kitchen table math, the sequel

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I can remember being gatekeepered out of 8th grade algebra back in the 70's, and the memory still makes me boil. In my case, I was a year younger than the other kids, so the teachers said I wasn't "developmentally ready" for abstract mathematics. So I wasted a year in consumer math.

Fast forward to today - I was utterly shocked to find out that my kids school gatekeepers 8th grade algebra (as well as a whole slew of other "advanced" courses). I had thought gatekeepering at such a young age had been discredited in the 80's. Why are they still doing it? We end up with a school system that is as tracked as the German system. And worse yet, in my district, the tracking criteria has nothing to do with whether a kid is good at math or not. It is all based on whether they are diligent at submitting homework that is neat and organized according to teacher standards.

However, this has nothing to do with Common Core in our district. They have been doing this for eons. At parents night at our high school last spring, the principal was complaining that we don't send enough students to schools like MIT and CMU. Well, you know, if you gatekeeper out all your most talented students in 8th grade, the messy, creative, smart ones, you won't have much talent left in the 12th grade.

Froggiemama on gatekeeping, part 2

At our middle school, when Chris was there, 7th-grade kids were gatekeepered in and out of Earth Science on the basis of "maturity."

"Maturity" meant, among other things, that the student was proactive (I think that was the actual term, proactive) in "seeking extra help."

(Code for: hire a tutor.)

One of the most talented students in the school was gatekeepered out of Earth Science on grounds that she was "anxious."

Anxious!

As I recall, this student had one of the highest scores on the enrollment test. But she was anxious, so no.

Ed and I got involved in that case because we happened to know the parents, who told us what was going on. (Involved in the sense that we could figure out the relevant statutes and knew people to consult.)

What it boiled down to:

Number one, if a high-achieving student has an emotional issue so disabling that she can't take Earth Science, the school is legally obligated to "identify" her as having special needs, which the school had not done (and was not proposing to do).

Number two, if the school had identified this student as having special needs, it could not keep her out of Earth Science on grounds that she had special needs.

Basically, the building principal was wrong on every conceivable ground.

The assistant superintendent intervened and the girl was enrolled.

Unfortunately, the assistant superintendent didn't last long in our district.

From the New York Times: Grouping Students by Ability Regains Favor in Classroom

It was once common for elementary-school teachers to arrange their classrooms by ability, placing the highest-achieving students in one cluster, the lowest in another. But ability grouping and its close cousin, tracking, in which children take different classes based on their proficiency levels, fell out of favor in the late 1980s and the 1990s as critics charged that they perpetuated inequality by trapping poor and minority students in low-level groups.

NYC is struggling with how to teach GT students.

Christine C. Quinn, the City Council speaker who is running for mayor, has proposed expanding the number of gifted classes while broadening the criteria for admission in hopes of increasing diversity. (The city’s Education Department has opposed the proposal, saying that using criteria other than tests would dilute the classes.)

And teachers?

Teachers and principals who use grouping say that the practice has become indispensable, helping them cope with widely varying levels of ability and achievement.

My instruction aimed at the middle of my class, and was leaving out approximately two-thirds of my learners,

Enjoy.

from a friend:

Education Next has made the Jacob Vigdor article (released online in October 2012) the lead story in the current Winter 2013 issue.

He argues that the achievement gap and generally dwindling math performance of US students has been addressed by making the math curriculum "more accessible" (i.e., it has been dumbed down). He then argues that it need not be dumbed down if the curriculum were differentiated between low and high performing students.

In fact, this is pretty much how it was in the 50's and 60's. Students did not need the 3 or 4 years of math in high school to get admitted into colleges. What he leaves out, however, is the quality of math education in the lower grades and how this has affected the number of students who might otherwise be high performing students.
...
There’s no disagreement that some kids are smarter than others. Most people know that you can’t just set a standard (like algebra in 8th grade) and do nothing else. But Vigdor overlooks overlooks that issue and then claims that the failed initiative defines some IQ/algebra correlation. There are many other variables to consider–which he doesn’t.

The “Math Wars” are about curriculum and teaching methods, but this article skips over that analysis. Most schools separate kids starting in 7th grade. In affluent areas, since “enough” students get onto the top math track in high school, (often due to tutors, learning centers, or help from parents), educators will not look for any fundamental issues in K-6. They only assume that it’s a relative problem.

Why not interview parents to see what is done (or not) at home and try to find out how the best students got there? There may see an IQ connection, but it’s not that simple. There are things one can do to separate the variables. But too many authors of the recent spate of articles about math, algebra and its need, either can’t or won’t.

