Examining calculator use among students with and without disabilities educated with different mathematical curricula

This study assessed if students with and without disabilities used calculators (fourfunction, scientific, or graphing) to solve mathematics assessment problems and whether using calculators improved their performance. Participants were sixth and seventh-grade students educated with either National Science Foundation (NSF)-funded or traditional mathematics curriculum materials. Students solved multiple choice and open-ended problems based on items from the State’s released previous assessments. A linear mixed model was conducted for each grade to analyze the factors impacting students’ self-reported calculator use. Chi Square tests were also performed on both grade’s data to determine the relationship between using a calculator and correctly solving problems. Results suggested only time as a main factor impacting calculator use and students who self-reported using a calculator were more likely to answer questions correctly. The results have implications for practice given the controversy over calculator use by students both with and without disabilities.     

The association of precollege use of calculators with student performance in college calculus

This study investigates how the use of calculators during high school mathematics courses is associated with student performance in introductory college calculus courses in the USA. Data were drawn from a nationally representative sample of 7087 students enrolled in college calculus at 134 colleges and universities. They included information about students’ demographics, standardized test scores, and high school mathematics course enrollment and performance. Factor analysis reduced ten items describing high school calculator usage to two composites: how extensively calculators were employed and teacher-imposed restrictions on their use. Hierarchical linear models predicted students’ college calculus grades, reported by their professor, while controlling for differences between colleges and student backgrounds. The more extensively students had used calculators in high school, the lower their grade in college calculus. However, students earned higher college calculus grades to the extent that their high school teachers had limited calculator use on quizzes and exams and had restricted calculator use until paper-and-pencil methods had been mastered, which offset the negative association of extensive calculator use with grades. The effect sizes of both calculator composites were very small. Overall, the findings raise doubts about any substantial long-term effects on college mathematics performance of calculator use in high school.     

Creating Meaning for and with the Graphing Calculator

In this study, we seek to describe how the meaning of a tool was co-constructed by the students and their teacher and how the students used the tool to construct mathematical meaning out of particular tasks. We report the results of a qualitative, classroom-based study that examined (1) the role, knowledge and beliefs of a pre-calculus teacher, (2)how students used graphing calculators in support of their learning of mathematics, (3) the relationship and interactions between the teacher's role, knowledge and beliefs and the students' use of the graphing calculator in learning mathematics, and (4) some constraints of the graphing calculator technology that emerged within the classroom practice. We found five patterns and modes of graphing calculator tool use emerged in this practice: computational tool, transformational tool, data collection and analysis tool, visualizing tool, and checking tool. The results of this study suggest that nature of the mathematical tasks and the role, knowledge and beliefs of the teacher influenced the emergence of such rich usage of the graphing calculator. We also found that the use of the calculator as a personal device can inhibit communication in a small group setting, while its use as a shared device supported mathematical learning in the whole class setting.This revised version was published online in September 2005 with corrections to the Cover Date.     

Mathematics Test Performance: The Effects of Item Type and Calculator Use

Previous research has provided conflicting findings about whether allowing the use of calculators changes the difficulty of mathematics tests or the time needed to complete the tests. Because the interpretation of results from standardized tests via norm tables depends on standardized conditions, the impact of allowing or not allowing examinees to use calculators while taking such tests would need to be specified as part of the standardizing condition. This article examines four item types that may perform differently under different conditions of calculator use. This article also examines the effect of testing under calculator and noncalculator conditions on testing time, reliability, item difficulty, and item discrimination.     

