Gambill Method - from ktm1

source:
Principal's Guide to Raising Math Achievement, pp. 81 - 82
by Elaine McEwan


Gambill method in a nutshell

• Teacher Carol Gambill has used her method of teaching algebra for 15 years. She has successfully taught algebra to students with disabilities, students of average ability, and gifted students.
  

• She assigns twenty to thirty problems for homework each night. Problems range from easiest to most difficult.
  

• ironclad rule: She assigns only those problems that have the answers printed in the textbook.
  

• She gives a daily quiz on the 4 or 5 most difficult homework problems. The first students to finish have their quizzes graded & recorded by Gambill; then these students become graders for next wave of students finished, and so on down the line. Total class time elapsed: 15 minutes.
  

• She uses "totally scripted lessons ... for each algebra unit that require absolute focus and attention, constant oral responses, and intense involvement from every student."

• She looks only at the homework of students who have failed the quiz.
  

• Students who didn't do the homework have detention that day, during which time they do the homework assignment under supervision.
  

• Gambill holds extra help sessions before school & at both lunch periods. She gives students her home phone number to call as a last resort. It is gratifying to see five to ten eighth-graders gathered around my chalkboard before school, excitedly discussing a difficult algebra problem. The kids love these chalkboard algebra debate sessions.
  

• textbook: Brown, Dolciani, & Sorgenfrey, 1994.

Gambill method for teaching algebra to mastery

The following passage is an excerpt from:
Principal's Guide to Raising Math Achievement
by Elaine McEwan

One of my favorite algebra teachers is Carol Gambill. She taught at the Sewickley Academy in the Pittsburgh area for many years and is now chair of the mathematics department and vice principal of the Littleton, Colorado, Prep Charter School. Carol has developed what her students call the "Gambill Method." I would hire Carol to teach algebra at my fantasy school in a heartbeat if I could. Here is the Gambill Method described in Carol's own words. Compare it to the way your students are learning algebra.


"Most students who enter my eighth-grade Algebra I or Honors Algebra I classes. in September each year are ill-prepared to learn algebra because most of them have not fully mastered arithmetic. To make matters worse, I have too few class periods to teach them the entire rigorous course when one adds up the drug education activities, annual class trips, report card day, vacations, snow days, exams, and parent-teacher conferences. These restrictions demand that the students put in extensive quality time. outside of class grappling with difficult problems and practicing for accuracy.


"I devised a method that I have used for 15 years with all students, those with disabilities, the average student, and those who are gifted. This method really works. Students make incredible gains during their year with me, because of the system the kids long ago dubbed the Gambill Method. Here's how it works.


"Twenty to thirty problems are assigned for homework every evening, ranging from the easiest to the most difficult of a given section of the text. I always assign the odd problems because their answers are in the back of the book. The answers provide the students with road maps to mastery. If they don't get the correct answer it means they turn back, take a detour, change a flat tire, or find a service station.


"On the day that an assignment is given I do the even problems with students in class using direct instruction. Although I use a traditional algebra textbook (Brown, Dolciani, & Sorgenfrey, 1994), I have developed totally scripted lessons for each algebra unit that require absolute focus and attention, constant oral responses, and intense involvement from every student. Direct instruction assures that all students leave my classroom that day with a thorough understanding and at least partial mastery of the concepts. I tell my students that doing homework does not merely mean writing out the problems, although that most assuredly is a component. I tell them they must master completely every problem of the assignment from the easiest to the most difficult. I would never assign a problem for which I had not given them the answer. The next day, when the students walk in the door I give them their daily quiz over the most difficult four or five problems from that assignment. Their answers and all of their work toward that end must be accurate. Some students work more quickly than others; the first students finished come up and have their papers checked by me, then they become student checkers and grade recorders, and so it progresses, with more and more checkers becoming available as the slower students finish their daily quizzes.


"Within 15 minutes, all students in the class have taken a daily quiz over the previous night's homework assignment. The quizzes have been graded and recorded and are back in the students' hands, thus providing daily immediate feedback to each student on his or her own progression toward mastery, and providing me, of course, with instant knowledge as to whether or not students did their homework.


"I never ask to see the homework of any student unless that student has failed the daily quiz. If I ask to see the homework of a student who has failed, and the student does not have it, he gets an immediate detention for the day. A detention simply means that students must stay after school that day and do under school supervision the assignment that they failed to do on their own. This, in my opinion, is a justifiable, logical consequence.


