calculators in standardized tests
Mike
on the
Texas TAPS test see: http://www.tasp.nesinc.com/ . Also note that I am
not criticizing all high school math teachers, just those that "teach
to the test,"
a problem not unknown among college faculty. -- Mike
Dear Editor,
I appreciated the stories in your March 10 issue on efforts being made
to improve the preparedness of students in Florida and Texas for
college. As a visiting faculty member at UNT [University of North
Texas] this semester I have been teaching two sections of a remedial
math course. The students are typical of many around the country in
that despite good intentions they are not ready for college level
work.
There are two changes Texas could make to the math components of it
testing regime (TASP, TAKS, etc.) that would yield some gains: do not
allow students to use a calculator on all questions, and do not give
them a formula sheet.
Unfortunately, some high school math teachers “teach to the
test.” Because the standardized tests allow free use of a
calculator, these teachers do the same. Many of my students cannot do
basic arithmetic. Some have no idea why 1 divided by 1/2 is 2. How can
they understand the behavior of an equation like y=1/x when free use
of calculators has robbed them of what math skills they had coming
into high school? While calculators are an important tool, their use
should be restricted to four or five test problems where they are
needed. After that students should use their minds.
Similarly, when students know all the formulas will be given to them
during the test, they learn not to learn. I have had students who do
not know the formula for the area of a triangle let alone the
quadratic formula.
These two changes, restricting calculator use and not giving out
formula sheets, would be cheap and easy. Each would reduce the damage
caused by those teachers who “teach to the test.”
Sincerely,
Michael Sullivan
Visiting Associate Professor, UNT
Associate Professor, Southern Illinois University at Carbondale
Herman Rubin
>Dear Editor,
It is not free use of calculators which has kept them
from understanding, but failure to teach the concepts
directly. Skills are easily forgotten, and often not
even worth teaching in the first place. But concepts
are not.
Concepts are not definitions or word groups; they are
the mental constructs which one makes when one finally
understands what is going on. Concepts can be taught,
but are not often derived by the student.
>Similarly, when students know all the formulas will be given to them
>during the test, they learn not to learn. I have had students who do
>not know the formula for the area of a triangle let alone the
>quadratic formula.
Knowing the formulas is not important. It is being
able to understand the derivation of the formula, and
knowing enough to know when to use it.
My experiences with teachers and prospective teachers,
and with graduate and undergraduate students, indicates
that almost everything the educationists are doing
hinders understanding. Even the use of multiple choice
tests should be abolished.
>These two changes, restricting calculator use and not giving out
>formula sheets, would be cheap and easy. Each would reduce the damage
>caused by those teachers who “teach to the test.”
No, it would increase it. Instead of getting some
understanding, it would be more memorization and drill.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Deptartment of Statistics, Purdue University
hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
Mike
I required my remedial students to derive the quadratic formula. In
order to do this they have to at least know the formula. You should
look at the formula
sheet at the link I gave. They do not even need to remember the
formula for the area of a rectangle. Students in good schools with at
least fair teachers
will learn suck basics, and there are many such schools and teachers.
But, for those students who do not get to go to the good schools, a
little drill in the basics is better than the nothing they are getting
now.
>
> My experiences with teachers and prospective teachers,
> and with graduate and undergraduate students, indicates
> that almost everything the educationists are doing
> hinders understanding. Even the use of multiple choice
> tests should be abolished.
>
I am against multiple choice tests as well. I am against gym teachers
teaching algebra. I think high schools need to pay math & science
teachers as much as accountants and engineers. But until utopia comes,
the minor changes I suggested would help more kids learn some basic
math.
> >These two changes, restricting calculator use and not giving out
> >formula sheets, would be cheap and easy. Each would reduce the damage
> >caused by those teachers who “teach to the test.”
>
> No, it would increase it. Instead of getting some
> understanding, it would be more memorization and drill.
