But I thought… Dept

This article talks about a public hearing to be held in Yuma AZ about Common Core standards to clear things up in the public’s mind, etc etc.

Of interest is one of the last statements in the article:

“Summaries of the standards emphasized that standards are not curriculum. Sheppard said the public frequently confuses the terms.

“The curriculum is the material used to teach the standards,” he said. “The instructional practices is what is the craft of teaching. The very best curriculum out there can only take kids so far. It cannot substitute the instructional excellence. That’s why you have the instructional practices and strategies to support the curriculum, which teaches the standards. So it’s really that relationship between all three.” 

Uh, what? What instructional practices? You mean the Standards for Mathematical Practice? Oh, so they ARE instructional practices and CC DOES dictate pedagogy. See, I thought CC DIDN’T do that. That’s what the website says and the people in charge of CC. Uh, speaking of people in charge of CC, where are they?

Pertinent to this discussion, Robert Craigen, a math professor at University of Manitoba, tells me “This notion that Curriculum = Instructional Resources seems a uniquely American idea. We don’t speak of the word Curriculum in that sense here in Canada at all. Curriculum is a document indicating what is to be taught. One picks resources based on curriculum, hopefully a resource which matches it well…”


Slow News Day at the Huffington Post, Dept.

Well, the Huffington Post wrote a headline that I think covers all the bases: “The Future of Learning: Project-based, Place-based, Experiential, Authentic, Constructivism”

This article is a paean to bad educational practices. “Real world” problems. Just get kids together with a real problem and they’ll learn what they need to learn to solve it. Sounds nice, and those that practice it find ways to make it seem like it’s working. Many parents know better. So do many teachers, but given that they want to keep their jobs, they keep their mouths shut.

“It all starts with a problem—a real problem like saving ocean species, global warming or the dangers of using plastic bags.

“As students get into exploring the depth of the problem and identifying possible solutions, they research the problem, interview experts, and present results in concise, highly readable and visual forms demonstrating their abilities to communicate. They are engaged, learning skills, gaining the knowledge and expertise the workforce is looking for. It totally changes how they learn and the teachers teach. As Ben Johnson, a career educator, put it for the educational website Edutopia:

” “Great teachers do not teach. They stack the deck so that students have a reason to learn and in the process can’t help but learn mainly by teaching themselves. This knowledge then becomes permanent and cherished rather than illusory and irrelevant.”

So there you have it. Any kind of educational practice other than constructivist, project-based, student-centered, inquiry-based BS is “illusory and irrelevant”.

And why is it that parents pay for Kumon, Huntington, Sylvan and other learning centers, as well as tutors, that use the illusory and irrelevant approach? Could it be because it works?

Developmentally Appropriate/Inappropriate, Dept.


Much of the criticism levied at the Common Core standards is directed to Kindergarten and first grades. The complaint is that some of the standards are difficult for some children to achieve, because they are “developmentally inappropriate”.

People like Dan Willingham and Ben Riley (of Deans for Impact) while not directly refuting such criticism, make a case that there are no set stages for when children develop. Children develop at different rates. Their reason for such statements may be a refutation of theories that developed from Piaget–notably from his disciple Constance Kamii who claims that teaching children standard algorithms prior to grade 4 does them harm because they are not yet “ready”. Doing so earlier eclipses the understanding, and results in a rote “math by doing” rather than “math by knowing”.

Point taken from Willingham and Riley. Nevertheless, there are some things we shouldn’t expect from all children at certain ages. So it is nice to see an article that articulates the “developmentally inappropriate” argument using the same framework that Willingham and Riley use.

“The average age that a child learns to be an independent reader is about six and a half. Some learn to read at four, and others at seven, and both extremes are developmentally normal. In fourth grade, kids who learned to read at four are typically not any better at reading than those who started at seven. Countries like Finland and Sweden, which outpace the United States in international testing, do not even start formal academic schooling until age seven.

“We need to respect children’s individual developmental timelines. The idea that “earlier is better” for reading instruction is simply not supported by research evidence. Children’s long-term achievement and self-identities as readers and students can be damaged when they are introduced to reading and literacy too early.”