"Because I am so strict with mastery of homework concepts, I assure the students that I will also do my part to help them be successful. Therefore, I conduct extra help sessions before school and at both lunch periods. It is gratifying to see five to ten eighth-graders gathered around my chalkboard before school, excitedly discussing a difficult algebra problem. The kids love these chalkboard algebra debate sessions. In addition, the students have my telephone number and are invited to call me as a last resort. Please note, however, that I seldom receive more than two calls per school year.


"My students win so many academic awards that students from other algebra classes cannot even play in their league. There is much hard work and yet the students l love my class, vote it their favorite each year, love math (even those who had despised it up until algebra) and remember their year with me as the one that led them to discover within themselves the power to determine their own destiny in the academic arena. All this is based on a simple system that nurtures and demands daily perfect mastery of each step in the course as it comes along. Other teachers who have adopted the Gambill Method have replicated my results" (Carol Gambill, personal communication, August 13, 1999).



One of the reasons I want Carol to teach math in my fantasy school is that she achieves remarkable success with her students. They have repeatedly won a variety of mathematics competition championships at the local, state, and national levels for the past 10 years. They took first place in the Pittsburgh MathCounts Competition for five consecutive years and won a Pennsylvania State MathCounts championship as well. And based on the outstanding achievements of Carol's students on the American Junior High School Math Exam, the NCTM presented her with the Edith Mae Sliffe Award. But awards are not the only or even the most important reason for my wanting Carol to teach in my school. Most important to me is that her students know exactly what is expected of them, and Carol is disciplined and structured enough to be consistent.

math class in the 1970s

from Robyn:

I went to school during the 1970's. Back then, children did not have tutors in elementary school. Parents did not reteach at home. But I learned math and am proficient with everyday math.

Today, suburban schools depend on educated, affluent parents to pick up the pieces from failed curricula.

Robyn is right. Our district just took a "math survey" of K-5 parents. That's a good development, but the questions weren't what I would have wished, including this item:

"I am able comfortably to assist my son/daughter with math homework."

Ed and I told the new assistant super that this question on the survey shows that the district relies on parents to reteach math at home.

She said it didn't.

I said: "Assist" doesn't mean "give your child a quiet place to work." It means "know math well enough to reteach when necessary."

She didn't agree.

She herself had to hire a math tutor for her son in high school and pointed out that one-on-one teaching is far superior to group teaching.

That observation is a heads-up for all of us.

Is it the case that administrators now universally assume parents are hiring private teachers for math the same way they hire private coaches for soccer? (I'm certain the superintendent believes something of the sort.)

If so, I'm going to have to do a lot of spaced repetition to dispel this notion, which confuses tutorials with tutoring.

The distinction is simple.

tutorials: good

tutoring: bad

If Christopher had spent this year learning algebra 1 from Carol Gambill with zero "help" from me he'd know a lot more algebra.

Yeah, sure, he'd probably know more algebra if Carol Gambill gave him private lessons than if Carol Gambill taught him algebra in her class. But the choice between a good teacher working with a good curriculum and an ineffective teacher working with a bad curriculum remediated by mom is no choice at all.

We did manage to point out that for many, many years kids took math at school and succeeded with no help from parents. We said that Ed took calculus in his high school, then took calculus at Princeton.

He had a tough time of it at Princeton because he was placed in the engineering course which was over his head. Nevertheless, he passed the course.

He did well in his high school calculus course with no help with homework and no tutoring.



on the Today show:

This morning on the Today Show there was a special regarding parents hiring Internet tutors from overseas locations due to the fact local tutors were so expensive. One mother was interviewed saying, “I believe teachers should be paid well. I just can’t afford them.” I couldn’t believe my ears. There was no hint of why aren’t the schools teaching our children or why is there this huge need for tutors. Needing tutors was a given. The story was what people are doing to secure tutors. What a nightmare!

in California

The Today Show post showed up at almost the exact moment I had looked up the CA Mathematics Framework 2005 and found this:

Whether students are underachieving, average, gifted, or in need of individual attention, parents should recognize their own and their children’s role in learning mathematics and achieving optimal success. They should know the specific academic standards their children are to meet at each grade level, and they should be able to monitor their children’s performance and provide extra help when needed. Parents should be responsible for obtaining information regarding their children’s progress and know how to interpret that information appropriately. Above all, they should encourage a positive attitude toward mathematics.

