Are you confused by terms that educators use? The ASCD Lexicon of Learning might be what you need.
Math Manipulatives contains two pages of resources:
Math Manipulatives (Page 1 of 2): Read a short essay about virtual manipulatives and their role in learning mathematics and access our list of virtual manipulatives on the web.
Math Manipulatives (Page 2 of 2):
There
are many kinds of online and hand-held calculators. Some are dedicated to
specific professional fields; others have features beyond the capabilities of
learners to use those, or features that learners might not be able to use on
state standardized testing. Some displays of online calculator input or
output are easier to work with than others. Therefore, educators should
help learners choose those appropriate for the level of math they are learning,
thus avoiding the potential problem of "teaching one way, but testing another
way."
Consider the following. A graphing calculator is an essential tool for learners in mathematics courses such as algebra, trigonometry, advanced math, and calculus. The visual display becomes a powerful tool for teaching and learning to show the link among conceptual, procedural, analytic, and investigative dimensions of learning mathematics. When it comes to using a graphing calculator (or some scientific calculators with certain non-graphing features) on state standardized testing, there may be restrictions on use that educators should be aware of depending on grade level of the learner taking the exam. For example, the Ohio Achievement Assessment (2011) policy on calculator use for standardized testing in grades 6-8 permits learners to use "most four-function and scientific calculators, including those with fraction capabilities" (para. 1). However, the policy prohibits graphing calculators and calculators with equation solving functions and geometric capabilities.
Manufacturers and technology organizations offer tutorials and manuals for elementary, financial, graphing, and scientific calculators. Examples follow:
Atomic Learning has a series of step-by-step technology tutorials, including for Texas Instruments calculators (e.g., TI-30XS, TI-84, and TI-Nspire handhelds). Under the option for types, select calculators. Readers might be particularly interested in TI-Nspire, which combines graphing capabilities with computer features (e.g., save and review work). You can see multiple representations of a problem on one screen, use "grab and "move" to observe patterns and relations, and much more. Texas Instruments teamed with Atomic Learning to provide online tutorials on the TI-Nspire handhelds.
Casio Education training videos for Casio calculators
Handheld Geometry "is for anyone who wants to use dynamic geometry to do mathematics on a handheld device, a graphic calculator, or the related computer software," according to site developer Nevil Hopley who is a math educator in Scotland. Content is geared toward math typically taught to students ages 11 to 18: straight lines, circles, triangles, quadrilaterals, optimizing, loci, percentages, ratio, connections, statistics, spatial, sequences. Video how-to's and notes accompany numerous graphic illustrations.
Hewlett-Packard calculators learning modules
Prentice Hall Graphing Calculator Help for TI-82, TI-83, TI-85, TI-86, TI-89, TI-92, HP48G, CFX-9850, Sharp EL9600C, and Casio FX2.
SimCalc MathWorlds software for TI-graphing calculators, computer, and TI-Navigator was developed by the University of Massachusetts-Dartmouth's James J. Kaput Center for Research and Innovation in Mathematics Education. Animations, real life examples, narrative stories, and more are used to explain math concepts. You'll find video tutorials at the site.
Sharp scientific calculators educational support
Texas Instruments Online Tutorials TI provides a number of interactive tutorials for basic and graphing calculators.
TI Math has activities for use with Texas Instrument graphing calculators (TI-Nspire, TI-Nspire CAS, TI-84 Plus Silver Edition and TI-89 Titanium) in various subjects, which include algebra 1, algebra II, geometry, precalculus, calculus, and statistics. Visit MathNspired, which is a collection of online lessons and tools for using the TI-Nspire handhelds for algebra 1, algebra 2, geometry, and calculus. TI-SmartView emulator software allows educators to project interactive representations of TI graphing and scientific calculators (TI-83 Plus and TI-84 Plus families, TI-30X/TI-34 MultiView, TI-73 Explorer) on their existing projection systems or interactive whiteboards. Note: Texas Instruments TI-Nspire CX and TI-Nspire CAS models have color screens for better math visualizations. Also look for the latest version software for the TI-Nspire.
