Barry's book !

Math Education in the U.S.: Still Crazy After All These Years

Very exciting!

Barry Garelick to speak at researchED!

researchED Conference Speakers

Very exciting!

Comments needed

If you have time to comment on Barry and Katharine's new article at The Atlantic, please do!

Way too much thinking

I've mentioned (a gazillion times -- sorry!) that I'm writing a book to do with the basal ganglia.

The basal ganglia handle nonconscious learning and intuition. (Turns out intuition is a real thing - ! Basically, intuition is nonconscious category learning.)

Meanwhile, the entire education world is obsessively focused on conscious processes.

Critical thinking.

Problem solving.

GROUP problem solving.

Cognitive science (and common sense) tell us that all of these activities depend upon nonconscious processes, but never mind.

Here's a typical passage describing current thinking (thinking!) in cognitive science:

A great deal of complex cognitive processing occurs at the unconscious level.

[snip]

It is largely accepted that lower levels of processing (e.g., motor reflexes, sensory analysis) can operate outside of perceptual awareness (implicitly) (e.g., Castiello, Paulignan, & Jeannerod, 1991). And although the existence of nonconscious computations at higher levels (e.g., semantic or inferential processing) has been controversial (Dixon, 1971; Eriksen, 1960; Greenwald, 1992; Holender, 1986), a range of empirical findings on the unconscious over the last several decades has led most cognitive neuroscientists today to believe that mental activity can occur outside of conscious awareness (Hassin, Uleman, & Bargh, 2005). Some have argued that all information processing can, at least in principle, operate without conscious experience, and that consciousness (C) may thus be of a different nature (Chalmers, 1996). This view goes along with the hypothesis that nonconscious processes can achieve the highest levels of representation (Marcel, 1983). A large amount of complex cognitive processing appears to occur at the unconscious level in both healthy and psychiatric and neurological populations. For example, evidence from patients with blindsight (Goebel, Muckli, Zanella, Singer, & Stoerig, 2001; Weiskrantz, 1986), prosopagnosia (Renault, Signoret, Debruille, Breton, & Bolgert, 1989), implicit awareness in hemineglect (Cappelletti & Cipolotti, 2006; Marshall & Halligan, 1988; Vuilleumier et al., 2002), nondeclarative learning even in amnesia (Knowlton, Mangels, & Squire, 1996; Knowlton, Squire & Gluck, 1994; Turnbull & Evans, 2006), and the “split-brain” syndrome (Gazzaniga, 1995) supports the idea that unconsciously processed stimuli can activate high-level cortical regions.

- The Neural Basis of the Dynamic Unconscious

Expertise is heavily nonconscious. Most of the time experts don't know how they do what they do,  they just do it.

Yet all of K-12 these days seems to be premised on the belief that being able to "explain your answer" equals "understanding."

That belief is nonsense on stilts.

Yes, experts think when they solve problems. But eureka moments come out of the depths.

We have no access to our nonconscious minds, and we can't explain what our nonconscious minds do.

What's more, if we didn't have nonconscious minds, we wouldn't solve problems.

So what happens to problem solving when you stop teaching the nonconscious mind?

What happens to problem solving when you believe that conscious "thinking" is all that matters?

Here's Barry on Explaining Your Answer.

Barry's book is out!!

Teaching Math in the 21st Century

I got my copy in the mail this week, opened it up to a random page, and instantly found a paragraph to post:

Well, OK, I like open response questions too, but I get rather tired of the "it's inauthentic if it's multiple choice" mentality. I took the math exam required in California to be certified to teach math in secondary schools. The multiple choice questions were not exactly easy; I would hesitate to call the exam "inauthentic." What I find inauthentic is the prevailing group-think which holds that judging math ability should be based on how well students in K-12 are able to apply prior knowledge to problems that are substantially different than what they have seen before. In the working world (which the education establishment tries to emulate by insisting that students be given "real-world" problems) most people employed in technical fields are expected to apply their skills to variants of well-studied problems. For those who need to solve problems of a substantially new nature, it takes weeks, months and years--they are certainly not confide to a two-to three-hour time limit.

I love that.

The real real world is so different from the real world constructivists imagine.

Speaking of which, my district is now committed to "instilling a culture of entrepreneurialism in our students."

