultivated and disseminated by young people with lots of time on their hands. Since I have spent a lot of time studying concept development, I utilized my “go to” method to help me understand what exactly a “meme” is: I perform a “search” on that word, and then click on “images” so I can view as many examples as I can. By looking at dozens of examples, I hoped to build a mental prototype of “meme.”

Using this method, I have determined that a “meme” is when you take a photo, place some snarky phrase over it in white using the font “Impact,” and then post it on Facebook, Pinterest or Tumblr.

But this didn’t account for the great interest in memes and their widespread dissemination. I decided I had to do more to investigate, so I searched for definitions. Here’s what I found:

  1. A meme is an element of a culture or system of behavior that may be considered to be passed from one individual to another by nongenetic means, especially imitation.
  2. A meme is a humorous image, video, piece of text, etc. that is copied (often with slight variations) and spread rapidly by Internet users.

Okay, this is beginning to make more sense, especially if I regard a “meme” according to the first sense. If this be the definition, I have reached the following conclusion: charter schools have become “memes.”

Which brings me to my story: I was at my school’s end-of-the-year shindig, which is usually sponsored by our parents’ association and takes place at a somewhat mid-scale but convivial eatery which will supply us with copious amounts of alcohol and fatty food to reward ourselves for a year well done.  There were about 30 of us in attendance, and we spanned a wide range of age, sexual orientation, skin color and height, which is why I love my school: we may be poor in money, but we’re super-rich in diversity.

Nearby was another long table loaded with a much less diverse crowd: it was primarily 20-something caucasian women with a few men of similar age and skin color sprinkled liberally among the crowd. There were one or two “adults” sitting in a clump at the head of the table, and I even spotted one of two people of color, but for the most part it was a pretty homogenous group, and they were clearly enjoying their margaritas. I concluded that this was not a law firm (too few geezers), nor were they celebrating the successful IPO of an internet startup (the restaurant was not fancy enough and there were too many women), and it certainly wasn’t a reunion of the Bethune-Cookman University “Wildcats.” 

I am nosey by nature, so I did a slow recon around the table and confirmed my suspicion: these were indeed the faculty and staff from a school. However, something was not right: the demographics were all off. I’ve worked in numerous private and public schools, and while teaching always attracts a lot of young, white women, even the most upscale private schools have a wide range of ages in their faculty and have embraced hiring policies which encourage diverse and inclusive teaching populations. Whatever this school’s mission was, diversity (at least in faculty recruitment) was not high on its list.

So I was quite miffed by this group: what kind of school has a nearly all white, all 20-something, all female faculty? I approached the maitre-de and offered to buy her a sandwich (my typical bribe) if she would tell me which school was being feted at the table nearby. She looked down at her clipboard and announced, “Oh, that’s the ….. School.”

I pride myself in having my ear to the ground on the goings on when it comes to schools in NYC (I’m a reluctant reader of Chalkface and even follow Beth Fertig on Twitter), so I was somewhat taken aback that one had escaped my notice. I whipped out my iPhone, conducted a search on the school in question and was chagrined by what I read. No, I was beyond chagrined: I was incensed. Here’s all you need to know:

  • Charter school
  • Hedge fund managers on Board of Directors
  • African-American student population

The NYC charter meme may include these uniforms, but it certainly won’t include these girls.

I didn’t read any further: this could have been the webpage for any number of charters that have sprung up over the New York City area. You have to admire the audacity in creating a school which fit the charter school mold so completely (this one was barely 3 years old.) All you have to do is throw in the khaki-pants-with-polo-shirt-with-school-logo uniform and a “no excuses” discipline code and >poof<, you done got a charter school!

This reinforces the saddness I feel whenever I hear the praises undeservedly heaped on the whole “charter school” movement, because it seems to me that the original intent of the charter school laws was to create “new” and “innovative” kinds of schools that “experimented” with different models of learning and instruction. Instead, what has emerged are endless numbers of cookie cutter schools which lack any individual identity or unique personality, where only the desperate and/or misinformed send their children, and where those who do not “make the cut” in the pressure-cooker classes are summarily “counseled out” to neighboring public schools which are obligated to educate those “rejects” (and my guess is that many of those “rejects” are going to emerge as some very brilliant and wonderful adults, if my 30 year tenure in education is any guide….)

