Practicing Math Online: Fun, Free, and Cool!

By: Center for Implementing Technology in Education (CITEd) (2008)

While teachers often encourage their students to read over the summer, research suggests that math skills actually suffer more from the long summer break (Peters, 2006; Cooper, et al., 1996). During the summer, students frequently forget what they have learned, and this forgetting may be more significant in children with special educational needs. (Cooper, et al., 2003). How can we get students to practice math over the summer, particularly students for whom math is difficult? "The hardest thing for the kids to retain all summer is their math skills and it's the hardest subject to get them to do during the summer without them knowing they're actually doing math." (Hernandez, 2008). How, then, can we get them to practice math? One way is by incorporating the math into games that they can play, either alone or with a friend or parent. Math applets can provide these games in a fun, computer-based format.

What are math applets?

Math applets are small, web-based programs that can help students in math in a variety of ways. Some are designed to illustrate specific concepts, while others provide practice to build skills. A hallmark of a good applet is that it is interactive; the user is actively engaged with the math. There are literally hundreds of math applets that are freely available on the web.

The interactivity of applets allows students to work with math concepts in concrete ways to help make a concept "real." For students who struggle with math or with language, an abstract explanation of a math task - for example, adding fractions or converting percentages to decimals - may not clarify the concept. They need to see the relationships and, better yet, physically manipulate the relationships to really understand the concept (Anstrom, n/d). Math curriculums classify this as the concrete-representational-abstract continuum of learning, but textbooks and curriculums often abandon this important learning sequence after the early primary grades. Virtual manipulatives like applets can support concrete and representational exploration and can even present quite sophisticated concepts in multiple ways to help students gain an abstract understanding of math concepts (see chart of Applets below).

How can math applets support learning?

Universal Design for Learning (UDL) is an educational framework that optimizes opportunities for all individuals to gain knowledge, skills, and enthusiasm for learning (Meyer & Rose, 2002; Rose & Meyer, 2006; Rose, Meyer, & Hitchcock, 2005). The "universal" in UDL does not imply one optimal solution for everyone, but instead underscores the need for inherently flexible, customizable content, assignments and activities, and assessments.

Three primary principles guide UDL and are present in interactive math applets.

Principle I: Provide Multiple Means of Representation (the "what" of learning)

As students differ in the ways that they perceive and understand information that is presented to them. Math applets support this principle by providing representations of abstract concepts and allowing students to interact with them, helping them to focus on the important features and relationships. Because they are digital, they also can provide many more examples of a concept than would be available in a traditional textbook, giving the student the chance to more firmly grasp the concept and avoid misconceptions.

Principle II: Provide Multiple Means of Action and Expression (the "how" of learning)

As students differ in the ways that they approach solving problems and express what they know. Math applets can support students in developing fluency in math skills such as computation. Many applets also provide students with opportunities to refine their problem-solving skills by developing and trying out strategies.

Principle III: Provide Multiple Means of Engagement (the "why" of learning)

As students differ markedly in the ways in which they can be engaged or motivated to learn. Students frequently find math applets engaging because of the interactivity and the ability to use them independently. In this environment they may feel more comfortable working on math skills. Many applets can be adjusted to match different levels of abilities, thus making them challenging without being so difficult that students give up. Some are presented in a game format that provides the addition of social interaction. Some provide feedback on a student's performance that can be used for self-assessment.

Playing games with math applets

Many math applets have been created as games that students can play by themselves, against the computer, or against another student. One type of game is based on the popular game Connect Four. Connect Four is a two-player game in which the players take turns in dropping alternating colored discs into a seven-column, six-row vertically-suspended grid. The object of the game is to connect four singly-colored discs in a row -- vertically, horizontally, or diagonally -- before your opponent can do likewise.

The Connect Four format is used in several online math applets, developed as a part of Project Interactivate, that focus on different math skills. Players must answer a math question correctly in order to place a disc. Players can set the difficulty level and time limit. In Arithmetic Four, players must solve whole number arithmetic problems - addition, subtraction, multiplication, or division. Other games include Fraction Four, Estimator Four, Order of Operations Four, and Algebra Four.

Other games can also provide practice in computation skills. Two examples, from the National Council of Teachers of Mathematics' Illuminations website are the Product Game and the Factor Game, which both focus on multiplication. Another game from this website, the Fraction Game, focuses on equivalent fractions. All of these games can be played either against another player or against the computer.

