Does Algebra Improve Thinking Skills?
For many years, it has been claimed that taking high school level and
college freshman level algebra courses will enable one to be a better
"thinker". It has often been proposed that the ability to
logically reason and symbolically reason improves as one takes
additional algebra courses. Recently, however; some non-fans of
algebra, such as Richard Cohen of the Washington Post, write "You will
never need to know algebra. I have never once used it and never once
even rued that I could not use it" in his article
What Is the Value of Algebra?. Others even claim that college math
requirements serve little useful purpose if they do not have direct
application in one's career. In this study, my objective is to
quantitatively determine if taking high school and college freshman
level algebra and calculus courses help one's symbolic and logical
reasoning skills by testing students at various levels of math.
A Four Question Logic and Symbolic Reasoning Test
I developed a four question test to be given at community colleges
with questions with the following format:
- Question #1 - Test
symbolic reasoning and logic skills in a problem that resembles a
typical IQ test problem. The student must substitute symbols with
- Question #2 - Test
symbolic reasoning and logic skills in a
elementary boolean logic type problem. This problem involves
logical skills often required of
- Question #3 - Test
symbolic reasoning by substituting values of variables into a
statistics formula that gives the confidence intervals for poll
data. Only beginning pre-algebra skills are required.
- Question #4 - Simply
inquires whether or not students have taken a computer programming
or logic course that specifically teaches use of if-then statements
with operators like and & or. The test I gave at Lake
Superior College with results shown below did not include this
The test was deliberately kept short so as to not use up too much
instruction time and thus get better participation by community
To See This Test Click Here.
The test will open in a new window. To print it out, use a 70%
setting and the entire test may be printed on one page.
More Results Are
Explanation of Results
The test given at Lake Superior College was limited to the first 3
questions. This test was given approximately at the middle of
the semester. So for example, results from the Calculus I group
were obtained from students about half-way through the Calculus I
course. I have since added Question #4 inquiring whether or not
students have taken a computer programming or logic course that
specifically teaches use of if-then statements with operators like
and & or. Future test results will include this additional
Although the results clearly suggest improvement in scores as students
take more math courses, more tests including the addition of Question
#4 should be given at other community colleges to determine if taking
other courses in logic or computer programming helped in answering
both Questions #1 and #2.
It seems very likely that additional algebra coursework led to
improved scores in Question #3. It seems logical to conclude
that as one takes additional algebra courses, they become less
intimidated by large formulas.
Do You Want To Participate?
To participate in this study, simple print out the test and give to
your students. Your college identity will be kept anonymous. Email me
the following results:
- What type of institution is this? Community College, 4-yr
College, High School, etc.
- What course are your students currently enrolled in?
- How many students took the test?
- How many got Question #1 correct?
- How many got Question #2 correct?
- How many got Question #3 correct?
- How many replied YES to Question #4?
Although I am primarily studying community colleges, data from high
schools, middle schools, 4-year colleges, or technical schools would
also be helpful. If you would like an answer key sent to you,
drop me an email.