In his report, he pooh poohs the idea of introducing Singapore Math into classrooms, citing the usual cultural differences argument which is specious. (Teachers in Singapore have better math background; students go to school all year round, so there’s no forgetting concepts during the summer; the culture promotes education and hard work, etc). He neglects the fact that Singapore’s texts present the material clearly and succinctly and that there have been successes in schools in the US that have used it.

I remember one day back in middle school, when C. had done well on one of his death-march-to-algebra math tests, we were taking a walk & discussing his triumph. At some point we got to talking about where he would now rank in Singapore terms. We figured probably on par with Singapore kids who have developmental disabilities.

I'm (half) serious.

Remember the Singapore Math pilot project in New Milford, Connecticut?

The SPED kids were ahead of the general ed kids.

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ドル 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ドル 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ドル 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.

re: Diane Ravitch writing in today's Times--

If every child arrived in school well-nourished, healthy and ready to learn, from a family with a stable home and a steady income, many of our educational problems would be solved.

Waiting for a School Miracle
By DIANE RAVITCH
Published: May 31, 2011

lgm writes:

Our nation and NY have many students who can be described as ideal. They have been placed in fully included classrooms with students who have severe issues and [they have been] denied access to an appropriate education. Remove that barrier, place by instructional need with competent teachers, and we as a nation will see education succeed. Continue to mainstream, and pretend to teach at an instructional level several years below the grade level over the door if it all, and we'll continue headbanging.

Yesterday's home and careers assignment for my 8th grader was similar to his 1st grade assignments before full inclusion: Take the alphabet. Under each letter, list two careers that start with that letter.

The majority of this school meets Ravitch's definition of ready to learn. But the idealists won't let the majority of children learn at their instructional level.

back to the future with Diane Ravitch

The history of tracking students in public education goes back to the early part of the 1900′s. By the 20′s and 30′s, 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. Students were tracked into the various curricula based on IQ and other standardized test scores as well as other criteria. By the mid-60’s, Mirel (1993) documents that most of the predominantly black high schools in Detroit had become “general track” institutions that consisted of watered down curricula and “needs based” courses that catered to student interests and life relevance. Social promotion had become the norm within the general track, in which the philosophy was to demand as little as possible of the students.

[snip]

By the early 80’s, the “Back to Basics” movement formed to turn back the educational fads and extremes of the late 60’s and the 70’s and reinstitute traditional subjects and curricula. The underlying ideas of the progressives did not go away, however, and the watchword has continued to be equal education for all. While such a goal is laudable, the attempt to bring equity to education by eliminating tracking had the unintended consequence of replacing it with another form of inequity: the elimination of grouping of students according to ability. Thus, students who were poor at reading were placed in classes with students who were advanced readers; students who were not proficient in basic arithmetic were placed in algebra classes. Ability grouping was viewed as a vestige of tracking and many in the education establishment consider the two concepts to be synonymous.

The elimination of ability grouping occurs mostly in the lower grades but also extends to early courses in high school. The practice of such full inclusion is now so commonplace that theories have emerged to justify its practice and to address the problems it brings. “Learning styles” and “multiple intelligences” are now commonplace terms that are taught in schools of education, along with the technique known as “differentiated instruction” to address how to teach students with diverse backgrounds and ability in the subject matter. Teachers are expected to “differentiate instruction” to each student, and to keep whole-group instruction to a minimum. To do this, the teacher gives a “mini-lesson” that lasts 10 to 15 minutes; then students work in small groups and told to work together. The prevailing belief is that by forcing students to solve problems in groups, to rely on each other rather than the teacher, the techniques and concepts needed to solve the problem will emerge through discovery, and students will be forced to learn what is needed in a “just in time” basis. This amounts to giving students easy problems, but with hard and sometimes impossible approaches since they have been given little to no effective instruction to the mathematics that results in effective mathematics problem solvers.

[snip]

Brighter students are seated with students of lower ability in the belief that the brighter students will teach the slower ones what is needed. And frequently this occurs, though the fact that the brighter students are often obtaining their knowledge via parents, tutors or learning centers is an inconvenient truth that is rarely if ever acknowledged. The result is that brighter students are bored, and slower students are either lost, or seek explanations from those students in the know. Another inconvenient truth is that in lower income communities, there are unlikely to be students who have obtained their knowledge through outside sources; they are entirely dependent on their schools.

[snip]

Through the efforts and philosophies of otherwise well-meaning individuals, full inclusion and equality for all has served as a form of tracking.

