[Numeracy 161] Re: Application vs. Theory
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Mon Feb 15 01:33:00 EST 2010
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Greetings Brooke and all,
Well, I'm glad this discussion is continuing and that we're not leaving it to the realm of agreement to disagree! And yes, I'll agree that absolute values do have a positive connotation, precisely because they have basis in empirically observable concrete and material reality. That was not, however, the thrust of my message your are responding to.
I'm only going to provide a short answer at this point. I am not a mathemetician and have not studied math beyond portions of the British advanced levels, except in its application of studies in logic, test design, and applied linguistic research. Pedagogically, I espouse the principle of understanding and avoid mastery of rules without trying to instill some measure of understanding of those very rules, that is, the reasoning that underlies them. This espousal extends to learners with the most basic levels of numeracy. Scaffolding is key here. I always strive for the "ah ha" moments, and remain convinced that much more learning can and does take place than we might expect. I've yet to work students whose dislike of math has not decreased in working with them. I consider the language-math connection to be a crucial one, because, ultimately, I view math as a language in its own right.
Rather than responding further to your comments at this time, I remain curious what other subscribers to this list might believe and hopeful that more contributions to this discussion lie ahead.
Michael A. Gyori
Maui International Language School
From: "Denney, Brooke" <denneyb at cowley.edu>
To: numeracy at nifl.gov
Sent: Sun, February 14, 2010 7:05:04 PM
Subject: [Numeracy 160] Application vs. Theory
Your comments leave me feeling as a mathematician curious of how you came about your “logic”. To use the term absolute value to mean, “one that knows no positives or negatives”, is a paradox. That is, if you are talking about the mathematical operation known as absolute value (which does, have a positive connotation). Additionally, your comments about negative numbers astonish me and my fellow mathematician colleagues. Is it important to know the mathematical proof that states the logic of why two negatives when multiplied together yield a positive result? Or, is it okay for people to just “know the rule”? Several researchers have stated that adult numeracy learners need to be taught within realistic contexts; otherwise educators jeopardize de-motivating learners to learn. Do not misinterpret my response, I love to learn about math theory and logic but without application the concepts are often nonrepresentational.
I understand why you would choose to utilize the Cartesian Coordinate Plane to discuss all real numbers. Nevertheless, many students would consider that lesson mindless prattle if they did not have a prior frame of reference to build their cognitive skills from. Conversely, many students do know what it means to be below sea level or overdrawn in their bank account (and the like). Their frame of reference allows them to relate to the idea of negatives better. Albeit true, it is subjective in nature but isn’t all mathematics subjective?
I leave it to the discussion board participants, is it better for numeracy students or developmental math students to understand the application of mathematics or learn about the theory that lies underneath?
Math & Numeracy Moderator
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