Comparing the effects of visual and algebra tile manipulative methods on student skill and understanding of polynomial multiplication.

摘要

This study examined the effects that manipulatives had on the learning of algorithmic skills and understanding. Specifically, the effects of using algebra tiles on students' learning of polynomial multiplication were examined. Whole class participation with rectangular tiles such as Lab Gear, Algebra Tiles, and Algeblocks was used as the manipulative teaching method. Visual teaching consisted of the use of pictures or graphs. Teacher demonstration without the use of any manipulative or picture setting was the non-visual/non-manipulative method of teaching,;The classes of the teachers who volunteered to participate were used as the accessible population and the sample. These consisted of Algebra I and Applied Math classes. Each class was a unit of analysis for the data.;The classes were randomly assigned to the three methods of instruction. Teachers were given a curriculum with examples, illustrations, and worksheets for each lesson to be taught in the concept of multiplying positive polynomials. All three treatments used the same or equivalent written examples and worksheets. The three methods of instruction are currently being implemented throughout South Carolina and the United States as illustrated in textbooks and research materials. These have become established and accepted methods of instruction.;A statistically significant difference between the non-visual/non-manipulative and the manipulative teaching methods was found in both the skill data and the understanding data. This difference also extended to the open-ended question asking students to explain the process of multiplying polynomials. The use of manipulatives had a positive effect in learning the algorithm of multiplying binomials and extending to the general situations of multiplying polynomials. The students who were taught using the manipulatives method were better able to explain the process of multiplying polynomials in a written paragraph. The use of manipulatives, pictures, and numbers and variables provided students with multiple representations of the concepts. Even through there was no statistically significant difference between the non-visual/non-manipulative and the visual methods, the data show that students using the visual method had a higher mean score in both skill and understanding and were better able to explain the process of multiplying polynomials.