Protecting Students from Learning: Raymond
by Barry Garelick

In my experience, when a school opts for "differentiated instruction," parents have no way to know whether their children are being taught the same curriculum as other children -- especially since differentiated instruction tends to go hand-in-hand with a reduction in quizzes and tests and the introduction of "standards-based" report cards parents don't know how to interpret.

A less-able child is treated equally in the sense of being placed in a classroom with more-able children.

But is the less-able child taught the same curriculum?

Is the less-able child given the same problems to do?

And, if he is given the same problems but can't do them, what then?

In Singapore, somewhere around 4th or 5th grade, less able children are given more time in the day to master the curriculum. Equality means that all children are taught the same curriculum.

I was just reading a short article in Education Week about Bill Gates' "Gold Star teacher" plan when I came across a letter criticizing the concept.

First, here's Gates:

Bill Gates closed the National Governors Association's 2011 winter meeting last week by urging the governors to consider increasing the class sizes of the best teachers.

Under the Microsoft founder's model, a school's most effective teachers would be given an additional four or five students. Less effective teachers could then work with smaller classes and receive professional development.

A 2008 study supported by the Bill and Melinda Gates Foundation determined that 83 percent of teachers would support increasing their class sizes for additional compensation. (The foundation provides grant support to Editorial Projects in Education, which publishes Education Week.) In 2009, a Goldwater Institute report argued for tying teacher effectiveness to a higher pupil-teacher ratio and a higher salary.

The endorsement by Mr. Gates now could push the proposal further into the mainstream, given the level of support shown at the NGA meeting.


Gates to NGA: Tie Class Sizes to Teachers' Skills
Education Week
Published Online: March 8, 2011
Published in Print: March 9, 2011, as Gates to NGA: Tie Class Sizes to Teachers' Skill

And here's the reaction from a letter writer:

What makes a teacher of young learners effective is his or her ability to work with individuals in ways that are appropriate to their needs. During whole-group lessons, such teachers move around their classrooms, spotting those who are having difficulty and taking the time to give a little help and encouragement. Later, when planning future lessons, they include modifications for the range of abilities in their classrooms and figure out ways to have most students working on their own or with a partner, so they can meet with small groups.

It is only the least-competent teachers who stand in front of their classrooms and give the same instruction to all, blind to the boredom of those who already know the material, the confusion of those who aren’t ready for it, and the tuned-out state of the few who don’t care.

Although the notion of getting extra pay for taking on more students might have seemed attractive to most of the teachers responding to a survey funded by the Bill and Melinda Gates Foundation in 2008, the situation at that time was only hypothetical.

Today thousands of teachers all over the country have classes of 30 and up. I wager that neither Bill Gates nor the governors who agree with him could keep order in such classrooms, much less teach anybody anything.

Linking Pay and Class Size Hurts Teaching Quality

And here is Doug Lemov:

[Many] to most of the top-performing urban charter schools of which I'm aware buck the otherwise orthodox belief in heterogeneous classroom grouping and solve this problem by homogeneously grouping classes.

Teach Like a Champion
p. 256

With homogeneous grouping, the teacher is always teaching to the level of the entire class because the entire class is on the same level.

Also: whole-group instruction does not mean whole-group lecture. Whole-group instruction means "Call and Response," "Pepper," "Cold Call," "Wait Time," "Everybody Writes," etc. In the well-taught homogeneously grouped classes Lemov describes, the situation is pretty close to 100% of students learning from the teacher 100% of the time because 100% of students are directly engaged with the teacher for 100% of the class. That's the goal.

How much time are students directly engaged with the teacher in a heterogeneous class?

Not much.

Say class time is 50 minutes and you've got 20 kids.

• 12 minutes for the mini lesson

• 2 or 3 minutes for transition-time (sit on the floor to observe mini-lesson; re-group for partner-work; sit on floor again for mini-lesson; etc.)

• 35 minutes for individual time with teacher

That's maybe 3 minutes of direct instructional time with the teacher per each two-child pair and another 12 minutes of time directly engaged with the teacher during the mini-lesson if the mini-lesson happens to be pitched to the child's level.

If the mini-lesson is not pitched to the child's level, then 3 minutes max.

One of these days I'll have to write up my notes from the 5th grade writing workshop I observed. I think it's fair to say that the two boys I was sitting closest to learned nothing at all for the entire class period. Learned nothing and practiced nothing.

I don't know whether the other kids were engaged in productive partner work.