Charters are not innovators in any way, shape or form, unless you consider it an “innovation” to underpay and overwork your novice, young faculty, discriminate against English language learners and those requiring special services, and focus relentlessly on high test scores. Of course, you need hedge fund sharks to fund the whole enterprise, and some young, white, primarily female teachers to staff the classrooms, but neither of these seem to be in short supply. Oh, and don’t forget the students…

Coming to a Tumblr blog near you!

Coming to a Tumblr blog near you!

I’m in favor of having all sorts of schools, where informed parents can rest assured that their children are getting a high quality education from a faculty that is professional, diverse and committed. However, I think that charter schools like these are not really schools at all: they offer nothing innovative or interesting; rather, they are memes, which is what seems to attract young people nowadays.

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Do “Americans” really stink at math? Let’s check the numbers.

Last week, journalist and statistical illiterate Elizabeth Green published a highly visible article in the New York Times Magazine that proclaimed that we, the citizens of these United States, “stink” at math. I castigated Green for her misuse of actual data to back up the enticing headline, and while the article had nothing new to say (Stigler and Stevenson had a go at the Asia/US comparison back in 1994), I thought for the most part her comparison of math teaching and the culture of education in Japan and the U.S. held up pretty well.

Now it’s time for my response: Ms. Green, you are wrong – in point of fact, Americans are very good at math, but forget the Japanese, we should be looking at France if we want to see what great math education looks like. How do I know this? I used data!

The Fields Medal is the world’s most prestigious award for mathematics achievement. It is given out every 4 years to a select group of mathematicians around the world for outstanding discoveries in mathematics. It is much more selective than the Nobel Prize,  and while the money is not so great, the distinction is far, far higher.

In its 78 year history, the Fields Medal has been awarded to 54 different individuals from around the world. Here are the standings for the top 10 countries:

  1. The United States of America: 12 winners
  2. France: 10 winners
  3. Russia/Soviet Union: 9 winners
  4. United Kingdom: 6 winners
  5. Japan: 3 winners
  6. Belgium: 2 winners
  7. Germany: 1 winner
  8. Australia: 1 winner
  9. British Hong Kong: 1 winner
  10. Finland: 1 winner

It seems to me if we look at these numbers, the United States looks pretty good – in fact, I would go so far as to say that we totally kick ass! However, before I paint a rosy picture of math achievement in the U.S.A., it should also be known that the last Fields Medal winner from the U.S. was back in, wait for it, 1998! Meanwhile, oh la la, those wacky French and those studious and  irrepressible Russians have been cleaning our clocks: both countries have taken home 4 medals apiece in the last dozen years. And where is Ms. Green’s beloved Japan in this race? Ha, they have only 1 medal, and that was almost a quarter century ago (1990.)

Is this the face of the next United States math education innovation?

What can we conclude from the above data? Well, contrary to Ms. Green’s assertion, and when use factual, measurable and realistic comparison with other countries, it seems like our educational system is doing a very good job at teaching mathematics. If you look at the top 10 institutions that created winners of the Fields Medal, half of them are located in the United States of America! However, I would still keep an eye on the French: three of their institutions were in the top 10, while, wouldn’t you know it, Moscow State University languished at 11th place, and Kyoto University was well at the bottom. The United States may only take up a tiny fraction of the earth’s surface area, but we’ve totally got a complete lock on mathematical research and innovation.

Nowhere in this field do you see the originators of the latest über trendy mathematics program, Singapore. It seems while they are able to get their students to perform highly on the international math tests, they can’t actually spawn a world class mathematician. Frankly, I don’t think this speaks very highly of their educational system. If we’re going to model mathematics education on the practice in any free country, it seems to me we should be following the French. Okay, their food is very fattening and they love Jerry Lewis, but if we want to continue leading the world in mathematics achievement, sacrifices must be made!

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Why the New York Times Stinks at Math

I love it when my hometown rag, The New York Times, attempts to publish something provocative about the state of mathematics and teaching. Yes, the Times has not aged well, and I often wonder if the editors of the various lifestyle sections, including “Style,” “Home,” “Food & Dining,” and “Travel” section live in the same economic climate as the bottom 99% of us, but I do admire the investigative reporting, especially when they decide to do something like pantsing that mendacious asshole, Andrew Cuomo.

