The Graphing Calculator: A Survey of Classroom Usage

The purpose of this study was to investigate secondary mathematics teachers' use of the graphing calculator in their classrooms, The study examined whether algebra teachers are currently using this technology in their classrooms, their perceptions toward the technology, and any changes in the curriculum or instructional practices. A survey methodology was used in this study. The findings indicated that the use of the graphing calculator is still controversial to many algebra teachers. Teachers of algebra I were using graphing calculators to a significantly lesser degree than teachers of algebra H. However, modifications of the algebra curriculum are beginning to appear in classes using graphing calculators. Finally, a majority of algebra teachers responded that the graphing calculator was a motivational tool.     

普通高中教育投入绩效评估实证研究——基于江门市47所高中调查的多层数据

基于江门市47所高中调查的多层数据,运用多层统计分析模型,进行普通高中教育投入绩效评估的实证研究,结果表明:中考成绩与学校绩效之间呈负相关态势;高考成绩最重要的决定因素是学生先前的知识储备和起始能力水平;教育经费投入对高考成绩有显著正影响;学校师资质量对提高学生学业成就有正影响;在47所学校中,有18所学校教育绩效较好,有27所学校教育绩效还有待进一步提高,相应的教育资源的配置需要进一步优化等,并提出相应的政策建议.     

Graphing Calculator Use in Algebra Teaching

This study examines graphing calculator technology availability, characteristics of teachers who use it, teacher attitudes, and how use reflects changes to algebra curriculum and instructional practices. Algebra I and Algebra II teachers in 75 high school and junior high/middle schools in a diverse region of a northwestern state were surveyed. Forty of the 75 schools (53%) returned a total of 109 individual surveys. Results indicated that: (1) While 78% of teachers have some access to the technology, only 28% use it regularly. (2) Statistically significant relationships exist between use and age, years of experience, teaching assignment, and teaching level. (3) Respondents view graphical solution methods as secondary to symbolic methods. (4) Teachers are more receptive to using technology to supplement rather than expand the curriculum.     

A Survey of High Order Schemes for the Shallow Water Equations

In this paper, we survey our recent work on designing high order positivity-preserving well-balanced finite difference and finite volume WENO (weighted essentially non-oscillatory) schemes, and discontinuous Galerkin finite element schemes for solving the shallow water equations with a non-flat bottom topography. These schemes are genuinely high order accurate in smooth regions for general solutions, are essentially non-oscillatory for general solutions with discontinuities, and at the same time they preserve exactly the water at rest or the more general moving water steady state solutions. A simple positivity-preserving limiter, valid under suitable CFL condition, has been introduced in one dimension and reformulated to two dimensions with triangular meshes, and we prove that the resulting schemes guarantee the positivity of the water depth.     

An Information-theoretic Approach to the Effective Usage of Auxiliary Information from Survey Data

In this paper, we propose an information-theoretic approach to the effective usage of auxiliary information from survey data, which is suitable for both simple and complex survey data. Our estimator under simple random sampling without replacement will be consistent and asymptotically normal. We show that the resulting estimates have smaller asymptotic variances than the usual estimates which do not use auxiliary information. For more complex survey designs, the resulting estimator is in essence asymptotically equivalent to a pseudo empirical likelihood estimator. Results of a limited simulation study show that the proposed estimators perform well among a number of competitors.     

Strategic Level MS/OR Tool Usage in the United Kingdom: An Empirical Survey

A survey of the practitioner members of the United Kingdom Operational Research Society was conducted to identify current levels of MS/OR tool usage at the strategic level. In this paper details of the survey will be outlined, the framework of strategic tasks will be described, and the MS/OR tool usage results for these strategic tasks will be presented and discussed.     

Assessing Students' Understanding of Functions in a Graphing Calculator Environment

In a classroom environment in which continual access to graphing calculators is assumed, items that have been used to assess students' understanding of functions often are no longer appropriate. This article describes strategies for modifying such items, including requiring students to explain their reasoning, using calculator-active items, analyzing graphs and tables, and using real contexts.     

The Quantity and Quality of Biology Laboratory Work in British Columbia High Schools

The purpose of this research was to survey the quantity and quality of laboratory work conducted by 11th- and 12th-grade biology students in British Columbia high schools to analyze student performance on laboratory-based questions on provincial examinations, and to examine the curriculum for recommended laboratory work. A pilot survey was used to produce a valid survey instrument that identified teachers' use of laboratory activities. Examination and curriculum data were extracted from Ministry of Education documents. The frequency of laboratory work was low, with quantitative activities much less frequent than qualitative. Laboratory exercises were confirmatory rather than investigative. Critical thinking and hypotheses formulation were seldom expected of the students. Many teachers reported that they infrequently or never used laboratory simulations or computer-based data collection. Although laboratories were equipped adequately, teachers claimed that the curriculum and provincial examination limited the scope for an inquiry-based course. Provincial examination results indicated that the frequency and type of laboratory work had no effect on scores on lab-based questions. Analysis of the laboratory activities recommended in the syllabus revealed that fewer laboratory activities were being conducted than are recommended in the curriculum guide outline. This study indicates that while the current philosophy of many biology teachers supports an investigative learning experience, little change in classroom practice has occurred in British Columbia schools.     

A Survey of Job Opportunities and Job Requirements and their Effect on the Mathematics Teaching for Early Leavers in Secondary Schools

A questionnaire survey was used to gauge the opinions of mathematics teachers about some history of mathematics material recently developed for use in the classroom. Teachers' opinions of the materials were generally favourable, but a sizeable proportion responded that they would not be prepared to actually use such material in their own teaching.

     

The Authority of the Calculator in the Minds of College Students

A group of 25 undergraduate students was given seven estimation tasks that involved computation of whole or decimal numbers. The subjects (10 elementary education majors, 7 mathematics majors, and 8 undecided or premajors) were selected because of high achievement in their current college mathematics class. They were asked to estimate an answer to a computational task and then use a calculator provided by the researchers to determine the exact answer. The calculator had been programmed to give incorrect answers that were increasingly higher than the actual answer (beginning with a 10% error and ending with a 50% error). While the majority of subjects produced reasonable estimates, only 7 of the 25 students questioned the accuracy of the answers produced on the calculator. The study points out the subjects’ lack of confidence in estimation skills, as well as a reluctance to question calculator produced results.