Up in my area of NY, folks (mainy blue collar [people who] work in NYC gov't agencies and came here for the 'good schools') could care less about charters. They see that concept as a waste of resources that would be better devoted to fixing public school. Essentially, they want the district to be the charter by having the state stop forcing full inclusion and go back to grouping by academic instructional need. Allow test out, allow honors courses, allow slow learner courses, have alternative school, but do not allow the inclusion of violent children, druggies, gang members, emotionally disturbed, mentally ill and severe needs to be an excuse not to offer a year or more's worth of curriculum to each unclassified child each year. They propose that unclassified disruptors/nonparticipants pay the difference in cost between the alternative school and the regular setting.

Additionally, they'd like to fire the teachers who are presenting rather than teaching or are incompetent or abusive. It's been six years since the middle school failed AYP and the taxpayers stopped the 'blame the student' game and funded 'extra help' and rTi. They want to cut costs by having the unclassified students learn the material in the classroom, not from the extra help/resource teacher.

On the other hand, some parents view this proposal as racist or elitist. They work behind the scenes rather than engage in debate at board meetings for continuing full inclusion. Homeschool, homebound, alternative, and private school numbers continue to increase as does the number of hours of 1:1 aides for the emotionally disturbed and behaviorally challenged, and the security guards to remove the violent and disruptive.

Group work can also increase engagement because individuals can be assigned roles that allow them to be "experts in something," so that they can be challenged at a level appropriate to their understanding, she says. To discuss and present various theories for why the Jamestown settlement failed or why the dinosaurs became extinct, for example, more advanced students may be "producers" charged with stopping their group periodically to summarize what is being said; those with attention deficits might be assigned to be "prop directors" to keep track of supplies needed to make a chart for the final presentation.
Unleashing the 'Brain Power' of groups in the Classroom: The neuroscience behind collaborative work
Nancy Walser
Harvard Education Letter
May/June 2010, p 2

Good thing we got rid of tracking.

What most middle class parents in Chicago are seeking when they have their children apply for the magnet and selective schools is classmates that are not two grade levels or more behind. If the teachers are also good, all the better. But many would choose humdrum teachers, in a grade-level or better classroom, over high octane teachers trying to teach to a large number of children with serious remediation needs in the same room as children already on grade level.

Funny how parents just aren't getting with the program on differentiated instruction.

Or anything else, for that matter.


children should struggle
mixing fast and slow learners
constructivism solves classroom discipline problems
ed schools and you
palisadesk on recent graduates of ed schools

It does seem likely we are headed toward a period where the heterogeneous classroom will be the only safe way to avoid constitutional scrutiny. That clearly impacts what can go on in the classroom. Imagine the range of math problems that would be needed for cumulative review by 8th grade in such a classroom.

It looks like we will be left then with ineffective and inefficient instructional models.

ABOUT THE STUDY METHODS

The study is based upon survey findings from a randomly selected, nationally representative sample of 900 public school teachers in grades 3 to 12, plus qualitative data from five focus groups, conducted in winter-spring 2008.

[snip]


DIFFERENTIATED INSTRUCTION

Heterogeneous grouping of students in a classroom implies that teachers will respond flexibly to the different learning levels among the students in their classroom. But teachers evince serious doubts about how well they are carrying out differentiated instruction in their own lessons.

More than eight in ten (84%) teachers say that, in practice, differentiated instruction is difficult to implement.


OBSERVATIONS

Differentiated instruction-the strategy whereby teachers adjust their material and presentation to the diverse array of academic abilities within a given classroom-is tricky to implement, according to teachers. Education experts and policymakers who believe that this is the optimal alternative to tracking should recognize that, from the perspective of teachers, it is easier said than done.

Survey:
In your judgment, how easy or difficult a mission is it to Implement differentiated instruction on a daily basis in the classroom?

Somewhat difficult: 48%
Very difficult: 35%
Somewhat easy: 12%
Very easy: 4%
Not sure: 1%

The following description of what it took for one teacher to try to make differentiated instruction work sounds like an engineering exercise requiring the most delicate and complex analysis and judgment. It also reveals substantial self-doubt about the execution:

"Language arts, we've really been struggling because we do have so many different levels of kids. They're always in the same classes all mixed together, so I do a lot of differentiated instruction with tiered lessons and flexible grouping. Where kids are really, really strong in writing they're with a particular group of students for writing activities. Then they might be in a different group altogether for reading, just depending on where their levels are. [Moderator: How do you identify that/] Some is teacher observation; some is testing and assessment scores. At the beginning of the year, a lot of it's based on the state standards test scores that they showed the previous year. Sometimes there's teacher observation that follows them [here] as well."

High-Achieving Students in the Era of NCLB
Tom Loveless, Steve Farkas and Ann Duffett
Thomas B. Fordham Institute
page 65

As far as I can tell, virtually every school district in the country has committed to differentiated instruction as its core principle of instruction and instructional grouping.

