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.
What are the calculator policies for Common Core Assessments?
PARCC Calculator Policy and Mathematics Reference Sheets released in 2012. Note, for example, that the PARCC Calculator Policy indicates: "PARCC mathematics assessments for High School will allow for a calculator with functionalities similar to that of a TI-84 graphing calculator."
As of December, 2012, SBAC has not determined its policy on the use of calculators for summative and interim assessments.
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 webinars for Casio calculators. Note: Casio's PRIZM graphing calculator offers picture plot technology in which users can upload their own images or photos to the calculator and then perform math equations on top of those, thus adding real-life meaning to mathematics. Lessons are also included.
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 Activities are for use with Texas Instrument graphing calculators (e.g., TI-Nspire, TI-Nspire CAS, TI-84 Plus Silver Edition and TI-89 Titanium) in various subjects such as algebra 1, algebra 2, geometry, precalculus, calculus, and statistics. MathNspired 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 on their existing projection systems or interactive whiteboards. Note: Texas Instruments also has apps for using TI-Nspire and TI-Nspire CAS on an iPad.
Buy additional resources via CT4ME.
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:
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.
Algebrahelp.com Calculator Index lists the online calculators provided at the site for solving and working with algebra equations, simplifying expressions, graphing functions, prime factoring numbers, operations with fractions, solving proportions, and so on.
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.
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 is "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. You can also download the calculator.
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.
HOT!: Graphing Calculator is free from Desmos.com and compatible with any computer or tablet. Examples of graphs possible are also at Chrome.Google, where you can also launch the app. It is full featured, and comes with support for using features. Multiple graphs can be placed on top of one another. You can show Cartesian and polar coordinates and zoom in and out of plots. Graphs can be saved or printed and axes labeled in terms of "pi" for typical trig graphs. There are options for displays in radians and degrees. Points can be plotted at users choice and tables of values shown on a graph can be displayed. Set notation can be used; inequalities can be graphed. 3D graphing is an option. There is a projector mode for class use. This is a winner for math educators!
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.
Online Statistics Calculators: There are five statistics calculators available from Alcula.com: measures of central tendency and dispersion, box and whisker plots, linear regression, correlation coefficients, and scatter-plots. Other online calculators for math are also available.
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:
Protractor by Silverview Consulting is compatible with iPhone, iPad, and iPod Touch. For a small fee ($.99), you can then find the number of degrees in angles using images on the Web or photos you've captured. Think of taking a picture of a roof, for example, and finding angles on it, or measuring the lean of an object.
TI-Nspire and TI-Nspire CAS (Computer Algebra System) graphing calculator apps for iPad are from Texas Instruments. These apps enable "comprehensive graphing, data entry and analysis, statistical modeling and calculating functionality" (iTunes Description section).
TouchCalc by Alexander Clauss is a free calculator app for iPhone and iPad. It comes with several modes. The scientific mode includes the usual functions and operations such as basic arithmetic, powers, roots, logarithms, trigonometry, and so on. A bit/integer mode offers logic operations and calculations in 8, 16, 32, or 64 bits. The statistics mode enables calculations of mean, median, mode, quartile values, variance, standard deviation, range, and so on.
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 and see when other math symbols were first introduced.
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. See the interactive demonstrations Approximating Pi at PBS Nova or Computing Pi at NCTM's Illuminations. You will experience how the Greek mathematician Archimedes determined a theoretical approach to the calculation of pi using a circle and finding perimeters of inscribed and circumscribed polygons. This took place around 250 BC and the demonstration is still useful.
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.
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