november 3, 2001ictcm conference1 applied calculus on the web applets & applications professor...

November 3, 2001 ICTCM Conference 1

Applied Calculus on the WebApplets & Applications

Professor Michael S. PilantProfessor Michael S. Pilant

Department of MathematicsDepartment of Mathematics

Texas A&M UniversityTexas A&M University



BackgroundBackground TeachingTeaching TrainingTraining ExplorationExploration AssessmentAssessment



BackgroundBackground Finite Math on the WebFinite Math on the Web Project – Project –

This began in 1998 as a way to present the core This began in 1998 as a way to present the core mathematics curriculum to students at Texas mathematics curriculum to students at Texas A&M University, a large public state university A&M University, a large public state university with approximately 35,000 undergraduate with approximately 35,000 undergraduate students.students.



BackgroundBackground Enrollments in 2000Enrollments in 2000

Finite Math - Math 166 – 2,152 studentsFinite Math - Math 166 – 2,152 students Business Math - Math 141 – 5,728 studentsBusiness Math - Math 141 – 5,728 students Applied CalculusApplied Calculus - Math 142 – 4,054 students - Math 142 – 4,054 students Total = 11,934Total = 11,934



BackgroundBackground Enrollments in 2001Enrollments in 2001

Finite Math - Math 166 – 2,070 studentsFinite Math - Math 166 – 2,070 students Business Math - Math 141 – 5,735 studentsBusiness Math - Math 141 – 5,735 students Applied CalculusApplied Calculus - Math 142 – 3,813 students - Math 142 – 3,813 students Total = 11,618Total = 11,618



BackgroundBackground

Use Use Finite Math on the WebFinite Math on the Web

as a model for as a model for

Applied Calculus on the WebApplied Calculus on the Web



Overall Design ConsiderationsOverall Design Considerations Initial use – to illustrate a concept, allow limited Initial use – to illustrate a concept, allow limited

interaction - interaction - teachingteaching Reinforcement of concepts – feedback, allow more Reinforcement of concepts – feedback, allow more

interaction - interaction - trainingtraining ExplorationExploration – full functionality and interaction – full functionality and interaction AssessmentAssessment – checkpoint for students and/or instructors – checkpoint for students and/or instructors



TeachingTeaching Finite Math on the Web Finite Math on the Web – – TopicalTopical

Counting and Probability,Counting and Probability,Conditional Probability, Conditional Probability, Statistics, Statistics, Probability Distributions, Probability Distributions, Financial ApplicationsFinancial Applications

Lines and Slopes, Lines and Slopes, Least Squares, Least Squares, Matrices, Matrices, Linear Programming, Linear Programming, Sets, Sets,



TeachingTeaching Applied Calc on the Web Applied Calc on the Web – Sequential– Sequential

Function Behavior, Function Behavior, Optimization, Optimization, Integration, Integration, Area, Area, Multi-variable ApplicationsMulti-variable Applications

Polynomial Functions, Polynomial Functions, Logarithmic and Logarithmic and Exponential Functions, Exponential Functions, Limits and Continuity, Limits and Continuity, Rates of Change, Rates of Change, Rules of Differentiation, Rules of Differentiation,



TeachingTeaching (Re-)Introduce basic concepts, for example:(Re-)Introduce basic concepts, for example:

Graph of a functionGraph of a function Intercepts (roots)Intercepts (roots) Intersections between curvesIntersections between curves Maximum, minimumMaximum, minimum Definitions of slopeDefinitions of slope



TeachingTeaching Initially, the applets should have very Initially, the applets should have very

simple “look and feel.”simple “look and feel.” Respond to mouse click and dragRespond to mouse click and drag Open with an image (or data) appropriate to Open with an image (or data) appropriate to

contextcontext



Basic AppletBasic Applet

Plots a functionPlots a function

set by HTMLset by HTML

<param> flag<param> flag




Zoom inZoom in

Rescale coordinatesRescale coordinates




Select functionSelect function

Show coordinatesShow coordinates




Show axesShow axes

Show gridShow grid





TrainingTraining Subsequently, the applet is used in such a Subsequently, the applet is used in such a

way as to reinforce basic concepts and way as to reinforce basic concepts and algorithmsalgorithms