Accessible Calculators --this list provides information on the types of accessible calculators and potential sources. It was developed at the Georgia Tech Research Corporation Center for Assistive Technology and Environmental Access.
Calc 3D is downloadable mathematical graph and charting software for geometry and statistics. The calculator can do statistics, best fits, function plotting, polar and parametric plotting, integration. It handles vectors, matrices, complex numbers, quaternions, coordinates (Cartesian, polar, spherical, cylindrical), regular polygons, and intersections. Find distances, volume, area, and more. The software handles several languages, too.
CalculateWhat.com features a variety of free online calculators for just about anything, with a large emphasis on math calculators for algebra, geometry, statistics, and general math. Each page also offers formula information and a brief background on each particular subject. New calculators are added regularly.
Calculators On-Line Center features over 19,000 calculators for mathematics, statistics, science, and engineering. Calculators for mathematics range from those suitable for basic mathematics through calculus and higher level mathematics. Don't miss this vast collection of specialized calculators by topic from J. Martindale.
Calculator Options for Teaching Learners with Multiple Special Needs.
Coolmath Online Graphing Calculator is free and has all the common operators and functions expected in scientific calculators and graphing calculators for graphing functions. Great alternative for students who forget their own handheld graphing calculator, such as the TI-83.
Cyberchase Talking Calculator is a free basic online calculator (add, subtract, multiply, divide) from PBS Kids.
EasyCalculation has a series of free online calculators set up as they relate to specific math concepts for number, algebra, statistics, geometry, trigonometry, calculus, and more. There are also some tutorials on the math concepts related to those calculations.
eCalc has "a free online calculator that supports many advanced features including unit conversion, equation solving, and even complex-number math. The calculator is designed to work directly in your browser and requires no special plug-ins." There is a basic calculator and a scientific calculator, the latter of which includes trig, log, and exponential functions, and decimals to fractions. Both have large keys for easy input. eCalc is not a graphing calculator. However, it's definitely worth investigation.
e-Tutor online graphing calculator is free and can be used to graph simple to advanced equations. Multiple equations can be shown on a single graph.
Fraction Calculator at Home School Math is free. Enter two fractions (including mixed numbers) to add, subtract, multiply, or divide. The answer is presented in reduced form and in mixed number form, as appropriate.
GCalc is a free online graphing calculator. "GCalc is designed to provide a basic, easy-to-use, well-balanced set of graphing functionality for algebra, pre-calculus, calculus and beyond."
GraphCalc is a Windows 2D/3D graphing calculator. Download it for free. The developers call it "an all-in-one solution to everything from everyday arithmetic to statistical analysis, from betas to Booleans, from cubes to calculus, from decimals to derivatives. GraphCalc combines all the features of a professional mathematics package with the simplicity of an easy to learn windows interface. It provides user-friendly help and tutorials to guide you through the easy and fun process of mastering GraphCalc." A Linux version is also available.
InstaCalc is a free online calculator that can interpret natural language expressions and equations. It also includes instructions for getting started. Results are displayed instantly, and can be shared. Perform basic math, convert units of measure and currency, use variables and rows, create charts similar to what you'd do with spreadsheets, work with trigonometry, logarithms, programming tools, and more. You can add notes and embed your calculations in your own web pages, too. It's amazing.
Microsoft Mathematics
4.0 is a FREE download! It includes a full-featured graphing calculator that’s designed to work
just like a handheld calculator. You can plot in 2D and 3D; there's
step-by-step equation solving, and additional math tools to help you
solve triangles, convert from one system of units to another, and
solve systems of equations. There's a library of equations and formulas
and ink handwriting support. This is a great teaching and learning tool,
which also comes with a teaching guide.
PDA Handheld Computing Resources on the Web is brought to you from the Shiawassee Regional Education Service District in Michigan. The collection includes links to ebooks, journals, peripherals, tutorial videos, hardware/software, assessment programs, math programs, and more to integrate the PDA into your instruction.
Statistics Calculators at DanielSoper.com are free for the research community with 21 categories available.