So it was with curious interest that I had a look at Elizabeth Green’s article in the July 23rd edition of the New York Times Magazine, “Why Americans Stink At Math.”  Me, I love a good screed disparaging Americans as much as anyone else, although I would like to point out to Ms. Green that “America” is composed of two continents, North and South, and that even if she were referring to North America, we do share this continent with Mexico and Canada. Oh, and then there’s that issue about those people who were here before there was an “America,” but let’s not get technical, okay?

This article is clearly well-researched, and I hope Ms. Green’s book sells well and that “Chalkbeat,” the website where she is the chief executive, gets a bazillion hits. However, it appears that Green herself is pretty poor at math herself, and the Times let her get away with it. Of course, perhaps the Columbia School of Journalism doesn’t require that their students take a basic course in statistics.

Where should we begin? Perhaps the title is a good place: if you’re going to write about how bad “Americans” are at mathematics, it’s probably a good idea to get some reliable and relevant data to back it up. Unfortunately, the “data” that is thrown down in this article is, to put it politely, piss poor.

The first place where Green goes wrong is when she cites “national test results”  about mathematics achievement in the U.S.. First, I wonder which “test results” Green is referencing here (you have to be suspicious when, in the days of the omnipresent interweb, a link is not included to the data supporting this point.)  It may be significant that 2/3 of all 4th and 8th graders are not “proficient” in math, but again, this is a national standard, not an international standard, so this only points to the fact that U.S. children are not achieving according to some standard that was created where, in some dark cave where Dick Cheney and his family reside?

Green goes on to state that half the 4th and 8th graders taking the National Assessment of Educational Progress could not read a thermometer, or that 3/4 of the test takers could not translate a simple word problem into an algebraic expression. Note that this is the National Assessment of Educational Progress – it doesn’t say anything about whether U.S. children are better or worse than anybody else around the globe; for all we know, 7/8 of  the children in Helsinki and 11/13 of the children in Ibaraki couldn’t successfully answer these questions either. Look, I’m not the sharpest pencil in the box, but even I know these numbers are insignificant without a context.

The one mention of an international comparison is that students in Massachusetts, which many of us know is a “state,” lag two years behind their counterparts in Shanghai, China, which if I understand it correctly, is a “city.” Yes, and would you be surprised to learn that the students at the Bronx High School of Science outperformed those in the village of Zhuangjiashan, China? Cherry picking data is never a good idea, except if you can use it to back up a sensational headline (or you are a best selling author.) Oh, and if Ms. Green bothered to do her research, she would have found out that the scores in Shanghai are cherry picked themselves: according to an investigative report by The Guardian, many children in Shanghai are barred from taking these kinds of tests.

Green goes on to cite how the picture does not get better into adulthood (I wonder if she is talking about her own understanding of statistics?) Green uses a 2012 study (which remains unspecified) about how U.S. adults ranked in the bottom 5 of 20 countries in numeracy. Which countries these are, we do not know. What the sample size is, we do not know. How the samples were chosen, we do not know. The only study I know of that was done comparing math proficiency in adults internationally was by the “Program for International Assessment of Adult Competencies” that compared 23 countries and put the U.S. third last.  However, that result had so many methodological flaws that I had to tear it down in a separate blog post that I titled “Is this the most ignorant article about the Common Core ever written?”  If Green has some better data on this, I would love to see it.

Green follows this up with some scary data about miscalculations in the medical profession, including doctors and pharmacists, just to help show how very afraid we should all be. However, this “evidence” is junky as well: does the U.S. rank higher in medical computational errors than other countries or not? Isn’t this an article that is putting forth the thesis that “Americans” are worse at math than everyone else? I wonder if other professions have higher rate of alleged innumeracy, including writers reporting on mathematics education? Ms. Green, would you mind calculating the integral of X squared for me?

I won’t even go on about the A&W burger story and fractions, besides the fact that I was unable to find a reference that it was actually true… the only mention I could find was a case study described in a blog post in 2013, which also, curiously enough, was unreferenced…. It sounds like a good story, but like many other urban legends, this might be one that stands alongside the worms in McDonald’s hamburgers?

Besides the dubious statistics Green uses to promote her cause, I would also like to take her to task by referencing the Louis CK debacle on “Common Core Mathematics.” I followed this story very carefully, and can tell you that the issue being described had nothing to do with the Common Core or mathematics education. What it really was about, in my estimation, is that parents should not really be helping their kids with math homework: it is a subject that is bound up in all sorts of emotions concerning intelligence and anxiety, and since the teaching of it changes every few years, parents inadvertently end up transferring their anxieties to their children. As someone who has worked in the field of teaching mathematics for the past 3 decades, I can tell you right now that the first piece of advice I give parents about promoting their children’s achievement in mathematics is butt out of helping with their homework assignments.

