In Defense of Jason Zimba, Dept.

I was a bit snarky in a previous post about Jason Zimba regarding his remarks about “fluency” vs “memorization”. He has clarified for me that he does draw a distinction despite my characterizing his position as waffling.

While I do not agree with everything Zimba says about Common Core Math Standards (nor do I carry his enthusiasm for the standards), I appreciate what he has done to clarify what the standards mean. In particular, he has said that the standard algorithms can be taught earlier than the year in which they appear. He even recommends starting the teaching of the multidigit addition and subtraction algorithm in first grade–and not waiting until the year in which they appear in the CC standards (Grade 4)

He states: “The Common Core requires the standard algorithm; additional algorithms aren’t named and they aren’t required.”

Fairly strong words, but despite such clarifications as he provided in this earlier column he wrote for Fordham’s “Common Core Watch” word is not getting out.  There are schools in which the standard algorithms are delayed in the belief that standard algorithms eclipse the “why” and instead promote the “how” (as in “rote”) in performing operations.

Teachers are sending home notes to parents with the students advising them: “Do not teach your child the standard algorithm for computation until he or she has learned it in school.”

I have said before that Common Core is the gasoline on the reform math fire that has been burning for the past 25+ years.  Although it is possible to implement some aspects of the CC standards in a sensible manner, the tide of reform math and its bad practices are difficult to turn back.

Wagons in a Circle, Dept

.Fordham’s now infamous survey showing that “Eighty-five percent of instructors report that parents misunderstand the new methods and are less likely to reinforce math learning at home” proved what Fordham wants us to believe:  I.e., that parents don’t know what they’re talking about, they’re against it because it wasn’t how they were taught, etc etc.  (They say nothing about the fact that standard algorithms are delayed for years, and in their stead, alternative methods are being taught–even though std algorithms MAY be taught earlier than the grade in which they appear in the standards, as confirmed by Jason Zimba and Bill McCallum.)

So just to make sure that everyone is on the same page with objections to CC math standards being all the fault of parents, and that multiple methods are good, and “rote learning” (which of course is the only other alternative) is bad, Fordham put together a little seminar of talking heads. At the same time, people could tweet comments to ‪#‎CCParents‬ which some did, but looking over the tweets, I was one of the few who had anything negative to say. NCTM seemed to weigh in quite a bit.

For the record, I don’t believe that the reaction we are seeing among parents to how CC is being implemented is unwarranted, nor should they be vilified. There is some credibility to their claims which should be taken seriously.

But if you’re up for more punishment, you can watch the video and decide for yourself what’s really being promoted and what’s really being dismissed. And then enroll your child in Kumon, like many are doing/have done.

The More Things Change, Dept.

Alice Lloyd has a pretty good article in the Weekly Standard on the Common Core crisis, how its being portrayed and the confusion over Fordham’s survey on same. She gives a good background history and articulates some of the problems in the math standard implementation. In fact, it tracks pretty closely with what I said in my talk at ResearchED last month in UK.
 
“Every stab at reform has had roughly the same aims. Common Core math is no different—it’s meant to make problem-solving processes simpler and more uniform and to let students build a grounding in basic “number sense” skills before they’d start to solve rotely. The reforms in the 1960s, when there was purportedly a numeracy crisis in America, and again in the late 1980s and 1990s, when “anti-racist math” was a thing, shared the lofty aim to make the deeper experience of math accessible to a wider audience.”
 
Yes, exactly right.
 
“Kick a number like 202 to the nearest multiple of ten, remembering the difference for your final answer: 617 minus 202 is not as easy as 617 minus 200, which is obviously 417; just remember to take away the 2 you knocked off on the front end when you’re done, and you get 415. Mentally it takes mere seconds, and explaining it is fairly simple. But that’s just where we hit a wall: Teaching multiple solutions, and letting children choose the one that comes most easily in practice, makes sense—but the more methods on offer, the more rules there are to govern them. Teachers new to these multiple methods stick to the rules, or else risk getting something wrong. And it’s not just teachers.
 
“I asked a young woman at the Fordham Institute talk, who turned out to be a math curriculum designer, if the standards intentionally ingrain intuitive math-problem-solving practices in order to make the kids’ little lives easier. She said no, not exactly: With addition problems, for instance, a third grader would have to draw a certain type of diagram a certain way to “show her work.” “
 
Not to mention the interpretation/implementation of CC in which the standard algorithms are delayed until 4th, 5th and 6th grades, because that’s when they appear in the standards. Nothing prohibits teaching them earlier, ensuring their mastery and THEN showing the alternative methods afterward. This is how it had been done in the days of traditional or conventional math teaching that are mischaracterized as having failed thousands of students. The alternative methods are nothing new and were taught for years. And of course the ever-pervasive “Students must understand or they will just be doing things by rote” mentality, thus preserving the false dichotomy between understanding and procedure.
 

