Interviews I never finished reading, Dept.

This one is from a blog called “Cool Cat Teacher” that ostensibly presents hip, new, ideas about education as a refutation of the stuffy old traditional methods that people have claimed “never worked”, or if they did, “only for a few people.”

This particular blurb is an interview with a history teacher called Keith “Hip” Hughes, who has some ideas about “flipping the classroom”.

The basic idea is to try to reduce the amount of time you’re talking to kids from the front of the room. I think sometimes we have this illusion that the kids are learning in the space between our mouths and their ears, and I’m not sure how much that might be happening. So “flipping” is saying, “Let’s have the kids get the content somewhere other than the classroom.” Many times, that could be a reader, but many times it could be a really great video that explains a concept that you would normally be explaining in front of the room. You’re probably still going to have to review it. But the idea is to free up time in your class so kids that are working through skill-based activities that might in the past have been done as homework. Now (those) can be doing that in class with your facilitation.  The next step is designing projects and really having kids doing authentic inquiry-based awesome stuff in your classroom, using the content.

First of all, I’m a traditional based teacher and if I facilitate, I do so using direct instruction methods followed with questions as has been done in the past.  For centuries actually.  Effectively, I might also add.

Second of all, I make sure to leave enough time in my class for students to get started on the “skill-based” activities known as homework so they can ask questions about it in class, rather than going home and not knowing how to do it.

Third, videos only go so far. Yes, you can rewind and replay as much as you want, but if you didn’t get something the first time, hearing the same explanation again without clarification isn’t going to help too much.  And if they’re that sold on doing learning at home rather than at school, have them read the textbook as preparation for the next lesson as is done in many university classes. It teaches them how to read a textbook rather than rely on videos and come to class with questions for the teacher.  Oops, I forgot. Textbooks are bad. Never mind!

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Biting the Hand that Fed You, Dept.

Keith Devlin, outspoken spokesperson (known as “the math guy” on NPR) on mathematics and who apparently has never backed down from a stated position, has this to say in a column written originally in 2011 and revised in 2014:

“As a nation, we should stop the current suicidal cry to turn back the clock to a form of math teaching that did no one any good and which those of us who became professional mathematicians first had to unlearn, and focus on making good, practical, sensible use of centuries old teaching tools (such as word problems) to produce a generation well equipped for life in the Twenty-First Century.”

He is not the only one to make such statement. What is more alarming than the statement itself is how often such statement is taken as truth and rarely if ever challenged.  The older forms of math teaching did no one any good? Really? Including him? Oh, he’s got that covered.  People like him (a professional mathematician) had to unlearn what he learned in his classes.  The word problems that he learned from did him no good whatsoever and he had to unlearn the problem solving techniques?

I get tired of the canard that “it never did anyone any good” particularly as uttered by those who, despite earnest claims with no evidence to support them, benefited from what they feel harmed many.  The ongoing mischaracterization of traditional math as “mindless computing” needs to be challenged.  Take a look at the students who go on into STEM majors and careers and the many problems they solved at home. Yes, they took on challenging problems, but also the very problems he says do not promote thinking and are mechanical and non-thinking in nature.  The “worked example” effect has its merits despite the claims of professional mathematicians who climbed the ladder and then kicked it down after they reached their levels of success, claiming that the ladder never did anyone any good.

Well, yes, but, Dept.

From Madison, Wisconsin comes this report about yet another parent math night, this time to introduce parents to the new math curriculum Bridges in Mathematics.  The math night consisted of math games that were actually used as part of the new curriculum so that the kids could guide their parents through them

Emerson teachers were on hand to speak with parents about the lessons and provide guidance as needed. Maria Cavicchio, a kindergarten teacher at Emerson, said students build on concepts taught in games like Spill Five Beans throughout the year. Although Hannah used the game to learn about number recognition, number writing and counting, the game also teaches the fundamentals of addition, subtraction and probability. “They do these sorts of games and they learn (the concepts,)” she said. “It’s not rote memorization, students really like (the activities) and learning is more meaningful.”

Yes, God forbid anyone memorize anything; that would be rote and would eclipse any “understanding”. Because math is about learning to problem solve (as opposed to learning how to solve problems–sorry for the digression but I still fail to understand how problem solve became an infinitive verb with a life of its own) and of course “explain your answer.”  Everyone knows if you can’t explain your answer, you lack understanding. I mean everyone:

“(Bridges) focuses on developing the students’ understanding of math concepts,” Davis said. “It is not about how students can memorize certain skills, but really around their ability to problem solve and look at math in more complex ways…and explain their reasoning to their teachers and peers.”

Never mind that understanding is many layered and true understanding can ONLY be built on mastery of skills. As my friend and frequent commenter here, SteveH, has said:

“If students can do problems without words, that is meaningless and rote? It’s all rubbish. There are too many skills to learn and understanding first is clearly not necessary or sufficient. However, true understanding is not possible without mastery of skills. Conceptual understanding (what they are talking about) is at best only the motivating baby steps of proper understanding.”

