Mathematical Functionality Gerd Kortemeyer Lyman Briggs College February 2011 LONCAPA Math Functionality Todays Session somewhat specialized topic Goal demonstrate how mathematical assessment is integrated into the ID: 541655
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Slide1
LON-CAPAMathematical Functionality
Gerd Kortemeyer
Lyman Briggs College
February 2011 Slide2
LON-CAPA Math Functionality
Today’s Session:
somewhat
specialized topicGoal:demonstrate how mathematical assessment is integrated into theLON-CAPA course management functionalitySlide3
LON-CAPA Course Management
Full featured course management system
Discussions
Drop boxes
MSU integration
Messaging
StatisticsSlide4
LON-CAPA Course Management
Structured Content
Embedded Assessment
Contextual Discussions
Time ManagementSlide5
LON-CAPA Course Management
Shared Learning Content ManagementSlide6
Particular Strength: Assessment
Randomized problems: different
numbers
formulasgraphsimagesoptions… for each student.
Student can collaborate without “cheating”
Randomized examsSlide7
LON-CAPA Mathematics
Mathematics Output:
typesetting
graphingGenerating Mathematics Problems:symbolic math functionalitystatistics packagesMathematics Input:
numerical
formula evaluation
sampling
symbolically
checking for propertiesgraphical inputbubble sheetsclickers
The grader is
inSlide8
WARNING
Today’s presentation is going to show some very specialized functionality.
Because you can does not mean you have to.Slide9
Mathematical Output
Typesetting:
LaTeX
can be embedded anywhere in the materialSlide10
Mathematical Output
Editor for non-native
LaTeX
speakersSlide11
Mathematical Output
Generated on-the-fly, can vary from student to student.Slide12
Mathematical Output
<algebra>-tag to pretty-print the output from computer algebra systems
Example:
$formula=“a*x^5” Slide13
Mathematical Output
One-source, multiple target
Looks good in print
Online:Print (dynamically generated PDF):Slide14
Mathematical Output
Dynamic Graphing
Data-Points
FunctionsLine-GraphicsInternally usesGNUplotSlide15
Mathematical Output
Data pointsSlide16
Mathematical Output
Data pointsSlide17
Mathematical Output
FunctionsSlide18
Mathematical Output
Line graphicsSlide19
Generating Mathematics Problems
LON-CAPA problems include
Perl Scripting Environment
MAXIMA Computer Algebra SystemR Statistics PackageProblems not just randomized,but randomly generated with desired propertiesSlide20
Generating Mathematics Problems
Direct calls to MAXIMA:
$result=&
cas(‘maxima’,$expression);Simple example: use computer algebra system to calculate a reduced fractionSlide21
Generating Mathematics Problems
Direct calls to R:
$result=&
cas(‘R’,$expression);$results=&cas_hashref(‘R’,$expression);Example: generate a distribution with certain properties:Slide22
Mathematics Input
Simplest input: numericalSlide23
Mathematics Input
Sampling – approximate functionSlide24
Mathematics Input
Symbolically: exactly one exact answer (but equivalent forms)Slide25
Mathematical Input
Checking properties
Using R:Slide26
Mathematical Input
Checking properties
Using MAXIMA:Slide27
Mathematical Input
Checking properties
Using Perl and MAXIMA:Slide28
Mathematical Input
Math editor for studentsSlide29
Mathematical Input
Graphical input
using
GeogebraSlide30
Mathematical Input
Rulesets
Function
First Derivative
Second Derivative
Integral
Symbolic, computed, or hard-coded rangesSlide31
Mathematical Input
Problems can also be rendered for bubble
sheets
Every student gets a
different versionSlide32
Mathematical InputSlide33
Mathematical InputSlide34
Mathematical InputSlide35
Mathematical Input
Numerical Clicker
in LectureSlide36
Mathematical Input
LON-CAPA can evaluate clicker data after lectureSlide37
Mathematical InputSlide38
Mathematical Input
i
>clicker2 integrated in LON-CAPASlide39
Interested?
Faculty Seminars
May 10-11, 2011
Can give departmental colloquiaWork one-on-oneLON-CAPA ConferenceVirginia Commonwealth University May 19-21, 2011LON-CAPA Workshop
MSU, late JuneSlide40
Thank You
Gerd Kortemeyer
Lyman Briggs College
andDivision of Science and Mathematics Educationkorte@lite.msu.eduhttp://www.lon-capa.org/