lon-capa mathematical functionality
DESCRIPTION
LON-CAPA Mathematical Functionality. Gerd Kortemeyer Explorations in Instructional Technology Brownbag Seminar February 2011 . LON-CAPA Math Functionality. Today’s Session: somewhat specialized topic - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/1.jpg)
LON-CAPAMathematical FunctionalityGerd KortemeyerExplorations in Instructional TechnologyBrownbag SeminarFebruary 2011
![Page 2: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/2.jpg)
LON-CAPA Math FunctionalityToday’s Session:
somewhatspecialized topic
Goal:demonstrate how mathematical assessment is integrated into theLON-CAPA course management functionality
![Page 3: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/3.jpg)
LON-CAPA Course Management
Full featured course management system
DiscussionsDrop boxes
MSU integration
MessagingStatistics
![Page 4: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/4.jpg)
LON-CAPA Course Management
Structured Content
Embedded Assessment
Contextual Discussions
Time Management
![Page 5: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/5.jpg)
LON-CAPA Course ManagementShared Learning Content
Management
![Page 6: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/6.jpg)
Particular Strength: AssessmentRandomized problems: different
◦numbers◦formulas◦graphs◦ images◦options◦…for each student.
Student can collaborate without “cheating”
Randomized exams
![Page 7: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/7.jpg)
LON-CAPA MathematicsMathematics Output:
◦ typesetting◦ graphing
Generating Mathematics Problems:◦ symbolic math functionality◦ statistics packages
Mathematics Input:◦ numerical◦ formula evaluation
sampling symbolically checking for properties
◦ graphical input◦ bubble sheets◦ clickers
The grader is in
![Page 8: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/8.jpg)
WARNINGToday’s presentation
is going to show some very specialized
functionality.Because you can does
not mean you have to.
![Page 9: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/9.jpg)
Mathematical OutputTypesetting:
LaTeX can be embedded anywhere in the material
![Page 10: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/10.jpg)
Mathematical OutputEditor for non-native LaTeX
speakers
![Page 11: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/11.jpg)
Mathematical OutputGenerated on-the-fly, can vary
from student to student.
![Page 12: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/12.jpg)
Mathematical Output<algebra>-tag to pretty-print the
output from computer algebra systems
Example: $formula=“a*x^5”
![Page 13: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/13.jpg)
Mathematical OutputOne-source, multiple targetLooks good in print
◦Online:
◦Print (dynamically generated PDF):
![Page 14: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/14.jpg)
Mathematical OutputDynamic Graphing
◦Data-Points◦Functions◦Line-Graphics
Internally usesGNUplot
![Page 15: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/15.jpg)
Mathematical OutputData points
![Page 16: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/16.jpg)
Mathematical OutputData points
![Page 17: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/17.jpg)
Mathematical OutputFunctions
![Page 18: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/18.jpg)
Mathematical OutputLine graphics
![Page 19: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/19.jpg)
Generating Mathematics ProblemsLON-CAPA problems include
◦Perl Scripting Environment◦MAXIMA Computer Algebra System◦R Statistics Package
Problems not just randomized,but randomly generated with desired properties
![Page 20: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/20.jpg)
Generating Mathematics ProblemsDirect calls to MAXIMA:
$result=&cas(‘maxima’,$expression);
Simple example: use computer algebra system to calculate a reduced fraction
![Page 21: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/21.jpg)
Generating Mathematics ProblemsDirect calls to R:
$result=&cas(‘R’,$expression);$results=&cas_hashref(‘R’,$expression);
Example: generate a distribution with certain properties:
![Page 22: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/22.jpg)
Mathematics Input
Simplest input: numerical
![Page 23: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/23.jpg)
Mathematics Input
Sampling – approximate function
![Page 24: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/24.jpg)
Mathematics Input
Symbolically: exactly one exact answer (but equivalent forms)
![Page 25: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/25.jpg)
Mathematical InputChecking properties
◦Using R:
![Page 26: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/26.jpg)
Mathematical InputChecking properties
◦Using MAXIMA:
![Page 27: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/27.jpg)
Mathematical InputChecking properties
◦Using Perl and MAXIMA:
![Page 28: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/28.jpg)
Mathematical InputGraphical
inputusing
Geogebra
![Page 29: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/29.jpg)
Mathematical InputRulesets Function
First DerivativeSecond Derivative
Integral
Symbolic, computed, or hard-
coded ranges
![Page 30: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/30.jpg)
Mathematical InputProblems can also be rendered for
bubble sheetsEach student has a different exam
![Page 31: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/31.jpg)
Mathematical Input
![Page 32: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/32.jpg)
Mathematical Input
![Page 33: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/33.jpg)
Mathematical Input
![Page 34: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/34.jpg)
Mathematical InputNumerical Clickerin Lecture
![Page 35: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/35.jpg)
Mathematical InputLON-CAPA can evaluate clicker data after lecture
![Page 36: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/36.jpg)
Mathematical Input
![Page 37: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/37.jpg)
Mathematical Inputi>clicker2
integrated in LON-CAPA
![Page 38: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/38.jpg)
Interested?Faculty Seminars
May 10-11, 2011Can give departmental colloquiaWork one-on-oneLON-CAPA Conference
Virginia Commonwealth UniversityMay 19-21, 2011
LON-CAPA WorkshopMSU, late June
![Page 39: LON-CAPA Mathematical Functionality](https://reader036.vdocuments.us/reader036/viewer/2022062520/56816069550346895dcf9312/html5/thumbnails/39.jpg)
Thank YouGerd KortemeyerLyman Briggs College
andDivision of Science and Mathematics
[email protected]://www.lon-capa.org/