 

Shut the Hell Up, Dept.

Another in a long line of stories about how parents need to be taught the inefficient, non-standard methods for simple math, so they can help their children “understand” .  And of course no such story would be complete without this trope of a quote:

“The important thing is explaining how you know what you know,” Timm told the class. That’s what he wants their kids to leave school with — a deeper understanding of math, beyond rote memorization.

It might be nice to interpret Common Core in an alternative way; the one that allows standard algorithms to be taught prior to 4th grade.  The one that allows students to gain proficiency in the (shudder) procedure before being shown alternative methods that then serve to spotlight the underlying concepts.  The way it used to be done when Brownell, (reformer of his day in the 40’s through 60’s and receives steady praise from today’s reformers including Alfie Kohn) wrote the textbooks that I used.  Distinguishing main dish from side dish would be such a welcome change.

It might also be nice to not require “explanations” from K-6 students

Maybe they wouldn’t need to have parents make up the slack–or have students enrolled in learning centers.

Love Notes of the Past, Dept.

This harkens back to the days when I was writing letters about ed school under the name John Dewey on a blog called Edspresso.  (These letters were compiled in a book along with another set of letters I wrote on the blog Out in Left Field under the name Huck Finn.  Info on the book is here.  )

This particular comment ranks up there for odd reasons I can’t quite put my finger on:

Your mission here, Mr. Dewey, is becoming painfully clear (and sad)–parrot the lines you see in the so-called anti-establishment blogs, and voila, you’re a revolutionary.

Yet one important characteristic separates your meandering missives from those sites who set themselves against the status quo . . .

They at least try to know what they’re talking about.

 

 

What Am I Missing Here, Dept.

I was going to put this in the category of articles I never finished reading, but I did read it, and re-read the following paragraph several times in a vain effort for it to make sense:

“Today, much of the public and private school curriculum is based on what is known as “Singapore Math” and, specifically, the so-called “number sense” — which makes physical associations between numbers and, for instance, toys that a child handles while counting. And while Singapore Math is a great starting point, it may not be enough in the forms currently taught in the schools. To put it plainly, our students need more rigorous training. After all, students from Mainland China rule the Math departments at the top U.S. universities today, not Singaporeans, and definitely not Americans.”

First of all I’m not aware that the techniques used in Singapore’s math programs are the dominant form of math education in the US. Yes, some programs borrow the bar diagram technique for solving problems and use it occasionally, and then point to it as evidence that “Look, we’re using Singapore’s techniques.  But most textbooks do not use Singapore’s full techniques, at least not in any consistent fashion. And does she really think that the statement that China rules the math departments in US universities but not Singapore stands as proof that Singapore’s methods are inferior to China’s?  Singapore’s population is a lot less than China’s as is the percentage of people who emigrate from there to the US. Might that be a more likely reason than concluding that Singapore’s math program is not effective?

I asked the author this question in an email.  She responded:

Having taught and observed several top U.S. Math programs, I can tell
you with certainty that I am yet to encounter one Singaporean. And, you
know, sample size is not an issue here. Either Singaporean Math is not
enough to get the kids into the top U.S. Math programs, or it kills the
kids’ desire to study Math — neither is a good outcome. Furthermore, I’ve
lived in Singapore and it never struck me as Math Capital of the world.

Clearly she knows better than some useless TIMSS exam. And clearly she never visited homeschoolers, or even California.

What am I missing here?

SteveH on the current slew of math reformer arguments

SteveH was commenting on a particular blog that, like many, holds that math as traditionally taught is passe, never worked, and that the blog authors’ ideas of math education are far superior.  I have left the particular blog unidentified since it is typical of the many:

The only thing I ever had to memorize was the times table, and that was only a fraction of all of our work. Does ______ think that students have to learn why different base number systems exist in third grade?

Never do we see their full promised-land curriculum of understanding and problem solving that leads to a proper preparation for the 7^th grade track to algebra in 8^th grade. If ____ is talking about alternate paths for high school students who are not headed for a STEM college degree program after a proper K-8 math preparation, I’m open to suggestions, but it has to be based on their career and job requirements.

Education based on teacher ego. Educators like _____ do NOT want the teacher totally as the guide on the side. They want the teacher as someone who impresses the students. It’s all about them and their turf. They define a different process, but don’t show examples of success.

 Where is their full curriculum and student end results?

 

Another Book I’ll Never Read, Dept.

Someone criticized me the other day for trashing a book he wrote that I hadn’t read.  I have many failings and yes, trashing books I haven’t read is one of them.  I bring this up because of a book I read about here:  “Reimagining the Mathematics Classroom: Creating and Sustaining Productive Learning Environments, K-6.”