Zooming in and out becomes proceduralizedZooming in and out becomes proceduralized




Show plot toolsShow plot tools






Zoom inZoom in

Zoom outZoom out

Show/Hide AxesShow/Hide Axes

Show/Hide GridShow/Hide Grid

ResetReset




Show functionShow function

ToolsTools






Enter functionEnter function

Plot functionPlot function

Show secantShow secant

Show tangentShow tangent

ClearClear



ExplorationExploration Once the basic concepts and processes Once the basic concepts and processes

become familiar, students can explore become familiar, students can explore Apply concepts to new situations (domains)Apply concepts to new situations (domains)



Investigating

limits of

Functions (e.g.

x*(sin(1/x))



AssessmentAssessment In order to provide feedback to the In order to provide feedback to the

instructor (and to the student!) some type of instructor (and to the student!) some type of assessment is required.assessment is required.



AssessmentAssessment Basic (declarative) knowledgeBasic (declarative) knowledge

Multiple choice, instant feedbackMultiple choice, instant feedback Algorithmic (procedural) knowledgeAlgorithmic (procedural) knowledge

Multiple choice, short answerMultiple choice, short answer Problem solving (strategic knowledge)Problem solving (strategic knowledge)

Workout, multi-step, applet basedWorkout, multi-step, applet based



AssessmentAssessment In order to provide meaningful assessment, In order to provide meaningful assessment,

we require the applet to we require the applet to Communicate with the browser via HTML Communicate with the browser via HTML

<param> …</param> tags<param> …</param> tags Allow communication via JavaScript through Allow communication via JavaScript through

public functionspublic functions



<applet name=“myApplet” …><applet name=“myApplet” …> … …<param name="background_color" value="ffffff"><param name="background_color" value="ffffff"><param name="xmin" value="-2.0"><param name="xmin" value="-2.0"><param name="xmax" value="2.0"><param name="xmax" value="2.0"><param name="ymin" value="-2.0"><param name="ymin" value="-2.0"><param name="ymax" value="2.0"><param name="ymax" value="2.0"><param name="function" value="sin(x)"><param name="function" value="sin(x)"><param name="show_grid" value="true"><param name="show_grid" value="true"><param name="show_axes" value="true"><param name="show_axes" value="true"><param name="show_plot_tools" value="true"><param name="show_plot_tools" value="true"><param name="show_function_tools" value="true"><param name="show_function_tools" value="true"></applet></applet>

Integration with HTML



Communication

with Scripts



Intersections

between two

curves (e.g.

sin(x), cos(x))



Finding the slope

of the tangent

to a curve



Finding curve

based on a

formula



Assessment methods using appletsAssessment methods using applets JavaScript (client-side)JavaScript (client-side) Cgi-bin scripts (client-server)Cgi-bin scripts (client-server) Assessment built into appletAssessment built into applet CookiesCookies Databases Databases

MySQL, PostgreSQLMySQL, PostgreSQL



JavaScript exampleJavaScript example

// Answer to Q10 is x=55/102=0.539 and p=745/306=2.43// Answer to Q10 is x=55/102=0.539 and p=745/306=2.43

// If x=0.539 is substituted, p = 2.44 results // If x=0.539 is substituted, p = 2.44 results

// allow 2.43 or 2.44 as answer// allow 2.43 or 2.44 as answer

// must encode this answer!// must encode this answer!

function checkAnswerQ10() {function checkAnswerQ10() {

var x = deleteSpaces( document.myform.Q10x.value )var x = deleteSpaces( document.myform.Q10x.value )

var p = deleteSpaces( document.myform.Q10p.value )var p = deleteSpaces( document.myform.Q10p.value )

