[Numeracy 174] Re: Application vs. Theory
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Mon Feb 15 19:30:45 EST 2010
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In my experience, it's when we "speak abstract" to students who live in concrete that we lose them.
Generally when we "teach theory" what we actually teach is further reinforcement that math is an arcane ritual in which we are to perform symbolic rites and written incantations with certain inscrutable patterns until they satisfy The Master. When I am writing those symbols down, they're connecting to all kinds of things in my mind... real applications... when my students read word problems, they are often not connecting the processes to somethign real; it's just adding a layer of complexity to the symbol manipulation. I work hard to help them see the connection, but that generally requires a whole lot more drawing and wishing I were a graphic artist ;)
Academic Development Specialist
Center for Academic Success
Champaign, IL 61821
sujones at parkland.edu
>>> "Denney, Brooke" <denneyb at cowley.edu> 2/14/2010 11:05 PM >>>
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