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Dr. Carroll: This panel is now open for comments from the audience
Audience member: I have a quickie question. I am aware of scientific research reported
in the Baltimore Sun and the Los Angeles Times "Reading by 9" series. If
you don't learn to read by age 9 you have a problem for the rest your life. Is there
scientific research that answers the question of if you don't learn a certain amount
of math by an age do you have a problem there after.
Panelist: From what little I know, there was a study to this effect. An educator
from Connecticut showed that if students do not learn to think abstractly between
age 11 and 14, they would have severe difficulties to do so later in life. But I
don't know how scientific the study was, unless Jim knows.
Panelist: From what we know, we know there are limitations, but there hasn't been
any real research on exactly the length of time the windows are open, when they open
and when they start closing. We just don't know. There is clear evidence that they
do close, though.
Audience member: My name is Tim and I'm a math resource teacher with Los Angeles
Systemic Initiative. I have a comment and a question. The comment is I think it's
unfair to have a panel so one side and to have these criticisms with math educators
and not have an educator on the panel and balance and give that point of view. My
question has to deal with the fact that in addition to A Nation at Risk report, the
center for the fork worse preparation in quality education also spoke of the criticisms
from the business community level of public education that employees failed to demonstrate
problem solving in the algorithms in school. My question is how are the standards
going to address problem solving and reasoning in this area and how are you going
to assess it, when on a multiple choice standardized test, the best you can do is
test basic fact and computational skills?
Panelist: A well-designed multiple choice test does not have to test just computation
and basic minimal skills. You can design a multiple choice test that requires multiple
links and substantial independent thought. The second thing I'd like to say with
students coming up without problem solving skills. My wife is a math teacher. (Inaudible).
I have many different series covering over a wide time period, over at least 20 years.
What we can see within the series, even though considered (Inaudible). Many of the
skills that lead to appropriate problem solving and are deleted from those books,
the quality of the problems, the number of problems that appear in the book of problem
solving problems, some require extension by the student. They are in later books
instead of earlier books. It's not just where you define the base line that makes
the difference, but text books are losing a lot of skills involved with real problem
solving. They are being out of the text books. Even traditional books.
Panelist: I might as well say a word. One issue here is a sloppy definition -- on
the part of math educators -- of mathematical problem solving. Part of the point
of the list of problems I put up was to show you exactly that. In fact with the traditional
training that I had 40 odd years ago, most of the students came out with an ability
to solve problems. They could handle unknown, unexpected situations, break them up
into pieces, take the pieces and analyze them, and then put the parts together to
make the best decision possible on the basis of the given data. What we are seeing
with problems of the kind I showed you here is a notion of mathematical reasoning
that makes no sense to us. What we, as professional mathematicians, understand to
be mathematical reasoning is replaced with a formulaic approach that doe not appear
to be reasoning at all. It is a strange thing and we can't recognize, describe or
even make a guess as to what it might be.
Audience member: How do we test the problem solving you described. (Applause). How
do we test the kind you described?
Panelist: Let me give you one example. "x squared + px + 4". That's a trinomial,
what's the biggest value of p for this trinomial so that it will always have real
Male student: If it is a multiple choice question I can take a random choice and
have a 1 out of 4 choice. That doesn't indicate my ability to solve the problem.
Panelist: Random choices would give an outcome of 25%. If the outcome is indeed 25%
then you know that students as a whole do not show much understanding on this question.
For sure some students would do better in multiple choice exams than others. So multiple
choice exams may not be an ideal way to test real understanding, but that is a fact"
of life. No matter what system you devise, it always discriminates against a certain
group of people and favors another group. Multiple choice, it discriminates against
one group of people, but on the whole it can be made very effective. I just demonstrated.
There are many other ways that demonstrate it too.
Audience member: My name is Ann and I'm a parent. My question is it's not clear to
me and it's really a general over all question for the conference at large. Whether
or not LAUSD is adopting the State Standards. You are talking about writing and rewriting.
It sounds like the professors and the other gentleman described specific standards
that sound good to me. I don't understand why we have to have all these people writing
and rewriting. Why are we not adopting the State Standards? (Applause) If we do,
how are you going to make sure this translates into what the classroom teachers are
doing? The teachers at my school think Mathland is the hottest thing. It really will
not reflect the Standards and how do we make sure that they will be able to get tests
and that we make sure a text like math land won't be allowed.