Parents are their children’s first teachers. A child’s early experiences with mathematics at home can provide an important foundation for learning the content standards for kindergarten (Saxe, Guberman, and Gearhart 1987). Parents and other family members can nurture and stimulate mathematics development in their children and, for many children, will need to be involved in their children’s mathematics program at all grade levels (Stevenson et al. 1990).

However, schools must take greater responsibility to support the early mathematics development of children who are less fortunate and do not benefit from an educated, supportive family environment. Such support may require after-school homework, transportation services to bring children to school early for extra tutoring, extended tutoring support, and similar kinds of programs.

(Chapter 7: Responsibilities of Teachers, Parents, Administrators)

This is remarkable. Here we have the state of California officially telling parents they must:

• "know" the specific standards for each grade level
• "monitor" their children's math performance
• "provide extra help when needed"
  
• be "responsible" for getting info from the school about how their child is doing (hah!)
  
• "know how to interpret" that information
• be prepared to do this until he graduates from high school

This is bizarre.

What parent apart from a person working in a math-related field can do this?

And how many parents working in math-related fields can do this? Pedagogical content knowledge is different from domain knowledge.

Next question: are parents expected to be able to do this for every subject their child will be "learning" at school?

I'm obsessed with my child's math education, and I can't do these things. I don't know what C. knows and doesn't know; I don't know how to assess his knowledge or when to assess his knowledge or how frequently to assess his knowledge; I don't understand the wording of the state standards; my ability to reteach math at home may not extend to helping with proofs in geometry (unless I can get there first & teach them to myself well enough to "assist"); barring a miracle I'm not going to be able to reteach calculus at home.

If I can't do these things, there aren't many parents out there who can.



where does this come from?

Why would these paragraphs appear in any state DOE document?

I have to assume we're seeing the effects of the past 25 years of ed school constructivism. This list isn't constructivism; it's the absence of instructivism. When educators spend all of their time in graduate school and professional development learning false theories of human learning..... and it comes time to write a Mathematics Framework..... maybe this is what you get.

Send in the parents.


CA Math Framework: responsibilities of parents
why do we have so many tutors?
parents are the problem

an amazing math teacher

My niece had a terrific algebra teacher freshman year. Scratch that: my niece had a terrific algebra teacher fall semester. Her school is on block scheduling so by January she was done with math for the next 9 months. Won’t take math again until the fall.

Here’s how he ran his class.

Every week his students have 3 chances to take a test on that week’s material. The test is short, perhaps 5 key problems. If they ace it the first time, they’re done. If they don’t ace it, they take it again; if they don’t ace it the second time, they take it one last time. The final grade stands.

The cool thing: the tests are cumulative.

The first week students take a test on the the first 5 problems; the second week students take a test on those five problems along with the next five problems; the third week they take a test on the first week’s 5 problems, the second week’s 5 problems, and the 3rd week’s 5 problems, and so on.

By the end of the semester they’ve worked up to a final exam covering everything they’ve learned in the course, which they remember because they’ve been re-tested on it every week of the semester.

The teacher also sends each parent a weekly email laying out in detail his child’s progress in the course. Parents can see whether or not their child mastered that week’s material, and they can see when he mastered it: 1st test, 2nd test, or 3rd. Parents can also see any set of 3 tests where his child did not master the material even with three tries. My sister says you could glance at the email and see exactly which material your kid barely squeaked by on.

The teacher explained his system on Back to School night and told parents not to panic when they got the initial emails because early on in the year the point total could suddenly drop 50 points when a student blew the first or second test. He told parents not to panic & not to yell at their kids because they’d have two more chances.

The emails don’t function as a veiled request for parents to kick in with reteaching and tutoring. They are information. Parents know what their kids are doing in the course. I assume that his emails do function as an invitation for parents to kick in with oversight and homework monitoring. Which is fine by me. Parents of students in his class know exactly what they need to know to manage the situation at home.

This may be especially important in my sister’s school because some kids intentionally blow off the class due to a complicated CA system whereby they get credit for “Math 1” even if they flunk Algebra 1. My sister and I agree that the problem these kids pose is school level, not teacher level. In my view (not necessarily my sister’s) the school needs to kick in with supervised homework sessions and the like. (See: LaSalle High School.) Working in a system that rewards kids for flunking algebra, this teacher deals with it by making sure parents know their kids have decided to flunk algebra, providing them with a weekly update on just how much algebra their kids have flunked to date.

