lon-capa mathematical functionality

LON-CAPAMathematical FunctionalityGerd KortemeyerExplorations in Instructional TechnologyBrownbag SeminarFebruary 2011

LON-CAPA Math FunctionalityToday’s Session:

somewhatspecialized topic

Goal:demonstrate how mathematical assessment is integrated into theLON-CAPA course management functionality

LON-CAPA Course Management

Full featured course management system

DiscussionsDrop boxes

MSU integration

MessagingStatistics

LON-CAPA Course Management

Structured Content

Embedded Assessment

Contextual Discussions

Time Management

LON-CAPA Course ManagementShared Learning Content

Management

Particular Strength: AssessmentRandomized problems: different

◦numbers◦formulas◦graphs◦ images◦options◦…for each student.

Student can collaborate without “cheating”

Randomized exams

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

WARNINGToday’s presentation

is going to show some very specialized

functionality.Because you can does

not mean you have to.

Mathematical OutputTypesetting:

LaTeX can be embedded anywhere in the material

Mathematical OutputEditor for non-native LaTeX

speakers

Mathematical OutputGenerated on-the-fly, can vary

from student to student.

Mathematical Output<algebra>-tag to pretty-print the

output from computer algebra systems

Example: $formula=“a*x^5”

Mathematical OutputOne-source, multiple targetLooks good in print

◦Online:

◦Print (dynamically generated PDF):

Mathematical OutputDynamic Graphing

◦Data-Points◦Functions◦Line-Graphics

Internally usesGNUplot

Mathematical OutputData points

Mathematical OutputData points

Mathematical OutputFunctions

Mathematical OutputLine graphics

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

Generating Mathematics ProblemsDirect calls to MAXIMA:

$result=&cas(‘maxima’,$expression);

Simple example: use computer algebra system to calculate a reduced fraction

Generating Mathematics ProblemsDirect calls to R:

$result=&cas(‘R’,$expression);$results=&cas_hashref(‘R’,$expression);

Example: generate a distribution with certain properties:

Mathematics Input

Simplest input: numerical

Mathematics Input

Sampling – approximate function

Mathematics Input

Symbolically: exactly one exact answer (but equivalent forms)

Mathematical InputChecking properties

◦Using R:

Mathematical InputChecking properties

◦Using MAXIMA:

Mathematical InputChecking properties

◦Using Perl and MAXIMA:

Mathematical InputGraphical

inputusing

Geogebra

Mathematical InputRulesets Function

First DerivativeSecond Derivative

Integral

Symbolic, computed, or hard-

coded ranges

Mathematical InputProblems can also be rendered for

bubble sheetsEach student has a different exam

Mathematical Input

Mathematical Input

Mathematical Input

Mathematical InputNumerical Clickerin Lecture

Mathematical InputLON-CAPA can evaluate clicker data after lecture

Mathematical Input

Mathematical Inputi>clicker2

integrated in LON-CAPA

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

Thank YouGerd KortemeyerLyman Briggs College

andDivision of Science and Mathematics

Educationkorte@lite.msu.eduhttp://www.lon-capa.org/