Resequencing Skills and Concepts in Applied Calculus Using the Computer as a Tool

Heid, M. Kathleen

doi:10.2307/749108

Cited by 115 publications

(69 citation statements)

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“…However, after a brief revision of routine skills, they improved to match the control students at routine problems whilst retaining their superiority in higher order skills. This is consistent with Heid's work in calculus (Heid 1988) where it was shown that students who use the computer for conceptual work and only carry out routine manipulation for a short time at the end of the course were better at higher level conceptual problems than control students following a traditional course and not significantly different in ability with routine manipulation.…”

Section: Reflectionssupporting

confidence: 76%

Encouraging versatile thinking in algebra using the computer

Tall

Thomas

1991

Educ Stud Math

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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 of versatile 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 nonequivalent expressions. We call such a piece of software a generic organizer because it 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.

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Section: Reflectionssupporting

confidence: 76%

Encouraging versatile thinking in algebra using the computer

Tall

Thomas

1991

Educ Stud Math

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“…(Heid, 1984, p. 2;1988) When students studied calculus using Mathematica, focusing on conceptual ideas and using the software to carry out the computations, it has been claimed that:…”

Section: Powerful Combinations Of Visual and Symbolicmentioning

confidence: 99%

Advanced Mathematical Thinking and the Computer

Dubinsky¹,

Tall²

2002

Advanced Mathematical Thinking

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“…[5][6][7][8][9][10][11]. These studies give a picture of CAS being a tool that students use in the classroom, once they have learned to master CAS, i.e.…”

Section: Cas In Mathematics Educationmentioning

confidence: 99%

Students’ use of CAS calculators – effects on the trustworthiness and fairness of mathematics assessments

Pantzare

2012

International Journal of Mathematical Education in Science and

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This is a submitted version of a paper published in International journal of mathematical education in science and technology.Citation for the published paper: Lind Pantzare, A. (2012 AbstractCalculators with computer algebra systems (CAS) are powerful tools when working with equations and algebraic expressions in mathematics. When the 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 12 th 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 lowachieving 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.

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Resequencing Skills and Concepts in Applied Calculus Using the Computer as a Tool

Cited by 115 publications

References 0 publications

Encouraging versatile thinking in algebra using the computer

Encouraging versatile thinking in algebra using the computer

Advanced Mathematical Thinking and the Computer

Students’ use of CAS calculators – effects on the trustworthiness and fairness of mathematics assessments

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