How does not knowing that 1 divided by 1/2 is 2 help a student
understand mathematical concepts? Is it really okay for a student not
to know how to find the area of a triangle without looking up the
formula, as long as they understand "triangleness"? It is better of
course if for a student to
be able to explain this and over formulas. But how does one explain
what one does not know?
Mike
Herman Rubin
Mike <mike_...@yahoo.com> wrote:
>hru...@odds.stat.purdue.edu (Herman Rubin) wrote in message news:<b538cf$s...@odds.stat.purdue.edu>...
>> In article <8df09e88.03031...@posting.google.com>,
>> Mike <mike_...@yahoo.com> wrote:
.......................
>> Concepts are not definitions or word groups; they are
>> the mental constructs which one makes when one finally
>> understands what is going on. Concepts can be taught,
>> but are not often derived by the student.
>> >Similarly, when students know all the formulas will be given to them
>> >during the test, they learn not to learn. I have had students who do
>> >not know the formula for the area of a triangle let alone the
>> >quadratic formula.
The problem is that they have been taught that knowing the
formulas is the only important part, or at least that is
the most important part. They have already been taught
well not to learn, but to act like a robot.
>> Knowing the formulas is not important. It is being
>> able to understand the derivation of the formula, and
>> knowing enough to know when to use it.
>I required my remedial students to derive the quadratic formula. In
>order to do this they have to at least know the formula.
Not so. They might derive a different version of the
quadratic formula, but they do not have to know the formula
to do so.
You should
>look at the formula
>sheet at the link I gave. They do not even need to remember the
>formula for the area of a rectangle. Students in good schools with at
>least fair teachers
>will learn suck basics, and there are many such schools and teachers.
>But, for those students who do not get to go to the good schools, a
>little drill in the basics is better than the nothing they are getting
>now.
There is nothing basic about knowing the formulas, or some
methods of computation. Knowing how to add is useless if
one does not know when.
>> My experiences with teachers and prospective teachers,
>> and with graduate and undergraduate students, indicates
>> that almost everything the educationists are doing
>> hinders understanding. Even the use of multiple choice
>> tests should be abolished.
>I am against multiple choice tests as well. I am against gym teachers
>teaching algebra.
Gym teachers did a much better job of teaching algebra 60
years ago than those with certificates in high school
teaching of mathematics do today. At least they had books
which did a better job of explaining, and were not even
used to a practice of dumbing down. Also, those taking
algebra then were either college preparatory, or planning
on using it.
I think high schools need to pay math & science
>teachers as much as accountants and engineers. But until utopia comes,
>the minor changes I suggested would help more kids learn some basic
>math.
You will have to start with those not brought up in the
present schools, and have to keep them out of the education
courses. The teacher who lowers the level so that those
who should not have graduated primary school can pass the
courses is the problem, as is the teacher who does not
understand the subject. I am not convinced that most of
today's math and science teachers are capable of understanding
those subjects, and having incompetent credentialed people
teaching is rarely better than not having teachers.
>> >These two changes, restricting calculator use and not giving out
>> >formula sheets, would be cheap and easy. Each would reduce the damage
>> >caused by those teachers who “teach to the test.”
>> No, it would increase it. Instead of getting some
>> understanding, it would be more memorization and drill.
>How does not knowing that 1 divided by 1/2 is 2 help a student
>understand mathematical concepts?
It does not help, but it does not hinder much. However, being
drilled in it, instead of seeing the concepts, does hinder.
Knowing how to do arithmetic does not hurt, if if comes after
knowing the concepts, and is derived from them. Being taught
by rote and drill seems to make it at least much more difficult,
and often impossible, to learn the concepts.
Is it really okay for a student not
>to know how to find the area of a triangle without looking up the
>formula, as long as they understand "triangleness"? It is better of
>course if for a student to
>be able to explain this and over formulas. But how does one explain
>what one does not know?