Evidence-based decision making is not a hallmark of public schools.

I just picked up my kids from a day of ski school.It was a great experience for everyone.The kids seemed to enjoy the day.And as a parent, I felt like they learned a lot and were challenged appropriately for the day.

The experience made me wonder: What if academic schools were taught like ski schools?Here are some things that might change:

1.Children would be grouped by ability, not age.

Ski schools are organized by ability group, with age separation only for adult vs child.This means that the classes have children with different ages.For example, my older son, who is 8 years old, was in class with 10- and 13-year olds.And my 5 year old was in class with 3 and 4 year olds. From what I could tell, instructors, parents and children weren’t rattled by this notion.

If schools were to do the same, children would be in class with their academic peers, not their age peers.This would make it easier on teachers and students, as students would be able to focus on building the skills that they need to build, not on some arbitrary standard that someone their age should be able to do, and teachers could focus on skill-building for *all* students in the class since they would have similar ability levels.

2.Parents would be given very specific feedback about what their child need to do to get to the next level.

At the conclusion of the day, I was given very detailed feedback.For example, my older son needed to stay on the “fall line” consistently as he did the moguls.When I probed further, the instructor told me in detail what my son needs to do because the instructor had a very clear idea of what a skier of a given level should be doing.

Imagine being given very specific feedback in a parent-teacher conference: “Currently, your son has mastered 456 of our 1,234 spelling words that students need to master at this level.To get to the next level, we are focusing on subset of 124 words, mostly dealing with long vowel sounds.Here’s a list of the reference words, with your son’s progress noted.”

It would make our job as parents easier, provide transparency into the classroom, and help me answer the question “What do you do all day?”

3.Students would only be allowed to advance to the next level when they have demonstrated mastery of the current level.

My older son is attempting to get to the next level.However, they will not advance him until he consistently demonstrates the skills that are required at that level.And there is no negotiating this point. Everyone recognizes that promotion without mastery is a disaster waiting to happen.

Imagine hearing something similar from your child’ teacher: “Your son/daughter needs to become proficient at all multiplication tables up to and including 12x12, as measured by our proficiency exam . . . he’s very close, but he’ll need to focus on these problems to advance to the next level.”

4.The instructional approach and techniques at the beginner level would look quite different from that at advanced levels.

In the beginning of ski instruction, instructors use the “wedge” to teach skiing.It’s an artificial construct to help students learn how to turn and shift their weight from ski to ski.As the student progresses, the wedge is abandoned as skiers are taught to ski with their skis “parallel”.In the final stages, independent use of upper and lower body is taught.Each of these stages looks quite different, yet no one worries that it won’t eventually work.

What if the same approach were used in reading instruction?You might get this in your child’s backpack:

“Dear Kindergarten Parents,

. . . In reading instruction, we are continuing to teach children letter/sound correspondences.We are limiting our instruction of vowels sounds (e.g., short a, long a, long “o”) to isolate the effect of an “e” has at the end of some words.During this phase, the stories your child is reading won’t be “authentic”.In fact, they will sound contrived and silly because we are focused on helping them to improve their tracking skills with decodable text, and teaching them how to use punctuation marks to identify sentences and paragraphs.Eventually, as they become proficient decoders, the stories will become more authentic and sound more like stories you are used to hearing as an adult.Please bear with us and help us make this phase of learning fun by emphasizing tracking, going left to right when they read, and helping them use punctuation marks to tell them how to group words.When they don’t know sounds, simply provide the sounds to them and help them feel good about their experience with reading.”

And here’s the kicker . . . everyone in the ski school system seems completely happy with it.There is no jealousy across groups because a skier who is a “4” would be completely unsuccessful skiing in a “5” group.And parents aren’t pushing for their child to be upgraded to another level because they know it would mean misery on the mountain.

If we could only get educators to realize the beauty of this approach . . .

A principal reason districts cite increasing staffing ratios—whether by adding teacher aides, instituting team teaching, or lowering class size—is the challenge of “differentiating instruction” to meet the needs of an educationally heterogeneous population in each class. But a far more effective—and less costly—solution is to change how classes are formed.

While much attention has been given to the size of classes, almost none has been directed to how they are formed. Classes are not chance aggregations of pupils; at least in principle, they are composed of students who have mastered the prerequisite skills and knowledge to function in the class. But in most American schools students are assigned to classes based on age—regardless of whether they have demonstrated such mastery. As students move up the grades, their teachers confront an increasingly unmanageable array of undiagnosed knowledge gaps among their students; these gaps impede the acquisition of new skills and explain the dismaying fall-off in student performance in the middle and high schools grades that is a hallmark of American schools. Exhorting teachers to address these gaps through “individual attention” or, to use the current buzzword, “differentiated instruction” is a fool’s errand.