Another game format available from Project Interactivate involves investigating the Cartesian coordinate system by directing a robot through a mine field laid out on the plane. The player enters the coordinates and the robot moves to that point. By continuing to enter coordinates, the robot moves toward a target while avoiding the mines in the field. Players can set the number of mines and choose to have the starting and ending positions set randomly. Two versions are available. In the first, the player works in only one quadrant, while the second uses all four quadrants of the Cartesian coordinate system.

Logic games, such as Nim, and Mastermind, are also available as math applets. Nim, available at the Illuminations website, is a game in which players alternately remove counters from the board, and the player who takes the last counter wins. In Mastermind, found at the National Library of Virtual Manipulatives, the object is to guess a hidden pattern of pegs. In these games players can discover what strategies are more likely to win the game as they play over time.

Exploring math applets

There are several websites that provide a wide variety of engaging math applets. The sites described below include instructions and suggested activities for each applet, and applets are categorized by content areas. Many provide feedback and keep track of the player's score, so that they could be used in a game-like way. Parents may find these a fun way to learn about math, too!

Illuminations

http://illuminations.nctm.org

Illuminations, developed through a partnership between the National Council of Teachers of Mathematics (NCTM) and MarcoPolo, has been designed as a companion to illuminate the NCTM standards for mathematics. It includes links to the standards and electronic examples from the NCTM website. Illuminations includes lessons that can be sorted by standard and by grade level. The lessons have detailed descriptions and are printable. It also includes interactive tools that support exploration of math concepts. Tools are categorized by grade level.

An additional feature is Web Resources, a list of links to web resources that have been reviewed by an editorial board of experts. These resources can be searched by grade level and standard.

National Library of Virtual Manipulatives for Interactive Mathematics

http://nlvm.usu.edu/

Developed at Utah State University and funded by the National Science Foundation, the National Library of Virtual Manipulatives is a library of web-based interactive virtual manipulatives and concept tutorials. Manipulatives are sorted by grade level and math content area, and each manipulative includes instructions, suggested activities, lesson plans, and connection to relevant NCTM standards. The manipulatives include some that are commonly used in teaching (base 10 blocks, pattern blocks, and algebra blocks).

Project Interactivate

http://www.shodor.org/interactivate/activities/

Project Interactivate is developed and maintained by Shodor Educational Foundation, a non-profit education and research organization that focuses on developing valid models to support understanding. It includes over 100 interactive tools and activities that allow students to explore mathematics. Tools and activities are categorized by math content (number and operations, geometry and measurement, function and algebra, and data analysis and probability). All include explanations of how to use them in teaching and why the activity is useful. Many are incorporated into lesson plans that are also available, and some of these include downloadable worksheets to use in lesson. Also included is a discussion section that models how to introduce or explains different concepts to students. An online dictionary provides definitions and links to relevant discussions.

Using math applets can be a fun way for students with learning disabilities to keep their math fresh over the summer break. They may even find new ways to understand difficult concepts, and parents might find that playing with the applets helps them to understand the math their children are learning and where they struggle.

Resources

Use the chart below to find an applet that might appeal to your student. See the ways to adjust the game listed in the third column. For example, if your student has a slow reaction time or gets frustrated by timed games, look for an applet that allows you to adjust the time given for responses. If your student is distracted by animation or sound, look for applets that allow you to turn the sound on or off or control the complexity of the game. If you want to practice a particular type of skill, look for those applets that list the skill or allow you to adjust the problem types. And finally, watch how your student does with a second player, some students concentrate better when they play games with the computer as an opponent rather than a friend or a parent. Most of all, help your student relax and have fun playing - it's the best way to learn!

Game name and URL	What does it teach?	What can you adjust?	How many players?
Arithmetic Four	Addition Subtraction Multiplication Division	Time Problem types Difficulty of problems	Two players
Estimator Four	Addition Multiplication Percentage	Time Level of difficulty Precision of answer	Two players
Fraction Four	Fractions Percents Decimals >Algebra	Time Level of difficulty Problem types	Two players
Order of Operations Four	Order of Operations	Time Level of difficulty Problem types	Two players
Algebra Four	Algebra	Time Level of difficulty Problem types	Two players
Maze Game	Cartesian coordinate system	Number of mines Size of graph Random vs. fixed	One player
Simple Maze Game	Cartesian coordinate system	Size of graph Random vs. fixed	one player
Product Game	Multiplication	Factors used in game Number of responses needed	Two players
Factor Game	Factors in multiplication	Numbers available	Two players or against computer
Fraction Game	Sound on or off	Fractions	one player
Fraction Track	Fractions		two players
Nim Games	Logic	Type of game Initial size Computer's mode of play	play against computer
Mastermind	Logic	Number of colors	one player

References