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1、Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Philosophy of the Math Department,Mathematical Literacy,All students must be mathematically literate,They must perform in the workplace,They will be lifelong learners,They must be pr
2、oblem solvers,Mathematical Literacy for Engineers,Used to learn engineering concepts,Apply concepts in real life situations,Be a lifelong learner in chosen profession,Mathematics is the,tool,that makes these possible,Demands of Advancing Technology,Todays engineer needs a working knowledge of,Patter
3、ns,Functions,Algebra,Spatial relationships,Geometry,Measurement,Data analysis,Probability,Competent use of technology,Use of Technology in the Classroom,We are riding on a wave of change,It is not going away,We cannot reject it or ignore it,ABET requires it,We must find a balance of how best to use
4、these new technologies,Without,sacrificing basic mathematical skills,Engineering programs must demonstrate that their students attain:,k)an ability to use the techniques,skills,and modern engineering tools necessary for engineering practice.,Concerns,Students who cannot envision basic functions,Inab
5、ility of students to evaluate the reasonableness of a calculator answer,Lack of basic skills with,Algebra,Derivatives,Integrals,Differential Equations,“students have become less familiar with,basic algebra and trigonometry.This change has been coincident with their heightened usage of,calculators Bi
6、ll Graff,Addressing Concerns,Stressing basic functions,drilling recognition,Repeatedly discussing whether an answer given by technology is reasonable,Requiring“Gateway tests to demonstrate/review basic derivative and integration skills without a calculator,Addressing Concerns,Repeated reminders that
7、 a calculator can be used both to,solve a hard problem and,make a very bad mistake,Learning to use the calculator as a,tool,Remember that misuse of the tool is not the tools fault,A hammer can be used to build a mansion or break a window,Good Uses of Technology,Discovery teaching,Making connections,
8、“Messy problems,Using a variety of solution strategies,Discovery Teaching,Example:Pose the problem of finding the derivative of ln(x)using the limit definition for a derivative,Messy Problems,Consider,Is the,decomposition,what we want the student to learn?,Or is it to be able to,use,it to do somethi
9、ng else with(inverse Laplace transform)?,Shift of Teaching Strategies,Our teaching goals are shifting from,Performance,of mathematical operations,To the,use,of mathematical concepts.,Assessment methods,Two tiered exams,Without the calculator to assess basic understanding of the material,With the cal
10、culator to assess problem solving skills,Shift of Teaching Strategies,Use various ways of looking at a problem,Formulas,Tables of values,Graphs,Textual descriptions,This aids,all,learning styles,Shift of Teaching Strategies,Consider the classical parachute problem,We must ask more than the usual“aft
11、er how many seconds will the parachutist hit the ground?,We give students direction by asking more detailed questions,Have them analyze the motion of the falling body,Geometrically,Numerically,and,Analytically.,Varieties of Solution Strategies,Try alternate methods to find a solution,Look at the gra
12、ph,Manipulate the formula,View the table of values,use regression to come up with a mathematical model,Implications of Available Technology,Our role as,guides,in the learning process is more important than ever,Must decide when to use/not use technology,The challenge for all of us,Take advantage of
13、the symbolic computation possibilities and do,more,mathematics,more,engineering,Philosophy of the Math Department,Problem,Consider f(x)=log,a,x,What if we try to use the definition for derivative using the limit,No way to break up this portion of the expression to let h,0,Possible Solution,We know t
14、hat the derivative is the slope function,What if we graph y=ln(x)and check the slopes plotting them,Slope Results,The table at the right shows the values of theslopes at various x values,What function might this be?,Appears to be,x,slope of ln(x)at x,0.001,1000.000,0.010,100.000,0.100,10.000,0.500,2.000,0.750,1.333,1.000,1.000,1.500,0.667,2.000,0.500,5.000,0.200,10.000,0.100,Derivative of the Log Function,For the natural logarithm,ln(x),For the log of a different base log,a,(x),
Philosophy of the Math Department - LeTourneau University 拉托纽大学数学系的哲学
