Comments on: Teaching Math: Abstract Equations Beat Reality http://www.outsidethebeltway.com/archives/teaching_math_abstract_equations_beat_reality/ Online Journal of Politics and Foreign Affairs Wed, 25 Nov 2009 22:29:17 -0600 http://wordpress.org/?v=2.8.5 hourly 1 By: The Loudest Cricket http://www.outsidethebeltway.com/archives/teaching_math_abstract_equations_beat_reality/comment-page-1/#comment-349842 The Loudest Cricket Tue, 29 Apr 2008 16:04:46 +0000 http://www.outsidethebeltway.com/archives/2008/04/teaching_math_abstract_equations_beat_reality/#comment-349842 <strong>The Death of the Story Problem?...</strong> I never thought that story problems should be used as a way of teaching math, but rather as a way of applying what is taught to the real world.  Most of the math tests I recall had two parts, the equation solving section (2...... The Death of the Story Problem?...

I never thought that story problems should be used as a way of teaching math, but rather as a way of applying what is taught to the real world. Most of the math tests I recall had two parts, the equation solving section (2......

]]> By: Grewgills http://www.outsidethebeltway.com/archives/teaching_math_abstract_equations_beat_reality/comment-page-1/#comment-348870 Grewgills Mon, 28 Apr 2008 18:27:36 +0000 http://www.outsidethebeltway.com/archives/2008/04/teaching_math_abstract_equations_beat_reality/#comment-348870 Real world examples tend to work quite well when teaching children to add fractions (ex 1 & 3), but are much less effective when explaining multiplication of fractions (ex 2 & 4). It does not appear from the examples given that different connectors were used to differentiate when combinations were additive or multiplicative. It would be interesting to see if using connective symbology would alter the results. Real world examples tend to work quite well when teaching children to add fractions (ex 1 & 3), but are much less effective when explaining multiplication of fractions (ex 2 & 4). It does not appear from the examples given that different connectors were used to differentiate when combinations were additive or multiplicative. It would be interesting to see if using connective symbology would alter the results.

]]> By: Wayne http://www.outsidethebeltway.com/archives/teaching_math_abstract_equations_beat_reality/comment-page-1/#comment-348810 Wayne Mon, 28 Apr 2008 16:29:57 +0000 http://www.outsidethebeltway.com/archives/2008/04/teaching_math_abstract_equations_beat_reality/#comment-348810 The problem many have with abstract math or anything outside of a basic or general system we typically use is their refusal to think outside the box. Just like in the experiment, if they are given something familiar they will become fixated on what is familiar. If you don’t allow them in the box then it easier for them to look for solutions outside the box. Of course giving them concrete examples helps. Like having a bowling ball and telling someone to draw a square on it. It helps to teach them Spherical geometry and that squares don’t have to have 90 degree angles just four equal angles. Explain this with words at a bar and you usually get nowhere with the consensus at the end by the patrons that all squares have four 90 degrees corners. Also I agree as stated previously, not all abstract mathematics have solid real world examples. The problem many have with abstract math or anything outside of a basic or general system we typically use is their refusal to think outside the box. Just like in the experiment, if they are given something familiar they will become fixated on what is familiar. If you don’t allow them in the box then it easier for them to look for solutions outside the box. Of course giving them concrete examples helps. Like having a bowling ball and telling someone to draw a square on it. It helps to teach them Spherical geometry and that squares don’t have to have 90 degree angles just four equal angles. Explain this with words at a bar and you usually get nowhere with the consensus at the end by the patrons that all squares have four 90 degrees corners.
Also I agree as stated previously, not all abstract mathematics have solid real world examples.

]]> By: Dutchgirl http://www.outsidethebeltway.com/archives/teaching_math_abstract_equations_beat_reality/comment-page-1/#comment-348016 Dutchgirl Sun, 27 Apr 2008 20:08:40 +0000 http://www.outsidethebeltway.com/archives/2008/04/teaching_math_abstract_equations_beat_reality/#comment-348016 Very interesting indeed, but I suspect that those using the concrete examples did worse because the examples aren't all that concrete: the water volumes are sometimes additive, sometime reflect a remainder, with no explanation of where the 'rest' went. Real world examples can be very useful math tools if they are in fact analogous to the abstract concept. Sometimes there is no real-world example for an abstract idea, where symbols function very well. Very interesting indeed, but I suspect that those using the concrete examples did worse because the examples aren't all that concrete: the water volumes are sometimes additive, sometime reflect a remainder, with no explanation of where the 'rest' went. Real world examples can be very useful math tools if they are in fact analogous to the abstract concept. Sometimes there is no real-world example for an abstract idea, where symbols function very well.

]]>