The rest of the article, when it avoided any mention of data, was a good read, and I always enjoy hearing about the work of the wonderful Magdelene Lampert, who is a legend in the world of education. Ms. Green may not know much about statistics, but you can’t beat her narrative ability; my only hope is that she’ll hire a statistician next time to help support her claims.



Posted in Common Core State Standards, International Assessments, The New York Times | Leave a comment

What Bad Assessment Looks Like, Go Math! Style….

As many of my loyal (and not so loyal) readers know, among the things I’m attempting this year is to help a K – 3 public school in an impoverished area of the Bronx implement an alleged “CCSS aligned” curriculum. I’m not a fan of most math curricula I’ve seen, and even the best require some kind of adaptation to be effective with the classroom population Go Math!, however, is among the worst of the worst I’ve encountered, and in my short tenure attempting to adapt it, I find myself mostly doing to the work of informing teachers what not to do, which includes correcting mistakes in terminology and developmental appropriateness.

In this post, I’m going to be discussing assessment: much of Go Math! relies on “end of chapter” exams that focus on multiple choice questions that are either poorly worded or completely inappropriate. One of the criticisms leveled at Go Math! has been its almost pathologic focus on procedures, without giving adequate coverage of concept development and higher order thinking (despite the fact that the graphic designers sprinkled the workbooks with “HOT Problem” logos that are not very “high” or require much in the way of “thinking.”)

The latest howler came in the 3rd grade chapter on area and perimeter. Most of the multiple choice questions don’t actually require any kind of thinking beyond remembering to count boxes when the word “area” appears in the question, or counting line segments when “perimeter” appears, which includes this task:

Can you figure out why this is a cruddy question?

Can you figure out why this is a cruddy question?

Okay, it’s not bad enough that most of the test asks exactly the same type of question over and over again, but if you really wanted to assess whether a student knows the difference between finding the area of a shape and perimeter, wouldn’t it be a good idea to provide shapes where the area and perimeter are not the same? 

My suspicion began when out of the 40 tests I looked at, each and every student got the question correct. Okay, it’s not a very difficult question to begin with, but when I looked at the work provided, I noticed that half the students had numbered the squares inside, and the other half numbered the line segments around the outside and came up with 22! Perhaps I’m a little misinformed here, but what exactly is this question assessing? (Let’s set aside the fact that Jake’s bedroom is 22 square meters, or 237 square feet, which makes it larger than the Superior Queen Room at the SoHo Grand in NYC.)

This is not to say that multiple choice tests are all evil; however, if you’re going to go through the trouble of wasting a child’s time with these type of assessments, at least make them interesting and meaningful. This is a garbage question that does nothing to help a teacher assess a student’s understanding of perimeter and area, and whatever 20-something year old editor who allowed this to appear should be fired, or confirmed as a replacement for Arne Duncan.

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Just to be clear….


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Is this the most ignorant article EVER about Common Core Math?

“Vox” is a website that claims to explain “everything you need to know in two minutes,” but it took me a lot less time than that to figure out this may the stupidest article about the Common Core math program I’ve ever read. Full disclosure: this is only true if what you mean by “read” is “look at this hideously stupid graph which the author used to support her point.”

And here it is!

stupid math graph

I’ve never actually heard of the “Program for International Assessment of Adult Competencies,” but I’m pretty certain CCSS or non-CCSS trained 7th graders know that a graph that lists the outcomes of a scored measurement without stating the highest possible score is immediately suspect. I’ll get to some assumptions later, but basically this is telling us that whatever sample of US adults took this test did 88% as well as the adults in the top scoring nation, Japan. I think that’s pretty damned good, considering the United States is second to the world in poverty, leaving Japan in the dust by over 10 percentage points (and I’m sure Japan uses a much higher economic benchmark for poverty than we do here in the US.) Of course, we all know that poverty is the single greatest predictor of poor school performance.

But let’s make an assumption: suppose the top score on this alleged exam was, what, 300? That means that the Japanese adults scored 288 out of 300, while the United States adults score 253 out of 300, which puts the Japanese at 96%, leaving us in the dust with a competency of 84.3%, which whittles the 25 point difference to less than 12 percentage points. This leaves aside that it is completely unknown whether the sample was somewhat random (Japanese engineers versus United States journalism majors, perhaps?) or even large enough to be statistically significant.

