This free Information Age Education Newsletter is written by David
Moursund and produced by Ken Loge. For more information, see the end of
this newsletter.
When I read the found the following newspaper article, I found it quite
troubling. Pay particular attention to the second paragraph that I have
quoted.
Alloway, Kristen and Rundquist, Jeanette (6/15/09).
N.J. Board of Education adopts tougher standards for 3rd, 4th grades.
The Star-Ledger. Retrieved from
http://www.nj.com/news/index.ssf/2009/07/nj_board_of_education_adopts_t.html#more
TRENTON. As part of an ongoing effort
to boost
academic expectations and achievement, the state today made it harder
for New Jersey's third and fourth graders to prove their proficiency on
annual tests.
Under the new standards adopted by the state
Board of Education, public school students who took the exams in May
needed to get 50 percent of the answers correct to show proficiency on
the language arts and math tests. Previously, the "cut scores" needed
to be deemed proficient were between 40 and 45 percent.
The
test scores are broken down in three categories—advanced proficient,
proficient and partially proficient. State officials immediately
cautioned that raising the bar could mean more students being found
"partially proficient" when districts receive the results later this
year.
Being "Proficient" with 50
Percent Correct Answers
Of
course, I do not know what questions are on the math test. However, in
my mind I image an adult trying to use math in our society and quite
often getting incorrect answers. Of what value is level of math
knowledge and skill to the person or to the people this person works
for and/or with?
From time to time I have heard the
assertion that the average adult in the United States performs in math
at about the sixth grade level. Perhaps this means that if adults are
given the New Jersey sixth grade math test, their median score will
fall in the “proficient” range.
This possibility suggests a number of things to me:
- It does not take a lot of math knowledge and skills to
function as an “average” adult in out society.
- The
average adult in our society does not have the math knowledge and
skills to effectively deal with the money-problem situations that they
encounter. (Think in terms of borrowing money and the related compound
interest; think in terms of saving and investing money for future uses.)
- The
secondary school math education system in the United States is not very
effective in providing future adults with long-term knowledge and
skills in the areas of math that the curriculum covers. The average
adult in this country has taken a number of school math courses above
the level of the sixth grade. Indeed, three years of high school math
(grades 9–12) are typically required for high school graduation.
Math Maturity
You have heard the
quote, “You can lead a
horse to water, but you can’t make it drink.” Our education system
leads students to math, and requires them to pass math courses.
However, the ideas discussed above suggest that for a majority of
students, the long-term residual impact—the long-term retention of
usable math knowledge and skills—is modest.
In recent years
I have thought about this situation in terms of math maturity. Math
maturity focuses on one’s long-term retention of usable math knowledge
and skills. It is one’s ability to think mathematically, using the math
that one has had an opportunity to learn. It is one’s ability to
communicate effectively (read, write, speak, listen) in the language of
mathematics. See
http://iae-pedia.org/Communicating_in_the_Language_of_Mathematics.
It is one’s ability to recognize and understand problems in which math
might be a useful aid in solving the problem. It is one’s ability to
quickly relearn math that one has previously studied, but has forgotten
some of the details. See
http://iae-pedia.org/Math_Maturity.
The
key to increasing math maturity is learning math with understanding.
Learning math through rote memorization and regurgitation contributes
little to increasing one’s level of math maturity.
Now,
let’s go back to the current emphasis on students throughout the
country being required to take math courses and to demonstrate they
have achieved a level of “proficient” or above on state and/or national
tests. What our math education system has learned is that it is
possible to “teach to the test” in a manner that will help a great many
students score at a proficient or higher level. Here are two widely
used approaches:
- Make sure that curriculum content,
instructional processes, and the teacher-developed assessment are
consistent with and supportive of learning to perform well on the state
and national tests. For example, math textbook writers and publishers
put a tremendous amount of effort into aligning their material with the
various standards that states have set.
- Teach students how to
do well on objective tests. This includes giving quite a bit of
practice in taking such math tests in an environment that is similar to
what is being used in the state or national test.
Each of
these approaches contributes to improving test scores. Neither of these
approaches focuses on increasing math maturity. Thus, our math
education system is putting a lot of effort into increasing student
math test scores, but this may well be having relatively little impact
on the average student’s ability to make long-term effective use of the
math he or she has covered in school coursework.
Constructed Responses Versus
Objective Tests
Today’s
tight school budget situations are leading to larger class sizes.
Consider a writing teacher faced by an increasing number of students.
The teacher might think: “How many written essays should I assign this
term? How long should I require them to be?” “I just don’t have the
time to provide as much feedback on student writing as I know I should.”
Math
teachers face the same type of question. “When I assign homework, how
much emphasis should I place on students providing responses that
require careful reading and analysis on my part in order to provide
useful feedback? Ditto for tests.”
One measure of math
maturity is performance in constructed response (open-ended response)
types of questions. Such questions are more challenging to students and
more challenging to teachers. In terms of state and national math
tests, it is quite expensive to find, train, and make use of test
graders who grade constructed responses relatively rapidly and in a
valid, reliable, and fair manner. See, for example,
http://www.michigan.gov/mde/0,1607,7-140-22709_31168_31773-97188--,00.html.
This leads many school districts and states to not use standardized
math tests with constructed responses.
Final Remarks
This IAE Newsletter
focuses mainly on
math education and the idea of math maturity. The same ideas apply in
each academic discipline. Thus, we can think about teaching history in
a manner that increases a student’s level of “history maturity.” Such
an approach to education in each discipline provides a strong argument
for having smaller class sizes and better-prepared teachers.
About Information Age
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