A Collection of Java Websites to Support Mathematics Education
An Article on the Use of Java Applets in Mathematics Education
| Uses of Java Applets in Mathematics Education | http://www.utc.edu/~cpmawata/instructor/tsukuba1.htm |
| A very readable overview of how Java applets can be used to
enhance instruction in the mathematics classroom. The author is Chris Mawata, who visited
Brisbane last year, and attended QAMT’s 75th anniversary dinner. |
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Archive Sites - Lots of Applets!
| Manipula Maths Collection | http://www.ies.co.jp/math/java/iesjava.html-ssi |
| One hundred and fifty eight applets, all
mathematical, from middle school to university. These applets are slick, and load very
fast. You hardly need to go past this site to view the best applets to support mathematics
education. There is a file containing nine applets that you can download. |
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| JARS | http://jars.developer.com/ |
| The Java Applet Review Service. Click on Search,
and type in your category. The applets are rated – top 1%, top 5%, top 25%. |
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| Educational Object Economy | http://209.249.14.50/index.html |
| A large collection of Java applets. Select Search
for Applets, type in your category, and click on [Search]. |
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| Developer.Com | http://www.developer.com/directories/pages/dir.java.educational.math.html |
| A website with over 200 Java applets for Maths
education, from lower primary to tertiary level. |
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Number
| A Simple Calculator | http://www.geocities.com/SiliconValley/7676/calculator.html |
| This isn’t actually a Java applet, but it is a handy
little 4 function calculator that loads quickly. |
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| The Big Calculator | http://www.geocities.com/SiliconValley/2548/BigCalculator.html |
| Set the precision to as many decimal places as you wish. So
you can show students, for example, that 1/97 is repeating decimal, with a period of 96.
Or find pi to 2000 decimal places (it takes about 30 seconds). |
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| The Game of Nim | http://www.csm.astate.edu/Nim.html |
| Nim is a classic game of logic. Except, if you know the
secret, you can usually win! And, surprisingly, the secret is based on binary arithmetic. |
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| Fractions – The Patterns Program | http://www.best.com/~ejad/java/patterns/patterns_d.shtml |
| A Java implementation of Pattern Blocks, which are common
manipulatives for introducing fractions and fraction operations. The site includes
instructions on how to use the applet, and exercises and activities for the students. |
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| Napier’s Bones | http://www.cut-the-knot.com/blue/Napier.html |
| A fast-loading Java implementation of this ancient
calculating device. One feature is that you can choose bases other than 10. The topic is
best taught with manipulatives, but this would be either a nice introduction to the topic,
or an interesting way to wrap up the unit at the end. |
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| Calendar Magic | http://www.cut-the-knot.com/SimpleGames/Calendar.html |
| Presents an interesting puzzle, based around a calendar. The
puzzle can be presented to students using an actual calendar, though the website does
allow the user to choose the month and the year. |
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| Eleven Times | http://www.learningkingdom.com/eleven/ http://www.LearningKingdom.com/five/ |
| I’ve always enjoyed mental arithmetic tricks. The first
URL is a very nice implementation of mentally multiplying by 11, while the second presents
a method of squaring numbers that end in 5. |
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| JavaSlide – A Java Slide Rule | http://www.comcen.com.au/~adavie/javaslide/javaslide.html |
| A slide rule is useful as a calculator, for example
multiplying 2 x 3, but the mathematics underlying its construction means it is even more
useful in the study of logarithms. If you have tossed yours out, well, here is a very good
Java implementation. And it even looks like my old slide rule. |
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Number Patterns and Algebra
| Traffic Jam | http://forum.swarthmore.edu/~morton/java/jam/Jam.html |
| Traffic Jam is a puzzle in which people try to
swap places following certain proscribed rules. It is best solved using real people, or
manipulatives, but for those that prefer it, the above URL is a Java implementation of the
game. The instructions can be found at http://forum.swarthmore.edu/workshops/sum96/traffic.jam.html. |
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| The Sum of the First N Numbers | http://www.cut-the-knot.com/ctk/pww.html |
| A "proof without words" that the sum of
the first N whole number is given by N(N+1)/2. This can be done with coins on an overhead
projector, but the Java implementation is fast and colourful. |
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| Math in the Kingdom demonstration | http://www.learningkingdom.com/math/demo/ |
| This is an interesting site from two viewpoints
– it is a demonstration of a commercial site that uses Java as its teaching engine,
and it is a very slick bit of programming that shows what is possible with Java. It is
probably a good example of the direction that on-line tuition is heading. The applets are
large, and take quite a while to load. |
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| Line Graphs | http://www.idbsu.edu/people/jbrennan/algebra/lines/graph_applet.html |
| The Graphing Applet allows students to move a
linear graph with their mouse, and see the effects of their actions on the y=mx
+ c rule. This is "backwards" from a graphing calculator where they
change the y=mx+b rule, and see changes happen to the graph. |
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| An Eye-Opener | http://www.cut-the-knot.com/pythagoras/tricky.html |
| A puzzle that can be used to introduce or
reinforce the fact that (n+1)(n-1) = n2 –1. Or maybe it is just a nifty
puzzle. |
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| PAT Online | http://domino.psy.cmu.edu/patonline.html |
| A Java implementation of an intelligent algebra
problem tutoring system being developed at Carnegie-Mellon University. The web interface
is quite slow, but the project has great potential, and it is worth the wait. |
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| Pascal’s Triangle | http://www.cs.washington.edu/homes/jbaer/classes/blaise/blaise.html |
| Pascal’s Triangle is rich in patterns. This
applet generates some fractal patterns that can be found in the triangle. A very useful
applet when studying modulo arithmetic. |
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Geometry
| Angles and Parallel Lines | http://www.ies.co.jp/math/java/angle.html | ||
| Six applets on this topic, and all very good.
