Whether they're in elementary, middle, or high school, students frequently have difficulty grasping and applying the necessary concepts to think and do mathematics. Fortunately, the Internet provides a wealth of tools ranging from calculators and virtual manipulatives to dynamic illustrations and interactive environments. Tools provide educators a variety of models to meet the needs of diverse learning styles and can be integrated easily into existing lesson plans. To build your tool chest, visit the following Web sites.
This meta web site sponsored by MathForum focuses on a variety of math tools. Its index starts with pre-K, and continues all the way up to discrete math. Selecting an index topic leads to a listing of tools, activities, supplemental materials, etc. Selecting a specific tool provides a description of the tool and its specific URL. This web site is developing a Math Tool Community that includes discussion areas, research updates, a newsletter and a very thorough site map of topics in mathematics. Add this web site to your tool chest.
Don't let the words "middle school" dissuade you. This meta web site contains an incredible assortment of all types of calculators, ranging from a 1885 Felt & Tarrant "Comptometer" adding machine (history) and Vector Calculator to an Astro-Psysical Calculator and a Linear Algebra Matrix Calculator. Many of the calculators allow users to convert data, such as converting to or from metric units or calculating the Cost of Living effect on consumer prices. This type of tool could be used in a whole class situation to test answers or confirm a hypothesis. In addition, students can use them to check their work. Note: Online calculators sometimes are not as accurate as actual calculators, especially when working with very large or very small numbers. However, these discrepancies could provide problem-solving activities for your students.
These tools from Vanderbilt University follow the fill-in-the-blank model using algorithms to factor polynomials, find derivatives and antiderivatives, fit polynomials to data sets, plot parametric equations, plot functions of polar coordinates and more. Each algorithm has options, such as, showing plots, solutions, calculations and sums. If you teach calculus, put this site in your tool chest.
This NSF-supported project created by Utah State University is a collection of interactive, web-based virtual manipulatives. Virtual manipulatives encourage active engagement in mathematical thinking and learning – helping students visualize relationships and applications. This site focuses on Numbers & Operations, Algebra, Geometry, Measurement and Data Analysis & Probability with activities clearly matched to NCTM standards. Teachers can use these manipulatives in whole class instruction or promote students working in partner-teams or individually. Because this is a PreK-12 web site, high school teachers with challenged students may want to investigate the Grade 6-8 section of tools.
NCTM illuminations provides models of mathematical teaching using engaging, interactive activities matched to the NCTM Standards. There are many facets to the illumination web site, but the following three areas are reviewed for you to add to your tool chest:
- Interactive Math Tools Interactive Math Tools are Java applets used to explore math and create interactive lessons. Grade 9-12 examples include tools that investigate the effects of varying the parameters in recurrence relations, visually describe congruence theorems, explore cryptography and shift transformations, provide an interactive geometry dictionary, support an isometric drawing tool and more.
- E-Example Index This index offers electronic illustrations of mathematical concepts. These examples are quite visual and students can readily see change. Grades 9-12 examples include tools that manipulate a velocity vector to control the movement of an object and to explore iterations and recursions. They also offer algebra to model and analyze the changing amount of medicine in an athlete's body, to focus on the connections between algebra and geometry, to explore three methods for measuring how well a linear model fits a set of data points, and to gain a better understanding of linear functions by exploring the relationship between symbolic and graphical representations.
- i-Maths i-Maths are online, interactive, multimedia investigations including math applets and video clips. Models are divided between single-day and multi-day activities. Grades 9-12 investigations include tools that focus on regression lines and correlations, explore rates of change, develop and analyze exponential models, use rational functions and more. Some i-Maths make cross-reference to the E-Examples.