The teacher is available every lunch hour and frequently after school for Extra Help. And: Extra Help actually helps. My niece went in twice when she wasn’t getting something. The reason she knew she wasn’t getting it was that she had barely squeaked by on the first two tests and still came up with a low score on the 3rd test.

She went for Extra Help after the 2nd test. My sister says the 3-test format taps into the Magic Number 3 that is embedded in the hearts and minds of children everywhere, as in: “I’m going to count to 3 and when I get to 3 you better be factoring trinomials or else.”

Clearly, the three tests serve as formative assessment. The teacher knows, the student know, and the parent knows whether the kid has or has not mastered the material covered in the course to date. That doesn’t happen in a normal math class. In a normal math class, as my sister points out, “Since no one grades homework, you don’t find out if they know anything until they flunk the test.”

This math class is far from normal because, as it turns out—and this came as a surprise—this teacher also grades homework. The way my sister and my niece found that out was that one day my niece blew off her homework: she just wrote down whatever came to mind and turned it in.
The homework came back with an “F” on top. The teacher had read her homework, corrected her homework, and graded her homework.

She went to see him and apologized. It had been years since a teacher had so much as looked at her homework and she’d assumed he wasn’t going to look at it, either. She asked if she could do it over again & the teacher said yes.

It will probably come as no surprise to learn that the homework sets weren’t burdensome. Perhaps because this teacher read and graded all the homework, or perhaps because he knew exactly how much homework the kids needed in order to master the concepts, he gave small problem sets. My other niece, whose teachers never so much as glanced at anything the kids did outside class, would be assigned dozens of problems every night; she’d sit and slave over her math and no one at the school would give it a second thought. As a result, the stuff they turned in was “the crappiest sh** you’ve ever seen.”

The kids in this teacher’s class, because their teacher was a collecter and correcter, learned to produce neat, readable solution set with the answers circled.

So:

• formative assessment

• distributed practice

• cumulative practice

I would put money on it the kids in this man’s class have some of the highest math achievement coming out of a public school Algebra 1 course in the country.

They better have, since it'll be 9 long months before any of them looks at the inside of a math book again.


the Gambill method

an administrative hassle

I missed the latest big math meeting.....this is the one in which 5th grade parents were going to be filled in on 6th grade math.

It's all a big mystery, as things here so often are.

A friend sent this reaction:

Tracking: first we’re tracking, then we’re not. Then we are, then we’re not. So, I don’ t know if we are or not. Changes were going to be made but the teachers in 6th couldn’t handle too many changes.

The deal here is that the middle school principal wants to get rid of the accelerated math course.

A month ago, at a principals' meeting with parents, he said they were dumping the accelerated course. Last year's principal wanted to dump it, too; he told us so.

Unfortunately the superintendent had already sent around a letter saying they'd be tracking kids in 6th grade, which two of us present at the meeting remembered clearly....so WIRES CROSSED!

Anyway, going into the 5th grade meeting I posted a series of The Trouble with Middle School Math posts on the Forum:

• Gambill method
• Singapore problems, 6A
• Singapore, Saxon, Trailblazers problems
• Kipp versus Irvington
• Your child. Not the little genius you thought, eh? (the trouble with Phase 4)
  

I love the internet.

At the meeting parents were concerned about what would happen if their kids did well in the non-accelerated track.

Could kids move to the accelerated track?

Apparently the new assistant superintendent for curriculum said "sure."

Then they asked the principal who said probably not, because moving kids from one track to the other would be an "administrative hassle."

Which was not the answer people were looking for.

I wish I'd been there, because I could have pointed out that moving kids OUT of the accelerated course is never an administrative hassle.

Moving kids OUT can be accomplished NOW, TODAY, RIGHT THIS MINUTE!

It's moving kids IN to the accelerated track that poses an insurmountable administrative hassle.

There's a discrepancy.


failure to cess

It bothers me that I have no idea why the principal would tell a roomful of parents he's never met that he won't be able to move their kids from the regular track to the accelerated track because it would be an administrative hassle.

There may be almost nothing worse he could have said, and he apparently chose to say this after the assistant superintendent had given the exact opposite response, which makes it even worse.