Find the angle sum of a triangle, and the sum of the exterior angles of a polygon, and
more. |
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| Quadrilaterals and Conservation of Area | http://www.ies.co.jp/math/java/quadri.html | ||
| There are some interesting applets in this
collection of 10 applets. Changing Border Line is a good example of an applet that
should only be used after students have tackled the problem themselves. |
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| Similar Figures | http://www.ies.co.jp/math/java/similar.html | ||
| The Pantagraph is my personal favourite, from
this collection of nine applets |
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| Miscellaneous | http://www.ies.co.jp/math/java/geomisc.html | ||
| The Solid of Solomon is a delightful diversion. |
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| Pythagoras’ Theorem | http://www.ies.co.jp/math/java/pythagoras.html | ||
| How many ways do you have to prove
Pythagoras’ Theorem before the kids say, ‘Enough already! I believe it!"
Will eight visual proofs be enough? My favourite is the applet simply labelled Pythagorean
Theorem. Also check out rhe Pythagorean Tree, and Origami. |
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| Pythagoras’ Theorem | http://SunSITE.UBC.CA/LivingMathematics/V001N01/UBCExamples/ UBCExamples/Pythagoras/pythagoras.html |
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| This Java applet was written by Jim Morey. It won
grand prize in Sun Microsystem's Java programming contest in the Summer of 1995. All that
students need to know to follow the proof is that triangles of equal height drawn on the
same base have equal areas. |
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| Spirograph Applets (1) | http://math.ucsd.edu/~dlittle/java/Spirograph.html http://www.csm.astate.edu/spirotest/spirotest.html http://www.csm.astate.edu/wheels/wheels.html |
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| Spirographs can be studied as an application of
modulo arithmetic, as just a bit of geometric fun in junior school mathematics, as an
application of parametric equations or an application of complex numbers in Maths C. The
first applet is the one to use when introducing the topic, as it demonstates how the
spirographs are made. The second one generates the final pattern must faster. The third
extends the idea to a wheel travelling around a wheel travelling around a wheel. Some
fascinating patterns emerge. |
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Fractals
| An Introduction to Fractals | http://www.best.com/~ejad/java/fractals/intro.shtml |
| This is not just a Java applet, it is an entire unit on
fractal geometry with interactive applets included as needed. |
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Statistics
| Histogram Applet | http://www.stat.sc.edu/~west/javahtml/Histogram.html | |
| This applet is designed to teach students how bin widths (or
the number of bins) affect a histogram. |
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| Centres applet | http://www.stat.wisc.edu/p/stat/course/st201-limt/public/html/ | |
| A neat little applet that demonstrates how the mean and the
median are affected by outliers. Very simple, and very effective. |
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| Sampling Distribution Simulation | http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/index.html | |
| Choose the parent population – normal, skewed, uniform
or custom. Then create a sampling distribution of the mean, or one of many other choices
of summary statistics. |
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| Normal Approximation to the Binomial | http://www.ruf.rice.edu/~lane/stat_sim/binom_demo.html | |
| Vary n and p in a binomial distribution, and investigate how
the binomial distribution approaches the normal approximation as p approaches 0.5 and n
increases. |
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| Confidence Interval Applet | http://www.stat.sc.edu/~west/javahtml/ConfidenceInterval.html | |
| This applet helps students understand confidence intervals. |
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| Central Limit Theorem | http://www.stat.sc.edu/~west/javahtml/CLT.html | |
| This applet demonstrates the central limit theorem using
simulated dice-rolling experiments. |
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| The Monty Hall Game | http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html | |
| As a motivating example behind the discussion of probability,
an applet has been developed which allows students to investigate the Let's Make a Deal
Paradox. |
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| Circle Zap | http://abacus.maths.uq.edu.au/~mrb/java/CircleZap/ | |
