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Fifty percent of college-bound students graduate from high school underprepared for mathematics at the post-secondary level. As a result, thirty-five percent of college students take developmental mathematics courses. What is even more shocking is the high failure rate (ranging from 35 to 42 percent) of students enrolled in developmental mathematics courses. Many studies in the literature have addressed this high failure rate from the prospective of environmental challenges, but very few explored the root of students' mathematical errors. This study sought to determine the error patterns of developmental mathematics students in real number computations. And, in addition, this study explores students' use the order of operations in simplifying arithmetic expressions and evaluating algebraic expressions. Lastly, this study explored the misconceptions that undergirded those errors and gave some possible reasons for those misconceptions. The study encompassed a mixed method design--both quantitative (item analysis) and qualitative (interview)--in order to answer the research questions. The results of the item analysis were used to determine which problems were missed due to procedural errors or misconceptions. The qualitative analysis included the examination of the students' paper and pencil tests and video interviews. The researcher (a) examined the solution to each test item on the students' tests, (b) discerned steps believed the students took to arrive at the solutions, and (c) coded the steps. A convenience sample of students enrolled in ten sections of Developmental Mathematics 0371 (DMTH 0371) taught by eight instructors during the spring semester of 2010 were used in this study. Data collection included: (a) students' test results, work, and scratch paper on the DMTH 0371 test; (b) video-taped interviews; (c) demographic information; and (d) the placement test and results used to place students in DMTH 0371, which were gathered from the Student Information System (SIS) and Banner. Two forms of the assessment instruments were used in this study: a selected-response (multiple-choice item format) test and constructed-response (open-ended response format) test. The results of this study identified four types of error patterns made by developmental mathematic students. Most of the students demonstrated a fragmented understanding of signed-number arithmetic (negative numbers), sign errors, fractions, distributive property (parentheses), and exponential errors in simplifying both arithmetic and algebraic expressions. The students also misinterpreted operations and executed buggy algorithms both arithmetically and algebraically. Thus, across all of the students' errors made in different problems, a weak understanding of negative numbers seems to be the fundamental sources of their different errors. These students simply ignored the presence of the "negative sign" in order to get an answer (i.e., these students try to "repair" a new situation). These findings typically suggest that any remediation program should go beyond students' procedural errors to the aspect of "conceptions." The information provided by this study could be of value to the instructional practices community colleges and universities developmental mathematics programs. However, this study should be replicated and extended to include a larger population to determine if the errors and misconceptions can be generalized to all developmental mathematics students with similar characteristics. Similar studies should be conducted to either validate or argue the results obtained in this study. Research should be done to determine appropriate remediation instructional strategies for the errors presented in this study. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

This practicum investigated the effectiveness of using music activities to reinforce basic money skills with 10 students, ages 12 to 21, with mental retardation in the trainable range. The program used a combination of music and visual aids as strategies for reinforcing basic money skills and improving student on-task behaviors in the classroom. Pretests and posttests as well as systematic observation were used to evaluate the intervention. Results indicated increased achievement levels of basic coin money skills for the target group. Students also demonstrated increased on-task behaviors. Appendices include student data of previous mastery of basic money skills, the coin money skills pretest/posttest, summary of pretest data, the observation form (used both before and after program implementation), summary of observation data, lyrics to coin money skills song activities, coin face manipulative reproduceables and coin identification chart, explanation of a schoolwide money skills student video project, and an attachment of recommended music resources to reinforce basic skills. (Contains 35 references.) (DB)

The present mixed-methods quasi-experimental study (embedding a case study and a mixed factorial within-between ANOVA test), conducted in a private English school in Limassol, Cyprus, investigated how the use of the schematic learning aids (researcher-made color-coded flash-cards and grids) influence year-2 children's ability to read, write and represent Hindu-Arabic numerals and how these number representations affect their arithmetic competency. This was achieved by comparing an intervention group (n = 16) and a control group (n = 17) before and after the 2-week intervention. It is concluded that the use of the place-value learning aids facilitates numeration system conceptual understanding, reading, writing and representing numbers (in canonical and non-canonical form) by thinking in terms of "100s", "10s" and "1s" (or in terms of color-coded cards). Students visually relate the face-value of the digits (e.g. "3" and "5") of the number (e.g. "35") with the number of flash-cards to be used for the canonical representation (three orange cards and five blue cards). Children also understand how "53" differs from "35" or "503". It is further concluded that the use of the learning aids facilitates addition and subtraction performance in terms of "hundreds", "tens" and "ones" (rather than just "ones") either mentally or by constructing canonical and non-canonical representations with the use of the flash-cards and grids or by constructing abstract representations on paper. Students realize that ten cards of one color can be exchanged with one card of another color (or vice versa). Students further understand how "35-2" differs from "35-20" and how "51-32" differs from "52-31". Quantitative data are in agreement with qualitative data, suggesting that children's arithmetic competency is enhanced when taught how to represent numbers, additions and subtractions with the use of the learning aids. The control group mean score increase from before to after intervention was 1,24 marks, compared to an increase of 11,06 marks for the intervention class. The medium to large Cohen's d effect sizes of 0,51 (comparing the intervention group score increase to the control group score increase) or 0,57 (comparing the intervention group score from before to after) indicate strong practical significance. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