I have no idea what to make of it.

daily quizzes beat concept maps

an oldie but goodie: the Gambill method

"the persistence of bad industry practices"

in the September Atlantic:

ALMOST TWO YEARS ago, my father was killed by a hospital-borne infection in the intensive-care unit of a well-regarded nonprofit hospital in New York City. Dad had just turned 83, and he had a variety of the ailments common to men of his age. But he was still working on the day he walked into the hospital with pneumonia. Within 36 hours, he had developed sepsis. Over the next five weeks in the ICU, a wave of secondary infections, also acquired in the hospital, overwhelmed his defenses. My dad became a statistic—merely one of the roughly 100,000 Americans whose deaths are caused or influenced by infections picked up in hospitals. One hundred thousand deaths: more than double the number of people killed in car crashes, five times the number killed in homicides, 20 times the total number of our armed forces killed in Iraq and Afghanistan. Another victim in a building American tragedy.

About a week after my father’s death, The New Yorker ran an article by Atul Gawande profiling the efforts of Dr. Peter Pronovost to reduce the incidence of fatal hospital-borne infections. Pronovost’s solution? A simple checklist of ICU protocols governing physician hand-washing and other basic sterilization procedures. Hospitals implementing Pronovost’s checklist had enjoyed almost instantaneous success, reducing hospital-infection rates by two-thirds within the first three months of its adoption. But many physicians rejected the checklist as an unnecessary and belittling bureaucratic intrusion, and many hospital executives were reluctant to push it on them. The story chronicled Pronovost’s travels around the country as he struggled to persuade hospitals to embrace his reform.

It was a heroic story, but to me, it was also deeply unsettling. How was it possible that Pronovost needed to beg hospitals to adopt an essentially cost-free idea that saved so many lives? Here’s an industry that loudly protests the high cost of liability insurance and the injustice of our tort system and yet needs extensive lobbying to embrace a simple technique to save up to 100,000 people.

How American Health Care Killed My Father

by David Goldhill

Atlantic Monthly September 2009

The subject of formative assessment came up in the Comments thread for Allison's post about middle school math pre-tests.^*

Sitting here in Evanston Hospital, keeping watch over my mom and reading the National Reading Panel Reports of the Subgroups in the lulls between crises,^** I had a blinding flash of recognition when I read the passage above.

My blinding flash was not about hospital sterilization procedures and physician hand-washing, however. No. My blinding flash of recognition was all about formative assessment, (aka collect & correct).^***

Ed and I have now been lobbying our school district to use formative assessment (pdf file) ("assessment for learning") for four years. Four years!

Moreover, the district has been paying formative assessment consultants to teach teachers how to use formative assessment for at least two years.

But do we have formative assessment?

No, we do not.

Not only do we not have formative assessment, we do have administrators sending FOILable emails to parents in which they openly refuse to provide formative assessment when directly asked to do so.

Formative assessment at its simplest means: find out what the kids learned, then reteach the stuff they didn't learn.

Can't get it; district won't do it. Or doesn't do it. Either one. I don't know any district that does.

And that is "deeply unsettling," as Goldhill says. How is it possible that parents have to beg schools to provide an essentially cost-free idea that stands a chance of getting kids to college ready to do college work?

update 1:49 Chicago:

This might have something to do with it.

Gambill method

$27,722 per pupil spending

can you FOIL the answers?

^* [news flash: at the moment, I can't log on to the old ktm site, which had a number of good posts about formative assessment. Usually when this happens the site eventually becomes available again, but we'll see. I really need to get it backed up, finally. Here's the URL for the search page: http://www.kitchentablemath.net/twiki/bin/view/Kitchen/CommentsSearch]

^** Do you know the meaning of the words meaning troponin leakage? I do.

^*** It's possible I have been writing an education blog for too long.

can parents be held accountable?

Instructivist has a post on "spreading the blame" in which he writes:

Home life has the greatest influence on a child's success or failure in school. It shapes the behavior of the child. It is where values and attitudes are communicated. Home life can be intellectually stimulating or impoverished. Attempts to remedy educational disparities also need to focus on this neglected aspect.

While these observations are certainly true (I always base my case against character education in this exact premise!), I'm not absolutely sure they have to be true.

We have a friend who is on the board of one of the successful charter schools in NYC (I've never been able to remember the name, unfortunately).

He told us that tiny little kids - in Kindergarten & 1st grade - come in with "attitude." They are hard and defended. Apparently they talk and sound like the're 18.

It takes a couple of months for the school to get through the shell, but get through it they do. The kids regain their sweetness, and start to focus and learn.

I don't think this school has any kind of remedy for the kids' home life. In fact, I'm sure of it, because I remember our friend expressing surprise that parents never come to school events, contact teachers, etc.

I think Siegfried Engelmann's philosophy is that you have to teach the kid you get - right?