| An applet that allows students to gather data on their
ability to use a mouse. |
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| Correlation | http://www.stat.uiuc.edu/~stat100/java/GCApplet/GCAppletFrame.html | |
| Match the scatterplot with its correlation coefficient. Quite
a neat little game. |
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| The Cereal Box Problem | http://www.mste.uiuc.edu/reese/cereal/cereal.html | |
| The Cereal Box problem gives rise to an exponential
distribution. After reading about the problem, follow the link to "Go on a simulated
shopping trip to get the prizes" to run the Cereal Box applet. |
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| Monte Carlo Simulation | http://polymer.bu.edu/~trunfio/java/montepi/MontePi.html | |
| This applet simulates throwing darts at random towards a
board that consists of a circle inside a square. How can we use this experiment to
estimate Pi? |
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| Regression Applet | http://www.stat.sc.edu/~west/javahtml/Regression.html | |
| The applet below is designed to teach students the effect of
influential points on a regression line. |
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Calculus
| A Collection of Calculus Applets | http://www.ies.co.jp/math/java/calcjava.html |
| A marvelous collection of 23 applets to support the teaching
of calculus. The ones that I feel are most useful for Maths B and C are: Surfing (Derivatives) Secant Line and Tangent Line Derivatives of Cubic Functions Rectangle Approximation Method The Number e (1) Limit of sin(x) / x |
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| The Little Deriver | http://user.tninet.se/~jml288p/derive.html |
| Type in an expression, and the Little Deriver will find its
derivative symbolically. A great way to check homework! |
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| The Coffee Cup Caustic | http://www.cacr.caltech.edu/~roy/Caustic/ |
| Not calculus, but I didn’t know where else to put it.
Have you ever seen a strange cresent of light in a cup of coffee that is held in bright
sunlight? This applet will show you how it is formed. It is simple, and effective. |
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Trigonometry
| Trigonometry Applets | http://www.ies.co.jp/math/java/trigjava.html |
| A comprehensive collection of applets on Trigonometry. The
Sine Box, Cosine Box, Tangent Box and the Six Trig Funtions are particularly neat. |
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| The Buffon Needle Problem | http://www.angelfire.com/wa/hurben/buff.html |
| It is a rather remarkable fact that we can estimate the value
of pi by repeatedly dropping a needle onto some lined paper. This applet simulates the
experiment, and provides an experimental value of pi. You will have to go elsewhere to
find the mathematics. |
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| Play a Piano | http://www.frontiernet.net/~imaging/play_a_piano.html |
| Set the frequency and the fade, play a note, and see the
waveform. Lots of trigonometry to be explored. |
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Complex Numbers
| Five applets for complex numbers | http://www.ies.co.jp/math/java/misc.html |
| This is part of the Manipula Maths collection of Java
applets, in my opinion the best collection on the web. |
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Parametric Equations and Polar Equations
| Parametric Equations | http://www.ies.co.jp/math/java/param/param.html | |
| A wonderful visual explanation of how the graph
of a pair of parametric equations is produced. |
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| Famous Curves Applet Index | http://www-history.mcs.st-and.ac.uk/~history/Java/ | |
| A very slick and very comprehensive website.
Choose your curve – the Pursuit Curve, the Lemniscate of Bernoulli, Neile’s
Parabola, and many, many others. |
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Functions
| The Pendulum | http://science.kongju.ac.kr/phys/shin/experiment/kjh/pendulum/index.html |
| A nice little applet that simulates the swing of a pendulum.
The viewer can set values for the mass, the angle and the length of the string, using
slider bars. If time is pressing this is a pretty good alternative to the real thing. |
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Mathematical Fun
| Find the Apple applet | http://science.kongju.ac.kr/phys/shin/experiment/kjh/pendulum/index.html |
| An enjoyable little logic game, for kids of all ages. |
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| The Animated Nekker Cube | http://www.sover.net/~manx/necker.html |
| A wonderful, whimsical implementation of the ‘wire
cube’ optical illusion. |
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