Oh, and incidentally, whoever made this graph would have lost a significant number of points on the 3rd grade New York State math exam because he/she did not label the “0″ on the horizontal axis, nor include an incremented scale…

The article goes on to feature two videos from the websites, LearnZillions and Khan Academy, which share the dubious distinction of being the epitome of what “bad” math teaching looks like. There are also quotes from Dan Meyer, a one-man publicity machine who believes he speaks for all math teachers, despite the fact that he spent exactly 5 years teaching in an actual classroom.

Finally, this article is yet another example of the “waking up on third base” phenomena, which posits that everything that you see in a Common Core math curriculum is the direct result of the implementation of the Standards. Nothing could be further from the truth: all of the items described on in the article have been documented, published and taught since the NCTM published its curriculum standards a quarter of a century ago. If you’ve been teaching math using a textbook that was published in the last 20 years, you’ve probably seen all this stuff before including, with all deference to Mr. Colbert, the infamous description of a “number sentence.” Telegram for Mr. Colbert: 1989 is writing to tell you to “LOL!”

I love it when people who know little to nothing about education (Libby Nelson, the author of this piece of junk, is a journalism major who has written for Politico and something called Northwestern Magazine) try to dip their toes into a controversial subject like the Common Core and then end up getting eaten alive by people like me. Actually, I don’t love it, but it does make me angry because a formerly respected organization like the NCTM actually tweeted the link to this worthless piece of codswallum, and smelling something rotten, I just had to follow the scent.




Posted in Common Core State Standards, Khan Academy | 2 Comments

Yo, @LouisCK : We Need To Have A Dad-to-Dad Talk About Math, Homework & the CCSS

Dear Louis CK:

Okay, I’m a fan and I love your work. End of fawning admiration. I want to talk to you dad-to-dad about your daughter’s homework, the Common Core, and the fate of the world. Seriously, I do.

I’m sorry your daughter got a math homework assignment that was so confusing and led to discord in your  tranquil home. I’ve been a math teacher for the past 30 years, and if your daughter had been in my class, I’m sure she would have come home with these types of assignments on a regular basis. It’s not that I want to torture your child or make you feel dumb. It’s just that part of the unspoken agreement between schools and parents is that children must get homework, and the more challenging it is, the better. This is because we’re currently in an educational era where teachers can get away with developmentally inappropriate assignments by citing the “fact” that we now have “high standards,” and that we’re trying to “challenge our students to do their best.”

This runs counter to the fact that homework has never been shown to be effective. If that isn’t bad enough, helping your child with homework does not lead to better long term outcomes. Sure, it may make you feel as if you are being a “good parent,” but there are lots of ways to be a good dad; unfortunately, getting involved in school just doesn’t happen to be one of them.

Let me cite my own personal history: I have a 22 year old daughter. When she was in elementary school, I took it upon myself to help her with her math homework. I mean, who would be better than a math teacher with an MS in elementary mathematics education? What could go wrong?

A lot, it turned out. First, as an “expert” on mathematics teaching, I was appalled at 90% of the homework that my daughter had to do. I frequently found it confusing, inappropriate and just plain dull. This did not endear me to my daughter or her teachers. Once, while I was attempting to help my kid with an activity that required her to order fractions, I was told that I didn’t know what I was talking about. This was followed by a door slam.

After several incidents like this, I finally waved the white flag and admitted defeat: imagine how humiliating it was to admit that the teacher who spent his days bringing great math to his students couldn’t do it with his own kid. At the same time, I had a realization: mathematics, despite its seeming neutrality, is the most emotional subject taught in school, for a variety of reasons. The most salient one is that it is the subject that we use to gauge our own intelligence. Other subjects, like language arts and social studies are “interpretive,” so there is certain amount of “wiggle room” when answering questions. By way of contrast, mathematics is about logic and process, and when you start engaging with your kid in these two domains, you’re asking for trouble.

My solution was to step down: I told my daughter that she should spend a reasonable amount of focused time doing her math homework, and if there were questions that were confusing or difficult, she would give it the old college try and then bring it into school. Her teachers were invariably understanding and she never felt singled out, as other kids in her class also found math confusing. It’s just the nature of mathematics: deal with it. If we tried to make it easier, it would no longer be mathematics.