If the kids you get have parents who aren't able to support their children's education - or are unwilling to do so - then you have to work within that reality.

For me that would mean, first and foremost: NO EXPECTATION OF HELP WITH HOMEWORK. When we talked to the new assistant superintendent she said this principle is an absolute for "turnaround schools." If you're trying to turn a low-performing school around you assume zero parental help with homework.

However, if I had a school full of kids who didn't get "easy" homework done, I'd take this a step further and stop assigning homework at all - or, rather, I would assign homework that would be completed under supervision at school, as "La Salle High School" does:

4. In their freshman year, all students are required to attend study halls during the hour or two when they are not in class. The study halls are also resource centers, which contain many of the books and references needed by freshmen in their courses. In such study centers, emphasis is placed on assisting students with their work. The teacher aide who runs the center is familiar with the assignments that freshmen receive. (This stands in contrast to study halls in other schools, which provide only custodial care during study periods.) Some freshmen who are deemed to be academically deficient are required to attend a separate study skills center adjacent to the freshman study hall. There, the intention is to provide more intense help than is available in the freshman study hall. Together, the freshman study hall and the study skills center serve to initiate freshmen into the academic culture of the school.

5. During their sophomore, junior, and senior years students who are experiencing academic or truancy problems are assigned to study halls during times when they are not in class. Again, emphasis is on providing academic assistance.

6. A few students exhibiting extraordinary behavioral problems are assigned to “supervised study.” In this room, custodial care is supplemented with a strong emphasis on interaction between the aide and the students. The room has only 12 desks, indicating that supervised study is necessary for only a tiny portion of the student population.

7. The school places a premium on student attendance in classes and has designed an effective monitoring system whereby parents are notified by the classroom teacher of class cuts on the same day that they take place.

I don't know how many teachers would be able to require students to do their homework under supervision without benefit of a well-thought out and well-staffed system like La Salle's.

Carol Gambill does, but she's working with kids who, by and large, are doing their homework successfully and are highly motivated.

I have no idea what I'd do if I were teaching in a school in which parents didn't supervise homework, the kids didn't do it, and there was no supervised homework option in the building. I'd probably try to spend as little class time as possible on instruction and as much class time as possible on homework.... ?



are there ways to hold students and parents accountable?

You could do things like fine parents whose kids don't show up for school - I think some communities have tried this, right?

I'm not sure what you can do to hold kids accountable apart from detention.

Kids should definitely have detention for not doing homework; rule should be enforced and consequences should be real.

This is another of my beefs with my own middle school. One of the teachers sends a student around to "check" to see whether the kids have done their homework. Naturally some of the kids simply write that day's date on an old homework assignment, and the student checker marks down that the homework is completed. This shouldn't be happening. The teacher shouldn't entrust homework checking to a student.



update from instructivist

Judging by most of the responses to my post, the thesis is widely misunderstood. I'm concerned with the environment parents create simply by being, i.e.having or lacking certain attributes. These attributes can be any number of things, e.g. providing a loving and nurturing environment conducive to the healthy emotional development of the child; valuing respect for others and teaching good manners; attaching value to education; providing an intellectually stimulating environment even in incidental ways. Contrast this with dysfunction and psycho- and sociopathology as is so often the case, a pathology that poses nearly insurmountable obstacles to education and perpetuates stratification. The thesis does not concern itself with minutiae like school board relations.

In this respect the thesis seems unremarkable.

True.

(So, can anyone tell I'm a little burned-out?)


here's Joanne Jacobs

My book, "Our School," is about Downtown College Prep, a San Jose charter high that targets low-achieving Mexican-American students. Many parents had an elementary education in Mexico and speak English poorly or not at all. The school assumes parents can't help with homework but asks them to check off a homework log showing that they saw their child doing something. If a student misses two or more homework assignments, a teacher-counselor calls the parents.

Students behind on homework must attend special study sessions during what otherwise would be free time and/or Saturday school. Getting kids to do the homework is a big job in ninth grade. If they do it poorly, that's not a huge problem. Once the work habits are in place, they will improve.

Ninth, tenth and 11th graders have a 75-minute study session at the end of the school day. Tutors are available on request with ninth graders getting priority.

Niki Hayes told me something interesting.

She said you have to establish homework habits in K-5, because the middle school years really are "hormonal," and that's the worst time to try to do it!

I had never thought of that, but it makes sense.