图形计算器与中学数学创新教育—几个值得思考的问题

图形计算器作为一种现代化教育技术，在中学数学创新教育中发挥着越来越大的作用，近几年来，北京市有40多所中学的几百名教师，利用图形计算器开展课题研究，使图形计算器进行中学数学创新教育的关键是教育观念的更新，重点是改进课堂教学过程，方向是实现现代教育技术与课程及教材的整合，开展课题研究则是进行创新教育的一种重要而有效的途径。     

Effects of Calculator Use on Scores on a Test of Mathematical Reasoning

A sample of college-bound juniors from 275 high schools took a test consisting of 70 math questions from the SAT. A random half of the sample was allowed to use calculators on the test. Both genders and three ethnic groups (White, African American, and Asian American) benefitted about equally from being allowed to use calculators; Latinos benefitted slightly more than the other groups. Students who routinely used calculators on classroom mathematics tests were relatively advantaged on the calculator test. Test speededness was about the same whether or not students used calculators. Calculator effects on individual items ranged from positive through neutral to negative and could either increase or decrease the validity of an item as a measure of mathematical reasoning skills. Calculator effects could be either present or absent in both difficult and easy items     

The Use of Curry Teaching Simulations in Professional Training

Summary

This article describes how a teacher changed her method of teaching after acquiring knowledge about graphing calculators in a Professional development program. It describes one particular unit on understanding variables and graph interpretation taught in a seventh-grade science and math class. The use of graphing calculators proved to be effective in increasing student understanding of relationships between variables, graphing, and experimental design. The teacher in our project also found graphing calculators to be effective tools for teaching constructively. Our study implies that math and science teaching can be improved through the use of graphing calculators.     

Gender Differences in Constructed Response Reading Items

To evaluate the effects of calculator use on performance on the SAT I: Reasoning Test in Mathematics, questions about use of the calculator on the test were inserted into the answer sheets for the November 1996 and November 1997 administrations of the examination. Overall, nearly all of examinees indicated that they brought a calculator to the test and about two thirds reported using them on one third or more of the math items. Some group differences in the use of calculators were observed with girls using them more frequently than boys and Whites and Asian Americans using them more often than other racial or ethnic groups. Use of calculators was associated with higher test performance, but the more able students were more likely to have calculators and used them more often. The results were analyzed further using multiple regression and differential item functioning procedures. The degree of speededness on different degrees of calculator use was also examined. Overall, the effects of calculator use were found to be small, but detectable.     

Prospect

ABSTRACT

The 1988 Education Reform Act introduced a schools’ quasi‐market intended to reward schools financially for recruiting pupils and to give them a financial incentive for ‘good’ educational performance. The paper examines this linkage by analysing data on financial performance for over 300 English Local Education Authority (LEA) and Grant Maintained (GM) secondary schools from 1990/91 to 1995/96, correcting for inflation and changes in LEA delegation ratios. On average over 6 LEA areas, real school budgets per pupil declined by 0.6% a year while examination performance at GCSE improved. Statistical analysis shows that while change in pupil numbers is the most important variable explaining school budget change, half as much is explained by variations in LEA and government financial policy, thus weakening market incentives. It was also found that the proportion of socially disadvantaged pupils, as measured by free school meals, is associated with a loss of pupils over time and hence a decline in budget. GM status had no discernible effect on pupil recruitment, once social disadvantage and other explanatory variables were taken into account. It is suggested that both ecological and open systems theories of how organisations change in response to external environmental pressures explain the differential success of schools in attracting resources.     

Personalizing college mathematics with technology

Abstract

This study investigated personalization as an innovation that can be used to impact college mathematics achievement. In the reported study, similar tasks using personalized data and teacher-selected data were implemented in courses in both 4-year and 2-year colleges. Pre- and posttests and student work were analyzed to examine the impact of personalization on student understanding. Our findings provide insight into how the use of the technology can influence students’ thinking and ability to connect with and use personally authentic data.     

Pre-service teachers learning mathematics using calculators: a failure to connect current and future practice

This study brings to the forefront pre-service teachers’ contrasting views between their own use of calculators and their views of appropriate use of calculators in the elementary school classroom. Using a Heideggerian perspective, this paper describes a course in which pre-service teachers study mathematics in a reform setting but may fail to connect their use of calculators and their views of how their future students could utilize technology in a similar manner. This study also demonstrates that, in contrast to commonly held beliefs about students’ overuse of calculators, most of the pre-service teachers did not rely exclusively on their calculators.     