Flipped classrooms, stations, and now pretend entrepreneurialism.

Barry's Rifle Range on grit

In all my classes, I required my students to answer warm-up questions at the beginning of class. I used two types of questions:. One was a review-type question to apply what they recently learned. The other required them to some apply their prior knowledge –or what was familiar—in a new or unfamiliar situation. Some may view this as an inquiry-based approach, or an application of the “struggle is good” philosophy that adherents of Common Core seem to say is necessary to develop perseverance in problem solving, as well as the all-important and frequently undefined “grit”. I view a short amount of struggle as appropriate provided that explanation is provided shortly after. That way, even if students do not succeed in solving a problem, most are receptive to explanations that they might otherwise tune out.

Saturday, December 20, 2014
Conversations on the Rifle Range, 19: Grant’s Tomb Again, Alice in Wonderland, and the Eternal Question

Asking students to spend a few minutes applying prior knowledge to a new problem arouses curiosity.

That's a good thing because, according to Jaak Panksepp, curiosity is one of the seven core emotions driving all human behavior. He calls it "SEEKING."^*

SEEKING may be the core emotion, in fact, the emotion without which the other six don't work.

So: arousing curiosity about math!

Good idea.

Panksepp's fantastic book: Affective Neuroscience: The Foundations of Human and Animal Emotions

And I see he published a new book in 2012!

Ordering it now -----

The Archaeology of Mind: Neuroevolutionary Origins of Human Emotions by Jaak Panksepp and Lucy Biven


^*It's probably more accurate to say that curiosity is a facet of SEEKING.

download this

I just checked out one of the articles Barry quotes and found this:

Paula Tommins asked, “How are we training the teachers and supporting the teachers because they’re going from downloading to coaching.” By “downloading” she meant imparting knowledge, she later said.
Parents question a new method for teaching math
Published: Wednesday, October 31, 2012

Just the other day I was thinking about the download scenes in The Matrix.

Neo would be in mortal danger so he would dial up the home computer and ask the guy they left back on the ship to download How to Fly a Getaway Helicopter into Neo's skull, and in under 5 seconds -- voilà. He could fly.

I was thinking those scenes are evidence that everyone's folk theory of learning encompasses the fact that knowledge stored on Google is not the same thing as knowledge stored inside your brain. I mean, the Warchowski siblings could have written the scenes differently, right? (If they'd gone to Teachers College, maybe they would have.) They could have had Keanu Reeves Google "How to Fly a Getaway Helicopter" and then have Google read him the directions really, really fast.

They didn't do that or anything like that because everyone understands that when it's a matter of life and death you have to know the instructions by heart.

p.s.: 'Downloading' new skills into our brains like characters on The Matrix set to become a reality, say scientists

p.p.s.: how to learn things automatically

explain yourself - Barry on the Common Core

Barry writes:

A few weeks ago, I wrote an article for TheAtlantic.com describing some of the problems with how math is currently being taught. Specifically, some math programs strive to teach students to think like "little mathematicians" before giving them the analytic tools they need to actually solve problems.

Some of us had hoped the situation would improve this school year, as 45 states and the District Columbia adopted the new Common Core Standards. But here are two discouraging emails I received recently. The first was from a parent:

They implemented Common Core this year in our school system in Tennessee. I have a third grader who loved math and got A's in math until this year, where he struggles to get a C. He struggles with "explaining" how he got his answer after using "mental math." In fact, I had no idea how to explain it! It's math 2+2=4. I can't explain it, it just is.

The second email came from a teacher in another state:

I am teaching the traditional algorithm this year to my third graders, but was told next year with Common Core I will not be allowed to. They should use mental math, and other strategies, to add. Crazy! I am so outraged that I have decided my child is NOT going to public schools until Common Core falls flat.

This may sound wildly off topic, but the struggle a third grader has "explaining" why two plus two equals four strikes me as being of a piece with the struggle basic writers have trouble writing a conclusion, especially a conclusion in a 5-paragraph essay, a highly compressed form that leaves you no room to "ask a rhetorical question" or "suggest future lines of inquiry" or "close with a quotation that captures your view" and the like.

With the 5-paragraph essay, when you get to paragraph 5 you've said everything you were going to say (if you're lucky), but the teacher wants you to say something more.