Direct Instruction post at Fordham

check yourself before you wreck yourself

Fordham draws the familiar analogy between scripting in medicine and scripting in education: do you want your physician to be inventing new concepts in hand-washing on the spot or do you want him to do it the way the Best Practices checklist says to do it?

What often goes unremarked in these discussions is the fact that master teachers and professors often write their own scripts. These scripts will be revised, edited, and polished over the years, but they are scripts nonetheless. Teachers of older students and professors who teach seminars write questions and create discussion structures they repeatedly use. Here, for instance, is a terrific set of videos of a professional development session in which the presenter explains how to write one's own DI questions. Again, these questions and structures are revised, edited, and polished from one semester or school year to the next, but the fact is that superb teachers and professors don't wing it. Nor do they reinvent each course from scratch each year.

Creative people use scripts.

Another point: creativity comes in many forms. There is no reason to assume that a 1st grade teacher following a script could be replaced by a robot following the same script. Here is Ken on the question of scripting: (you may have to hit refresh to bring the page up)

Inevitably, whenever Direct Instruction (DI) is discussed the subject of “scripting” is raised. One frequent objection is that the scripts stifle teacher creativity. Nothing could be further from the truth.

Before we jump in, let’s first look at some sample scripts. Here’s a sample script on Writing Fractions. Here’s one on Subtraction. And, here’s another. (pdf files)

In DI, teachers use pre-designed scripts when teaching. The scripts are based on extensive research regarding student retention, and every aspect of every script is based upon results that were demonstrated through research. The great advantage of this approach is that every teacher using the script becomes the beneficiary of that research and will probably teach much more effectively than if left to her own devices.

DI designers test the programs carefully before publishing them and each DI program is extensively revised based on specific student error data from the field test. Scripting the lessons allows sharing of these “polished stones” across teachers. Also scripting helps reduce the amount of teacher talk. Children learn by working through the sequence of tasks with carefully timed comments from the teacher. Children learn little from straight teacher talk. Too much teacher talk decreases pupil-motivation, draws out the lesson length unnecessarily, and often causes confusion by changing the focus of the tasks, disrupting the development of the larger generalization, of which a teacher the first time through is usually unaware.

Also, without guidance, teachers may use language that students do not understand or that distracts students’ attention from examples. Scripts also allow aides, parents, and other paraprofessionals to assume teaching responsibilities, resulting in increased quality instructional time.

Moreover, even though the DI programs are carefully tested and scripted, successful use of them requires training in the special techniques of delivery. Teachers must make many decisions in response to the children's performance. Some of the most important decisions involve placing each child appropriately and moving the children through the lessons at a pace that maximizes their learning potential.

Lastly, the scripted presentations do not comprise the whole lesson, and the lessons do not comprise the whole school day. There are opportunities for group and independent work. A good DI teacher also creates additional activities that allow students to make use of their learning in various situations. So, there is a great deal of teacher creativity involved in the interpretation and presentation of the script, in attending to the needs and progress of all students and in designing expansion activities.

why is scripting used in Direct Instruction?
big concepts in DI
Explicit Direct Instruction professional development videos (brief - very worthwhile)
Carol Gambill in a nutshell

differentiated instruction in action

C's math class has graduated from Glencoe Algebra to Glencoe Geometry, thank God.

I say "Thank God" because last fall my neighbor managed to track down a Teacher Wraparound Edition of Glencoe Geometry, which she's loaned to me.

I do not have a Teacher Wrapround Edition for Glencoe Algebra. I've been working without a net. In order to check C's homework — which I have to do because here in Irvington Union Free School District (per pupil funding: $22,000) teachers stop collecting and correcting homework around grade 3 — I have to work every homework set myself, check my answers against C's, then figure out which one of us is wrong when the answers don't agree, and, finally, after all that is out of the way & my book deadline has receded further into the distance, have C. re-do the problem(s) in question if he's the one who got them wrong.

I have to do all this because the school refuses to supply answers to kids or their parents.

All the answers are belong to us.

For geometry, I have the answers. (The answers, they are belong to me.)

Boy, does that save time.

I work the problems quickly and efficiently, then I check my answers in the book.

If an answer is wrong, I re-do quickly and efficiently. I can afford to be quick and efficient, because I have the answers.

"speed and accuracy": the KUMON mantra. Have I mentioned the fact that KUMON provides the parent with the answer key? The parent quickly checks her children's work, then has them re-do problems they missed.