The SABIS model of class formation proposes an alternative. The SABIS International Charter School in Springfield, Massachusetts enrolls 1,574 students in kindergarten through twelfth grade and has the largest waiting list, nearly 2,700 students, of any Massachusetts charter school. Tenth graders from low-income families outperform their peers in the Springfield district schools by 45 percentage points on the state’s respected MCAS test (92 percent proficient or advanced, compared to 46 percent) in English and 50 percentage points in Math (83 percent versus 33 percent proficient or advanced) and for the past seven years every SABIS Springfield high school graduate has been admitted to an institution of higher learning.39 The school has literally closed the achievement gap by race and income; tenth-graders in the low-income and African-American NCLB subgroups outperform the average student statewide. In 2008, Newsweek named the school just one of three urban “top U.S. high schools” in Massachusetts.40

Students are placed in grades by skills level, not age. From phonics in kindergarten through AP classes in high school, students are taught each learning objective to mastery. Through electronic assessment tightly keyed to the curriculum, their teachers are alerted immediately when they fail to demonstrate mastery of a skill they have just been taught. Rather than move forward, their teacher re-teaches the concept or arranges for tutoring of individual students by their peers so that knowledge gaps do not form that undermine later learning. A schoolteacher can no more successfully introduce algebra to students who have not mastered division than a college professor can teach an advanced chemistry class to students who have not completed basic courses in the subject.

So equipped, SABIS teachers routinely succeed with classes of thirty students. Ralph Bistany, SABIS’s founder, sees it is as SABIS’s mission to demonstrate that a world-class education can be delivered affordably and scoffs at those who claim thirty children cannot be taught effectively in one classroom. “First, we need to define the word ‘class,’” he says. “Every course has a prerequisite—concepts that the course is going to use but not explain. That list of concepts determines who belongs in the class and who doesn’t.” If the course is German, and one student is fluent and others cannot speak a word of the language, the students obviously should not be taught together, he explains. At SABIS, students in a class have the same background but neither, he hastens to say, “the same ability nor the same knowledge.” So formed, it doesn’t matter whether the class has ten students or fifty. “In fact, fifty is better,” he adds. “We have worked with classes of seventy in countries where it is allowed, and it has worked like a charm.”

The Efficient Use of Teachers by Steven F. Wilson Ascend Learning, Inc.
A Penny Saved: How Schools and Districts Can Tighten Their Belts While Serving Students Better

“fifty is better”

palisadesk recommends:

The Principals' Partnership
Research Brief
Tracking & Ability Grouping

From Today's EdWeek

'Algebra-for-All' Push Found to Yield Poor Results

Spurred by a succession of reports pointing to the importance of algebra as a gateway to college, educators and policymakers embraced “algebra for all” policies in the 1990s and began working to ensure that students take the subject by 9th grade or earlier.

A trickle of studies suggests that in practice, though, getting all students past the algebra hump has proved difficult and has failed, some of the time, to yield the kinds of payoffs educators seek.

[snip]

“There’s no question that taking advanced courses boosts student achievement,” said Adam Gamoran, a professor of education policy studies and sociology at the University of Wisconsin-Madison. His 2000 study on algebra and tracking helped catalyze the interest in expanding access for all students to algebra courses.

“Where the area of disagreement comes,” Mr. Gamoran added, “is what should we do with students who performed poorly previously. In my judgment, the reason studies like mine show that students even with low levels of achievement do better in advanced classes is because the low-level classes are practically worthless.”

“And there’s no simple solution to this problem,” he added, “because we also know that when tracking is eliminated, students at high levels don’t gain as much as they do in high-level or [Advanced Placement] classes.”

[snip]

Tom Loveless, the author of the report from the Washington-based Brookings Institution on “misplaced” math students in algebra, said the issue is even more complex.

“No one has figured out how to teach algebra to kids who are seven or eight years behind before they get to algebra, and teach it all in one year,” said Mr. Loveless, who favors interventions for struggling students at even earlier ages.

Nationwide, research findings may diverge because testing content varies—the TIMSS test has more algebra content than many state exams taken by 8th graders—and because course content varies from classroom to classroom.