Mr. Tarr: I will work on that one. As far as Mathland and so forth is concerned,
I work primarily in science, but in terms of the texts, one problem has been that
if we have a multitude of texts, then you have a great variety between one school
and another in terms of what's being taught. I know there is an effort to lower the
number of approved texts in the district. As to adopting the State Standards, we
are a State-funded organization. The State Board of Education said "these are
the standards". Of course the Standards are voluntary, but on the other hand,
if all the assessments are set to those Standards, then we are definitely doing a
disservice to the students if we don't teach to those Standards. We are definitely
going to teach to the standards. In terms of curriculum, there is more to the curriculum
than just the standards. If you look at the 6th grade science standards, I think
that's 2 pages. For a 6th grade science teacher, we can't just give them 2 pages
and say "Here you go, teach for a year and you figure it out". The Standards
gives us the material that has to be taught. However, curriculum design is more than
just saying "Okay, here is your list. Teach to it." What we are trying
to do is say, "What would you do in your classroom to address these Standards",
so we can be sure the students actually have been exposed to the Standards. More
importantly, how do you know the kid knows the Standards? You can't sit there and
recite to the kids, here are the Standards. What are the activities, what are the
units of study in that classroom that are going to deliver those Standards? The Standards
are saying by the end of grade 6 the student will know this. When did that material
get presented? Did you present some of that material in grade 4 and some in grade
5 so they know the material by the end of grade 6? That's what we look at. It's not
that we looked at the Standards and said we were going to rewrite them all and make
new curriculum. We are saying we expect students to know this material by the end
of grade 8 on the focus of physical science for example. Does that mean we tell the
teachers that's grade 8 material so you can't teach it in grade 5, 6, or 7? Because
that's the grade level where the Standards are. We have to design something so that
teachers know, okay, if I teach this concept and that concept in grade 6 and this
concept in grade 7, by the time the student is in grade 8, they will know it. That's
the grade level at which we expect it to be assessed. That is curriculum design.
One of the difficulties with, say benchmark standards, is with a K-3 span. If you
are a second grade teacher, what are you supposed to teach? Do we wait until grade
3 and then teach everything? The point behind what we are doing and grade level standards
is to say okay, if this is the point at which we are going to assess, what do we
have to do to get there?
Audience member: My name is Mr. Morton and I'm here representing the PTA for all
of Santa Clara County. I have two questions. One for the gentleman in the middle.
Although the State Board in developing these Standards and Frameworks and so on,
did accept public testimony, it clearly ignored most of that public testimony, especially
from teachers, curriculum developers and people in a variety of other develops. That
leads you and your colleagues the task of trying to achieve the buy-in of 250,000
people that have to teach math in the classrooms. After they have already felt trampled
upon and I'm concerned about the possibility of doing that. I'd like to know how
you think you might approach that. I have a second question for two people. May I
say that too? They are related. This is for Dr. Wu and Dr. Milgram. The State Board
put forth the notion and the organization expressed the notion that what is being
done is research based and proven. This is the only right way to do things. But Dr.
Wu told the public audience that this was an experiment and we have to wait and see
how it turns out. This is coming from the people attacking other kinds of curricula
as experimental and shouldn't be tried until they are proven. If this is an experiment,
one, why are we testing on 5.7 Million children at once. It seems a pilot might be
in order. What if the experiment fails. How do you know when to pull the plug?
Panelist: I think you confused 2 things.
Audience member: No.
Panelist: I am not a psychologist, but the "research base" you mentioned
refers to a research base for instructional methods. That is a research requirement.
The experiment I was referring to is the fact that for the first time in a very long
time, we are trying to teach the correct kind of mathematics in the schools. The
kind of mathematics in the Standards and Framework is the kind of mathematics that
professional mathematicians like myself and my colleagues here recognize as mathematics.
Unfortunately you ask somebody to define what mathematics is, it's what mathematicians
practice. We are trying (Inaudible).
Audience member: That alone make its experimental.
Panelist: That should tell you (Inaudible)
Audience member: Then there is a chance it will fail. Then what? how will we know?
Panelist: Are you concerned that we do an experiment (Inaudible)
Panelist: Of course I know where you are coming from and that you have test it is
yourself and that's okay.
Audience member: Not exactly.
Panelist: I think it is relevant that you say "some professional mathematicians".
The community is diverse. One thing we do not like to do is be bothered with requests
that are not directly involved in the particular research we are doing. We like to
do our work and be left alone. The few of us who get to the point where we have to
try to do something are in a tiny minority.
David, not so long ago, in response to pressure from his own school was forced to
send a letter out asking the mathematical community in California what their view
was on these issues. Were the Standards that had just been passed representative
of the math community or the tiny minority suggested by certain elements within the
Cal State system?
There are about 500 practicing mathematicians in California and they are every bit
as difficult to get responses from as any other busy group, if not more so. But fully
one hundred of them responded, agreeing with the view that these new standards are
representative of the views of the mathematics community.
In the math community it is unheard of that such a high percentage would even respond.
To say or even imply that our views here, mine and Wu's, represent a minority position
within the mathematics community is grossly wrong and, flat-out, insulting.
Audience member: I didn't say that.
