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November
3
,
2001

ICTCM Conference

1

Applied Calculus on the Web

Applets & Applications

Professor Michael S. Pilant

Department of Mathematics

Texas A&M University


November 3, 2001

ICTCM Conference

2

Applied Calculus on the Web

Applets & Applications



Background


Teaching


Training


Exploration


Assessment

November 3, 2001

ICTCM Conference

3

Applied Calculus on the Web

Applets & Applications



Background


Finite Math on the Web

Project




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

November 3, 2001

ICTCM Conference

4

Applied Calculus on the Web

Applets & Applications



Background


Enrollments in 2000


Finite Math
-

Math 166


2,152 students


Business Math
-

Math 141


5,728 students


Applied Calculus

-

Math 142


4,054 students


Total = 11,934

November
3
,
2001

ICTCM Conference

5

Applied Calculus on the Web

Applets & Applications



Background


Enrollments in
2001


Finite Math
-

Math
166


2
,
070
students


Business Math
-

Math
141


5
,
735
students


Applied Calculus

-

Math
142


3
,
813
students


Total =
11
,
618

November 3, 2001

ICTCM Conference

6

Applied Calculus on the Web

Applets & Applications



Background



Use
Finite Math on the Web



as a model for


Applied Calculus on the Web

November
3
,
2001

ICTCM Conference

7

Applied Calculus on the Web

Applets & Applications



Overall Design Considerations


Initial use


to illustrate a concept, allow limited
interaction
-

teaching


Reinforcement of concepts


feedback, allow more
interaction
-

training


Exploration



full functionality and interaction


Assessment



checkpoint for students and/or instructors

November 3, 2001

ICTCM Conference

8

Applied Calculus on the Web

Applets & Applications



Teaching


Finite Math on the Web


Topical

Counting and Probability,

Conditional Probability,

Statistics,

Probability Distributions,

Financial Applications

Lines and Slopes,

Least Squares,

Matrices,

Linear Programming,

Sets,

November 3, 2001

ICTCM Conference

9

Applied Calculus on the Web

Applets & Applications



Teaching


Applied Calc on the Web


Sequential

Function Behavior,

Optimization,

Integration,

Area,

Multi
-
variable Applications

Polynomial Functions,

Logarithmic and
Exponential Functions,

Limits and Continuity,

Rates of Change,

Rules of Differentiation,

November 3, 2001

ICTCM Conference

10

Applied Calculus on the Web

Applets & Applications



Teaching


(Re
-
)Introduce basic concepts, for example:


Graph of a function


Intercepts (roots)


Intersections between curves


Maximum, minimum


Definitions of slope

November
3
,
2001

ICTCM Conference

11

Applied Calculus on the Web

Applets & Applications



Teaching


Initially, the applets should have very
simple “look and feel.”


Respond to mouse click and drag


Open with an image (or data) appropriate to
context

November 3, 2001

ICTCM Conference

12

Applied Calculus on the Web

Applets & Applications


Basic Applet


Plots a function


set by HTML

<param> flag


November
3
,
2001

ICTCM Conference

13

Applied Calculus on the Web

Applets & Applications


Basic Applet


Zoom in

Rescale coordinates


November 3, 2001

ICTCM Conference

14

Applied Calculus on the Web

Applets & Applications


Basic Applet


Select function

Show coordinates

November 3, 2001

ICTCM Conference

15

Applied Calculus on the Web

Applets & Applications


Basic Applet


Show axes

Show grid


set by HTML

<param> flag

November 3, 2001

ICTCM Conference

16

Applied Calculus on the Web

Applets & Applications



Training


Subsequently, the applet is used in such a
way as to reinforce basic concepts and
algorithms


Zooming in and out becomes proceduralized

November 3, 2001

ICTCM Conference

17

Applied Calculus on the Web

Applets & Applications


Basic Applet


Show plot tools


set by HTML

<param> flag

November 3, 2001

ICTCM Conference

18

Applied Calculus on the Web

Applets & Applications


Basic Applet


Zoom in

Zoom out

Show/Hide Axes

Show/Hide Grid

Reset



November
3
,
2001

ICTCM Conference

19

Applied Calculus on the Web

Applets & Applications


Basic Applet


Show function

Tools


set by HTML

<param> flag

November 3, 2001

ICTCM Conference

20

Applied Calculus on the Web

Applets & Applications


Basic Applet


Enter function

Plot function

Show secant

Show tangent

Clear

November 3, 2001

ICTCM Conference

21

Applied Calculus on the Web

Applets & Applications



Exploration


Once the basic concepts and processes
become familiar, students can explore


Apply concepts to new situations (domains)

November 3, 2001

ICTCM Conference

22

Applied Calculus on the Web

Applets & Applications

Investigating

limits of

Functions (e.g.

x*(sin(1/x))


November
3
,
2001

ICTCM Conference

23

Applied Calculus on the Web

Applets & Applications



Assessment


In order to provide feedback to the
instructor (and to the student!) some type of
assessment is required.