The title alone tells me it’s a book I won’t like.  I’m tired of being told to “reimagine” things as if such things desperately need to be reimagined. In this case, what he reimagines in terms of math education in K-6 are (I’m guessing) the conventional or traditional mode of teaching math which the author of the book describes in the interview:

For most teachers, myself included, K-6 grade mathematics emphasized following procedures to get answers without much concern for how or why these strategies worked, were related or could be adapted to new problems.

One can find by examining textbooks from previous eras, such as the 50’s and 60’s evidence that there were explanations for procedures or strategies, as well as many problems for students to apply such knowledge.  Something that does not get talked about in articles such as this, is that over almost three decades, math in K-6 has undergone a transformation thanks in large part to the 1989 math standards of the National Council of Teachers of Mathematics (NCTM) (revised in 2000, and then clarified to little avail in 2006).

Such standards as well as those adopted by states which imitated them carried an underlying message that “Memorization is bad; struggle is good”.  This message has been extended somewhat by the Common Core math standards, which carry the “dog whistles” of math reform, as Tom Loveless of Brookings Institution refers to them.  The result is that K-6 math education has become a no-STEM zone, in which understanding is given priority over learning procedures. If anything needs to be “reimagined” perhaps it is what has emerged as a result of the previous reimagining. If a child cannot explain their reasoning, the child is held to not understand underlying principles. Students are given one-off problems that do not generalize well, but appear to be “mathy” and real-world like. Traditional problems are held in disdain for being predictable, easy, and not teaching students to “think like a mathematician”, this last despite the fact that they are novices, not experts, and have to think like children, just as mathematicians once did.

I’m also tired of people who hold in disdain the very things they have benefited from.  When pressed on this by pointing out that they seemed to do all right with the down-trodden and eschewed traditional methods, they will respond that “Yes, but there were plenty that did not” without providing much in the way of evidence other than “Look how many people say they hate math” or “Look how many adults cannot do _____” in which the blank is generally some procedure that they may not have used for many years.  (I myself have to brush up on certain math procedures that I haven’t done in years; it usually comes back fairly easily.  Oh, right, that’s me, and I’m the exception.)

What they offer to replace the methods that helped them succeed are summarized in this statement:

The methods I used in the 1990s, which led to significant improvement in my students’ outcomes in mathematics, are becoming more widely adopted today. These include giving students opportunities to productively struggle with an unfamiliar task designed to extend and/or challenge their prior knowledge, requiring students to communicate with peers about their mathematical reasoning, and using students’ mathematical ideas as the basis for calling attention to key mathematical relationships and properties.

Well, these sound an awful lot like the coveted Standards for Mathematical Practice (SMPs) contained in the Common Core math standards.  These purport to teach students to think like mathematicians and are frequently implemented by teaching “habits of mind” of, say, algebraic thinking, well outside of any proper algebra course in which such habits would arise as a result of what’s being taught and practiced. On the subject to the SMPs and thinking like a mathematician, I rely more on the wisdom of a real mathematician, Steve Wilson of Johns Hopkins, who provided this perspective:

There will always be people who think that teaching kids to “think like a mathematician,” whether they have met a mathematician or not, can be done independently of content. At present, it seems that the majority of people in power think the three pages of Mathematical Practices in Common Core, which they sometimes think is the “real” mathematics, are more important than the 75 pages of content standards, which they sometimes refer to as the “rote” mathematics. They are wrong. You learn Mathematical Practices just like the name implies; you practice mathematics with content.

You’ll forgive me then if I choose not to read this book or to write a nuanced review of same.

 

 

 

 

 

Shameless self promotion, Dept.

I’ve started writing what will be another book about math education.  For those of you who haven’t read my previous books, this self-promotion will provide a link to Amazon where you can buy said books, read them, and recommend to your friends and enemies.

 

 

Oh, please! Dept

I’m OK with some of the computerized learning programs, but why is it that almost every article about ed tech (particularly those written by NPR like this one) has this ubiquitous paragraph embedded within?

Just learning reading and math the way it was done 100 years ago is not going to prepare anyone for the future. Up to 70 percent of the tasks in most jobs are on track to be automated, leaving only the most creative, empathetic, technically fluent, collaborative work for humans. Students need to find motivation and meaning, and take a playful attitude that makes it safe to try and fail. It’s as though half the world’s children were 100 years behind on learning to walk, but everyone now needs to dance.

I agree that the future will be different than the present, but does learning to read and to do math have to be done via interpretive dance, or while learning how to use the internet, or while texting the person sitting next to you?  Computer skills are probably the one thing that kids are picking up on without any training.  Why not teach children how to speak English incorrectly, and how to write sentences without capitalization or punctuation since that’s the prevailing style?  Or, to teach children to “learn how to learn” rather than learn facts and procedures since we all know you can look up those things on Google.