Enriching Teaching with Technology
Oliver Knill
11/8/2003, draft
Abstract
Here are some general thoughts about the use of technology in the classroom. This is a working draft.
Variety for learning
Learning works best when many different channels are used.
Lectures in Classes sometimes with demonstrationsReading textbook, handouts usually done in privateHomework assignments usually from bookComputer based quizzes QA tool, ”webwork” etc.Online activities for example with Java appletsQuestion Center in public location, CA/TF staffedOnline Question Center www.math.harvard.eduElectronic voting system Project Galileo at HarvardLabs using technology Mathematica computer algebra projectsProblem sessions by course assistantsMeeting with instructors office hours
The use of technology provides many opportunities to enhance a lecture. How it is done depends of course personalpreferences and taste.
Available Technology
I) CAS systems
• Mathematica
• Maple
• Matlab
• Mathcad
• Macsyma
II) Problem Solving
• Webwork
• Multiple Choice quizzes
• Electronic Voting systems
• Gateway exams
III) Webpages
• Javascript interactive pages
• Dynamic HTML
• Java applets
• Flash pages
IV) Multimedia
• Graphics
• Movies
• Animations
• Slideshows
V) Databases
• Online Encyclopedias
• Online Courses
• Databases of problems
• Chatbots
VI) Communication
• Email, ICQ
• Course Websites
• Online Discussions
• Taped lectures online
• Electronic conferences
1
Pitfalls in using technology
The question, how a teacher should enrich class room experience is difficult. It is easier to list some pitfalls.
I) Technological challenges
Technology should not be used forthe sake of using technology. Pit-falls:
• teacher is not comfortablewith technology
• cable forgotten, projectorcompatibility not tested.
• application crashes, machineneeds to reboot.
• projector needs adjustments,i.e. picture not sharp.
• overhead projector using slideswhich are unreadable
II) Illustrating the obvious.
Enrichment which focus on simplis-tic concepts only offend the intelli-gent mind. Examples:
• Applets illustrating the ”rateof change” using the tangent.
• Interactive matrix multiplica-tion
• Animating the Riemann sum
• Animating a function liketraveling wave
III) Overuse
Too much technology can be likeadding too much salt to a wellprepared dish.
• A teacher is proud about aspecific software program andspends time explaining the in-ner details of it.
• Online problems which areroutine and boring and of thesame multiple choice type.
• Students sit behind computersin classrooms. No class-timeleft to cover essential material.
IV) Too much Complexity
A in class or online demonstrationshould be memorable, fun and stilleasy to use.
• Assignments in CAS, whichneed serious programmingfrom the student.
• Assignments which challengethe CPU of the computer toomuch and don’t run on oldermachines.
• Assignments with unnaturalproblems.
• Assignements requiring toomuch background knowledge.
V) Big brother
Technology can be used to gaugeand monitor the learning progress ofstudents.
• Monitored online homework isas stressful as an exam.
• Computer security is known tobe lax at educational institu-tions.
• Students fear that scores areused for grades and letter ofrecommendations.
VI) Laziness
Technology can enhance but not re-place the direct student-teacher in-teraction. Pitfalls:
• Using technology to save hu-man resources.
• Automated grading does notreveal key obstacles.
• Series of lectures in power-point format.
• Too much information onoverhead.
• Reusing problems for exams.
VII) Lack of time to prepare
Preparing a class using technology needs lots of time
• Testing equipment and program before class.
• Having alternative in case of failure
• Embed the module with didactic merit
• Try out many many things and throw what doesnot work.
VIII) Outdated/emerging technology
Languages for the web like SVG,VRML,AIML,MathML, Flash are evolving and changing.
• Emerging not yet fully standardized technologydoes not yet work.
• Older technology is often no more supported.
• Even simple programs need attendance.
Department of MathematicsOne Oxford StreetHarvard UniversityCambridge, MA 02138
email: [email protected]: (617) 495-5549fax: (617) 495-5132url: www.math.harvard.edu/ k̃nill
2
Interactive examples
Interactive Flash Example
The shown example from the center of technologyand teacher education is quite useful. It allows thestudent to experiment a bit get the idea for Rollestheorem. Flash works pretty well on all browsers.Disadvantages are that one needs proprietary soft-ware on limited operating systems to develop thecode.
Interactive Javascript Example
Simple javascript programming can be quite effectiveto do simple things. The example allows students toplay with Gausss-Jordan elimination.
Interactive Java Example
Java is widely used in educational pages. Unfortu-nately, certain combinations of browsers and Javaversions do not work properly. This example allowsstudents to measure the area of simple regions usingthe planimeter.
Interactive Virtual Reality Example
Virtual reality allows to explore surfaces and objectsby moving around in a virtual world. It is effectivefor demonstrations in class. There are plug-ins forVRL for most browsers.
3
Multimedia examples
Presentation software
Presentation software like Power-point or Keynoteare suitable for introduction meetings or reviews. Us-ing presentation software for lectures is dangerousbecause the teacher does no more see the need todevelop the thoughts and is in general too fast. Onesees this often in conferences.
Quicktime Video
Here is the example of a movie published 1995 bythe geometry center. It is originally published inthe quicktime. In order that one can see the movieon every platform, one has to place the movie indifferent formats.
Other Video Formats
The same movie embedded into a flash movie or con-verted to the avi format. The flash version is a fifthof the size and viewable on any browser. The avi sizeis of less quality and a 10’th of the original movie.
Slideshow
The web browser is a decent presentation softwaretoo. It can be used for example to present an exhibitof graphics.
4
Interactive Problems
Online Quizzes
Multiple Choice quizzes, which are graded instanta-neously are easy to build and maintain, work. Stu-dents like them.
Online Homework
Webwork is an internet based method for deliv-ering homework problems over the internet. Stu-dents get instant feedback and progress can be mon-itored. Webwork was developed at the University ofRochester.
Diagnostic Tests
Internet based diagnostic tests are of similar formthe above two examples. In this case, students haveto do the test supervised.
5
Online resources
Just a few examples
Connected Curriculum Project
One of the best collection of interactivelearning materials is the CCP project.http://www.math.duke.edu/education/ccp/
Mathworld
One of the best collection of online knowledge withsometimes interactive demonstrations is Mathworld.
Mactutor
One of the best collection of articles on Mathhistory and Biography is the Mac Tutor His-tory of Mathematics archive http://turnbull.mcs.st-and.ac.uk/history/.
6
Computer algebra systems
Just three examples. The highest obstacle for a student in all CAS systems is to learn the graphics user interface(GUI), which are often confusingly built, unstable and too complex.
Mathematica
Mathematica is one of the best CAS for beginners.
Matlab
Matlab has the possibility to build nice interfacesand is strong in linear algebra.
Maple
Maple is similar to the above mentioned CAS. It isalso widely used at many places.
7
Interfaces
A Chatterbot which knows math and can access CASsystems is in development by a project supported bythe Provost at Harvard.
8
Top Related