kitchen table math, the sequel: instructional grouping vs differentiated instruction

Tuesday, March 16, 2010

instructional grouping vs differentiated instruction

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”


Crimson Wife said...

Grouping children by where they are in the curriculum rather than by age such a no-brainer to me. I don't understand why only a handful of schools use the practice.

Catherine Johnson said...

It's ideological.

Goes back to --- the 1980s? I think it's the 1980s. Jeannie Oakes was the leader of the anti-tracking movement, I gather.

I assume she and the rest were mostly motivated by the fact that the bottom track was oversubscribed by black students.

Of course today what you see is special education oversubscribed by black students - but I don't know if those two facts are causally related. (That is, I don't know whether, once it became politically incorrect to track black students into lower tracks schools then resorted to 'placements' in special education as opposed to tracking.)

In any case, public education is deeply opposed to grouping of any kind. (Except for the 'fluid' groupings of guided reading ---- grouping is making a comeback there.)

Genevieve said...

It seems like tracking in the past didn't work very well for the students in the lower tracks. I understand the desire to change that.
I just don't understand why we can't fixed what didn't work about tracking (children being put in the wrong track because of stereotypes, inability to change tracks, inadaquate teaching in the lower tracks, etc).

SteveH said...

Tracking is not good if schools don't help students learn. Then it just reflects SES. It also doesn't help if the tracks teach different material, rather than cover the same material at a slower pace. Then again, the current solution is to put all kids on the slow track and hide the SES effect at home.

SteveH said...

You mean they don't trust the spiral? Imagine! And they have a huge waiting list.

Anonymous said...

I think you mean "principle" in the opening sentence. Otherwise, great article and totally on target.

Crimson Wife said...

Grouping by place in the curriculum is different that traditional tracking because you'd have high, middle, and low achievers in the same class. But unlike traditional heterogeneous classes, the teacher wouldn't have to worry about the kids being all over the map in terms of where they are in the curriculum.

I'd much rather teach a range of ages all at the same place in the curriculum than a bunch of kids the same age who may be several grade level equivalents apart.

Catherine Johnson said...

That's funny: I just checked the spelling of "principal" in the original -- it's 'principal'!


I'm going to correct it.

I'm sure it will be corrected in the book.

Catherine Johnson said...

I'm broadly in agreement with this article but we've seen the limits of his experience here.

A lot of the kids in C's class, who were not placed in Honors math in high school, were put into 'accelerated' math.

What that meant was that as freshmen they were put in a sophomore math class. The 9th grade kids were miles ahead of the other kids because they had already completed Math A, which is (or was - now abandoned) a 1 1/2-year sequence.

(I need lgm to weigh in here...I still don't entirely understand how Math A worked...)

Anyway, point is: the accelerated freshman were far ahead of the non-accelerated sophomores and spent weeks covering material they already knew & getting scores of 100+ on every quiz and test.

Parents tell me it was pretty much a wasted year.

I think the sophomore class may also have included juniors who were moving through the math sequence very slowly.

Meanwhile C., at Hogwarts, took Algebra 2 Advanced Honors - and made it through that course under his own steam, no tutors & no parent reteaching or help with homework - earning a B+.

Taking kids who've spent 5 years in a super-accelerated track and putting them in with kids who have never been accelerated and who are not necessarily interested in math (or motivated by this point) is the wrong way to go.

Catherine Johnson said...

This goes back to Attewell's "Winner Take All" study.

Attewell found that the kids most damaged by winner-take-all schools are high performing boys who score 2.5 SD above the mean on SAT.

A white male student scoring 2.5 SD above the mean on SAT has a .42 probability of taking the AP math exam in a school that is 1 SD below the mean for percentage of high scores & affluent families & only a .30 probability of taking AP math exam in a school with many high scorers & affluent families.

lgm said...

Every district in my area does their math sorting and class offerings differently. It seems to be a function of the teacher competency as well as the student diversity, competency, motivation, acheivement, and ability. Some offer honors classes to unaccel as well as accel. Some let a student switch into honors at several points. Mine doesn't offer any honors classes.

Here, accel isn't streamed with unaccel until Alg. II, and that's done in order to keep the class size appropriate as the district doesn't want to run undersubscribed classes. This district has double period classes though, so an accel student wouldn't be in with someone who found math difficult...he'd be in a single period class with an unaccel student who can do the work easily enough to maintain an above 80 average, but didn't have the study habits or the right political background to make the accel cut in 7th. I'd have to ask if the accel guy is getting a gpa boost for that, since the content is the same..I think they do get +4% for taking it accel.

I'm guessing your frosh who were done with Math A were taking Math B with sophs? Sounds like a mistake was made if that much review of Math A was needed - course it could just be how the course is run and anyone with mastery has an advantage.

My district has spend $$ on Acuity to see what everyone in middle school knows. No word on how that's going to be used to adjust the math class sorting.

Jenny said...

Crimson Wife,
I agree with your comment, "I'd much rather teach a range of ages all at the same place in the curriculum than a bunch of kids the same age who may be several grade level equivalents apart."

I have been placed in a middle school math classroom while completing my teacher certificate program in Washington, and have noticed the huge gap in achievement between students. During this process I have often wondered how we can address the needs of every student, so they will be successful. That's the point of school, right?

Instead, we've been placing students of all abilities into the same classes, crowded the classrooms, and expect all of the students to perform at the same level in the same curriculum. Then, the state wonders why not all students are passing standardized tests. How can a student that doesn't know their basic multiplication facts be expected to multiply fractions, without access to additional help at school? Then the student just gets pushed ahead, falling further and further behind until they’ve failed and have had their academic confidence destroyed.

I hope that more people will realize the benefits of instructional grouping and that it can help us achieve our goal as teachers – ensuring the success of all students.

palisadesk said...

That's funny: I just checked the spelling of "principal" in the original -- it's 'principal'!

.....I'm sure it will be corrected in the book.

No, it won't be corrected in the book, because it is correct as it stands.

"Principal" as an adjective, as used in the sentence cited, means most important, foremost, chief, primary. That's exactly the meaning implied -- the main reason, primary reason that districts cite for their staffing ratios ......(etc.)

"Principle" (ending with -le) is a noun and generally has some meaning synonymous with axiom, law or guiding assumption. A useful mnemonic for remembering which is which is to associate "principle" with "rule" (both ending in -le)

The "al" principal can be a noun or an adjective but in either case has the connotation of primacy.