the arithematic of differentiated instruction

Concerned Teacher on differentiated instruction:

Differentiated instruction is a total scam. You MUST teach in order for students to learn, and you must offer practice time during which you are available to lend assistance. No superteacher can do both at multiple levels and through multiple modalities daily in the course of a single 55 minute period class, and do it well.

Teachers are not the folks who have perpetrated this myth. Teachers have had this myth forced upon them by administrators, and as far as I know, colleges have promoted this nonsense.

Concerned Teacher responding to Protecting Students from Learning

The arithmetic of differentiated instruction doesn't add up.

Put 20 kids at all levels of abilities and interests in the same classroom for 55 minutes.

Seat them in pods.

Have the teacher deliver a 10 minute mini lesson, after which she moves around the class working one-on-one with 20 different children.

While the teacher is making her way around the room, the other 24 children do whatever they've been told to do without being able to ask a question or get feedback. If they've been told to work together, then a lot of them are going to be copying whatever the quickest child in the pod is doing.

The total number of productive minutes an individual child can experience is 12 to 15 out of the 55, max, and that's assuming that the mini lesson was pitched to the child's level.

If the lesson was over a child's head, he or she has just two or three minutes of comprehensible direct instruction from the teacher.

If the lesson was below a child's level, he or she also has just two or three minutes of useful direct instruction from the teacher. If that.

Hunter Writing System

looks interesting:

Is this a whole-language approach to teaching grammar?

Yes and no. Yes, to the extent that whole-language instruction requires involvement of all the senses in learning. It is my recommendation that teachers have students say their rearranged sentences out loud (or, at least, subvocally) not only to test whether they are meeting the criteria for some grammatical element but also to hear what correctly spoken English sounds like. Of course, they do write and read the sentences as they carry out the exercise material.

No, because this system for immersing students in structure does not--and cannot--teach grammar through literature or through the students' own writing. Students must learn the structure of the sentence systematically, building from the known to the unknown in an experience-based and carefully sequenced way. This ownership of structure cannot be learned in random order nor without "interactive" types of exercises.

How does this way of teaching grammar relate to the process approach to teaching writing?

Nancie Atwell, a chief proponent of the process approach to teaching writing for middle school students, recommends occasional 10-minute mini-lessons in grammar primarily for the purpose of fixing some usage error. (Her reasoning is that the indispensable, if not sole, means to becoming a better writer is to do personally meaningful writing--as opposed to learning grammar as a means.)

Although my program would provide ideal subject matter for 10-minute mini-lessons, the primary instruction would have to be in the fundamentals of grammar (not in rules of usage); it would have to be virtually daily, not occasional, in occurrence; and it would have to be accompanied by extensive practice. It would have to include incrementally developed lessons on how sentences and their parts work and interact and would address usage errors only as sufficient background to understand and consistently apply them have been absorbed.

The philosophy of the proponents of the process approach to writing is that improvement in the mechanics of writing will take place with students' heightened desire to make sure that their message is read and acted upon and without formal instruction in grammar. (There remains the troubling question as to whether such experiences can lead to the remedying of most, let alone all or the most serious, mistakes. Then there is the question of permanency of the error-free writing.) Is it not reasonable to believe, too, that any lasting improvement in the mechanics of writing might occur just for the brightest of students or for those immersed in correct usage of English in their homes?

My philosophy regarding mastery of writing on the part of middle school students--in fact, all students--is entirely different. My philosophy is that immersion in grammar--that is, an experiencing of the roles of the key parts of the sentence by means of hands-on strategies, strategies that initially involve the rearrangement of sentence parts--is a prior and, for many (if not most) students, an indispensable means to self-confidence and competence in writing....

It is in light of this that I recommend that my grammar program--in accompaniment with on-going composition work--be the initial component of any foundational writing program (and, therefore, of any middle school program). My teaching suggestions in the next section offer some insights.

Competing Philosophies

slower math students in Singapore

from the Air report on math education in Singapore:

The topic structure in Singapore’s framework is efficient because topics are not taught and retaught as students move through the primary grades. Instead of repeating topics that students have already learned, teachers simply reintroduce them as a foundation on which to build new mathematical content. This practice, however, may not be suitable for students who have more difficulty with mathematics. The Singapore system recognizes that students who have trouble with mathematics may not attain mastery by following Singapore’s regular program of mathematics instruction and that these students may need special assistance to attain competence.

Beginning in grades 5 and 6, Singapore identifies its weaker students on the basis of a general examination of mathematics and language competency. These students receive special assistance and are taught according to a special fifth- and sixth-grade mathematics framework. This special framework mandates that students in the slower track

• receive approximately 30 percent more mathematics instruction than students in the regular track, and

• be exposed to the same mathematical content as students in the regular track, although at a slower pace.