In this practicum students' (n=27) learning styles were used to develop teaching lessons and strategies that would improve mathematics learning in a second grade classroom. Each child's learning style was determined through the Swassing-Barbe Modality Index (SBMI). Pretests for mathematics concepts were given. Each concept was then taught incorporating each of the learning styles. Posttests indicated an increased level of understanding and achievement by the target group. Daily logs and records indicated an improvement in work habits and attitudes. It was determined that testing learning style preferences and teaching to these preferences can result in an increase of learning and achievement. Included in this study are the purpose, research and solution strategy, method, results, and recommendations. Appended are a sample of daily records, copies of pretests and posttests, lesson plans, and a sample of a SBMI record sheet. (Author/KR)

The goal of this practicum was to involve parents in their children's mathematics learning. To accomplish this aim, efforts were made to improve children's performance and attitudes toward mathematics; to enable teachers to recognize the value of activities and games as an alternate to learning by rote; and to offer opportunities for parents to participate in workshops in order to obtain the knowledge necesary to help their children with mathematics, to explore various activities, and to have a hands-on experience with math materials to use at home. The implementation consisted of meeting with children in grades three through six to introduce them to exciting and stimulating math activities in order to show them that math can be an enjoyable subject. Six workshops for parents were designed to discuss pertinent information and mathematical activities they could use at home to improve their children's achievement and attitude towards math. Measurement of objectives was achieved by observation; the feedback of children, teachers, and parents; and responses to an evaluation form designed to reveal parental reactions to the program. Included are the introduction, study of the problem, anticipated outcomes and evaluation instruments, solution strategy, results, discussion, and recommendations. Appended are the evaluation forms, recommendations for parents, letters to parents, description of number tricks, sample of children's activity sheets, description of games played, sample of activity sheets distributed to parents, and math challenges. (Author/KR)

This practicum was designed to expand the scope of the inservice mathematics manipulative training program to address the lack of parent and teacher understanding of the use of manipulatives that are used by Chapter I math tutors to remediate students. A second aim was to acquaint and assist parents and teachers with remediation of educationally deprived elementary school aged children by using manipulatives. A parent survey and needs assessment was used to develop and facilitate inservice mathematics manipulative training sessions which focused on helping parent and teachers understand manipulatives for remediating basic mathematics skills. Included in this study are the: (1) "Introduction"; (2) "Study of the Problem"; (3) "Anticipated Outcomes and Evaluation Instruments"; (4)"Solution Strategy"; and (5) "Results, Conclusions and Recommendations". Appended are a copy of the parent survey, pre- and post- parent/teacher surveys, and miscellaneous documents. (Author/KR)

Mathematics teachers are trained to assess students' abilities and instruction needs. Many teachers use creative teaching strategies, games, and various media to meet those needs. Teachers, though, are constantly searching for instructional strategies, time savers, games, materials, and other ways to improve teaching in mathematics classrooms. Since they have such busy schedules and lack the time to get together with fellow teachers to share ideas and visit each others' classrooms, a mathematics publication was developed to address these needs. The publication was written by and for teachers. Mathematics teachers shared ideas with other teachers in the district in articles which were published in the issue. A target group was pre-surveyed before the publication and post-surveyed after the publication was distributed. The knowledge and usefulness expressed by the target group indicated the desire for future issues of the publication within the school district. Included in this report are the purpose of this project, a brief literature review, a description of the project methods, results of the project, and recommendations. Copies of memos, surveys, and letters are appended. (Author/CW)

Activities were provided for a target group of third grade students who were experiencing difficulty in mastering the skills required to solve problems involving money. The program's aims were to remediate these students by giving them the opportunity to use instructional software that would increase their mathematical vocabulary, strengthen the logic behind their thought patterns, and assist them in mastering the skills necessary to solve word problems with confidence and success. Developed and implemented was a computer program that included reading, understanding, analyzing, estimating, and computing with regard to the solving of word problems having to do with money and the making of change. Each of the students in the target group was given a pretest, an attitudinal survey, and a posttest. Results indicate that the students in the target group improved their ability to solve word problems concerning money and the making of change. The attitudinal survey indicated that the students gained both confidence and a feeling of success. Included in this study are the purpose, research, method, results, and recommendations. Appended are the minimal standards for the county and state in which the research was done, sample tests, parental survey form, software evaluation form, letters from both principal and teachers, and a documentation packet on the computer program that was used. (KR)