The Jiu Jitsu of Lesson Planning

There are a slew of math textbooks out now that build in a constructivist approach to teaching math, yet temper it with direct instruction. It is as if the publishers have had their ear to the ground view Twitter, edu-blogs and other gathering places in which teachers vent about what they prefer in teaching.  The publishers have gathered that there is some rebellion against student-centered, inquiry-based learning, and an equal amount against direct, explicit and whole-class instruction.

The result are textbooks that bridge this gap by proclaiming as “Big Ideas Math” series does on the front cover, as part of the title, the words “A Balanced Approach”.  In the case of Big Ideas Math, their idea of balance is to start with an activity that is usually ill-defined as to what the goal of the activity is or what is to be discovered, followed by an explicit direct-instruction lesson.  Some of the ideas from the activity are then incorporated into the direct-instruction lesson.

The idea of an activity in which the goal is not stated is like teaching someone how to get from point A to point B, by not telling them where Point B is, nor how it figures in the general layout and giving them some paths to follow. Based upon the paths, the person being led is supposed to then know when Point B has been reached. Or not. In any event, at some point they will be told.

Teachers who despair of such techniques (or hold to Anna Stokke’s rule of thumb which she wrote about in a CD Howe report,  for “balance” being 80% direct and 20% student centered, activity/inquiry-based) will probably do the following:  Incorporate the crux of the activity into a ten minute intro for the direct- and whole-class instruction lesson.  Or, after mastery of material, have students do an activity, now having the prior knowledge to appreciate it and actually learn from it.

Because some schools monitor teachers closely and may not allow such latitude, I offer as a public service, this advice from the late Grant Wiggins and his co-author Jay McTighe who unwittingly provide a way out of this mess.  These two masters are generally respected by those who subscribe to the edu-group-think that passes for “best practices”. Teachers can go outside the textbooks while claiming that they are still adhering to student-centered principles per Wiggins and McTighe. In the Japanese art of jiu jitsu, it’s a way of turning the opponent’s force away from you and towards them. It’s a strategy worth a try at any rate. Here it is.

More generally, weak educational design involves two kinds of purposelessness, visible throughout the educational world from kindergarten through graduate school. We call these the “twin sins” of traditional design. The error of activity-oriented design might be called “hands-on without being minds-on”—engaging experiences that lead only accidentally, if at all, to insight or achievement. The activities, though fun and interesting, do not lead anywhere intellectually. Such activity-oriented curricula lack an explicit focus on important ideas and appropriate evidence of learning, especially in the minds of the learners.

A second form of aimlessness goes by the name of “coverage,” an approach in which students march through a textbook, page by page (or teachers through lecture notes) in a valiant attempt to traverse all the factual material within a prescribed time. Coverage is thus like a whirlwind tour of Europe, perfectly summarized by the old movie title If It’s Tuesday, This Must Be Belgium, which properly suggests that no overarching goals inform the tour.

As a broad generalization, the activity focus is more typical at the elementary and lower middle school levels, whereas coverage is a prevalent secondary school and college problem. No guiding intellectual purpose or clear priorities frame the learning experience. In neither case can students see and answer such questions as these: What’s the point? What’s the big idea here? What does this help us understand or be able to do? To what does this relate? Why should we learn this? Hence, the students try to engage and follow as best they can, hoping that meaning will emerge.

 

Clear as Mud, Dept

.Jason Zimba one of the lead writers of the CC math standards, when asked to explain whether there is a distinction between being “fluent” with math and “memorizing” offered some explanations.

First, on the issue of whether CC requires memorization:

“The standards require students to know basic facts. Here is the language for multiplication (page 23): ‘By the end of Grade 3, know from memory all products of two one-digit numbers.’ We can debate the best ways to help students meet this expectation, and we can debate the best ways to assess whether students have met the expectation. Those are good discussions to have. But there is no room to debate the expectation itself. The language in the standards is unambiguous.”

Then he distinguishes between “fluency” and “memorization”

“Fluency pertains to an act of calculation. In particular, to be fluent with these calculations is to be accurate and reasonably fast. However, memory is also fast, so the difference between fluency and memory isn’t a matter of speed. The difference, rather, has to do with the different nature of calculating versus remembering. In an act of calculation, there is some logical sequence of steps. Retrieving a fact from memory, on the other hand, doesn’t involve logic or steps. It’s just remembering; it’s just knowing. The mental actions of calculating and remembering are different. The standards expect students to remember basic facts and to be fluent in calculation. Neither is a substitute for the other.”

