160 research outputs found
Encouraging versatile thinking in algebra using the computer
In this article we formulate and analyse some of the obstacles to understanding the notion of a variable, and the use and meaning of algebraic notation, and report empirical evidence to support the hypothesis that an approach using the computer will be more successful in overcoming these obstacles. The computer approach is formulated within a wider framework ofversatile thinking in which global, holistic processing complements local, sequential processing. This is done through a combination of programming in BASIC, physical activities which simulate computer storage and manipulation of variables, and specific software which evaluates expressions in standard mathematical notation. The software is designed to enable the user to explore examples and non-examples of a concept, in this case equivalent and non-equivalent expressions. We call such a piece of software ageneric organizer because if offers examples and non-examples which may be seen not just in specific terms, but as typical, or generic, examples of the algebraic processes, assisting the pupil in the difficult task of abstracting the more general concept which they represent. Empirical evidence from several related studies shows that such an approach significantly improves the understanding of higher order concepts in algebra, and that any initial loss in manipulative facility through lack of practice is more than made up at a later stage
Mathematically gifted and talented learners: Theory and practice
This is an Author's Accepted Manuscript of an article published in International Journal of Mathematical Education in Science and Technology, 40(2), 213-228, 2009, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/00207390802566907.There is growing recognition of the special needs of mathematically gifted learners. This article reviews policy developments and current research and theory on giftedness in mathematics. It includes a discussion of the nature of mathematical ability as well as the factors that make up giftedness in mathematics. The article is set in the context of current developments in Mathematics Education and Gifted Education in the UK and their implications for Science and Technology. It argues that early identification and appropriate provision for younger mathematically promising pupils capitalizes on an intellectual resource which could provide future mathematicans as well as specialists in Science or Technology. Drawing on a Vygotskian framework, it is suggested that the mathematically gifted require appropriate cognitive challenges as well as attitudinally and motivationally enhancing experiences. In the second half of this article we report on an initiative in which we worked with teachers to identify mathematically gifted pupils and to provide effective enrichment support for them, in a number of London Local Authorities. A number of significant issues are raised relating to the identification of mathematical talent, enrichment provision for students and teachersâ professional development
Gender Differences in Visuospatial Abilities and Complex Mathematical Problem Solving
Mathematical problem-solving and spatial visualization are areas in which performance
has been shown to vary with sex. This article describes the impact of gender on spatial
relations measured in 331 secondary school students (202 males, 129 females), 145
(105 males, 40 females) of whom had been selected to participate in a mathematical
talent stimulation project after passing a complex problem-solving test. In the two tests
administered, the Differential Aptitude Tests-Space Relations (DAT-SR) and the Primary
Mental Abilities-Space Relations (PMA-SR), performance was assessed on the grounds
of both absolute scores and the ratio to the number of items answered. The students
participating in the talent program earned higher scores on both tests, although no
interaction was identified between mathematical abilities and gender in connection
with the differences in spatial habilities observed. In PMA-SR, boys answered more
items and scored higher, whereas in DAT-SR girls tended to omit more items. None
of the indicators studied exhibited differences between the sexes in both tests and in
some cases the differences in the absolute values of the indicators were absent when
expressed as ratios
Mathematical talent in Braille code pattern finding and invention
The recognition of patterns and creativity are two characteristics associated with mathematical
talent. In this study, we analyzed these characteristics in a group of 37 mathematically talented
students. The students were asked to find the pattern the Braille code had been built upon and
reinvent it with the aim of making its mathematical language become more functional.
Initially, the students were unable to identify the formation pattern of Braille, but after
experiencing the difficulties that blind people face when reading it, they recognized the
generating element and the regularity. The results were in contrast with those of a control
group, and it is noted that the students with mathematical talent were more effective in using
visualization to identify the regularity of the pattern and their invention proposals were more
sophisticated and used less conventional mathematical content.This research is part of the R+D+I project EDU2015-
69,731-R (Spanish Government/MinEco and ERDF)
Research On and Activities For Mathematically Gifted Students
This Topical Survey offers a brief overview of the current state of research on and activities for mathematically gifted students around the world. This is of interest to a broad readership, including educational researchers, research mathematicians, mathematics teachers, teacher educators, curriculum designers, doctoral students, and other stakeholders. It first discusses research concerning the nature of mathematical giftedness, including theoretical frameworks and methodologies that are helpful in identifying and/or creating mathematically gifted students, which is described in this section. It also focuses on research on and the development of mathematical talent and innovation in students, including connections between cognitive, social and affective aspects of mathematically gifted students. Exemplary teaching and learning practices, curricula and a variety of programs that contribute to the development of mathematical talent, gifts, and passion are described as well as the pedagogy and mathematics content suitable for educating pre-service and in-service teachers of mathematically gifted students. The final section provides a brief summary of the paper along with suggestions for the research, activities, and resources that should be available to support mathematically gifted students and their teachers, parents, and other stakeholders
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