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Descriptors:
Disabilities; Academic Achievement; National Competency Tests; Class Activities; Learning Activities; Factor Structure; Grade 4; Educational Indicators; Achievement Gains; Performance Factors; Teacher Education; Professional Development; Access to Computers; Mathematics Achievement; Reading Achievement; Science Projects; Technology Uses in Education; Factor Analysis; Educational Opportunities; Calculators; Benchmarking; Predictor Variables; Student Characteristics; Item Response Theory; Standardized Tests; Individualized Education Programs; Measurement Techniques

Abstract:
Opportunity to Learn (OTL) stems from the basic premise that there is an important relationship between the quality and intensity of classroom instruction and students' levels of academic success. For many students with disabilities, an emphasis on OTL has become national priority, yet measuring its impact is a complex challenge. The first purpose of this study was to explore the factorial validity of OTL using indicators found in the 2005 4th grade National Assessment of Educational Progress (NAEP). The study entailed confirmatory factor analyses for potential OTL factors including teacher preparation, professional development, classroom activities, and access to technology. Separate factor analyses were conducted using the reading and mathematics datasets. The authors then looked at the degree to which OTL factors influenced NAEP estimates of ability for both students with disabilities and their non-disabled peers. The following three OTL factors differentially predicted student scores: classroom activities (reading), student constructed projects (reading), and using calculators for instruction (mathematics). For the remaining three reading factors and seven mathematics factors, there were no differences in the relationship between the factors and scores for students with and without disabilities. (Contains 13 tables.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Foreign Countries; Mathematics Tests; Calculators; Computer Assisted Testing; Equipment; Internet; Integrated Learning Systems; Electronic Learning; Engineering Education; Undergraduate Students; Instructional Effectiveness

Abstract:
WIRIS quizzes are an online mathematics tool for educational purposes that upgrade Moodle quizzes and allow the development of personalized quizzes using random data and conditional instructions. WIRIS quizzes can be used in any mathematics or science degree; their complex operators allow it to be used to solve electrical circuits. This tool promotes autonomous student learning and enables teachers to monitor that learning and make adjustments if necessary. Therefore, this tool improves teaching quality. It can also be used as an assessment tool by both the teacher and the student. This paper shows how WIRIS quizzes have been integrated into the virtual campus of the Polytechnic University of Catalonia (UPC), Spain, to teach electrical circuits. Lessons learned in performing and using WIRIS quizzes with second-year students at the UPC are shown. (Contains 9 figures and 1 table.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Algebra; Mathematics Tests; Calculators; Credibility; Mathematical Formulas; Questionnaires; Evaluation; Mathematics; Mathematics Education; Trigonometry

Abstract:
Calculators with computer algebra systems (CAS) are powerful tools when working with equations and algebraic expressions in mathematics. When calculators are allowed to be used during assessments but are not available or provided to every student, they may cause bias. The CAS calculators may also have an impact on the trustworthiness of results. In this study students' use of the CAS calculator in their work with released assessment items from TIMSS Advanced 2008 is studied using two approaches. Eight students familiar with CAS, from two mathematics classes in the 12th form, were video filmed when encouraged to think aloud during their work with the items. In addition, a questionnaire was distributed to all 33 students in the two classes who had been working with a CAS. The main finding is that even if the students are used to working with the CAS calculator, they are not using the calculator to a large extent. The analysis indicates that the difference in performance between the high- and low-achieving students has slightly increased due to the use of the calculator. From a validity perspective one could therefore argue that the CAS calculator is no major threat to the trustworthiness of the assessment. Nevertheless, the result indicates that those students in the study, mainly high achieving, who know how to use the CAS calculator, get an additional advantage. The advantage brings an amount of unfairness into the assessment and could be a threat to the trustworthiness and fairness. (Contains 2 tables and 5 figures.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Foreign Countries; Teacher Education Programs; Preservice Teacher Education; Special Education Teachers; Visual Impairments; Braille; Music; Calculators; Assistive Technology; Visual Aids; Online Courses; Blended Learning; Videoconferencing

Abstract:
Introduction: This study gathered data on methods and materials that are used to teach the Nemeth braille code, computer braille, foreign-language braille, and music braille in 26 university programs in the United States and Canada that prepare teachers of students with visual impairments. Information about instruction in the abacus and the preparation of tactile graphics was also gathered. Methods: A faculty representative from each university completed a 39-question online demographic survey during fall 2011. Frequency counts for each item were tabulated, and comments were reviewed and categorized. Results: All 26 university programs provided instruction in the Nemeth braille code. Most also provided introductory information on foreign-language braille, computer braille, and music braille. There was a high rate of consistency across the programs in what constituted a braille error. The university programs required students to prepare tactile graphics and learn computation on the abacus. The delivery of courses through a hybrid model was most common. Discussion: University programs are providing instruction in the Nemeth braille code, though there is variability in the topics that are covered, the books that are used, and the assignments that are required. Most university programs are also exposing their preservice students to specialized braille codes and are teaching them to produce tactile graphics and to perform computations on the abacus. Future studies are needed to look at the quality of instruction and, if the amount of instruction in the different topics is sufficient, to prepare future teachers of students with visual impairments adequately. Implications for practitioners: Data gathered from this study will assist university programs to evaluate the content of their courses on the topics that were studied. Adjustment in the content of courses may result, which may subsequently affect the skill set of practitioners as they complete university preparation. (Contains 3 tables.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Mathematics Achievement; Student Attitudes; Calculators; Grade 9; Mathematics Instruction; Secondary School Mathematics; Foreign Countries; Scores; Mathematics Tests; Comparative Analysis; Program Effectiveness; Educational Technology