Talking Calculator from Premier Assistive Technology is an onscreen full-function talking calculator that can be used with or without a screen reader. "Every button and edit area talks. It is easy to use with large keys and contrasting colors. It has three display areas, so when the user adds a series of numbers, the total is always displayed, even as you are entering a new number, while always displaying any numbers in memory." Further, "it displays your entries and results as you work. It actually displays the equation so that you can easily see or hear your last process. When students are required to show their work, they can simply cut and paste the steps into a document." A free download is available.
Unit Conversion from PDFConverter.com is a free series of unit converters with multiple options for converting mass, time zones, area, angle, length, volume, pressure, temperature, and data storage. Quick and easy to use.
WebGraphing.com provides online graphing (1D, 2D, & Interactive 3D) of functions, equations, systems of equations, inequalities in one and two variables, and piecewise functions, with tutorial analyses appropriate for students of algebra, precalculus, and calculus. There is also a forum for the different math levels. What sets the function graphing calculators apart from other graphing calculators is the automatic display of asymptotes and discontinuities in standard mathematical notation, and the automatic determination of an optimal graphing window--one that includes all mathematical features of interest.
Zona Land's graphics calculator, EZ Graph, enables you to graph almost any polynomial, rational, exponential, logarithmic, or trigonometric function.
180-in-1 Math Calculator by Charles Vu is compatible with iPhone, iPod touch, or iPad. It's available in iTunes for a couple of dollars. The 180 solvers cover topics in basic math, algebra, geometry, analytic geometry, probability and statistics, matrices, and trigonometry.
Calculator Options for iPhones: CalcGuy reviewed several iPhone calculator apps in his August 13, 2010 article. See:
Easy Geometry for the iPad is available in iTunes for a couple of dollars. With this app developed by JMS Soltutions, you can "explore the basic family of geometry shapes from the closed plane curves, quadrilaterals, triangles, polygons and geometric volumes. Learn the basic equations that describe each geometric shape as well as each shapes properties and interesting facts." The "Interactive Geometry Calculator allows you to choose the parameters used to solve the basic geometric shape" and explore the boundaries of each (Description section).
Graphing Calculator --software compatible for use with iPhone, iPod touch, and iPAD developed by Gabor Nagy. Available at iTunes for just a couple of dollars.
Pomegranate Software Calculators for Mobile Devices:
Trigonometry Pro HD by voi nguyen can be used on an iPad. It is available in iTunes for a couple of dollars. This "Interactive Trigonometry Calculator contains 13 Modules: Geometry, The Right Triangular Shapes, 30/60 Degrees Triangular Shapes, 45 Degrees Triangular Shapes, Oblique Triangular Shapes, Trigonometry/Geometry Equations, The Ultimate Units Converter, Animated Sin/Cos/Tan Graphs Functions, Interactive Central Angle, Interactive Unit Circle, Circle Functions, Lines, Point & Slopes Plot Functions and the bonus module is: The Arabic Numerals System."
Here's a bit of history for you!
From Slates, to Slide Rules and Software!
Does anyone remember the slide rule? "Throughout American history, teachers and parents have used objects--from colonial--era slates to modern electronic calculators--to help students master abstract mathematical concepts," according to The Smithsonian Institute, which has posted a highly informative display called Slates, Slide Rules, and Software: Teaching Math in America. Read developments in math education and teaching with manipulatives from the Early Republic, to the Cold War, and Information Age. Additional resources are provided. http://americanhistory.si.edu/teachingmath/
Did you know?
"The
slide rule has a long and distinguished ancestry … from William Oughtred
in 1622 to the Apollo missions to the moon ... a span of three and a half
centuries … it was used to perform design calculations for virtually all
the major structures built on this earth during that long period of our
history … an amazing legacy for something so mechanically simple" (Source:
The Oughtred Society,
History of the Slide Rule). Read more about it and other
calculating instruments at the Oughtred Society.
Can you guess the origin of the radical sign from the picture?
Get a little of the history
of the radical sign.
The
irrational number 
is the ratio
of the circumference of a circle to its diameter. It is often used
in mathematics approximated as 3.14, but a computer has calculated its
value to over 6 billion decimal places! Learn more about the
history of pi.