But what?

One thing I always liked about William J. Kerrigan's X-1-2-3 approach is the fact that he didn't bother with introductions and conclusions. The introduction was 1 sentence - Sentence X - and the conclusion was 1 sentence, too. Kerrigan called the final sentence the "rounding off" sentence, as I recall. Really, that's all anyone should do in a very short paper; otherwise your introduction & conclusion - 2 paragraphs out of 5 - take up 40% of the essay.

I've had to abandon Kerrigan's one-sentence policy, though, since I'm pretty sure other instructors don't look kindly upon one-sentence introductions and conclusions, not that I've asked.

So my students, like the 3rd grader trying to explain 2+2, solve the problem they've been set and then struggle to say something else about the something they've just said.

a math revolution too

Barry's in the Atlantic!

Mumford High, RIP

A beautiful piece from Barry on The Destruction of Education and the Preservation of Inequity:

From the fall of 1964 through June 1967, I attended Mumford High School in Detroit.... My brother and sister also attended Mumford and graduated in 1962 and 1958. As I write this, Mumford is in the process of being demolished. The demolition is part of the $500 million Detroit Public Schools Capital Improvement Program started in 2009. Because of a shrinking student population, the state is in the process of shutting down almost half the schools in Detroit. The school district is attempting to sell the shut down schools for redevelopment, an effort that has earned over $10 million since 2009.

But although Mumford is being destroyed, a new version of the high school has been built on what had been the original Mumford’s athletic field. The new school cost $52 million to build, secured by a bond issue in a city where almost half of its schools have been shut down. From the web page for the new Mumford, it is described as a “LEED Silver Certified state-of-the-art facility and will offer academic core areas, a high-tech media center, modern science laboratories, a courtyard student quad, and a community health clinic.” Mumford is one of 15 schools that has been taken out of the Detroit Public School system and assigned to Michigan’s Educational Achievement Authority–a statewide district set up for managing struggling schools. The new Mumford will open in the fall.

For those of us who grew up in a city that was at one time vibrant and had one of the best school systems in the country, it has been difficult to watch its decay.

[snip]

It is fairly easy to dismiss the decline of education in Detroit on its failing economy and its accompanying social ills and even for some to make sweeping accusations about the low cognitive ability of Detroit’s student population. But the decline of education is not limited to Detroit. It has been happening across the U.S. for quite some time, although not as catastrophically as in Detroit. The vision of education in this country for many decades has been education and equity for all. In fact, the history of the equity problems and their solutions in the U.S. has its parallels in the history of education in Detroit. It is a story of how the fight to eliminate inequity in education has actually increased it.

[snip]

During the period of the 50’s and early 60’s, Mumford had been one of the premier high schools in Detroit, competing with Cass Tech—a magnet school in the downtown area that had admission requirements—for the academic achievements of its students. Mumford was located in northwest Detroit which was a mix of working class, middle and upper middle class neighborhoods. Though predominantly Jewish, the northwest section was also home to upper middle class African Americans who attended Mumford (Graham; 1999).

[snip]

Mirel (1993) (an education professor at University of Michigan who has done much research in the history of the Detroit Public School system) points out that during the depression of the 30’s in Detroit as in the U.S as a whole, the push in education was to keep graduation rates steady and prevent drop outs. With the deficit of work, the thinking was that it was better to have young people in school than out with nothing to do. The general curriculum in Detroit at that time was experiencing a large number of failure rates. To keep the students off the streets, courses were made easier. “Descriptive” science courses were introduced in lieu of lab-based courses and focused on useful topics such as how vacuum cleaners worked. “Relevance” was the watchword just as “engagement” is now. Topics such as traffic safety were woven into classes such as civics, and schools offered courses in personal standards, focusing on topics such as diet, dress, etiquette and personal hygiene. Girls were offered courses on “Appearing to Advantage, “Homemaking”, “Use of Leisure Time” and “Bride and Trousseau”.

This pattern continued long past the depression, past World War II and into the 50’s and 60’s, during which time the influx of African Americans from the south into Detroit continued because of the well-paying factory jobs. Curricula in high schools had evolved into four different types: college-preparatory, vocational (e.g., plumbing, metal work, electrical, auto), trade-oriented (e.g., accounting, secretarial), and general.