Abstract:
Three calculator tests were administered to a national sample of 1,469 Irish students in Grade 9--the last cohort to study mathematics without calculators (Phase 1). Three years later, the same tests were administered to a similar sample with calculators (Phase 2). Scores on a test of calculator-inappropriate items showed no significant change over the 3 years. For a test of calculator optional items, students were divided randomly into 2 groups, 1 with calculator access and the other without. In both phases, the students with calculators achieved significantly better than the students without calculators. Achievement on a test of calculator appropriate items showed significant improvement over the 3 years. Students' attitudes toward calculators also improved over the time. (Contains 6 notes, 11 tables, and 2 figures.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Mathematics Achievement; National Competency Tests; Problem Solving; Calculators; Grade 8; Grade 4; Mathematical Concepts; Computation; Mathematics Education

Abstract:
This article summarizes research conducted on calculator block items from the 2007 fourth- and eighth-grade National Assessment of Educational Progress Main Mathematics. Calculator items from the assessment were categorized into two categories: problem-solving items and noncomputational mathematics concept items. A calculator has the potential to be used as a problem-solving tool for items categorized in the first category. On the other hand, there are no practical uses for calculators for noncomputational mathematics concept items. Item-level performance data were disaggregated by student-reported calculator use to investigate the differences in achievement of those fourth- and eighth-grade students who chose to use calculators versus those who did not, and whether or not the nation's fourth and eighth graders are able to identify items where calculator use serves as an aide for solving a given mathematical problem. Results from the analysis show that eighth graders, in particular, benefit most from the use of calculators on problem-solving items. A small percentage of students at both grade levels attempted to use a calculator to solve problems in the noncomputational mathematics concept category (items in which the use of a calculator does not serve as a tool to solve the problem). Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Mild Mental Retardation; Visual Aids; Program Effectiveness; Calculators; Decision Making; Intervention; Outcomes of Education

Abstract:
Background: Previous research has demonstrated that people with mild intellectual disabilities (ID) have difficulty in "weighing up" information, defined as integrating disparate items of information in order to reach a decision. However, this problem could be overcome by the use of a visual aid to decision making. In an earlier study, participants were taught to translate information about the pros and cons of different choices into a single evaluative dimension, by manipulating green (good) and red (bad) bars of varying lengths (corresponding to the value ascribed). Use of the visual calculator increased the consistency of performance (and decreased impulsive responding) in a temporal discounting task, and increased the amount of information that participants provided to justify their decisions in scenario-based financial decision-making tasks. Methods: The present study examined some practical aspects of visual calculator training, using a pen-and-paper version of two temporal discounting tasks. Participants with mild ID were tested, individually and in a group setting, before and after training in the group setting, and 2 months later. Results: (i) The visual aid improved temporal discounting performance using pen-and-paper presentation in a group setting as effectively as previously demonstrated using computer-based individual presentation. (ii) Following withdrawal of the aid, improvements in temporal discounting performance were maintained at 1 day post training, but lost following a 2-month hiatus; however, participants showed perfect retention, over 2 months, of how to use the aid. (iii) In addition to decreasing impulsivity in a hypothetical task, as previously demonstrated, use of the visual calculator also increased the ability of impulsive participants to wait in real time. Conclusion: The results suggest that the visual calculator has practical applicability to support decision making by people with mild ID in community settings. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Program Effectiveness; Calculus; Algebra; Foreign Countries; Mathematics Education; Universities; Computer Uses in Education; Educational Technology; Calculators; Mathematics Achievement

Abstract:
Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one where students learn and are examined with a computer algebra system (CAS) and another where students can only use scientific calculators. This study compares the performance of 1240 students as they transitioned to traditional university-level mathematics and according to whether they learned intermediate mathematics with or without the assistance of a CAS. This study concludes that students without CAS show a slight advantage, but the most important factor affecting student performance is the uptake of advanced-level mathematics studies in secondary school. (Contains 6 tables.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Evidence; Action Research; Academic Achievement; Calculators; Algebra; Computer Assisted Instruction; Teaching Methods; Mathematics Achievement; Foreign Countries; Secondary School Students; Mathematics Instruction

Abstract:
When a Computer Algebra System (CAS) is used as a pedagogical and functional tool in class and as a functional tool in exams, its effect on student achievement can be quite profound. The timing of when students are first introduced to a CAS has an impact on gains in student achievement. In this action research project, the CAS calculator was introduced to students and used to varying degrees in Years 10, 11 and 12. The effects on students' final year results were examined in terms of the timing of the introduction of the CAS device and the extent of its use in the classroom. There is some evidence of greater improvement in learning by introducing the calculator in Year 10 rather than Year 11. This gain is evident for low, average and above average mathematics achievers. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Intervention; Word Problems (Mathematics); Calculus; Subtraction; Mathematics Instruction; Mathematical Concepts; Number Concepts; Arithmetic; Teaching Methods; Problem Solving; Calculators

Abstract:
The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research on improving children's understanding and use of the principle of inversion through interventions has only been applied to the solving of a + b - b = ? sums. The main aim of the intervention described in this article was to study the effects of teaching children about the explicit use of inversion as part of the relational calculus needed to solve inverse addition and subtraction problems using a calculator. The study showed that children taught about relational calculus differed significantly from those who were taught numerical procedures, and also that effects of the intervention were stronger when children were taught about relational calculus with mixtures of indirect and direct word problems than when these two types of problem were given to them in separate blocks. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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