Also visit the Joy of Pi.
Φ The golden number, Phi (Φ)
1.618..., is an irrational number, like .
It is found in many places, as in properties of the human body, in
plants, DNA, the solar system, art and architecture (its uses date back
to the ancient Egyptians and Greeks), the stock market, the Bible and
theology (think of the book Da Vinci Code), population growth, and so
on. Learn more about it at
GoldenNumber.net.
Get the scoop on the history of the internet, a timeline of computer history, and learn about the people involved in making computers what they are today. Visit the Computer History Museum.
Did you know that slates are alive and well?
Consider the modern updated slate: the netbook and iPad, for example.
The Amazon widget below shows electronics using the search phrase: calculators math. You can also use the widget to search with other key words or to search for specific electronic products or virtual manipulatives. Suggestions include:
Help your students to understand the beauty of mathematics found in nature.
View the short video, Nature by Numbers, created by Cristóbal Vila, which was inspired by numbers (e.g., Fibonacci and Golden Ratio), geometry, and nature. This is truly beautiful and eye-opening. Then visit Dr. Ron Knott's web site for more on Fibonacci numbers and the Golden Section in nature. You will also find activities to do with your learners. Note: The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ... (add the last two to get the next).
The Exploratorium in San Francisco features the Geometry Playground, which will change how you view geometry in nature. It contains three sections: The Geometry of Seeing with a photo exhibition of the invisible geometry of light; The Geometry of Moving on the arcs, angles, and shapes created when people and things are in motion; and the Geometry of Fitting Things Together. Each includes hands-on activities for grades K-8. The Geometry Garden features curiosities found in nature from crystals to seashells to sculptures. The site was made possible by the National Science Foundation and the Gordon and Betty Moore Foundation.
Learn about fractals.
The
PBS television series , NOVA, has a one-hour program about fractals called
Hunting the Hidden
Dimension. There are five chapters, which can be viewed separately.
Learn about fractals in nature, including those in the human body.
There are links and books, a teacher's guide, and an email newsletter for
learning more. You can also design your own fractal using NOVA's
interactive generator.
Fractal Keys: A Pattern Paradise from the MathScience Innovation Center is a must see site for an adventure into learning all about fractals and where you can find them--everywhere, including music! Learners in grades 5-12 will benefit. Begin by clicking on the Welcome Center and viewing What are fractals?
Explore fractals with this unit by Cynthia Lanius, which is appropriate for elementary and middle schools learners and even adults. You will learn about the importance of fractals, properties of fractals, create a few, and get a series of links to other sites on the Web that address this topic.
NCTM Illuminations Fractal Tool applet, designed mainly for middle school learners, is a virtual manipulative to see how various shapes are fractals. Users can play with shapes that grow, shrink, and change over several stages and explore self-similarity and patterns in fractal measurements.
Amazing Seattle Fractals! will benefit high school learners and above.
The developer provides tutorials to learn more about fractals and how to
create fractal art. Users can download free fractal software
programs and view some fractal art galleries.
If you wish to generate 2D or 3D fractals and those with animation, consider ChaosPro, which is freeware for MS Windows. It includes tutorials and a gallery of examples.
Pomegranate Software offers the program called Fractals, which is designed for use on iPad, iPhone, and iPod Touch. It “renders as you move and pinch to explore Mandelbrot and Julia set fractals in real-time.” See the exciting displays and learn more about fractals at this site.
Ohio Achievement Assessment (OAA) - Policy for Calculator: Grades 6, 7 and 8. (2011, November 4). Ohio Department of Education. Retrieved from http://education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspx?Page=3&TopicRelationID=222&Content=114821
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See
related topics: Math Resources and
Standardized Test Preparation.
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Deubel, P. (year from last revised). Math manipulatives: Calculators and related resources. Retrieved Month, Day, Year, from Computing Technology for Math Excellence Web site: http://www.ct4me.net/math_manipulatives_2.htm
Last revised 04/30/12
CT4ME Author: Dr. Patricia Deubel
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