Learning Mathematics with Virtual Manipulatives

Abstract concepts are essential to understanding and performing mathematics. They are also a

source of difficulty for many students who struggle with mathematics, many of whom find even

basic mathematics concepts difficult to understand. A popular approach to help students

understand abstract concepts is the use of manipulatives. Manipulatives enable students and

teachers to represent concretely the abstract concepts that they are learning in mathematics class

and to link these concepts to prior knowledge. It is useful to introduce new concepts to all

students.

For the most part, classroom use of manipulatives has involved concrete, or physical,

manipulatives. However, with the advent of the World Wide Web, there is a new category of

manipulatives. Virtual manipulatives are basically digital “objects” that resemble physical

objects and can be manipulated, usually with a mouse, in the same ways as their authentic

counterparts. Virtual manipulatives are a relatively new technology and are modeled after

existing manipulatives such as base ten blocks, coins, blocks, tangrams, spinners, rulers, fraction

bars,algebra tiles, geoboards, geometric plane, and solids figures. They are usually in the form

of Java or Flash applets. Virtual manipulatives allow teachers to allow for efficient use

of multiple representations and to provide concrete models of abstract mathematical concepts for

learners of mathematics. Research suggests that students may also develop more connected

understandings of mathematical concepts when they use virtual manipulatives (Moyer,

Niezgoda, & Stanley, 2005)

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Brief description about Factor Tree Virtual Manipulatives.

Factor Tree, is ideal for giving students the additional assistance they may need to more fully

grasp the concept of prime factorization. It allows either computer-choice or student-choice

selection of numbers to be factored. In its basic operation, the program deals with one number at

a time. The more advanced mode uses two numbers, determines the prime factorization, greatest

common factor (GCF) and lowest common multiple (LCM).

How virtual manipulative (technology) is used in teaching the Factors and Multiples?

1) Log-in as ‘Student’, if the computer is not already running with desktop visible.2) Left CLICK mouse on the Internet Explorer. When the Internet is open,3) Type http: //nlvm.usu.edu/ into the address line of your toolbar, and Left CLICK ‘GO’ or

select ‘ENTER’ on your keyboard.4) Left CLICK mouse on Number and Operations / 6-8

5) Scroll down to the Factor Tree and left CLICK on the icon.

6) Pupils are shown the virtual manipulatives software online by the teacher. Teacher shows how to use the software.

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Type a number you think is a factor of the provided number into the left hand box, the computer will fill in the right hand box with a multiple whose product will be the top number and press ENTER. Repeat, to find all prime factors.

7) When satisfied and understand how to get prime factorizations of any number, scroll to the bottom of the screen and select TWO. The computer will provide two different numbers.

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8) Once both numbers are factored, a blank Venn Diagram will appear below the trees. Place the cursor over a prime factor and drag it to the appropriate section of the overlapping circles. This will display common factors between the two numbers.

9) Finally, fill in the boxes at the bottom of the screen for GCF and LCM.

10) Pupils try out the software in pairs using the computer option and also the user option.

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Why virtual manipulative (technology) is used in teaching the Factors and Multiples?

Provide learners with visual images. It can be manipulated as physical manipulatives and provide students opportunities for

constructing mathematical knowledge. To promote effective teaching.

What are the benefits?

It can help students visualize relationships and engage students learning actively. Useful to help the students to understand better. It will arouse students’ interest in learning mathematics. Pupils can work out the answer faster by using the virtual manipulatives.

Virtual manipulatives are helpful in breaking down math concepts, as well as making them seem more interesting.

Most virtual manipulatives make a game out of the math, which tends to keep the student's interest alive while helping to teach concepts that otherwise may seem too obscure.

The student becomes more focused and retains more information.

Virtual manipulatives allow for learning to occur in a multimedia environment where the

learner experience sound, images and animation.

Immediate feedback provides the learner with praise if they have solved the problem

correctly and corrects the learner if they have not completed the task correctly.

Allows for self-directed learning.

Assist students to develop mathematical concepts.

Increase students’ problem solving skills.

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What the concepts and skills to be learned from the virtual manipulatives activities?

Can make connections between the concepts, extension and generalizations in order to solve the problems.

Identify prime and composite numbers.

Find factors and multiples of whole number less than 100 and identify which are prime or composite.

Identify common factors of a set of whole numbers.

To manipulate and change the representations, thus increasing exploration possibilities to develop concepts and test hypotheses

Know how to use technology.

Learn by using factor tree method through games.

To develop their relational thinking and to generalize mathematical ideas

Related Technological Activities to Factors and Multiples

http://www.mathgoodies.com/factors/factor_tree.asp

http://www.math-play.com/Factors-and-Multiples-Jeopardy/Factors-and-Multiples- Jeopardy.html

http://www.toonuniversity.com/flash.asp?err=499&engine=14

http://www.mathplayground.com/factortrees.html

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References

Read more: How Math Manipulatives Help Elementary Students Learn | eHow.com http://www.ehow.com/facts_7295642_math-manipulatives-elementary-students-learn.html#ixzz1lKuIXByQ

Read more: Pros & Cons of Using Manipulatives in the Classroom | eHow.com http://www.ehow.com/info_7981856_pros-cons-using-manipulatives-classroom.html#ixzz1lKtjnUAO

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