Audience member: My name is Michael and I teach ESL at Van Nuys High School here
in Los Angeles. My question is about assessment. I also want to say that I am tremendously
encouraged by this conference that by the emphasis on the storing factual information
to a higher place in education in California for a long time. My question is about
assessment. I'm just had been trained to score the STEPS test which is the other
assessment device that's supposed to go along with implementing standards to determine
whether students advance to the next level of a class. And I want to know what you
feel about -- so the STEPS tests are performance-based tests as opposed to objective
tests. In the area of English writing, performance tests are a very good way, I believe,
of assessing how someone writes. However, I want to ask mathematicians what they
think about assessing science and math the performance-based way. Is it effective
in your opinion and cost effective?
Mr. Metzenberg: Well, assessment isn't really my field, but there is an interesting
study by the RAND corporation you might have seen or might be interested in, which
followed up on some performance assessments and looked at their cost-effectiveness.
I can't remember exactly the numbers they came up with. One thing they pointed out,
was many of the assessments that have been tried in this State were heavily subsidized
in many ways. There was quite a bit of volunteer work which you wouldn't expect to
continue. It was many many 10's of dollar per students if you include development.
Going into a cafeteria and setting up rows of work-stations so that students can
take the assessment without looking next door to see what the next kid is doing.
There were lots of unforeseen problems -- if you give a child materials to see if
they float or sink in water, lots of pieces of pumice will sink. The apparatus may
break. The security on an exam like that is horrendous because everybody in the State
is doing the same experiment and kids talk to each other. Basically the conclusion
was, you compare it with a multiple-choice test which measures different things,
but the value of that is tremendous. It's dirt cheap the security is good. If there
is a place for performance-based assessment, it must be a very small place.
Mr. Tarr: I'd love to talk about the STEPS test. When we look at AB1626 and social
promotion, the key is that for our kids this all kicks in in a year. As of July 1,
1999, the students have one year and by July 1, 2000 we are saying to students that
don't meet the Standards, you will not promote. Chicago tried this and wound up retaining
30,000 third graders. That doesn't work. The key is you have to look at what is the
role of assessment? Is it something you give at the end of a course to make it a
"gotcha."? Now you're going to have to do this again? We also know retention
doesn't work. In other words, a student that doesn't make it in third grade, in other
words, they haven't managed to learn what they are supposed to learn by the end of
third grade so we retain them. They have just proven the one thing they didn't get
is third grade the way we taught it. If we retain them, we do the one thing we know
doesn't work, again. So if we look at the role of assessment, on-going performance
assessment is used to inform instruction. At grades 4, 8, and 10 in the District,
the state will administer the CAAAS assessment. So with STEPS at grades 3, 7, and
9, we are hoping for that to give us a "heads up" on the problem a year
before the other assessments kick in. The other thing is even if we look at AB1626,
it says that students are promoted or retained on the basis of multiple assessments.
Do we want to have the only assessment for our students, their score on Stanford
9? On that one day -- maybe their dog was run over the day before? I don't know.
On that one day they have the flu and on the basis of that one day, you say "Okay,
you have to repeat 4th grade", or put them in an intervention program based
on one day of testing. AB1626 says you can use multiple assessments. You are saying
we have Stanford 9. That's one assessment with the augmentation. We have the teacher
grade, how the student did on the course, and then we have a performance assessment
which would be STEPS. We have multiple measures, three measures by which we design
a matrix to determine whether to promote or retain.
Moderator: Before I take the last question, we have an open microphone for additional
Audience member: I feel funny that the dude behind me ((Inaudible)
Listening to the 2 gentleman in front of me, the person who asked the question about
the value of multiple choice exams I think was an excellent question. I went through
the school system in New York City and they had exams called Regents. They were basically
multiple choice and short answer exams. Algebra and trigonometry and all the sciences.
Certain instruction in the way you had to know something to pass them. That's only
one aspect of having an exam like that. The other one is the students knew they had
to pass it. Certainly in New York City. You had to get a 65 % or more or they left
you back to repeat the course. The exams had value in themselves and you couldn't
just pass by guessing, but the greater value of the exams was that they established
a mind set of the students and teachers and the higher state that the student his
to learn trigonometry by the end of 10th grade. Everyone will concede from the New
York system to a point in time, it was one of the most excellent systems in the world
and produced great scientists and musicians and artists in this country.
For the gentleman in front of me, I forgot his name, but this was an experiment,
how do we know it works? Give me a break. Nobody said the traditional education was
perfect and there are certainly flaws. By God, there is no evidence whatsoever (Inaudible)
there is not you lay your money down on something anyway. Lay it down on what these
people are proposing. Now the question I originally had. I'm sorry.
Dr. Carroll: You are out of time. Why don't we take a coffee break and otherwise
Audience member: All right.
Dr. Carroll: Thank you for your comment. We will close the session and reconvene
at 20 after the hour. Thank you very much again.