Graphic abilities in relation to mathematical and scientific ability in adolescents

Background:?The study investigated a small range of cognitive abilities, related to visual-spatial intelligence, in adolescents. This specific range of cognitive abilities was termed ‘graphic abilities’ and defined as a range of abilities to visualise and think in three dimensions, originating in the domain of visual-spatial intelligence, and related to visual perception and the ability to represent space. The educational importance of graphic abilities has received minimal attention from the educational community and, consequently, plays a limited role in educational practice.

Purpose:?In order to understand the particular educational importance of this range of cognitive abilities, we investigated how graphic abilities are connected with the performance and the subject preference of adolescents in several academic areas. Our hypotheses were, first, that there is a high degree of correlation between developed graphic abilities and high performance in mathematics and science, and second, that there is a high degree of correlation between developed graphic abilities and personal subject preference in these two areas.

Sample:?The sample consisted of 60 14-year-old students (30 girls and 30 boys) attending a public secondary school in a small town in northern Greece. The entire sample had followed the same mathematics courses, which did not involve any geometry or spatial representation tasks.

Design and methods:?We identified and defined a specific range of three graphic abilities, related to visual-spatial intelligence, and we investigated these abilities in the sample through several visual-spatial tasks designed for the study and measured the sample's performance in these tasks. The degree of adolescents' graphic performance (that is, the performance in these visual-spatial tasks) was correlated with their performance in mathematics and science and with their subject preference (mathematics, science and language).

Results:?Our findings confirmed both hypotheses. A high degree of correlation was found between developed graphic abilities and high performance in mathematics, and a lower but still significant degree of correlation was found between developed graphic abilities and high performance in science. The findings support the second hypothesis as well, suggesting that children with developed graphic abilities reported that their favourite subject was mathematics and second favourite subject was science.

Conclusions:?The research suggested that there is a particular relation between the level of graphic abilities performance and children's performance and in preference for mathematics and science. That is, children with developed visual perception, visual thought and representational skills are actually better with numbers and physical concepts. This particular relation might be relevant to the overall cognitive development of children, especially with respect to the increasingly developing communication technologies, and it would seem to deserve more attention and extended research from the educational community. The authorial position is that education would gain from a better understanding of: the nature of graphic abilities, how we can develop this range of abilities and how the development of visual thought and graphic expression contributes to several curriculum subjects.     

What can evidence-use in practice learn from evidence-use in policy?

Abstract

Background: This paper approaches evidence-informed practice from the perspective of evidence-informed policy-making. Using the findings of a recent study of evidence-use by educational policy-makers to raise questions about evidence-use by educational practitioners, it seeks to explore what such a study might tell us about how to understand and improve evidence-use by educational practitioners.

Purpose: The paper aims, therefore, to identify potential connections, shared insights and common issues between evidence-use in policy and evidence-use in practice. It does this by focusing on two specific areas: the nature of the evidence (i.e. what evidence is used) and the nature of the use (i.e. how evidence is used). The paper outlines what was found about each of these aspects of evidence-use in policy, and then considers what questions and issues these findings might raise for evidence-use in educational practice.

Sample: The empirical study on which this paper is based was an in-depth study of the use of evidence within educational policy development in Australia. It focused on the development of three specific education policies within one Australian state education department and involved interviews with 25 policy-makers who were actively involved in the development of these policies.

Design and methods: The policy-based study involved the following data collection processes: (i) in-depth semi-structured interviews with 25 policy-makers who were involved in the development of the selected policies; (ii) documentary analysis of policy documents, background research reports and other relevant papers relating to the selected policies; (iii) unstructured observation (where possible) of meetings and events connected with the development of the selected policies; and (iv) feedback from 40 wider policy staff who took part in a verification workshop to discuss the project’s emerging findings.