}}



JavaScript exampleJavaScript exampleif ( eval(x) == 0.539 && Math.abs(eval(p)-2.43)<0.02 ) {if ( eval(x) == 0.539 && Math.abs(eval(p)-2.43)<0.02 ) {

Tried[9] = "Incorrect"Tried[9] = "Incorrect"

alert( "Watch your units!" );alert( "Watch your units!" );

}}

else if ( x == "539" && Math.abs(eval(p)-2.43)<0.02 ){else if ( x == "539" && Math.abs(eval(p)-2.43)<0.02 ){

Tried[9] = "Correct"Tried[9] = "Correct"

}}

elseelse

Tried[9] = "Incorrect"Tried[9] = "Incorrect"

alert("Question 10: Answer has been graded.\n"alert("Question 10: Answer has been graded.\n"

+ "Click Done to have your grade recorded.");+ "Click Done to have your grade recorded.");



Cgi-bin scriptsCgi-bin scripts

<form name=“myForm” method=“Post”<form name=“myForm” method=“Post”

action=http://server/cgi-bin/script.pl>action=http://server/cgi-bin/script.pl>

… …

<input type=hidden name=“var1” value=val1><input type=hidden name=“var1” value=val1>

… …

</form></form>



Cgi-bin scriptsCgi-bin scripts

<script language=“JavaScript”><script language=“JavaScript”>

……

document.myform.action=document.myform.action=

http://server/cgi-bin/newscript.plhttp://server/cgi-bin/newscript.pl

document.myform.submit( );document.myform.submit( );

……

</script></script>



Assessment built into appletAssessment built into applet1.1. Data encoded into applet is very secureData encoded into applet is very secure

2.2. Parametrically generate problems from built in Parametrically generate problems from built in templatestemplates

3.3. Specialized grading and evaluation algorithms Specialized grading and evaluation algorithms can be built into appletcan be built into applet

Example: Example: Venn DiagramsVenn Diagrams



CookiesCookies

function setCookie (name, value) {function setCookie (name, value) { var str;var str; if (value != null)if (value != null) str = name + "=" + escape(value);str = name + "=" + escape(value); var now = new Date()var now = new Date() var nowplus1 = now.getTime() + (52*7*24*60*60*1000)var nowplus1 = now.getTime() + (52*7*24*60*60*1000) now.setTime(nowplus1)now.setTime(nowplus1) str += top.cookieString;str += top.cookieString; str += ";expires="+now.toGMTString();str += ";expires="+now.toGMTString();document.cookie = str+";";document.cookie = str+";";}}



CookiesCookies

function getCookie(name) {function getCookie(name) {

var cookie = " " + document.cookie;var cookie = " " + document.cookie;

var search = " " + name + "=";var search = " " + name + "=";

var setStr = null; var setStr = null;

var offset = 0;var offset = 0;

var end = 0;var end = 0;



CookiesCookies

if (cookie.length > 0) {if (cookie.length > 0) { offset = cookie.indexOf(search);offset = cookie.indexOf(search); if (offset != -1) {if (offset != -1) { offset += search.length;offset += search.length; end = cookie.indexOf(";", offset)end = cookie.indexOf(";", offset) if (end == -1) { end = cookie.length; }if (end == -1) { end = cookie.length; } setStr = unescape(cookie.substring(offset, end));setStr = unescape(cookie.substring(offset, end)); }} }} return(setStr);return(setStr);}}



DatabasesDatabases Simple – file systems on serverSimple – file systems on server Cookies – on clientCookies – on client SQL – MySQL, Access, SQL Server, SQL – MySQL, Access, SQL Server,

PostgreSQL, …PostgreSQL, … Connect viaConnect via

Embed-perl, php, cgi-bin scripts, jdbcEmbed-perl, php, cgi-bin scripts, jdbcAdvantages: SecurityAdvantages: SecurityDisadvantages: ComplexityDisadvantages: Complexity

november 3, 2001ictcm conference1 applied calculus on the web applets & applications professor...

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