[snip]

During the period of the 50’s and early 60’s, Mumford had been one of the premier high schools in Detroit, competing with Cass Tech—a magnet school in the downtown area that had admission requirements—for the academic achievements of its students. Mumford was located in northwest Detroit which was a mix of working class, middle and upper middle class neighborhoods. Though predominantly Jewish, the northwest section was also home to upper middle class African Americans who attended Mumford (Graham; 1999).

[snip]

Northwest Detroit started to experience the phenomenon of white flight starting in the late fifties. The flight began in the twenties, starting in a more central area of Detroit—an area that would be the site of the riots to occur in the summer of 1967—that had also been predominantly Jewish in the 20’s through the 40’s. The flight’s trajectory continued and by the 60’s included northwest Detroit where I was living, and would continue to the suburbs. The demographic of Mumford was changing as well. According to Mirel (1993), 22 percent of black students were in the general track by 1967 with whites making up only 2 percent of the general track despite it being one of the most academically oriented high schools in the city.

After graduation, most boys who were in the general and vocation tracks in Detroit were drafted and sent to Viet Nam. Boys in the college prep track who went on to college, on the other hand, were given a draft deferment status which students in the general and vocational tracks did not receive. The role of the draft policies at the time of Viet Nam played no small part in contributing to the recognition of inequity between white and blacks.

[snip]

The summer of 1967 brought the riots that ultimately escalated the white flight to the suburbs, and brought in its wake racial rifts from which some say Detroit has never recovered. In the years shortly following the riots, there were efforts to decentralize and desegregate schools—met with protest from the white communities that would be affected. A friend of mine attended Cooley High School (located a few miles away from Mumford). In 1968 he witnessed a race riot that occurred at the school in April of that year, shortly after Martin Luther King was assassinated. He described it as follows:

“It really was a travesty, particularly in that the kids fighting were the ones in tech programs, being streamed into Viet Nam. Cooley was half black, half white and a powder keg as long as I was there. I went back to visit a year after I graduated — the white exodus occurred and Cooley had become almost entirely black. Achievement was up, violence was down — it had transformed into a 50!s middle class school.”

My friend’s description is apt in a way that he may not have realized when he wrote it. To his eyes, achievement looked like it was on the rise as it did in many schools. Change had in fact come to Northern to address the protest of a few years back and it came to Cooley, Mumford and other predominantly black schools in Detroit. But the change came in the form of more “relevance”, focusing on black history, black culture, the arts, dance, and creative writing.

[snip]

The reforms in the Detroit schools were consistent with reforms brought about across the U.S. during the 60’s and 70’s, by the prevalent radical critics of schools at that time.... “Traditional” schooling was seen as an instrument of oppression and schools were recast in a new, “hipper” interpretation of what educational progressivism was supposed to be about. In moving away from the way things were, the education establishment’s goal was to restore equity to students rather than maintaining the tracking that created dividing lines between social class and race. The end product however was a merging of general track with college prep with the result that college prep was becoming student-centered and needs-based with lower standards, and less homework assigned. Classes such as Film Making and Cooking for Singles were offered, and requirements for English and History courses were reduced if not dropped. Social class and race were no longer a barrier for such classes as evidenced by the increasing numbers of white students who began taking them. With the requirements for graduation being diminished in the “general” track as a result of the student-centered fad, this track saw an increase in students from 12 percent in the late 60’s to 42 percent by the late 70’s. (Ravitch, 2003).

[snip]

Currently, high schools have an honors/AP track, and a general track. The general track consists of less rigorous courses and represents a lower level of education. Qualification for the honors/AP track starts before high school, and in elementary and middle schools, there is also a two-tier system. The higher tier (starting at about third grade) is the gifted and talented track. In general, this track provides teacher-directed traditional instruction at or above grade level. For students who do not qualify (and the criteria for qualifying vary, with differing definitions of what constitutes “giftedness”), they are placed in classes with students of varying abilities. As such, they are subjected to a one-size-fits-all curriculum that involves student-centered group activities, and project-oriented approaches to learning. This educational approach is guided by an undying faith led by the educational establishment that all we need to do is teach students how to learn, how to think critically and that facts and content are things they can look up (on Google) on a “just in time” basis whenever they really need to know. For many students, the approach is a guarantee that they will not be able to handle honors or AP courses in high school.