Findings: Drawing on the findings from the original policy study, two areas of potential connection to evidence-use in practice are explored. First, in relation to ‘varieties of evidence and uses’, the negotiation of diverse evidence types and the potential for using evidence in multiple and varied ways appear to be features of evidence-use that are common to educational policy-makers as well as educational practitioners. Secondly, in relation to ‘narrowness of evidence sources’, there is potential for both policy-makers and practitioners to use a narrow (rather than broad) selection of evidence, due to a tendency to work with certain evidence types as a starting point (e.g. performance data) and a tendency to draw on certain evidence sources more frequently (e.g. well-known, familiar research sources).

Conclusions: This paper emphasises: (i) the need for more integrated (or joined-up) understandings of evidence-use across contexts of practice and contexts of policy; (ii) the importance of continued efforts to understand and represent evidence-use more effectively within educational practices; and (iii) the value of paying careful attention to the quality and qualities of evidence-use within and across the different settings of educational practice and policy.     

The New ‘Functional Mathematics’ for Learners with Down Syndrome: Numeracy for a Digital World

ABSTRACT

This paper explores the challenge of determining the mathematics curriculum for students with Down syndrome in our digital age where the tools of mathematics including electronic calculators and smartphone applications are readily available. Aspects once considered essential for ‘functional mathematics’ such as written calculation, using cash and telling time can be undertaken with easily accessible devices. Deeper concepts such as generalising through algebra, making decisions about money, and engaging in mathematical problem solving and applications are now a possibility. This paper explores the challenge through the theoretical perspectives of Educational Quality of Life and Numeracy Development, presenting five principles for mathematics curriculum planning. The possibility exists of using year level appropriate mathematics curriculum to build lifelong numeracy – ‘functional’ mathematics for a new age.     

Conclusions About Frequently Studied Modified Angoff Standard-Setting Topics

Test makers are struggling with the issue of whether to provide a standard calculator for all participants or allow students to bring in their own calculators. A within-subjects design was used to examine (a) effects of calculator type (own calculator vs. standard calculator) on student performance and (b) differential impacts of calculator type for children from a variety of backgrounds. Fifty Grade 8 students completed a set of National Assessment of Educational Progress problems and a set of timed computation tests with their own calculators and comparable sets of problems with a standard calculator. Performance on mathematical items (i.e., time, accuracy) and the ways in which students used the calculators (e.g., number of keys pressed, calculator difficulties) were not affected by calculator type. No performance advantages associated with calculator type were related to student background characteristics (e.g., socioeconomic status, ethnicity, sex, math ability). However, calculator preference depended on the complexity of the student's own calculator relative to the standard one.     

Using quality enhancement processes to achieve sustainable development and support for sessional staff

Abstract

Consistent with quality enhancement, we report on how we used a continuous improvement cycle to formalise and embed an academic development and support programme for our School’s sessional staff. Key factors in establishing and maintaining the programme included: local change agents supported initially by institutional project funding; School support for key academic and administrative roles; timely access to reports and tools from nationally-funded projects and sessional staff input. Reviewing our approach against national standards highlighted ongoing actions while collaboration with academic developers is critical for advancing our understanding and reviewing our approaches in our continuously changing context.     

Professional autonomy versus managerial control: The experience of teachers in an english primary school

This article examines the relationship between primary teachers' professional autonomy and the increasing managerial control over teachers' work. It considers how the education policies of successive Conservative and New Labour administrations in Britain have tightened central control over education undermining teacher discretion and directly impacting upon the labour process of the professionals concerned. The research was undertaken in an English primary school and data gathered in a variety of contexts including observations of the teachers in classrooms and the staff room, a governors/parents meeting, informal conversations and a series of semi-structured interviews with staff. The study explores how teachers make sense of the managerial culture in education, and how this is reconciled with their ideas about teaching and learning, and their professional interests and individual career aspirations. Structuration theory (Giddens, 1976, 1979, 1984) is used as a theoretical framework to explore whether there is conflict between teachers' professionalism and the new managerialism and examine how primary teachers make sense of this inextricable relationship.