In many cases, one can deduce it. Being taught the formulas,
which is the present practice, and which is fostered by not
making them available, seems to ensure that students will not
get any understanding.
amanda
I AGREE; I am not a teacher nor a faculty but I had done some
tutoring. The most recent one being in Chemistry to a high school
student. I did my Master's in Chemistry 8 years ago.
My student was bright; her Mom ( a former teacher hersulf) knew that
too. I was shocked that during a tutoring section, for a simple
calculation, like 8/4 something like that, she reached for the
calcuator.
Even thoguh I tried to show her by my approach that when integers are
involved and the digits are small, she could just use her head (I
did't say anything; I just tried to show by doing it in front of her)
but she PAID no attention to that saying her teacher allows to use
calculator.
> >
> > My experiences with teachers and prospective teachers,
> > and with graduate and undergraduate students, indicates
> > that almost everything the educationists are doing
> > hinders understanding. Even the use of multiple choice
> > tests should be abolished.
> >
>
> I am against multiple choice tests as well.
As a grad student in Computer Information System, I am required to
take a management course which my advisor lets me take at a community
college. I thought of taking at my university but to save money, I am
taking at the community college. I have a midterm exam today which
will be in multiple choice.
> I am against gym teachers
> teaching algebra.
My student's Chemistry teacher has a degree in English. She also
teaches other subjects. And this is a private school. (A Christian
school.)
> I think high schools need to pay math & science
> teachers as much as accountants and engineers. But until utopia comes,
> the minor changes I suggested would help more kids learn some basic
> math.
>
>
> > >These two changes, restricting calculator use and not giving out
> > >formula sheets, would be cheap and easy. Each would reduce the damage
> > >caused by those teachers who “teach to the test.”
> >
> > No, it would increase it. Instead of getting some
> > understanding, it would be more memorization and drill.
>
> How does not knowing that 1 divided by 1/2 is 2 help a student
> understand mathematical concepts?
Exactly.
> Is it really okay for a student not
> to know how to find the area of a triangle without looking up the
> formula, as long as they understand "triangleness"?
Good one.
tom
www.geocities.com/reformeducation
mike_...@yahoo.com (Mike) wrote in message news:<8df09e88.03031...@posting.google.com>...
Donna Metler
"Alberto Moreira" <junk...@moreira.mv.com> wrote in message
news:3e7c453...@news.mv.net...
> Said tmc...@eudoramail.com (tom) :
>
> >Here's my take on the situation:
>
> needs arithmetic.
>
This is what the TCAP test in TN does. The section of the test which is
arithmetic and requires basic math does not allow calculators to be used.
The problem solving section, where they are allowed, doesn't require
arithmetic, and if the student focuses on the calculator, they'll probably
not finish the test.
>
> Alberto.
>
>
gduffell
chord with me, remote as I am from your situation in Texas. I have
seen the same debates. Calculators can be used in classrooms as
computational tools, as aids to the learning of essential skills, or
as substitutes for essential skills. Invariably, it is the last aspect
that causes the most contention - what are essential skills and what
are not?
Similarly for the debate over formulae sheets. The critical questions
are about what essential knowledge and skills being tested, and the
learning priorities in the classroom. The mathematical curriculum is
not so light that teachers are free to devote the time that each topic
deserves. More likely, frequent compromises have to be made.
Conspicuous compromises like the use of calculators, or homework, or
the comprehensiveness of tests tend to be the most readily targeted .
My response is that there are more deeply underlying problems. The
resources provided in schools - reflected in classroom sizes,
facilities, assistance for children with special or remedial needs;
and the support provided to teachers - curriculum strategy, classroom
issues, professional development, are more fundamental issues. The
questions being debated, after all, are not new. (We can date the
calculator disagreement back 30 years, but the other is much older.)
If they were the heart of the issue there would have been some
resolution by now.
My understanding is that your education system, as in my country, is
inadequately resourced because there are higher priorities on our
federal governments' agendas. These priorities don't match with our
children's needs.
Without this being addressed, the fundamentals about what happens in
the classroom and what happens in testing will never go away.