kitchen table math, the sequel: Barry Garelick on mini lessons and inequality

Friday, May 27, 2011

Barry Garelick on mini lessons and inequality

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.


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.


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.


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.


Redkudu said...

Yes. That. All of it. Every day, in my classes.

The lower-level students are embarrassed, ashamed, and hostile for fear of being unable to answer questions in front of their peers. Also, they become bored when they cannot participate because their native language seems foreign to them as the content reading becomes more complicated, but their reading level, already low and un-adressed through intervention, stays the same.

The higher-skilled kids are often embarrassed, ashamed, and hostile for fear of being used as models of excellence (for which they are teased or bullied), and resentful when "group grades" represent NOT the work they put into the assignment but the lack of work their peers did. In effect, in my mind, they are being penalized for not teaching their peers well enough.

Bonnie said...

If less able children in SIngapore are given more time in the day, does that mean they have a longer day? And who pays for that? And do parents of the other kids start complaining that their kids aren't being given the same time?

Bonnie said...

I went to an untracked junior high in KY, in the 70's. It was horrific, really horrific. I remember sitting in 9th grade civics next to a kid who could not read. He was completely illiterate. He would sit and light cigars in the bottom of his desk throughout the class. Most of the kids in the class could read a little, but not well. So we spent the whole year taking turns reading the textbook out loud. Each time, when we would get to the kid next to me, he would simply say something nasty, and we would move on.

In 8th grade language arts, we had to work in pairs. Each "smart" kid was paired with one of the kids who couldn't read. My "teammate" used to threaten me if I didn't do her homework for her.

I am generally a progressive when it comes to education. I don't like this "direct instruction" stuff, I think Khan Academy is shallow -the illusion of education rather than the real thing - and I truly believe in small class sizes. But on tracking, I agree with conservatives. Untracked schools may be OK in very homogenous, well funded districts like Westchester County. But in struggling systems with large disparities, like my KY junior high, untracked classes are a disaster for everyone.

FedUpMom said...

My Older Daughter attends a Quaker school, which espouses the Quaker principles of radical equality and simplicity.

At the same time, they track the $&%^! out of the kids. It's a total contradiction to the Quaker ethos, but it makes real academic learning possible. They do actual math in the math class!

Glen said...

I just "track" my own kids. What choice do I (or you) have? The difference between consistently teaching a kid at exactly his current level vs. randomly teaching him at other people's levels for a few minutes then telling him to go teach himself is the difference between apparent genius and good student or between good student and "just not cut out for school".

Grace said...

Following up on what Redkudu wrote, this breeds destructive cynicism among some of the students on both ends of the spectrum. This is probably the exact opposite of what educators expect. In their ideal world, all the students are working together and learning to understand each other. That's a dream.

lgm said...

>>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 my NY district's elementaries, every unclassified child receives the same math curriculum which is based around the Regent's objectives for the grade level. The less able child is given the same problems in whole class, but is referred to rTi if he struggles after a 1:1 on the spot 'reteach' in the classroom. He may receive other more scaffolded problems, then go on, or he may have a reduction in the class assignment. If he falls behind he will be offered summer school. In middle school, the classes are grouped by acheivement level, and he will receive more support and more problems than a child in a section of children who all acheive at a higher level.

The biggest problems I see are that many teachers are presenting, rather than teaching. Many use solely auditory techniques, which are just inappropriate for topics that need visual demos..reminds you of Charlie Brown cartoons 'wah, wah' from the direction of the chalkboard. And of course, the ones that understand and can teach fractions are few and far between so it is accepted that the middle school will make up those topics.

The other problem is that some teachers are still shoving off studying to the parents in the non Title I elementaries rather than taking the responsibility, for ex., of making sure that 4th graders know their math facts and can speedily write them down. This goes along with the lack of classroom control, when they are allowing these children to blab instead of work since the admin won't back up the discipline.

Those who want to learn do not spend time teaching those of low acheivement either b/c a) they do not know how to break the lesson up into small bites for special ed or b) the nonsped children who do not want to learn will not try; they disrupt instead of asking or listening to peers who try to help. It is embarrassing to not 'get' anything your teacher says and they really shouldn't be placed in that position in math class - they should be placed appropriate to their instructional need.

lgm said...

>>If less able children in SIngapore are given more time in the day, does that mean they have a longer day? And who pays for that? And do parents of the other kids start complaining that their kids aren't being given the same time

In the US, the children who are less able to keep up with the work go out for rTi. The ones still in the classroom have idle time. This is a big problem with those parents and the admin here has ended up agreeing to offer band and free reading, rather than have the aide slowly read the Weekly Reader and waste the 45 minute time slot. The parents on the other hand will tutor at child's pace at home - just too much left out of the grade level curriculum.

In high school, the parents are upset that athletics and extracurriculars are cut to pay for double period remedial. They know these are disruptors and have explicitly stated that they want the parents of the disruptors to pay for alternative, summer school, transport to alternative&summer school and for double period as they have to pay community college books and fees for all math above Alg. II - since all the math teachers have been moved out of Trig, Pre-Calc and Calc in order to provide enough remedial.

If it gets any more heated, I think they'll be asking for civil penalties for lack of parenting.

SteveH said...