Take my advice: let your kid do her math homework on her own, and if she finds it frustrating, tell her she’s most likely not alone, make her a nice cup of chamomile tea, sit on the couch and read a book together. That’s what good dads do.

Which brings me to the Common Core: I agree, the Common Core State Standards are idiotic, but not for the reasons you may think. My disagreement is more than the fact that they are vague, poorly written and inappropriate; my problem is that they will never accomplish what they claim. They will not create a new generation of new “college and career ready” children, they will not make them more likely to get good jobs, and they will not make them good citizens in this poorly functioning democracy. In fact, it will not lead to a great future for our kids, or for anybody else for that matter. This is because no matter whether CCSS sticks around or dies a slow death, the future for our children is going to suck, and when our grown children are fending off the marauding hordes and baking away during the 140º summers, the issue of the viability of the Common Core State Standards is going to be as relevant to our survival as the current size of a Kardashian butt.

The real danger of the CCSS is that it distracts us from the real problems of the world, which includes the plots hatched by mendacious assholes like the Koch Brothers who are busy polluting our environment, stripping away our basic rights and pushing poor slobs like us into financial ruin. The advocates of the CCSS have made lots of noise about  “raising the bar” and all sorts of other nonsense relating to world competitiveness (which I have covered here), but in the end, it’s probably best to pay no attention to that man behind the curtain. Seriously, speaking dad-to-dad, you’ve got better things to do with your time. Now would you get back to making us laugh?

Posted in Common Core State Standards, Math Anxiety, Research | Leave a comment

“Waking up on third base” & Why CCSS Boasts Are Hollow

Jim Hightower, whom many of us in the over-40 set will remember as the plainspoken former Texas politician, once described former “president” George H.W. Bush as someone who “was born on third base and thinks he hit a triple.” Hightower was speaking about Bush the Younger’s proclamation of accomplishments that were, in fact, “inherited” through his family connections.

I feel the same way when I hear the constant comments from the CCSS supporters who are claiming that education has been “transformed” as a result of the implementation of these most dubious of “standards.”

EngageNY, New York’s own propaganda organ for the CCSS, and John King, New York’s own “Commissioner of Education,” have entertaining Twitter feeds that are continuously guilty of the “waking up on third base” claim. Let’s look at some of my favorites:

Jonathan King’s claim: “It was great to see how hands-on and comfortable students at JD George are with Common Core standards.”

My comment: Really? Compared to what? Do you have any proof that the students were not “hands on” and “comfortable” before Common Core standards were implemented? Many CCSS proponents seem to have a “before CCSS” and “after CCSS” view, as if one day everybody woke up and realized “hey, we haven’t been allowed to teach interesting lessons under the ‘old’ system. But CCSS has arrived and liberated us! Huzzah, huzzah!”

I’ve been in education for the past 30 years, and believe me, if you’re a well trained teacher who has been keeping abreast of contemporary methodology and practice, the CCSS will not seem “new” or “novel.” (They will, however, seem confusing, arbitrary and inappropriate.) Furthermore, the CCSS may actually inhibit teachers from doing all the higher level thinking they did before CCSS arrived to save U.S. education, especially if your school adopted one of those cruddy “Common Core Aligned” textbooks that focus on low levels of thinking.

Here’s another howler, this time from the EngageNY Twitter feed:

“Parents are hearing that their children feel more prepared for college with Common Core.” 

I didn’t have to get more than 2 seconds into the linked video to shut it off and whisper under my breath: THE PLURAL OF ANECDOTE IS NOT DATA, THE PLURAL OF ANECDOTE IS NOT DATA! On what basis is this claim even remotely true? Was there a double blind experiment performed in which a large sample of students from non-CCSS schools and CCSS implemented schools were compared to see who had better success rates at their comparable colleges? Were the subjects “pre-tested” to compare the difference between “before CCSS” and “after CCSS” cohorts? Where there linear regressions, and Kruskal-Wallis tests performed, maybe an ANOVA here or there? Can this claim withstand any claim of “rigor?” Even more important, would a student who was not educated using CCSS be able to smell the rampant BS in this video?