The elimination of inequity and tracking, therefore, has evolved to a two track system starting in lower grades and continuing on in high school. Those students not considered “smart enough for the gifted programs” are consigned to the lower track.

[snip]

In the meantime, there is a push for more technology in the schools, as if SmartBoards in every classroom and an iPad for every student is the answer. The tearing down of Mumford and the building of a state-of-the-art high school are indicative of what education has now become.

The complete article here.

just-in-time learning

Barry's new article. In my comment, I left a passage on memory consolidation from John Medina's Brain Rules:

It takes years to consolidate a memory. Not minutes, hours, or days but years. What you learn in first grade is not completely formed until your sophomore year in high school.

Direct Instruction in Grammar

From the study guide for the California Teachers of English Learners Teacher Certification Exam:

"Direct instruction in grammar and spelling has had disappointing effects on students' writing.  Teachers have not achieved much success with extensive error correction either.  The most successful teaching of language conventions has been the presentation of well-written materials.  A good reader becomes a good writer as the self editing process develops and good models are available.  A teacher is most likely to be successful if he/she keeps a variety of well-written and easily understood examples of both written and spoken English available to the students."

Study guide was prepared by XAMonline.com and has no affiliation with the California Teacher Credentialing Dept. nor the testing companies that California uses.  The above quoted passage doesn't seem that far out of line from what I've seen presented in ed school classes.

dysteachia, part 2

A popular textbook on special education (Rosenberg, et. al, 2008), notes that up to 50% of students with learning disabilities have been shown to overcome their learning difficulties when given explicit instruction.
Mathematics Education: Outwitted by Stupidity Barry Garelick

So the sequence is:

a. Collaborative group inquiry with spiraling
b. Huge increase in children diagnosed w/learning disabilities
c. Provision of explicit instruction (w/o spiraling?) to children diagnosed w/learning disabilities
d. Followed by 50% of learning disabilities resolving

Back on my home planet, we didn't bother with Steps A, B, and D.

dysteachia

In a well-publicized paper that addressed why some students were not learning to read, Reid Lyon (2001) concluded that children from disadvantaged backgrounds where early childhood education was not available failed to read because they did not receive effective instruction in the early grades. Many of these children then required special education services to make up for this early failure in reading instruction, which were by and large instruction in phonics as the means of decoding. Some of these students had no specific learning disability other than lack of access to effective instruction. These findings are significant because a similar dynamic is at play in math education: the effective treatment for many students who would otherwise be labeled learning disabled is also the effective preventative measure.
Mathematics Education: Being Outwitted by Stupidity by Barry Garelick

The effective treatment for many students who would otherwise be labeled learning disabled is also the effective preventative measure.

and see Galen Alessi's classic: Diagnosis Diagnosed

math and race in Iowa

Among the possible explanations offered for the decline [in ITBS scores] are increased drug use in the mid-60′s, permissiveness, increase in divorces and single family homes, as well as the progressivist trends in education resulting in student-centered and needs-based courses. (See  Protecting Students from Learning for a more extensive discussion of this last item.) Another explanation offered is that the population of test takers starting around that time began to include more minority students, resulting in a dilution effect. That argument fails to explain, however, why the same pattern of declining test scores for the SATs exists for the ITBS and ITED test scores which were not limited only to college bound students. Also significant is the fact that the population of test takers in Iowa, Minnesota and Indiana remained primarily white which has been noted by Bishop (1989) and Murray (1992). Specifically, the U.S. Census of 1950 shows that the population in Iowa was 99.2 percent white, declining by 0.7 percentage points to 98.5 percent white by 1980. Similarly, the populations of Minnesota and Indiana were 99 and 95.5 percent white in 1950, dropping respectively to 98.2 and 92.8 by 1970. (Hobbes, 2002).
Barry Garelick: The Myth About Traditional Math Education
Education News

fractions in a 1940 arithmetic text

Terrific new article by Barry G: The Myth About Traditional Math Education.