“If you take what’s called algebra class, and you look at the actual distribution of allocated time, you find that many of those teachers spend a very large portion of that year on basic arithmetic,” said Mr. Schmidt, who is a distinguished university professor of education at Michigan State’s East Lansing campus. His research on U.S. classrooms has found, in fact, that nearly a third of students studying algebra are using arithmetic books in their classes.

"Once a child is identified as being three years behind it shouldn't matter whether they are purple, from the planet Ork; they need placement that is appropriate to get them back on track. Anything less is just child abuse disguised as political correctness."

And yet where I live (Montgomery County, MD) the drive is precisely toward heterogeneous classrooms, and away from homogeneous grouping. They they are rolling out something called The Seven Keys to College Readiness. Benchmarks are being set that are unrealistic for some students, and too low for others. Advocates who call for more homogeneous grouping and a differentiated gifted curriculum are painted as elitists and even racists.

Elitists and racists, no doubt. Parents are stinkers.

Still and all, it could always be worse (and, if experience is a guide, it will be). At least the concept of college readiness has caught the attention of the folks running Montgomery schools.

Unlike here. The folks running my own district (per pupil spending: 26,718ドル) will have no truck with college readiness.

Last fall I asked the administration to include "college preparation" on the new 21-page Strategic Plan.

They said no.

Actually, they didn't even say 'no.' What they said was:

The strategic plan does not have specific mention of college readiness or international benchmarks. However, as a practice we are reviewing the Standards for Success—which you know is based on University preparedness.

Yes, indeed, I do know. I happen to own the book. Also, I possess all of the pdf file downloads that comprise the book, and I know where to find them on my hard drive. Ed read the history standards & says they are sound.^*

So this is a terrific resource, and we can all sleep soundly at night knowing it is being "reviewed." But it's not on the Plan.

You can find all of the Standards for Success material here. (Click on "ordering information" for pdf files.) College work samples in English, Mathematics, Natural Sciences, Social Sciences, and Second Languages here.





Universities Push to Influence State Tests for High School Students
Understanding University Success
review of College Knowledge by David Conley

^* for passersby: Ed is a historian

In our sample of schools in western Kenya, for example, the median first grade class in 2005 (two years after the introduction of free primary education, and prior to the class size reduction program we exploit here) had 74 students; average class size was 83; and 28 percent of first grade classes had more than 100 students. These classes are also very heterogeneous: Many of the new students are first generation learners and have not attended preschools (which are neither free nor compulsory in Kenya). Students differ vastly in age, school preparedness, and support at home. These challenges are not unique to Kenya. They confront many developing countries where school enrollment has risen sharply in recent years: understanding the roles of tracking and peer effects in this context is thus particularly important.

Peer Effects and the Impact of Tracking: Evidence from a Randomized Evaluation in Kenya (pdf file) Esther Duflo1, Pascaline Dupas2, and Michael Kremer3, 4
NBER abstract

Abstract

...This paper provides experimental evidence on the impact of tracking primary school students by initial achievement....One hundred and twenty one primary schools which all had a single grade one class received funds to hire an extra teacher to split that class into two sections. In 60 randomly selected schools, students were randomly assigned to sections. In the remaining 61 schools, students were ranked by prior achievement (measured by their first term grades), and the top and bottom halves of the class were assigned to different sections. After 18 months, students in tracking schools scored 0.14 standard deviations higher than students in non-tracking schools, and this effect persisted one year after the program ended. Furthermore, students at all levels of the distribution benefited from tracking. A regression discontinuity analysis shows that in tracking schools scores of students near the median of the pre-test distribution score are independent of whether they were assigned to the top or bottom section. In contrast, in non-tracking schools we find that on average, students benefit from having academically stronger peers. This suggests that tracking was beneficial because it helped teachers focus their teaching to a level appropriate to most students in the class.

Conclusion

This paper provides experimental evidence that students at all level of the initial achievement spectrum benefited from being tracked into classes by initial achievement. Despite the critical importance of this issue for the educational policy both in developed and developing countries, there is surprisingly little rigorous evidence addressing it, and to our knowledge this paper provides the first experimental evaluation of the impact of tracking in any context.

After 18 months, the point estimates suggest that the average score of a student in a tracking school is 0.14 standard deviations higher than that of a student in a non-tracking school. These effects are persistent. One year after the program ended, students in tracking schools performed 0.16 standard deviations higher than those in non-tracking schools....students who were very close to the 50th percentile of the initial rank distribution within their school scored similarly at the end line whether they were assigned to the top or bottom section. In each case, they did much better than their counterparts in non-tracked schools.

