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: 798954
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Slide1
LON-CAPAMathematical Functionality
Gerd Kortemeyer
Lyman Briggs College
February 2011
Slide2LON-CAPA Math Functionality
Today’s Session:
somewhat
specialized topicGoal:demonstrate how mathematical assessment is integrated into theLON-CAPA course management functionality
Slide3LON-CAPA Course Management
Full featured course management system
Discussions
Drop boxes
MSU integration
Messaging
Statistics
Slide4LON-CAPA Course Management
Structured Content
Embedded Assessment
Contextual Discussions
Time Management
Slide5LON-CAPA Course Management
Shared Learning Content Management
Slide6Particular Strength: Assessment
Randomized problems: different
numbers
formulasgraphsimagesoptions… for each student.
Student can collaborate without “cheating”
Randomized exams
Slide7LON-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
in
Slide8WARNING
Today’s presentation is going to show some very specialized functionality.
Because you can does not mean you have to.
Slide9Mathematical Output
Typesetting:
LaTeX
can be embedded anywhere in the material
Slide10Mathematical Output
Editor for non-native
LaTeX
speakers
Slide11Mathematical Output
Generated on-the-fly, can vary from student to student.
Slide12Mathematical Output
<algebra>-tag to pretty-print the output from computer algebra systems
Example:
$formula=“a*x^5”
Slide13Mathematical Output
One-source, multiple target
Looks good in print
Online:Print (dynamically generated PDF):
Slide14Mathematical Output
Dynamic Graphing
Data-Points
FunctionsLine-GraphicsInternally usesGNUplot
Slide15Mathematical Output
Data points
Slide16Mathematical Output
Data points
Slide17Mathematical Output
Functions
Slide18Mathematical Output
Line graphics
Slide19Generating Mathematics Problems
LON-CAPA problems include
Perl Scripting Environment
MAXIMA Computer Algebra SystemR Statistics PackageProblems not just randomized,but randomly generated with desired properties
Slide20Generating Mathematics Problems
Direct calls to MAXIMA:
$result=&
cas(‘maxima’,$expression);Simple example: use computer algebra system to calculate a reduced fraction
Slide21Generating Mathematics Problems
Direct calls to R:
$result=&
cas(‘R’,$expression);$results=&cas_hashref(‘R’,$expression);Example: generate a distribution with certain properties:
Slide22Mathematics Input
Simplest input: numerical
Slide23Mathematics Input
Sampling – approximate function
Slide24Mathematics Input
Symbolically: exactly one exact answer (but equivalent forms)
Slide25Mathematical Input
Checking properties
Using R:
Slide26Mathematical Input
Checking properties
Using MAXIMA:
Slide27Mathematical Input
Checking properties
Using Perl and MAXIMA:
Slide28Mathematical Input
Math editor for students
Slide29Mathematical Input
Graphical input
using
Geogebra
Slide30Mathematical Input
Rulesets
Function
First Derivative
Second Derivative
Integral
Symbolic, computed, or hard-coded ranges
Slide31Mathematical Input
Problems can also be rendered for bubble
sheets
Every student gets a
different version
Slide32Mathematical Input
Slide33Mathematical Input
Slide34Mathematical Input
Slide35Mathematical Input
Numerical Clicker
in Lecture
Slide36Mathematical Input
LON-CAPA can evaluate clicker data after lecture
Slide37Mathematical Input
Slide38Mathematical Input
i
>clicker2 integrated in LON-CAPA
Slide39Interested?
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 June
Slide40Thank You
Gerd Kortemeyer
Lyman Briggs College
andDivision of Science and Mathematics Educationkorte@lite.msu.eduhttp://www.lon-capa.org/