Dear Colleagues,
Partly in response to Garfunkel/Mumford, David Bressoud, former MAA president made these comments in a recent post.
http://launchings.blogspot.com/2011/10/ ... ersus.html
Regards,
Joe
Quantitative literacy and mathematics
Moderator: Sol Garfunkel

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Quantitative literacy and mathematics
Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
email:
malkevitch@york.cuny.edu
web page:
http://york.cuny.edu/~malk
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
email:
malkevitch@york.cuny.edu
web page:
http://york.cuny.edu/~malk

 Posts: 1364
 Joined: Tue Aug 28, 2007 2:52 pm
 Location: Jamaica, New York
 Contact:
Re: Quantitative literacy and mathematics
I tried to post this on the Launchings site but I guess it was too long, so I am posting it here.
Regards,
Joe
How does someone who thinks mathematics is important object to Quantitative Literacy (QL)? One certainly does not want a quantitatively illiterate society. However, I am made nervous by the idea of quantitative literacy for the same reason I am made nervous by Standards movements. What does one do with people who are taught arithmetical and mathematical material but don't master it or forget it quickly after they were found to have learned it? What does one do with real world people who have troubles with learning what one thinks is important? In particular, with mathematics, I think it is critical that students get to be aware of the great range of mathematical tools that they or mathematical experts can bring to bear on questions which arise in the world, as well as the excitement of aesthetically pleasing mathematics. Good curriculum may not mean that everyone masters what one would like them to master but it may have a staying power on scales other than being able to answer questions about factoring polynomials and percentages on standardized high stakes tests. One metaphor I like to use is that students should learn enough about the nature of mathematics and its applications to know when "to call a mathematician."
While I applaud the quantitative literacy movement's concern with teaching using contexts and the applicability of mathematics, I am nervous that nearly all the domains I see involving QL deal with are very traditional topics in arithmetic. Questions about percentages, fractions, and number size, while important, also seem to me rather "dry." Yes, one sees "bloopers" regularly on TV and in the press but what is far worse is that high school graduates have no inkling of the power of mathematics and its importance in the development of new technologies that are changing our way of life so dramatically. In a general way I would like to see the importance of mathematical modeling stressed, particularly models that use elementary mathematics. Shouldn't this be in our curriculum, too?
For example, despite QL how many graduates of high school understand the role mathematics has played in making compact cell phones possible? When asked, lay people invariably see cell phones as gifts from physics and engineering, and while this is true, there is wonderful mathematics that is no more complicated than many arithmetic, algebra, and trigonometry topics taught in K11 but have been "banished" by the CCSSM. More specifically, your cell phone works because of:
a. Error correction codes (Richard Hamming)
b. Data compression codes (David Huffman)
c. Frequency assignment algorithms (graph coloring algorithms)
d. Global positioning technology
Mathematics has played a very significant role here. Another way to think of the issues is to look at specific modeling domains that many students find highly interesting as sources of questions: operations research and fairness questions. How can we improve voting and election processes including redistricting? Is the method used to assign each state a number of representatives in the House of Representatives fair? Is the weighted voting system used by the European Union fair? In the domain of OR there are problems like the Chinese Postman Problem (things to be done on the edges of a graph or weighted graph) and the TSP (things to be done at the vertices of a graph or weighted graph). There are also lots of wonderful applications of mathematics using elementary tools to studying genomics.
Why aren't data compression codes and error correction code ideas taught in K  11? It seems to me the reason is that the mathematics community has tied itself to a curriculum which views Calculus as an entry point to STEM disciplines, thereby writing off large numbers of students whose mathematical talents and interests lie with more discrete and geometrical mathematical thinking. Furthermore, the current curriculum (here I mean the CCSSM) poorly serves future parents and those who will pursue careers that stray from STEM majors.
Best,
Joe Malkevitch
Regards,
Joe
How does someone who thinks mathematics is important object to Quantitative Literacy (QL)? One certainly does not want a quantitatively illiterate society. However, I am made nervous by the idea of quantitative literacy for the same reason I am made nervous by Standards movements. What does one do with people who are taught arithmetical and mathematical material but don't master it or forget it quickly after they were found to have learned it? What does one do with real world people who have troubles with learning what one thinks is important? In particular, with mathematics, I think it is critical that students get to be aware of the great range of mathematical tools that they or mathematical experts can bring to bear on questions which arise in the world, as well as the excitement of aesthetically pleasing mathematics. Good curriculum may not mean that everyone masters what one would like them to master but it may have a staying power on scales other than being able to answer questions about factoring polynomials and percentages on standardized high stakes tests. One metaphor I like to use is that students should learn enough about the nature of mathematics and its applications to know when "to call a mathematician."
While I applaud the quantitative literacy movement's concern with teaching using contexts and the applicability of mathematics, I am nervous that nearly all the domains I see involving QL deal with are very traditional topics in arithmetic. Questions about percentages, fractions, and number size, while important, also seem to me rather "dry." Yes, one sees "bloopers" regularly on TV and in the press but what is far worse is that high school graduates have no inkling of the power of mathematics and its importance in the development of new technologies that are changing our way of life so dramatically. In a general way I would like to see the importance of mathematical modeling stressed, particularly models that use elementary mathematics. Shouldn't this be in our curriculum, too?
For example, despite QL how many graduates of high school understand the role mathematics has played in making compact cell phones possible? When asked, lay people invariably see cell phones as gifts from physics and engineering, and while this is true, there is wonderful mathematics that is no more complicated than many arithmetic, algebra, and trigonometry topics taught in K11 but have been "banished" by the CCSSM. More specifically, your cell phone works because of:
a. Error correction codes (Richard Hamming)
b. Data compression codes (David Huffman)
c. Frequency assignment algorithms (graph coloring algorithms)
d. Global positioning technology
Mathematics has played a very significant role here. Another way to think of the issues is to look at specific modeling domains that many students find highly interesting as sources of questions: operations research and fairness questions. How can we improve voting and election processes including redistricting? Is the method used to assign each state a number of representatives in the House of Representatives fair? Is the weighted voting system used by the European Union fair? In the domain of OR there are problems like the Chinese Postman Problem (things to be done on the edges of a graph or weighted graph) and the TSP (things to be done at the vertices of a graph or weighted graph). There are also lots of wonderful applications of mathematics using elementary tools to studying genomics.
Why aren't data compression codes and error correction code ideas taught in K  11? It seems to me the reason is that the mathematics community has tied itself to a curriculum which views Calculus as an entry point to STEM disciplines, thereby writing off large numbers of students whose mathematical talents and interests lie with more discrete and geometrical mathematical thinking. Furthermore, the current curriculum (here I mean the CCSSM) poorly serves future parents and those who will pursue careers that stray from STEM majors.
Best,
Joe Malkevitch
Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
email:
malkevitch@york.cuny.edu
web page:
http://york.cuny.edu/~malk
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
email:
malkevitch@york.cuny.edu
web page:
http://york.cuny.edu/~malk
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