" the introduction of "standards-based" report cards parents don't know how to interpret."

The problem is that this approach converts raw information from tests into many other vague categories, like problem solving and numeracy. This is what our state test does, and our schools try to match it. They think it provides more information, but it doesn't. When our schools get the results from the state, they look at the poor numbers for "problem solving" and then come to the amazing conclusion that they need to work harder on problem solving, whatever that is. They don't look at the results for a specific skill, like two-digit multiplication, and decide to work harder on that. That information is lost when it's converted into rubric form.

I would look at my son's (1-5) rubric report card with 5 to 10 categories for each course containing numbers I couldn't relate to his homework and tests. (The report card had about 100 numbers on it.) That's partly because we hardly ever got back homework and tests. They went into portfolios that were hidden away at school. The schools told us that we don't understand, and that we just want what we had when we were growing up.

I had one teacher blow it all off by saying that it's really no different than before, they just now use numbers. I disagreed. When the raw test information is converted into the rubric categories, the results change from a raw percentage correct score into a non-linear and judgment-based result, even for something as non-subjective as math. But that teacher was wrong. The schools made a BIG effort to explain that a '3' was good. It was meeting expectations. It was not a 'C'. It was more like a 'B'. It's all made up. All of the rubric categories are fuzzy and defy calibration.

Our schools started off with a 1-4 rubric, where most kids got 3's. It was very non-linear. They would hand out 2's to try and give kids a little push, and they would hand out 4's if kids were putting in a lot of effort. Effort. What they found was that kids gave up trying to get a 4. It required more effort than learning. Why bother?

Then our schools went to a 1-5 rubric scheme. It was still non-linear and effort-based, but it gave them a finer control over motivation. A 5 is not an 'A', however. You could argue that according to the rubric it's even more than an A+. A rubric grade always includes a judgment factor because that's how the categories are defined. To get a rubric grade, you don't just combine grades from tests with a weighted formula. You put the results into a judgment-based rubric bucket. A judgment factor, like class participation is not separated into it's own category with it own weighting factor, it's incorporated into every rubric bucket.

This vagueness allows teachers to not give a 5 to kids who would have received a 97 on a test. When my son was in 7th grade, I tried to map his raw percent correct scores on his math tests to the rubric grade he received. It was clear that the mapping was non-linear.

With differentiated instruction, kids get different levels of expectations. Notice that I don't say different levels of instruction or material. It's too easy for teachers to translate differentiated instruction into differentiated grading. Rubrics have enough leeway to allow them to do that. They do the 10-15 minute intro before breaking kids into groups, so where is the differentiated instruction. There isn't any. (Our schools actually used the term differentiated learning.) At best, it comes when the teacher works with the kids who need the most help. For the more able kids, it's just differentiated expectations and grading. One teacher told me that because my son was more able, she would expect more from him. She thought this would please me. I wanted to ask whether she was teaching him more. Of course not. Teachers are guides on the side and they have their hands filled with the lowest level kids.

lgm said...

We have the 1-4 rubric. It came in when full inclusion came.

3 is meeting grade level expectations at mastery level. 4 is meeting above grade level expectations at mastery level. 4 is rare as most teachers won't test for it and none will teach to it...students scoring at that level are highly gifted or they are afterschooled. 2 is working towards expectations..and qualifies the child for 'extra help'. 1s are in lots of daily extra help from specialists and get tested for LDs if parents allow.

The objective is for everyone to be a 3; no resources are put towards 4 for those that walk in at 3 level and subject acceleration isn't allowed anymore.

Catherine Johnson said...

If less able children in SIngapore are given more time in the day, does that mean they have a longer day? And who pays for that? And do parents of the other kids start complaining that their kids aren't being given the same time?

I hope Cassy can chime in -- I'm sure she remembers the particulars of Singapore school days better than I do.

OK, from memory (PLEASE correct me, everyone):

First of all, the state pays for education.

Singapore kids attend school from age 6 through 16, I think. I don't know how many days they attend school each year.

As I recall, academic subjects are covered in the morning. I have a vague memory that kids go home for lunch (?), then return to school for afternoon classes, which I believe are what we would call 'specials' or perhaps 'enrichment.'

During that time, kids who need more time to learn the curriculum continue to do so. They spend less time in specials.

I'll check the AIR report & see if I can confirm this quickly.

Catherine Johnson said...

In the US, the children who are less able to keep up with the work go out for rTi. The ones still in the classroom have idle time.


I wonder if that happens in my district.

I had the impression that rti kids here go to other teachers.

The district has 5.5 "reading specialists," which the administration refuses to concede are remedial reading teachers.

We've been told the reading specialists are just as essential to the strong readers as they are to the struggling readers.

What do the reading specialists do for the good readers?

No one knows.

Anonymous said...

What do the reading specialists do for the good readers?

stay out of the way.
if we're lucky.

ChemProf said...

My mother was a reading specialist for about a decade back in the 70's. Sometimes a good reading resource teacher can help a classroom teacher with advanced students, by suggesting alternative materials, etc. My mother did, but she was also interested in gifted education, so I doubt that is typical.

The vast majority of her time was absolutely spent with struggling readers. And she never had any contact with typical "good" readers. Why would she?