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Does Algebra Improve Thinking Skills?

Introduction
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 variables.
  • Question #2 - Test symbolic reasoning and logic skills in a elementary boolean logic type problem. This problem involves logical skills often required of a computer programmer.
  • 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 question.

The test was deliberately kept short so as to not use up too much instruction time and thus get better participation by community college instructors.

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.

Test Results

More Results Are Shown Here


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 question.

Conclusions
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.

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