Peer Effects and the Impact of Tracking: Evidence from a Randomized Evaluation in Kenya (pdf file) Esther Duflo1, Pascaline Dupas2, and Michael Kremer3, 4
NBER abstract

This will have no effect whatsoever on the folks running our public schools.


stagnation at the top - Fordham report
Tracking: Can It Benefit Low Achieving Children?
Linda Valli on tracking in 5 Catholic high schools, 1
Linda Valli on tracking in 5 Catholic high schools, 2
"school commitment" in Valli's study of tracking in Catholic high schools
7th grade depression starts in 1st grade

ability grouping in Singapore
characteristics of schools where SAT scores did not decline
The Other Crisis in American Education by Daniel Singal
Hiding in Plain Sight: grouping & the achievement gap
tracking: first random-assignment study

SAT equivalence tables
SAT I Individual Score Equivalents
SAT I Mean Score Equivalents

chickens have come home to roost
the deathless meme of the high performing school
Allison on the naturals

On April 28th NAEP results for 2008 were released. Sam Dillon has an article in the NY Times where he uses these results to bludgeon NCLB for failing to close the black/white achievement gap.

Between 2004 and last year, scores for young minority students increased, but so did those of white students, leaving the achievement gap stubbornly wide, despite President George W Bush’s frequent assertions that the No Child law was having a dramatic effect.

The article provides some great graphs that show black/white children's scores for reading and math for the last 37 years. Interestingly, the graphs show steady improvements for both subjects and both demographics that Dillon ignores. James Taranto has a provocative response questioning whether Dillon would have been happier had the data shown static white achievement and increasing black achievement.

So minority kids are doing better than before. But because white kids are also doing better, and therefore the "gap" remains, the Times suggests the law is a failure. By this measure, it would have been better to pass a law that only benefits minorities than one that benefits everyone.

To be fair, closing the racial gap was one of the stated goals of No Child Left Behind. But what a strange, uncritical attitude the Times has toward the federal government when it reports with a straight face that the law is a failure because it seems to have helped children of all races, rather than observing that this calls into question whether the goal made any sense in the first place.

Ouch!

It made me think of a more problematic question. The graphs show a gap that's been pretty stubborn for 37 years and although the article was written to criticize NCLB as ineffective law since it hasn't closed the gap it was written to address, there's a bigger story here. The only significant gap reduction follows school desegregation and then, essentially nothing. In fact you could use the graphs to make a pretty good case that the last 37 years have seen nothing but improvement in math while in reading, NCLB seems to have reversed a bit of white decline and black stagnation. The real question to ponder here is why the gap seems immune to change.

You certainly can't claim there hasn't been a lot of effort expended in trying to close the gap. I would argue that much of the curricular turmoil of the last two generations is driven in large part by these very attempts. Federal and state involvement in local schools has also been accelerated by this effort. The evidence says that pushing on teacher quality, curriculum, administration, pedagogy, unions, pay, charters, vouchers, and everything else in the kitchen sink has accomplished little by way of closing the gap.

The gap represents about a three year difference in grade level. Could it be that having classrooms populated with kids exhibiting this gap, being fed a curriculum designed for the median student in the room is a problem? The one thing I've never seen addressed (except in very limited settings) is this curricular mismatch.

The graphics lay it out starkly. These are two completely different sets of kids. Three years difference is huge. Keeping them together in the name of racial equality or equal access is never going to close the gap. Everything we've done is piddling on the edges of a conflagration. If you really mean to close the gap then that educational goal has to stand in line ahead of our social goals until it's fixed, doesn't it?

Could it be that the slopes we see on these graphs are due to all the piddling around the edges while the gap is due to ignoring the obvious need to provide appropriate curricula? Could it be true that the shallow slope is an artifact of having an inappropriate mix in the classroom. And finally, would the slopes of both demographics improve with more appropriate placement?

Once a child is identified as being three years behind it shouldn't matter whether they are purple, from the planet Ork; they need placement that is appropriate to get them back on track. Anything less is just child abuse disguised as political correctness.

stagnation at the top - Fordham report
Tracking: Can It Benefit Low Achieving Children?
Linda Valli on tracking in 5 Catholic high schools, 1
Linda Valli on tracking in 5 Catholic high schools, 2
"school commitment" in Valli's study of tracking in Catholic high schools
7th grade depression starts in 1st grade

ability grouping in Singapore
characteristics of schools where SAT scores did not decline
The Other Crisis in American Education by Daniel Singal
Hiding in Plain Sight: grouping & the achievement gap
tracking: first random-assignment study

SAT equivalence tables
SAT I Individual Score Equivalents
SAT I Mean Score Equivalents

chickens have come home to roost
the deathless meme of the high performing school
Allison on the naturals