Well, I was educated in the New York State public school system (Jericho High School, class of ’77), decades before CCSS was a glimmer in Bill Gates’ eye, and somehow I learned the skills necessary to “write arguments to support claims with clear reasons and relevant evidence” (that would be CCSS.ELA-LITERACY.W.6.1.A, in case you were wondering….) I intend to apply that standard to this Twitter statement, which, if you are reading this blog post, should convince you that I, in fact, possess these “before CCSS” skills.

Let me proceed:

The “sample size” in this video is all of 2 students, one of whom is in college, while the other is in 8th grade. And just so you don’t think there was any “sample bias” here, the “expert” who is telling us this story is… wait for it… their mother! The “evidence” presented is thin at best, and is based on an “opinion” rather than an actual “fact.” Furthermore, it is my claim that this may be an example of “cherry picking,” and not a representative sample, based on the fact that this was promoted by the leading propaganda source for CCSS in New York State, EngageNY. Using my non-CCSS implemented writing and analytic skills, I can conclude that this Twitter statement is lacking any sort of veracity.

There are a few teachers out there who truly believed that the CCSS has “improved their game,” but if I was one of them, I would not want to admit to that, the implication being that I was one of those “plug and play” educators who never taught anything beyond the basic skills (unless you were trained in the “back to basics” movement….) In my field of mathematics education, the NCTM Standards and Focal Points are old hat: we knew how to design and implement curricula that were based on conceptual understanding, problem solving and procedural fluency decades before the shining light of CCSS shone upon us. Seriously, I don’t understand how CCSS proponents can claim that anything in the standards are “forward thinking,” unless you define “forward” as “backwards.” In an era where the word “literally” is a synonym for “figuratively,” this might be a little true.

Posted in Common Core State Standards, Junk, Uncategorized | 2 Comments

Now that she’s got the kids, where to find teachers?

If you remember a previous post, I pointed out that the Success Academy Charter Schools was advertising for students in some very interesting places, which included my neighborhood of Park Slope, as well as a website where I publish educational materials. How happy I was that the deadline passed, and  no longer have to look a these ads begging me to fill out a form so that my child can enter their “lottery.” (Yeah, like I would buy a ticket for that contest, even if it was free….)

Well, now that Eva has gotten all her eager young students ready to grace her halls this coming fall (including the building where she is going to displace a program for handicapped students who will have to travel miles away), it looks like she’ll be needing teachers to educate those eager young minds. So what do I see when I log into my TeachersPayTeachers account? You guessed it:


Want to join the team? Eva's got room for you (well, not if you're too expensive, that is...)

Want to join the team? Eva’s got room for you (well, not if you’re too expensive, that is…)


and this!


It gets even better when you arrive at the web site: prospective applicants are told the following:

At Success Academy, we make history every single day. Our schools rank in the top 1% in math and top 7% in reading among all New York schools. 100% of all scholars passed the 2013 science exam with 99% earning the highest possible rating. We provide an exploration driven curriculum for grades K-8, focused on the whole child. Chess, art, and other specialized subjects bring excitement to the school day and foster a lifelong love of learning. Our communities are calling for more, and we are meeting this urgent demand with rapid expansion.

If that doesn’t qualify as hyperbole, I don’t know what does, especially because much of what is in this paragraph is not actually “true.” But then again, everyone loves working with a winner, so why not invite all those eager, underemployed, impressionable and disposable youths to do this:

Are you ready to join this movement and make an indelible mark on education reform across New York City?

That is, if the “movement” is funded by such right-wing “philanthropies” like the Walton Family Foundation or pseudo-educational foundations intent on compromising public education like Bill & Melinda Gates, not to mention the billionaire hedge-fund managers who crashed the economy and threw tens of thousands of people out of work. Yes, this is the type of ‘movement’ I want to join!

I’m truly tempted to “apply now,” if only to see whether I could actually game something beyond a cursory “thank you for your application; we’ll contact you if you have any positions open in your area.”

Of course, being a 54 year old man finishing his 30th year in education in a “high needs” area (math and science), I’m a most unlikely candidate for any position at Success Academy, where young, inexperienced teachers probably fit their needs a bit better. I probably couldn’t put up with the demands of the work day (at 54 years old, teaching for 8 hours with just a lunch break is most likely beyond my stamina), and being bossed around by an “education manager” who has 2-3 years in “people management” is probably going to grate on my nerves (especially when I’ll have to spend most  of my time improving test scores and making sure kids look ‘straight ahead’ at all times.)

On second thought, I’ll keep my day job.


Posted in charter schools, Uncategorized | Leave a comment