Essay - Manipulatives: What? Why? How? Manipulatives What? Why? How? Objective the...


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manipulatives: what? Why? How?

MANIPULATIVES

WHAT? WHY? HOW?

OBJECTIVE

The objective of this work is to research hands-on manipulatives use in mathematics. This work will explore the historical perspective, the effects on education, the supporting *****ories, and ***** research has been thus far conducted. Finally, this work will research the special benefits of using algebra tiles.

INTRODUCTION

***** of ***** hottest topics among mathematics educators and researchers is that of 'manipulatives'. Manipulatives serve in so many areas of *****struction ***** ***** and are so helpful with the special needs of students that manipulatives, although being quite ancient in theory ***** even ***** are ga*****ing new respect in today's challenging and increasingly diverse classroom.

***** ARE MATH MANIPULATIVES?

Math manipulatives are traditionally concrete objects ***** one is able to manipulative that ass*****ts the individual in completion ***** math operations such as add*****g, subtracting, multiplying, division, and ********** on ***** more complicated ***** such as Algebra. One of the first manipulatives utilized in the ma*****matics classroom instruction was the abacus. This instrument is used in counting in numbers larger than ten human fingers can represent and historically were ***** by merchants for calculation purposes. The ***** preceded the inventions ***** ***** used for counting and continually evolved in its appearance since ancient civilization. The abacus is pictured in the figure below labeled Figure 1 and ***** the copy of a cover of ***** manual ***** Lee Kai-chen published in 1958 and has 4 decks *****in its design. Kai-chen claims that it is easier to perform both division and multiplication using ***** modified version of the abacus and ***** square roots ***** numbers and cubic ***** of ***** are much easier determined using this board.

Modified Version of Abacus

Source: Bagley (2004)

Manipulatives al***** include objects ***** as calcula*****rs, the slide-rule and compasses used in the Geometrical mathematics.

*****. 'WHY' USE ***** MANIPULATIVE?

The work of Burns (1998) documents the fact that: "...two-thirds of Ameri*****s loathe or hate mathematics." (Furner and Qu*****n, 2001) A TIMSS study stated findings that as American students travel from the fourth through the twelfth grade in school they ***** "...doing poorer in mathematics as compared to other students around the world (Schmidt, 1998)." (Furner ***** Qu*****n, 2001) For this reason, it is critical ***** ***** mathematics teacher have a sound knowledge- education- and experience-base ***** draw upon in ***** instruction. Th***** is most particularly so in ***** highly technological society for practical ***** and to develop more positive dispositions toward mathematics learning. It is documented in the ***** of Bush, Lamb ***** Alsina, (1990); Fullan (1983); Kessler (1985), McGalliard (1983); Silver (1985); and Thompson (1984) that "teaching behavior is profoundly or subtly affected ***** teachers beliefs concerning mathematics." (***** and Quinn, 1998)

Thompson (1984) states findings that the opinions and belief of ***** teacher impact their instructional practice ***** may be because of ***** teaching methods that are inappropriate (Ferrini-Mundy, 1986) Ongoing research again and again emp*****izes the need for *****s to re*****m education in promoting mathematics instruction

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