Good Grief, Dept.

This article gives supposedly good advice on what Common Core standards are all about, including this gem:

“Today’s students are learning math differently than their parents, but they are also showing a more sophisticated understanding of math problems and how the answers are derived, rather just than memorizing facts.”

In fact, the emphasis on alternative methods for basic computations in lieu of teaching standard algorithms first often results in confusion and frustration. It used to be that standard algorithms were taught first, and then the alternatives were presented as a “side dish” that provided short cuts as well as additional understanding of how the algorithm worked. Jason Zimba  on of the lead writers of the CC math standards has stated that the CC standards do NOT prohibit teaching the standard algorithms earlier than the grade level in which they appear and recommends teaching the standard multi-digit algorithm for addition and subtraction, starting as early as first grade. Nevertheless, the prevalent interpretation of CC standards is to delay teaching the standard algorithms until 4th, 5th and 6th grades, resulting in years of inefficient methods, picture drawing and lack of understanding, despite claims that students show “sophisticated understanding” of math problems.

The article also states:

“Students who are good at listening and following instructions may not be as successful in a Common Core classroom. More emphasis is placed on critical thinking and taking time to explain their thought process, according to The Santa Barbara Independent.”

While the CC web site claims up and down that it does not dictate pedagogy, on the other hand the CC website states: “Students who lack understanding of a topic may rely on procedures too heavily.  But what does mathematical understanding look like?” And how can teachers assess it? One way is to ask the student to justify, in a way that is appropriate to the student’s mathematical maturity, why a particular mathematical statement is true, or where a mathematical rule comes from.”

The underlying assumption here is that if a student understands something, he or she can explain it—and that deficient explanation signals deficient understanding. The result has been for students in lower grades to “explain their reasoning” in solving problems so simple that they defy explanation. This passes for “understanding” and “critical thinking” but is really an exercise in frustration for most students, with more important matters like procedures and skills left by the wayside.

Group-Think, Dept.

This article from The  Toronto Star exemplifies the ever-pervasive group-think about why the traditional method of teaching math won’t work.

From the article:

“Many parents want to get rid of “discovery math,” broadly defined as “doing it weird.” If only that loopy Liberal government would teach math the way we learned it when we were kids, the theory goes, there’d be no problem. Sure, great, except for one thing. Very few parents I’ve met can perform more than the most rudimentary arithmetic for themselves. If you all learned math so well, why do you inch toward Junior’s algebra homework with a cross and a bulb of garlic?”

First of all, not all parents are like that. Second of all, there are some aspects of math that parents haven’t done in a while, so they are rusty. Unless you use something often, you forget how things are done. I myself have to brush up on percentages if I haven’t worked with them for a while. Same with calculus, linear algebra and other topics. It doesn’t stand as proof that the traditional method failed. Also what does he mean by “very few parents I’ve met”?

He goes on:

“This summer I made my stepson spend some time on Khan Academy, an educational website, to brush up his math before he enters Grade 8. He was briefly baffled by questions that asked, say, 6 1/4 – 3 3/4. One way to do it is to convert both sides to improper fractions. But it’s easier if you simply recognize that 6 1/4 is the same as 5 5/4. You can do the differences in your head in about two seconds. The question is, how do you produce the kind of students who will make that insightful leap?”

Khan Academy is very traditional–a detail this author conveniently ignores. And recognizing that 6 1/4 is the same as 5 5/4 comes after being instructed in the procedure (which Khan provides) and practicing with it. It doesn’t come intuitively for most people. So that “insightful leap” as he puts it, is more like procedural fluency giving way to doing it in your head–as he likely learned it years ago.

He goes on:

“All I know for sure is that you don’t do it by teaching a bunch of rules students will learn by rote — the beloved “old-fashioned way.” That may work for basic math facts….But very quickly, math becomes so complex you can’t have a rule for everything. Khan Academy teaches and tests 111 different skills at the fifth-grade level alone. You’d go crazy learning a rule for each skill. You must be able to intuit a useful method for each situation.”

