Presented by JOY Center of Learning
Math to fit your personal style
and unique students.
Professor B Mathematics
Activating the Contextual Learner
Articles, Information, and Help
The Frustration and "Failure" of the Truth Seeker in Traditional Math EducationCopyright © Everard Barrett, 1998
Teacher, why do you "bring down" (in long division)? Why do you move the decimal points (when dividing one decimal by another)? Why do you count the decimal places (when you multiply one decimal by another)? Why do you skip a space (when you multiply by the second digit in a two-place multiplier)? Why do you divide the larger denominator by the smaller denominator and multiply the numerator by that answer (to find the missing numerator)? Why do you 'multiply across' (when you multiply fractions)? Why do you cancel 'up and down' (when multiplying fractions)? Why do you multiply the whole number by the denominator and add on the numerator (when you change a mixed number to an improper fraction)? Why do you divide the numerator by the denominator (when changing an improper fraction to a mixed number)? Why do you invert and multiply (when dividing one fraction by another)? Why teacher? Why? Why? Why?
Do you remember hearing these types of questions over and over again in your math classes from first through seventh grades? It is very likely that you asked many of them on many occasions yourself. Do you recall the teachers' responses? "Just do it. That's how you get the answer." Does this type of response to children's math questions sound familiar to you? Did you hear it a lot or just a few times? The vast majority of us have heard it over and over again from elementary through high school.
In this article, I will consider some of the dire consequences of these "answers" to children's math questions.
What kind of response do children want when they ask a question? Let us do an experiment. I want you to look up from this page and, with the customary furrow in your brow, vocally ask this question: "Teacher why do you bring down?" As you were doing that, did you feel the tension (in your mind) of something that needs to be cleared up? You generally feel this type of mental tension whenever you ask questions (including math questions). Now let us assume you get such a meaningful verbal response that it "floats" into your mind and everything "clicks" together so well that you exclaim with excitement, "Oh! I see." Now, once again, I want you to look up from this page and say, "Oh! I see." As you were doing that, did you feel the relief? The tension has rapidly dissolved and there is actually a look of relief on your face.
All children know this experience. They may not articulate it, but they feel the sensation of mental tension when asking a question and they feel the sensation of relief when receiving answers that "make sense" to them. This is why I often refer to virtually all children as "truth-seekers." Young truth-seekers strongly yearn for responses that dissolve the mental tension caused by their questions.
In the article entitled "You Could Be the Difference-Mathematical Excellence or Mediocrity for Your Children" on our web page, I made the point that ninety-five percent of all statements made by all of our math teachers from first through seventh grade (and beyond) were either untrue or meaningless. Untrue and/or meaningless statements deactivate the gift (owned by virtually all human beings) for making connections and, thereby, deriving meanings and retention. Consequently, truth-seekers' desire to dissolve the tension of their questions through meanings and understandings is totally frustrated by traditional mathematics eduction.
When children receive totally meaningless responses to their math questions day after day, week after week, month after month, year after year, through all their years in school, the only way they can prepare for tests is to "memorize the steps" which they tend to forget after the test is over (this assumes that they remembered the steps during the test). Some of those who are blessed with excellent memory and good discipline are able to get good grades and may even achieve "honor student" status. But, as many parents ruefully recall, a math honor student in eighth grade very often falls short of honor status in algebra, geometry, trigonometry and precalculus later on in high school. Many students, who hold on to honor status in high school, go on to college and become rather average math students. Consequently, honor student status, as a result of the traditional rote-mechanical, remember-the-steps approach to teaching and learning math is an illusion.
How do the minds of good problem solvers function as they "lock horns" with a problem? They relish the experience of grappling with the tension of the problem until the point at which it dissolves, as the set of connections representing or leading to the solution emerges. Problem solving is all about making connections. Consequently, the yearly "bombardment" of children's psyches with memorization of utterly untrue and meaningless "steps" (nonsense, because it makes no sense) creates a conditioning of their minds that virtually debilitates their natural capacity to make mathematical connections and solve problems. Clearly, truthful and meaningful statements and responses, through the years of children's experience with arithmetical computation, will powerfully facilitate their innate capacity to make mathematical connections and (thereby) solve problems.
Concerning the low grades of so many truth-seekers in mathematics, should we conclude that their failure was in mathematics or was theirs a failure to assimilate nonsense?