So, they don’t mean the same thing, except when they do. Here, read it and tell me what it means. I’m having a beer.

Articles I Never Finished Reading, Dept.

Bechtel Corp gave a $10 million grant to Calif State U’s ed schools “to train current and future teachers on new math and science standards.”

There’s the usual intro rhetoric:

” “For California and the nation to continue leading in the world’s key economic sectors, we must continue to ensure our teachers are equipped with the latest teaching strategies that support high standards, innovation and creativity,” CSU Executive Vice Chancellor for Academic and Student Affairs Loren Blanchard said in a written statement.”

Then there’s this:

“Math, for example, has gone from a subject in which students needed only to memorize math operations to one in which students need to master collaborating with fellow students to get the right answer as well as orally critiquing and analyzing how other students solved a problem.”

Yes, we’ve heard this one before and we know how it ends, thank you very much.

Nailed it, Dept

Nice op-ed from a 37-year veteran teacher who nails it to the wall, regarding what teaching has become–a slave to reform ed ideas. And how veteran teachers survive it.

“The education reform movement has choked, stifled and smothered veteran teachers. It has poo-poo-ed their historic knowledge and the vast wealth of experience they have collected. Education reform has replaced it with ridiculous chants, mantras, beliefs and a bowing before the goddess of data and technology. A great false association has taken place. It is believed that because shiny new green teachers (the ones who quit in mooing herds within their first five years) are adept at computer usage they are also are harbingers of true new fix-it-all education. And this works for principals who desire compliant teachers to implement the new stuff. Who better to do it than flexible indentured newbies who feel indebted to the principal for employment.

“Veteran teachers have seen the following elementary educational fixes. And we survived them. Well, some of us did.

“MATH: Math Their Way, Math Land, Mathematics Unlimited, Callifornia Math, Excel Math, Math Expressions, Dot Math, Math Manipulatives, New Math, Common Core Math … and more.

“The How of Teaching: Self-contained classes, blended (switching classes), Team teaching, combination classes, combination bilingual classes, after school programs, learning centers, projects, leveled ELA, Immersion cooperative groups, pair-share, No Child Left Behind, Race To The Top, Common Core, Goals and Standards numbered and written on the board, behavior modification plan this, behavior modification plan that and more.”

Couldn’t have said it better. And I’ve tried, believe me!

Alfie Kohn’s Letter to Future Apostles of Bad Practices

 

Alfie Kohn, the education critic, in a book about education, devoted a chapter on the downsides of teaching math in the traditional manner. Here’s an excerpt:

“The teacher begins by demonstrating the right way to do a problem, then assigns umpteen examples of the same problem (except with different numbers), the idea being for students to imitate the method they were shown, with the teacher correcting their efforts as necessary.”

Yes, traditional math can be done poorly, it’s no lie. But that doesn’t mean that it is always done poorly. Good textbooks and good teachers scaffold problems so that they increase in difficulty and are variants of the original worked example. Students are expected to stretch and move beyond, using reasoning based on the original structure.

“It’s a pretty sharp contrast, between math defined principally in terms of skills and math defined principally in terms of understanding. But if we are persuaded by a constructivist account of learning, even the latter isn’t enough. When traditionalists insist that it’s most important for kids to “know their math facts,” we might respond not only by challenging those priorities but by asking what is meant by know. The key question is whether understanding is passively absorbed or actively constructed. In the latter case, math actually becomes a creative activity.”

In Alfie Kohn’s world (and in the world of others who think similarly) there is a dichotomy between procedures and understanding. And even then, “understanding” must come via constructivism. In his world, there are no “aha” moments when being directly instructed. Homework problems do not entail any discovery, in his view.

I could go on, but you get the message. He wrote this in 1999, but the thoughts contained in his epistle to the masses have become scripture and are taken up by the likes of Jo Boaler and others. Be aware of it. If you teach a class in an ed school make it an exercise for students to describe “what’s wrong with Alfie’s picture”. And if they don’t know, then enlighten them.

But chances are that if you’re reading this and you teach in an ed school, you’re probably wondering why I’m bothered so much by what Alfie has to say.

The Hang-Up on Perimeter vs Area–and “understanding”

I get a bit tired of the trope that students today are subjected to boring math with boring procedures and boring problems. (Although I must say, I find the real-world problems that are supposedly interesting to be quite tedious and boring). Essays abound with links to something called Lockhart’s Lament which was written by a mathematician named Lockhart and is a lamentable whine about how he found math in K-12 boring. Continue reading