\doc\web\98\05\mastmath.txt
You have to master arithmetic before
tackling Algebra
Date sent: Fri, 24 Apr 1998 10:53:00 -0400
To: "Donna Garner"
From: Carol Gambill
Subject: Re: My Response to a Good Question
Copies to: "education consumers"
Donna,
As an algebra teacher at the 8th grade level, I would like to heartily
endorse your statement:
">It is still imperative for my students to spend time outside
>class learning their material. Even though we work every minute in class,
>students still must spend time on their own mastering the concepts by going
>through the thought processes on their own time. Individual differences
>require that some students spend more time than others learning the
>material."
Most students who enter my 8th 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, as
I have stated before, about 120 days/class periods to teach them the entire
rigorous course. These restrictions demand *absolutely* that the students
do extensive "quality
time" outside of class grappling with difficult problems and practicing for
accuracy.
I have devised a method which I have used for 15 years now with all
students, from the handicapped ones I used to teach to the "normal" and
gifted ones I currently have, to ensure each of them does homework with
care and accuracy. 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."
Briefly:
1) 20 to 30 problems are assigned for homework, from the easiest to the
most difficult of a given section of the text. I assign the odd problems
from a section, because their answers are in the back of the book. On the
day for that assignment, however, I do the even problems from the same
assignment with the students in class using Direct Instruction. Direct
Instruction assures that all students leave my classroom that day with a
thorough understanding and at least partial mastery of the concepts.
2) I tell my students that "Doing Homework" does *not* mean writing out the
problems, although that most assuredly is a component. I tell them that my
assignment to them is to *MASTER COMPLETELY* EVERY PROBLEM OF THE
ASSIGNMENT FROM THE EASIEST TO THE MOST DIFFICULT. I would never assign a
problem for which I have not given them the answer. The answers are their
"road maps" to mastery. Not getting the correct answer means turn back,
take a detour, change a flat tire, or find a service station.
Then, the next day, first thing, when the kids walk in the door, they have
their Daily Quiz over the most difficult 4 or 5 problems from that
assignment. Their answers and all 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 slowest 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.... Providing daily immediate
feedback to each student on his own progression toward mastery, and
providing me, of course, with instant knowledge as to whether or not each
student did his 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" means simply that the student must stay after
school that day and do the assignment, under school supervision, that he
failed to do on his own. This, in my opinion, is a justifiable, "logical
consequence."
Because I am so strict with "mastery" of homework concepts, I tell the
students that I have to do my part also. Therefore, I conduct extra help
sessions before school and at both lunch periods. It is gratifying to see
5-10 8th graders gathered around my chalkboard before school, excitedly
discussing the next step in a difficult algebra problem. The kids love
these chalkboard algebra "debate" sessions. In addition, the students have
my phone number and are invited to call me as a last resort. Important to
note, however, that the giving of the phone number is more an establishment
of "trust" and my doing "my part." I haven't had more than 2 phone calls
this entire school year.
I apologize for taking so much space to explain this system, but I have
found it to be nearly miraculous in effecting huge academic gains in all
students.
My students win so many academic awards that others cannot even play in
their league. Last Saturday, every algebra student I have, honors and
regular, signed up voluntarily to take the 15-county Annual Algebra I
Contest at 9:00 morning. The results of the Preliminary are the same as
they have been for the past 7 years, with my students "totally dominating,"
taking 95% of the top places. This is in competition with students at
least as bright as they are.
Hard Work! And yet, the students love my class, vote it their favorite
each year, love math (even those who had despised it up until algebra), and
remember my year as the one that led them to discover within themselves the
power of determining their own destiny in the academic arena.
And all this is based on the simple concept of a 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
--------------
At 1:54 PM -0000 4/23/98, Donna Garner wrote:
>(Please notice the comment at the bottom of this e-mail to which I am
>responding.)
>
>You and I are probably "dinosaurs." I do not know how old you are; but
>from your response, I am surmising that you may be in my same generation.
>When we were in school, our teachers assigned homework; and we graded it in
>class. We seldom if ever cheated because we knew cheating was dishonorable
>and because we were afraid we would get caught. Our parents would have
>been terribly disappointed in us if we had cheated, and we seemed to have
>enough "character" about us that we believed the maxim which said,
>"Cheaters never win." That was then; and this is now.
>
>Now there is such rampant cheating that I do not dare take an actual grade
>on homework because it would be a meaningless evaluation. When a teacher
>puts high stakes on homework grades, he just opens the door for blatant
>cheating. In fact, now we teachers cannot write a student up for cheating
>unless we have the actual piece of evidence! Now our word is not enough.
>The other day a fellow teacher was giving a test and saw two girls looking
>at each other's papers. She sent them to the office for a demerit and was
>told that since she did not have the actual "proof," the charge would not
>stand. In other words, a teacher's word or observation will not suffice.
>
>The part that is hard for the public to understand is the large numbers of
>parents who live in denial of their children's misdeeds. Whenever we have
>had an incident where we knew cheating occurred, it is amazing how many of
>the parents will fight us all the way to the school board. I guess that is
>why the administration now insists that we have hard evidence and not just
>a teacher's observation.
>
>Knowing all the problems with cheating still does not resolve the homework
>problem. It is still imperative for my students to spend time outside
>class learning their material. Even though we work every minute in class,
>students still must spend time on their own mastering the concepts by going
>through the thought processes on their own time. Individual differences
>require that some students spend more time than others learning the
>material.
>
>Therefore, I had to devise a system which would cause the majority of the
>students to do their homework -- to at least work with the material in an
>attempt to get them to internalize the concepts. My homework system gives
>them an instant reward. They get either a homework 100 or a 0 (homework
>counts 20% of their total six-weeks' grade -- we usually have over 25
>homework grades) if they completed the work on time and followed the
>directions -- even if every answer is wrong! Now, what does this system
>accomplish? This takes away the "high stakes" and makes it hardly
>worthwhile to cheat. After all, what does a student have to gain by
>cheating under my system? However, at the same time, it encourages him to
>do his homework by at least getting involved with it which is the intent.
>
>Now when the students come to class, they have at least looked at the work.
> I take the up or down homework grade, and we then check every answer
>together. Because there was no incentive for them to cheat, normally most
>of my students have their homework and have actually done it themselves.
>As we check over their answers together, they are not focusing on "grading"
>the work but are focusing on the content of the assignment. When they find
>something they missed, we stop and talk about those particular questions;
>and they are ready to listen at that point because they are generating the
>questions.
>
>Homework grades are actually an indication to parents, to administrators,
>and to me regarding how hard the student is trying. Any student should
>have all 100's if he is really doing his part to learn. Even weak students
>(including special education, Section 504, at-risk) feel they have a chance
>under this system. Nobody has an excuse for not doing his homework. Most
>of my students do their homework, and that is the end result I am after.
>All other grades on quizzes, major tests, compositions, book reports,
>projects, etc. are graded for accuracy and content by me; and those are the
>grades in the gradebook which are weighted more heavily.
>
>By the way, teachers are required by federal and state law to offer
>modifications/accommodations to our at-risk students. The reason I put
>this at-risk strategies list on the loop is so that the public will
>understand what we teachers are required to do. The days of us teachers
>standing in front of the class and lecturing have long since ceased. Our
>classrooms are very different now, not particularly by choice.
>
>Donna Garner
>dggarner@swbell.net
>----------
********************
Carol Gambill
Sewickley Academy
EDUCATION CONSUMERS CLEARINGHOUSE