[Numeracy 163] Re: Application vs. Theory
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Mon Feb 15 09:49:17 EST 2010
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I am not a mathematician, but have 16 years in adult education, and am one of the lead facilitators for the Texas ABE Math Initiative. I also teach an ASE/GED level math class. Personally, I can see that theory is important, and may lead to some deeper math understanding; however, in the real world, if I can get my students (and fellow teachers) to understand the application of math, I feel I have done my job. When teaching integers, I stress the addition rules using a number line, thermometer, check book - whatever works. When we hit subtraction - I use two strategies - one is that the subtraction is the "range" between the numbers using the number line, and two, this is the rule, and "Momma said so, so do it." (By this point in my class, I have created a level of trust and safety in the room, so they will take this direction very easily.) I understand that the mathematicians on this list are cringing right now, but this works for me and my students. They choose the strategy that works for them, and we move on. As long as they can continuously and consistently apply the rules, I am happy.
Also, in the real world of adult education, most teachers do not have the time or expertise to teach theory. Our math initiative has been created to work with teachers to give them strategies so they can work through their own fear of math. I cannot even see a practical way to introduce the theory that has been discussed here. My teachers would run out of the room, screaming.
Thank you for providing this forum.
Abilene, TX Adult Education
Texas ABE Math Initiative, Facilitator
From: numeracy-bounces at nifl.gov [numeracy-bounces at nifl.gov] On Behalf Of Denney, Brooke [denneyb at cowley.edu]
Sent: Sunday, February 14, 2010 11:05 PM
To: numeracy at nifl.gov
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