Abstract
Achieving proficiency in mathematics appears to be a particular area of challenge for students in the United States. The Trends in International Mathematics and Science Study (TIMSS) recently released results for 2003 testing, and revealed that eighth graders in the United States rank 15th among 46 participating countries (Snell, 2005). Although these results are a significant improvement from the 1995 performance, the United States students still rank near the bottom when compared to other students from industrialized nations. Research in the area of mathematics achievement has examined a number of explanations as to why some students will test proficient and many will not (e.g., Hyde, Fennema, & Lamon, 1990; Mason, & Scrivani, 2004; Mevarech, Silber, & Fine, 1991; Rangappa, 1993, 1994). Using data extracted from the Education Longitudinal Study (ELS, 2004), the present study investigated the impact of student reading ability, student math self-efficacy, teacher expectations, and the use of computers in the teaching of mathematics in predicting student math achievement. Findings reveal that 56% of the variance in student math achievement can be explained by students’ reading ability. The results of the final regression model also revealed that higher levels of math-self-efficacy and higher levels of teachers’ expectations were associated with higher math achievement scores. However, a negative association between computer-assisted instruction and student math achievement scores was found.
Highlights
―Communication is an essential part of mathematics and mathematics education‖ (National Council of Teachers of Mathematics [NCTM], 2000, p. 60)
It enables students to reflect upon concepts through interactions with others engaged in the same activity as well as allow students to become familiar with certain ways of describing mathematics while they are doing mathematics— providing students opportunities to become more knowledgeable (Lee, 2006)
There is empirical evidence supporting the cognitive benefits of manipulative use (e.g. Moch, 2001; Warrington & Kamii, 1998), mathematical writing (e.g. Jurdak & Abu Zein, 1998; Kenney, 2005), and mathematical discussion (e.g. Mercer & Sams, 2006; Hiebert & Wearne, 1993)
Summary
―Communication is an essential part of mathematics and mathematics education‖ (National Council of Teachers of Mathematics [NCTM], 2000, p. 60). The process described involves transitioning from manipulating concrete materials to creating images from the student’s perception of the concept, and to the development or adoption of some form of symbolic notation representing the concept Throughout his descriptions of using manipulatives to move students from concrete to abstract understanding, Bruner (1973) describes language as an integral part of manipulative use. Moch, 2001; Moyer, 2001; Stein & Bovalino, 2001) illustrates written and verbal communication as part of manipulative use, and the converse has been discussed (Kroll & Halaby, 1997; Whitin, 2004), an interactive relationship between these cognitively benefitting practices would appear to exist. Using student-created representations and engaging in class discussion, students were able to find solutions to problems such as ―1/3 of 1/3‖ which is written symbolically as ―1/3 x1/3.‖ By learning to think of the problems in this way, students were able to transition to using the symbolic representation more than if it had been introduced first as a normal multiplication problem
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