Without the answer key, I work problems painstakingly, doubting myself at every turn, sometimes re-working because I think maybe the answer could be wrong. From time to time an answer will come out the same wrong-seeming way 3, 4 times in a row, so that's more time, and in the end I still suffer doubt.

Having to work every problem without an answer key is a huge waste of time. A FWOT, actually. As Carolyn used to say.

So glad the paid professionals who teach my kid don't have to do it.


differentiated instruction 'round Glencoe way

Back on topic. The topic being: differentiated instruction.

I think a lot of us have wondered what differentiated instruction actually is when it's taking place inside the black box.

Sure, sure, I know the concept: if you have 20 students in a class, they are taught in 20 different ways. That is the concept here in Irvington, anyway, or so I gather from the Principal's Message in the Main Street School newsletter.

But what does that look like?

What might those 20 different instructional ways be on any given day?

Tonight, looking up the answers in my neighbor's Glencoe Geometry Teacher Wrapround Edition, I noticed that the book includes, in each Lesson, a "Daily Intervention" labeled "Differentiated Instruction."

Here is the Differentiated Instruction for Lesson 1.4 Angles Measures:

Auditory/Musical A metronome is a tool used to keep a constant tempo in music. It is composed of a pendulum that swings back and forth at varying speeds. The fulcrum of the pendulum acts as a vertex of the angle through which the pendulum swings. Demonstrate this by holding two pens at an angle in one hand and tapping another pen between the first two, creating a series of "ticks."

source: Glencoe Geometry Teacher Wraparound Edition
North Carolina Edition, p. 30
ISBN 0078601789

Daily Intervention Number 2: Inferential Thinking Activity

I am going to infer from the above that:

• it is normal for a high school geometry teacher not to know what a metronome is, what it looks like, or how it works
• a differentiated instruction activity is likely to command the attention of all 20 or 30 students in the room, seeing as how it involves the teacher performing a noisy classroom demonstration
• a differentiated instruction activity accompanying a lesson on angle measures doesn't have to have anything to do with angle measures, necessarily
  

I don't think this differentiated instruction thing is going to work out.


update from redkudu:

This is not a differentiated strategy. It is an engagement strategy. This is what I talk about when I say there is such little knowledge about the difference between the two.

That clears things up.

redkudu had mentioned this earlier and I didn't know what she meant.

She's absolutely right.

These are engagement strategies, pure and simple -- although they are labeled with the type of learner the "strategy" is supposed to address (auditory/musical; ELL; etc.)

What a mess.


update 2-13-2008: Steve H analyzes the US News & Newsweek rankings of high schools in the Comments thread.


woo hoo, Friday edition
differentiated instruction in action
can you FOIL the answers?
the Gambill method

second request

Hi---

Where are we on the Teacher’s Manual for Mathematics A?

TEACHER’S MANUAL W/ANSWER MATHEMATICS COURSE A
ISBN: 1567655475

As I mentioned, I’d like to order a copy so I can begin preteaching next year’s Math A content to Christopher over the summer. I discovered recently that when I briefly preteach material his mastery shoots up. It’s amazing. He is now finding math “easy” and his grades are moving towards the A range.

I own a copy of the Teacher’s Manual for Dressler’s Integrated Mathematics, which I’ve used to check Christopher’s homework and have him re-do problems he’s missed. But there are no copies of the Teacher’s Manual for Mathematics A available online, so I need the school’s help.

Ms. Urban sent Xeroxed copies of the answer key home with students, and all contemporary math textbooks contain answers to half the problems in the back of the book. Carol Gambill, winner of the Edith Mae Sliffe Award from the NCTM and one of the best 8th grade algebra teachers in the country, assigns only problems that have the answers in the book. Here’s what she has to say about this practice:

“Twenty to thirty problems are assigned for homework every evening, ranging from the easiest to the most difficult of a given section of the text. I always assign the odd problems because their answers are in the back of the book. The answers provide the students with road maps to mastery. If they don't get the correct answer it means they turn back, take a detour, change a flat tire, or find a service station.”

Providing an answer key to students is standard practice.

I’d be thrilled to have a Xeroxed copy of the answer key, but if copyright laws are a problem, I’m happy to pay for a copy of the Manual itself. I’m sure other parents would feel the same way.

So let me know.

Thanks ----

Catherine Johnson


all the answers are belong to us
email to the math chair
second request
teacher's manual
it would be unusual
more stuff only teachers can buy
inflammatory
2 weeks off
the return of Ms. K