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

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manipulatives: what? Why? How?


*****? WHY? HOW?


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


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


Math manipulatives are traditionally concrete objects that one ***** able to manipulative ***** assists the individual in completion of math operations such as adding, subtracting, multiplying, division, and then on ***** more complicated operations such ***** 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 *****ly were used by merchants for calculation purposes. The abacus preceded the inventions ***** ***** used for counting and continually evolved in its appearance s*****ce ancient civilization. The abacus is pictured in ***** figure below labeled Figure 1 and ***** the copy of a cover of a manual that Lee Kai-chen published ***** ********** and ***** 4 decks within its design. Kai-chen claims that it is easier to perform both division and multiplication using this modified version of the abacus and that square roots of numbers and cubic ***** of numbers are much easier determined ***** this board.

Modified Version of Abacus

Source: Bagley (2004)

***** al***** include objects ***** as calculators, the slide-rule and compasses ***** in the Geometrical mathematics.


The work of Burns (1998) documents the fact *****: "...***** 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 ***** twelfth grade in school they are "...***** po*****er in ***** as compared to other students around the world (Schmidt, 1998)." (Furner and Quinn, 2001) For this reason, it is critical that the mathematics teacher have a sound knowledge- education- and experience-base to draw upon in ***** *****struction. Th***** is most particularly so in ***** highly technological society for practical ***** and to develop more positive d*****positions toward mathematics learning. It is documented in the ***** of Bush, Lamb and Als*****a, (1990); Fullan (1983); Kessler (1985), McGalliard (1983); Silver (1985); and Thompson (1984) that "teaching behavior ***** profoundly or subtly affected ***** teachers beliefs concerning mathematics." (Furner and *****, 1998)

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


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