November 3, 2001

ICTCM Conference

24

Applied Calculus on the Web

Applets & Applications



Assessment


Basic (declarative) knowledge


Multiple choice, instant feedback


Algorithmic (procedural) knowledge


Multiple choice, short answer


Problem solving (strategic knowledge)


Workout, multi
-
step, applet based

November
3
,
2001

ICTCM Conference

25

Applied Calculus on the Web

Applets & Applications



Assessment


In order to provide meaningful assessment,
we require the applet to


Communicate with the browser via HTML
<param> …</param> tags


Allow communication via JavaScript through
public functions

November 3, 2001

ICTCM Conference

26

Applied Calculus on the Web

Applets & Applications


<applet name=“myApplet” …>




<param name="background_color" value="ffffff">

<param name="xmin" value="
-
2.0">

<param name="xmax" value="2.0">

<param name="ymin" value="
-
2.0">

<param name="ymax" value="2.0">

<param name="function" value="sin(x)">

<param name="show_grid" value="true">

<param name="show_axes" value="true">

<param name="show_plot_tools" value="true">

<param name="show_function_tools" value="true">

</applet>

Integration with HTML

November 3, 2001

ICTCM Conference

27

Applied Calculus on the Web

Applets & Applications

<script language="JavaScript">


function showSelection(){


var str = document.myApplet.plot2d.getSelectedObjectType();


document.myForm.object.value = str;


}

</script>




<form name=myForm>

<input type=button value="selected object"


onClick="showSelection();">

<input name="object" type=text size=30>

</form>

Communication with JavaScript/Forms

November 3, 2001

ICTCM Conference

28

Applied Calculus on the Web

Applets & Applications

Communication

with Scripts


November
3
,
2001

ICTCM Conference

29

Applied Calculus on the Web

Applets & Applications

Intersections

between two

curves (e.g.

sin(x), cos(x))


November 3, 2001

ICTCM Conference

30

Applied Calculus on the Web

Applets & Applications

Finding the slope

of the tangent

to a curve


November
3
,
2001

ICTCM Conference

31

Applied Calculus on the Web

Applets & Applications

Finding curve

based on a

formula


November 3, 2001

ICTCM Conference

32

Applied Calculus on the Web

Applets & Applications


Assessment methods using applets


JavaScript (client
-
side)


Cgi
-
bin scripts (client
-
server)


Assessment built into applet


Cookies


Databases


MySQL, PostgreSQL

November 3, 2001

ICTCM Conference

33

Applied Calculus on the Web

Applets & Applications


JavaScript example


// Answer to Q
10
is x=
55
/
102
=
0.539
and p=
745
/
306
=
2.43

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

// allow
2.43
or
2.44
as answer

// must encode this answer!

function checkAnswerQ
10
() {


var x = deleteSpaces( document.myform.Q
10
x.value )


var p = deleteSpaces( document.myform.Q
10
p.value )


}

November 3, 2001

ICTCM Conference

34

Applied Calculus on the Web

Applets & Applications


JavaScript example

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



Tried[9] = "Incorrect"



alert( "Watch your units!" );


}


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



Tried[9] = "Correct"


}


else



Tried[9] = "Incorrect"



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


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

November
3
,
2001

ICTCM Conference

35

Applied Calculus on the Web

Applets & Applications


Cgi
-
bin scripts


<form name=“myForm” method=“Post”


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






<input type=hidden name=“var
1
” value=val
1
>






</form>

November 3, 2001

ICTCM Conference

36

Applied Calculus on the Web

Applets & Applications


Cgi
-
bin scripts


<script language=“JavaScript”>







document.myform.action=




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



document.myform.submit( );






</script>

November
3
,
2001

ICTCM Conference

37

Applied Calculus on the Web

Applets & Applications


Assessment built into applet

1.
Data encoded into applet is very secure

2.
Parametrically generate problems from built in
templates

3.
Specialized grading and evaluation algorithms
can be built into applet

Example:
Venn Diagrams


November 3, 2001

ICTCM Conference

38

Applied Calculus on the Web

Applets & Applications


Cookies




function setCookie (name, value) {


var str;


if (value != null)


str = name + "=" + escape(value);


var now = new Date()


var nowplus1 = now.getTime() + (52*7*24*60*60*1000)


now.setTime(nowplus1)


str += top.cookieString;


str += ";expires="+now.toGMTString();

document.cookie = str+";";

}

November
3
,
2001

ICTCM Conference

39

Applied Calculus on the Web

Applets & Applications


Cookies


function getCookie(name) {


var cookie = " " + document.cookie;


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


var setStr = null;


var offset =
0
;


var end =
0
;



November 3, 2001

ICTCM Conference

40

Applied Calculus on the Web

Applets & Applications


Cookies




if (cookie.length > 0) {


offset = cookie.indexOf(search);


if (offset !=
-
1) {


offset += search.length;


end = cookie.indexOf(";", offset)


if (end ==
-
1) { end = cookie.length; }


setStr = unescape(cookie.substring(offset,
end));


}


}


return(setStr);

}

November 3, 2001

ICTCM Conference

41

Applied Calculus on the Web

Applets & Applications


Databases



Simple


file systems on server


Cookies


on client


SQL


MySQL, Access, SQL Server,
PostgreSQL, …


Connect via


Embed
-
perl, php, cgi
-
bin scripts, jdbc

Advantages: Security

Disadvantages: Complexity