The dissertation must represent an original contribution to applied mathematics, pure mathematics, or statistics, and must be of such quality as to be publishable in an appropriate professional journal. A final public oral examination devoted to the defense and evaluation of the dissertation is administered after the dissertation has been approved by the dissertation committee.

Jones, Rich Wilson, and Shalini Bhojwani This article will discuss techniques that have been demonstrated to be effective with secondary students who have learning disabilities in mathematics.

Secondary students with learning disabilities generally make inadequate progress in mathematics. Their Dissertation multimedia mathematics is often limited by a variety of factors, including prior low achievement, low expectations for success, and inadequate instruction.

This article will discuss techniques that have been demonstrated to be effective with secondary students who have learning disabilities in mathematics. The body of research on mathematics instruction for secondary students with learning disabilities LD is not developed well enough to describe a specific and comprehensive set of well researched practices, but it is sufficient for defining a set of procedures and issues as clearly associated with effective instruction and increased student achievement.

In this article, data- based investigations of procedures that have evaluated the effectiveness of mathematics instruction with secondary students with LD will be discussed.

Although this discussion will be based primarily on studies that were limited to secondary students with LD, some research on the instruction and achievement of younger students or higher achieving populations will be considered. This discussion considers six factors that predictably confound efforts to increase the effectiveness of instruction.

Each of the factors is particularly relevant in the case of instruction for secondary students with LD. These factors are a students' prior achievement, b students' perceptions of self efficacy, c the content of instruction, d management of instruction, e educators', efforts to evaluate and improve instruction, and f educators' beliefs about the nature of effective instruction.

Prior achievement Although students with LD spend a substantial portion of their academic time working on mathematics Carpenter,severe deficits in mathematics achievement are apparent and persistent.

McLeod and Armstrong surveyed junior high, middle school, and high school math teachers regarding mathematics achievement. The teachers reported that skill deficits in basic computation and numeration were common.

Specifically, McLeod and Armstrong found that secondary students with LD had difficulty with basic operations, percentages, decimals, measurement, and the language of mathematics.

Algozzine, O'Shea, Crews, and Stoddard examined the results of 10th graders who took Florida's minimum competency test of mathematics skills. Compared to their general class peers, the adolescents with LD demonstrated substantially lower levels of mastery across all subtests.

These persistent skill deficits, combined with limited fluency of basic fact recall i. For secondary students with disabilities, the adequacy of instruction in mathematics will be judged not merely on how quickly basic skills can be learned. Students must also acquire generalizable skills in the application of mathematical concepts and problem solving.

The task of designing instructional programs that result in adequate levels of acquisition and generalization for students who have experienced seriously low levels of achievement for a large proportion of their academic careers is indeed a challenging one.

Perceptions of self-efficacy attributes for failure or success Individual differences in cognitive development certainly affect the achievement of academic skills. In earlier years, many professionals readily accepted that individual psychological differences accounted for failure to learn in school.

Students' expectations for failure frequently develop as a result of prolonged experiences with instruction that fails to result in successful performance. By the time students with LD become adolescents, they have typically endured many years of failure and frustration. They are fully aware of their failure to achieve functional skills in the operations and applications of mathematics.

Although research supports the argument that perceptions of self-efficacy are task specific and fairly accurate, it does not reveal that learning disabilities are consistently associated with lower general self-concepts Chapman, Chapman concluded that students who come to doubt their abilities a tend to blame their academic failures on those deficits, b generally consider their low abilities to be unchangeable, c generally expect to fail in the future, and d give up readily when confronted with difficult tasks.

Unless interrupted by successful experiences, continued failure tends to confirm low expectations of achievement, which in turn sets the occasion for additional failure. Pajares and Miller's study of self-efficacy and mathematics has implications for teachers who attempt to remediate low math achievement.

They found that students' judgments of their ability to solve specific types of mathematics problems were useful predictors of their actual ability to solve those problems. Specific student estimates of self-efficacy were more accurate predictors of performance than prior experience in mathematics.

Extending the results suggests three important issues.

First, judgments of self-efficacy are task specific and generally accurate. Second, student judgment of self-efficacy may provide insights that will be valuable supplements to teacher assessments of performance skills.

Third, negative expectations and motivational problems may be reduced by interventions to eliminate deficits in specific mathematics skills. The fact that student ratings of self-efficacy are accurate for both successful and unsuccessful students suggests that this is not a chicken-or-the-egg-type issue.

Instead, it suggests that initially there is a fairly direct path from instruction to performance and, subsequently, to perceptions of self-efficacy.NSF's mission is to advance the progress of science, a mission accomplished by funding proposals for research and education made by scientists, engineers, and educators from across the country.

Southern Arkansas University - the most affordable, fastest growing university in Arkansas. PhD Dissertation The dissertation must represent an original contribution to applied mathematics, pure mathematics, or statistics, and must be of such quality as to be .

I no longer understand my PhD dissertation (and what this means for Mathematics Education) Earlier this week I read through my PhD dissertation.

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