And many of these skills grow from basic traditional instruction in procedures which give way to transfer. He ends on this note:

“Second, support students by giving them more practice time. The only way to learn how numbers work together is by tackling incrementally more difficult questions, lots of them, over time. Kids need to practice insight just as their parents practiced times tables.”

If  what he means by practicing insight is practicing procedure which in many cases leads to understanding, well then: I guess he and I are saying the same thing: Traditionally taught math works well.

Wayne Bishop Weighs In

For those who don’t know him, Wayne Bishop is a long-term veteran of the math wars in California and beyond. He is a professor of mathematics at Cal State LA. He played a role in getting the California math standards that preceded the CC standards, adopted in California.

He has been sharply critical of Common Core, as well as the tests that support the ineffective math philosophies that inform CC’s interpretation and implementation.

From his guest editiorial in the San Gabriel Valley Tribune:

“The idea that the Common Core standards and associated assessments are more rigorous and provide greater opportunities for California students is based on ignorance or, worse, is completely disingenuous.”

Read every word!

UPDATE: A commenter named George Tyrebiter (who has commented before and seems extremely knowledgable about what has gone on in math education in California) wrote the following comment on Wayne’s piece:

“Professor Bishop was too kind… Phil Daro, the BA in English who was hired in 2008 to be the Chair and Lead Author of the Common Core State Standards for Mathematics, was also the chair for the drafting of the Mathematics Framework for California Public Schools in 1992, the reason the crazy ways of doing math in Common Core looks just like the crazy ways to do math that greeted my son in the first grade in 1995. It took years for the sanity of real mathematics professors to push that out of California schools only for Common Core to push it back in.”

Lucy, You Have Some ‘Splainin’ To Do, Dept.

Last November, the online Atlantic published an article that Katherine Beals and I wrote on the current trend to have students explain their work in math.

Our main point was that doing so was in many cases superfluous to the mathematical process. That is, showing one’s work in solving a problem can be the explanation itself. Asking for more tends to be make-work and for students in lower grades whose articulation skills are still developing, a waste of time.

There was quite a flurry of both agreement and protest about this article. (Despite all the complaints, however, it will resurface in the annual anthology “Best Math Writing of 2016” which will be released around December.)

There is a back-story to the article. In the article there is a sample of a student’s explanation of a particular problem. I had solicited such explanations while I was assisting math teachers at a middle school. I had given students some instruction on how to solve particular types of percent problems, and then gave them a problem, asking them to explain their answer. I had them use a template that the school was recommending: “Need/Know/Do”.

There was only one student who got the answer right; and that was the one I used and which appears in the article. It turns out that I really should have also used an example of a wrong answer–complete with incorrect explanation, which might have better made the point. (Though I doubt that there would have been any less criticisms of the article).

I say this because of a meta-study conducted by psychologist Bethany Rittle-Johnson of Vanderbilt University. Rittle-Johnson examined 85 studies and one of her conclusions was “If kids are just off explaining their own thinking without guidance, then they can be spending their time essentially justifying stuff that’s wrong.”

21st Century and Jobs That Don’t Yet Exist, Dept.

Mark McCourt, whom I had the pleasure of meeting at the ResearchED conference in Oxford earlier in June, capsulizes the idiocy of the thinking about 21st century learning. I.e., that we shouldn’t focus on teaching students facts, because that only prepares them for what has happened in the past. It doesn’t prepare them for the future for jobs which haven’t yet been created.

He states the fallacy succinctly:

“Many of the jobs that I have done in my life, many of the decisions I have taken, could not have been predicted by my teachers, were not understood by the society that I grew up in, were not yet invented and were unimaginable. Many of the ways in which I lead my life, such as the use of Twitter or this very blog, are the preserve of this new future that I exist in, unimaginable to the school system of my childhood. Yet, I have been successful in my career, I am able to make decisions, and I can cope in this unimaginable world of technology.” …

“It isn’t rocket science. The idea that there is something radical that needs to change in schools is correct, but only insomuch as we need to strip schools back to these core purposes. Head teachers need to be left alone to create institutions focused on creating learn’d young men and women with the confidence to make their way in the world no matter what that world becomes. Make children really bright. Everything else will follow.”