The mathematics framework for students needing compensatory assistance adds review material to strengthen students’ understanding of previously taught content. For example, topics on numbers and geometry taught in grade 4 are repeated at a faster pace in grade 5. The introduction of some new concepts such as ratios, rates, and averages, which are normally introduced in grade 5, are delayed until grade 6 for the weaker students (Ministry of Education, 2001a). What is important, however, is that because slower students spend extra time studying mathematics, topics usually taught in grades 5 and 6 do not have to be completely sacrificed to make room for repetition.6

To support the framework for slower students, Singapore has developed a Learning Support Program to help educators identify these students and provide them with extra help (Ministry of Education 2003c). Mathematics Support Teachers (MST), who receive on-the-job supervision and specialized training to ensure that they are professionally competent, deliver compensatory assistance.

In the United States, we expect all students to meet the standards in state frameworks, but the standards do not help teachers address the needs of slower students. In fact, U.S. standards do not acknowledge that students learn at different rates. No Child Left Behind addresses the needs of failing schools, but it does not directly require that failing students receive help. Although some research evidence supports the belief that students benefit when the curriculum is adjusted to match their ability levels (Loveless, 1999), a distinct alternative curriculum would raise concerns in the United States about potential harm to students from ability grouping. Singapore’s approach differs from traditional ability grouping in that Singapore establishes a framework that requires students to master the same content as other students, not a watered-down curriculum as often happens in U.S. ability grouped classrooms. Singapore also provides extra assistance from an expert teacher.

What the United States Can Learn From Singapore’s World-Class Mathematics System: An Exploratory Study (and what Singapore can learn from the United States)

Apparently teachers in Singapore do not deliver 10-minute mini lessons followed by 40 minutes of one-on-one work with the students who are "struggling."

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.

[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.

bring back recitation

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.

scripted

Guided reading is scripted.

Miss Brave:

Before I actually became a first-year teacher, I was all about the workshop model. I thought it would be helpful, as a new teacher, to have a script of sorts to follow. After all, every mini lesson sounds a little something like this, but with all the blanks filled in:

"Boys and girls, we have been working hard on _____. Today I want to teach you that ____. Let me show you what I mean. ________. Boys and girls, did you see the way I ______? Now let's try it together. Turn and talk to your partner about _______. Boys and girls, today and every day I want you to remember that _______. Now off you go!"

A month and a half into the school year, the workshop model is pretty much the bane of my existence. Remembering the script and keeping the mini lesson to a scant 10 minutes is not as easy as it sounds. Neither is trying to shoehorn all the aspects of my lesson into the workshop model framework. I'm used to teaching in a style where I ask lots of questions of my students and invite lots of discussion. During the workshop model mini lesson, there are no questions allowed from the students and no discussion (except during the active engagement); it's all the teacher, all the time. I see my students raise their hands with these hopeful looks on their faces because they have something they want to share or something they have a question about, and it breaks my heart to keep saying, "Hands down, it's my turn now."

I think the workshop model probably does work for the population of students in the school where I teach. After all, taking advantage of those "teachable moments" that lead the lesson astray can be really confusing for students whose native language is not English, like the students at my school. But at the same time, the workshop model feels really one-sided. I can tell that there are kids who are confused, who aren't getting it, and I'm supposed to pull those kids for a 2-minute "re-teach" at the rug instead of changing tack and trying a different method?

This weekend, I took two New York State teaching certification exams (because my teaching license is from another state, I have to pass New York's exams to get my New York license). Mostly they were a joke, but they included lots of samples of class discussions -- and I realized that's something I miss. In my workshop model lessons, there's no back and forth, no "What do you think?", no "Who else has an idea about this?" I don't get to invite my students' opinions, their knowledge, their ideas. All I get to do is tell them how to punctuate their sentences and then eavesdrop on them while they try it. And even though I allegedly have more freedom as a cluster teacher, I've still been told by the powers that be that every class I teach should start with a mini lesson. It's hard enough being a first-year teacher as it is, but trying to shoehorn every lesson into a framework I'm not all that comfortable with is overwhelming.

Apparently the workshop model is mandated for use in schools throughout New York City, so...I should use it or lose it, I guess? Or I should, as someone suggested, plan two lessons: one to be taught the way I want to teach, and one workshop model to pull out when I'm being observed.

I don't think I'm ready to be that much of a renegade just yet.

Can we conclude from this that 'it's scripted' isn't the real objection the education establishment has to Direct Instruction?