The equal division of three cupcakes among four people, or the equal division of a 3 inch line into four parts, is an extension of the idea of division of a whole number by a lesser whole number, which students have already mastered. Students already know that if 12 cupcakes are equally divided among four people, then each person gets 12/4 cupcakes. This idea is extended by starting with the problem of 3 divided by 4, and expressing 3 as 12 fourths. The problem is now stated as 12 fourths divided among 3 people, so that each person receives 3 fourths. This idea is then applied to a line three inches long, so that fractions are ultimately related to a number line, and the final point made that fractions are a representation of division. This is a key concept and ultimately underscores an idea of representing a fractional part as a unit unto itself. That is, 3/4 of an inch can be thought of as a unit (i.e., there are four such units in a three inch line) which is a cornerstone idea when fractional division is studied later.

And here's Barry's chart showing the rise and fall in test scores:

SAT math question

I have two questions, actually, but I'll post just one for the time being.

Here it is.

For me, SAT math questions are non-routine. They are problems, as opposed to exercises.

Here's my question.

Is that true for kids scoring 700 and 800 on the SAT?

Or is it true for me because my math knowledge is still pretty tenuous?

When I watch Salman Khan work SAT problems, I don't feel like I'm watching a person solve problems.

I feel like I'm watching a person do exercises.

Am I wrong?

Barry's open letter to Deborah Ball

at Out in Left Field

Barry Garelick at Jay Greene

The Educationist View of Math Education

it isn't the culture, stupid

Barry G on the new international comparisons

The news last week that Shanghai students achieved the top scores in math on the international PISA exam was for some of us not exactly a wake-up call (as Secretary of Education Arne Duncan characterized it) or a Sputnik moment (as President Obama called it).

We've seen this result before. We've seen the reactions and the theories and the excuses that purport to explain why the US does so poorly in math. In fact, there are three main variations used to explain why Chinese/Asian students do so well in international exams:

Version 1: They are taught using rote learning and then regurgitate the results on exams that test how well they memorize the procedures of how to solve specific problems.

Version 2: They are taught using the reform methods of a "problem based approach" that doesn't rely on drills, and instills critical thinking and higher order thinking skills

Version 3: The teacher or the culture produces the proper conditions for learning

This argument is based on the observation that the education-valued culture manifests itself in ways that are unlikely to happen here: long school days, after-school math “clubs” in which math facts and procedures are drilled (pointed to by some as evidence that students in China are engaging in rote learning), long hours studying and teachers who know the subject matter extremely well. . . . The “culture argument” also paints a picture of U.S. culture as totally oblivious to educational values and ignores the subcultures that place a value equal to that seen in China and other countries. Those are the students whose goals are to enter the top universities in the US, who work very hard and take AP classes and exams. Some of the parents of those students have protested against the adoption of substandard math programs such as Investigations in Number, Data and Space, and Everyday Math. These are the parents who have been told by school boards that the traditional method of teaching math may have worked for some, but not for all. Those are the parents who have discovered that the traditional methods of teaching math (in the 50’s and 60’s) work very well indeed, and are similar in some respects to how it is taught overseas.

decline at the top

Speaking of our best students, the other reaction to mediocre U.S. performance on international tests I've seen -- which shows up in the comments to Barry's article -- is the claim that our best students are doing as well as the best students elsewhere. This is a variant of the 'culture' argument: American  slackers are bringing down the mean.

Not true.

Here's a passage from the Baltimore Curriculum Project video. In this section, William Schmidt, who headed one of the TIMSS studies, is talking about the best American students:

8:05 Schmidt: This system of ours has failed the elite kids, too. This is a little known fact because it wasn't emphasized very much, but in the early TIMSS study there was a high school specialist exam for those kids that were the AP physics kids and those that were the AP calculus kids. Those kids were last among their counterparts in the rest of the world. That is, if you took the elite track in the French system that was leading to math and science, these [American] kids were at the bottom. So we're failing those kids just as much as we're failing the kids on the other spectrum.

William Schmidt Baltimore Curriculum Project
Dr. William H. Schmidt of Michigan State University
Leading Minds K-12 Math Education Forum, April 24, 2008 in Baltimore.
U.S. TIMSS NATIONAL RESEARCH COORDINATOR
MICHIGAN STATE UNIVERSITY
12th grade