High School Mathematics at Work Essays and Examples for the Education of All Students (1998) / Chapter Skim
Currently Skimming:
Part One: Connecting Mathematics with Work and Life
Part One: Connecting Mathematics with Work and Life
Pages 7-56
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_ J :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: NQ 1Qnger and defense. For student s' it opens floors to careers.
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text by T · ~ Ale rea Dowels IS In earnlng5 and suggests that lit- students engage In mathematical thinking, they dL Con ~ 7 C:7 Cop · ~ · ~.
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. High school students win `'college" competition.
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1 ~ . ~ 1 1 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: their heads with facts through lectures 2~ IDS AT that
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ing the 15
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rl'h~nlrm ~EXTh~r ~nn11 n~alirm thm ImC!
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He has served as a University Professor, College President, and for ten years as the President and Chief Executive Officer of the American Association of Community Colleges. He has served as a consultant to the National Science Foundation and has served on many national commissions?
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Net impact, even factoring in the error rate, is a significant sales increase. On the other hand, most of the time, the errors cause us to ship the wrong item which then needs to be mailed back at our expense, creating an impression in the customers that we are not well organized even though the original error was theirs ~ It, It, ``Final point.
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Perhaps the most important is one not often mentioned, and Shall is the ability to convert an important business question into an appropriate mathematical one to solve the mathematical problem and then to explain the implications of the solution for the original business problem This abilit to inhabit simultane Y ously the business world and the mathematical world, to translate between the two, and, as a consequence, to bring clarity to complex, real-world issues is of extraordinary importance. In addition, the participants in this conversation understood and interpreted graphs and tables, computed, approximated, estimated, interpolated, extrapolated, used probabilistic concepts to draw conclusions, generalized from CO##ECTI#8 MATHEMATIOS WITH WOll AND LIFE the liaby 2'
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He has previously served on the Mathematical Science Education Board, and on the National Alliance for State Science and ~[athematics Coalitions (NASS~[C)
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courses (es em p
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Teachers Colle e and the Center for in, 01 this approach nave not nag much 1nterac ~.
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large cities' such as Aviation High School in 27
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Berkeley? CA National Center for Research in Vocational Education.
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He is also Director of the Institute on Education andL the [Economy andL Director of the Community College Research Center, both at Teachers College. National Center for Research in Vocational Education.
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l t :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: n _4 EB: '1' ~ my local paper, The Times of Trenton, IDS AT
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ye]
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as we ~ ~ ~q ~ fit ~ ~ o! 10U calculus
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She is currently a member of the Board of Directors of the American Association for the Advancement of Science and formerly chaired its Section A Nominating Committee. She has served as Vice Presidlent and as a Member-at-Large of the Council of the American Mathematical Society and served on its Executive Corn~nittee and its Nominating Conarnittee.
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AIL F n U L ~11 F ~R :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely Cures and r.~n~hl" ``f ~ torn n~rlFPr~tir~r, Each ~,~ relet t,h" ar"~t,P,at, art Burn ,~hr`~;`r human passions, remote even from the pitiful facts of nature? the generations have gradually created an ordered ~OS=OS7 where pure thought can dwell as in its nature home?
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to 7 What makes the world turn against me and all who look like me' I won nothing, IL survey nothing, when I ask this question, the luxury of an answer that will fill volumes does not stretch out [before one. When I ask this question, nay voice is filled with active participants in the schoolts activities eneraY and effort' In a tracked.
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he eck the thickness of the paint once it has . technology To TV ~ ~ '~ A to 01 me "rv coaling.
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Altbou many of the sponsors initially indicated that there Here no mathematical dimensions to their Corks students omen mere able to show sponsors places Were the mathematics we were studying was to be Fund. For example, Jackie worked with a crop and soU scientist She was intrigued by the way in Enrich measurement of weight is used to count seeds.
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Nev~ York: Teachers College Press.
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To assist his research in mathematics teaching and learning, he has taught algebra at the high school level. His interests include teaching mathematics by examining student ideas, using computers to support student exploration, and the potential for the history and philosophy of mathematics to ~ AM Y .
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ambulance companies Cit logs record the y date, the time of the ca cornpan and the response time for each Y 1 call (Table 1)
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t rn n d t h th r r r e s ~ a a suc as ese emus esa p ocluctive mixture of mathematics common sense, and intellectual detective work. It's the kind of reasoning that students should n this response time is a little longer-4 3 minutes to Graphs of the response times (Figures 1 and 2)
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drapes of the response time versus the time of da ~ Y (Figures 3 and 43 shed some light on these questions These graphs show that Arrow's response +- ~ ~ ~ ~ ~ C.~^ A AA ~ Limes were ~asL except between a! an ^'v' and 9 00 AM, when they were about 9 minutes about 5 minutes slower Perhaps the local Metro more susceptible to the afternoon - 1 1 1 1 11 ~ 1 1 l 1 1 1 1 _ _IIL 11 .
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on the other hand determining whether 5 200 , , ~ Finn ~ ~` ~ ~ ~ or u,~uu Is a ~eLLer esumaLe IS not necessary, Careful reasoning with everyday observant exact answer (if there is one) Fermi esti .
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_ in,, _ ,;;, ., component factors vary greatly from for the teacher are how man classes he Y or she teaches how many stuclents are in I each of the classes how much experience , ~ has the teacher had in general and has the teacher previously taught the classes and certainly as part of teaching style the l l kind of homework the teacher assigns, not changes might the teacher make to reduce the amount of time? The calculation above offers four possibilities Reduce the time .
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would cons fain 9Q QQO square feet of floor space giving I , a rough idea of the size . I le estimates that 1 6.S m dents Fermi Questions are useful outside the works place Some Fermi questions have political .
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cost in lost .
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Though the calculate find the optimal solution. Such a systematic Psearch of the assible solution space is important in many modeling situations where a formal optimal strategy is not ~BY On t he the some strategies Generally/ one of ~ ~ ~' .
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are relevant Start by establishing the kind of building-a hotel an office building an l l apartment builcling7 How many people are . on the cli~erent floors7 What are their norm mal destinations (e g primarily the ground .
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and C are finished so much sooner than elegy vator A, there is likely a more efficient solute tion. s1:op at floors relatively slowly.
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is clearly not optimal Luring Perio~s of low use and much of the ineffi~ ciency is related to the first hypothesis for rush hour optimization. that each rigor is servecl by a single elevator.
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mum time. A location that minimizes the the least average time of response.
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ICS AT The average ll:emperature for the day is then taken to be 58 degrees. Subtracting that result: Over five consecutive days, for example, if the average temperatures were 58 50 60 67 r r r r and 56 decrees Fanrenneit the calculation ~ I Yields 7r 1 5r 5r Or and 9 heatinq-deoree-davs respectively!
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because most people would not turn on their heat if the tem~era1:ure outside is above 65 cle~rees ~. Newtonts law elf cooling, which states 1:hat 1:he or heating oil usage is based primarily on average temperature is above 65 degrees, no heating should be requirecl, and 1:heref~vre tnat of last winter because ~ ~ us /4 203 = .
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From page 56... ...
, where T is the average temperature and U is the gas usage Note . that the slope,-~251, is the gas usage per heating-degree-day, and 65 is the cutoff.
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