John Monaghan

University of Agder

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Social and Cultural Anthropology

John Monaghan Peter Just

1. FIELDWORK AND ETHNOGRAPHY 2. CULTURE 3. SOCIETY 4. SEX AND BLOOD 5. CLASS AND CASTE, VILLAGE AND CITY, HOME AND THE WORLD 6. LANGUAGE AND SOCIAL LIFE 7. THE CULTURALLY CONSTRUCTED SELF 8. THE FUTURE OF ANTHROPOLOGY FURTHER READING INDEX.

Cultural Anthropology

Social anthropology

10.1093/actrade/9780192853462.001.0001

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Citations (66)

Adolescents' understanding of limits and infinity

John Monaghan

AIM To investigate mathematically able adolescents' conceptions of the basic notions behind the Calculus: infinity (including the infinitely large, the infinitely small and infinite aggregates); limits (of sequences, series and functions); and real numbers. To observe the effect, if any, on these conceptions, of a one year calculus course. EXPERIMENTS Pilot interviews and questionnaires helped identify areas on which to focus the study. A questionnaire was administered to Lower Sixth Form students with 0-level mathematics passes. The questionnaire was administered twice, once in September and again the following May. The A-level mathematicians had received instruction in most of the techniques of the Calculus by May. Interviews, to clarify ambiguities, elicit reasoning behind the responses and probe typicality and atypicality, were conducted in the month following each administration. A second questionnaire, an amended version of the first, was administered to a larger but similar audience. The responses were analysed in the light of hypotheses formulated in the analysis of data from the first 5ample. PRINCIPAL FINDINGS Subjects have a concept of infinity. It exists mainly as a process, anything that goes on and on. It may exist as an object, as a large number or the cardinality of a set, but in these forms it is a vague and indeterminate form. The concept of infinity is inherently contradictory and labile. Recurring decimals are perceived as dynamic, not static, entities and are not proper numbers. Similar attitudes exist towards infinitesimals when they are seen to exist. Subjects' conception of the continuum do not conform to classical or nonstandard paradigms. Convergence / divergence properties are generally noted with infinite sequences and functions. With infinite series, however, convergence / divergence properties, when observed, are seen as secondary to the fact that any infinite series goes on indefinitely and is thus similar to any other infinite series. The concept that the hut is the saue type of entitiy as the finite tens is strong in subjects' thoughts. We coin the term generic hiuit for this phenomenon. The generic limit of 0.9, 0.99, is 0.9, not 1. Similarly the reasoning scheme that whatever holds for the finite holds for the infinite has widespread application. We coin the term generic law for this scheme. Many of the phrases used in calculus courses (in particular hut, tends to, approaches and converges) have everyday meanings that conflict with their mathematical definitions. Numeric/geometric, counting/measuring and static/dynamic contextual influences were observed in some areas. The first year of a calculus course has a negligible effect on students conceptions of limits, infinity and real numbers. IMPLICATIONS FOR TEACHING On introducing limits teachers should encourage full class discussion to ensure that potential cognitive obstacles are brought out into the open. Teachers should take great care that their use of language is understood. A-level courses should devote more of their time to studying the continuum. Nonstandard analysis is an unsuitable tool for introducing elementary calculus.

Infinity

Cardinality (data modeling)

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Citations (16)

Developments Relevant to the Use of Tools in Mathematics

Mathematics education library (2016)

John Monaghan

Section (typography)

10.1007/978-3-319-02396-0_7

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Citations (3)

Award announcements

Rapid Communications in Mass Spectrometry (1995)

John Monaghan

10.1002/rcm.1290091429

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Citations (0)

Bridging the divide--seeing mathematics in the world through dynamic geometry

Teaching Mathematics and its Applications An International Journal of the IMA (2011)

Hasan Emre Aydın John Monaghan

In TMA, Oldknow (2009, TEAMAT, 28, 180–195) called for ways to unlock students’ skills so that they increase learning about the world of mathematics and the objects in the world around them. This article examines one way in which we may unlock the student skills. We are currently exploring the potential for students to ‘see’ mathematics in the real world through ‘marking’ mathematical features of digital images using a dynamic geometry system (GeoGebra). In this article we present, as a partial response to Oldknow, preliminary results.

10.1093/teamat/hrq016

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Citations (12)

Real mathematics: One aspect of the future of A-level

The Mathematical Gazette (1988)

John Monaghan

The “real” in the title refers to real numbers rather than real life. I expect, and hope, that many articles on the future of A-level will expound the cognitive and mathematical necessity of making A-level more practical. While I applaud and try to practise this, classroom teaching and research have convinced me that the notion of the real number line has subtle conflicts that will not go away by simply not mentioning them; they need to be addressed. Moreover teacher-led explorations of the real number line are essential if we are to lead students to an understanding of higher mathematics.

Real line

Real number

Line (geometry)

Number line

Real analysis

10.2307/3619940

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Citations (1)

1. A Retrospective Look at the Ethnology Volumes of the Handbook of Middle American Indians

University of Texas Press eBooks (2000)

John Monaghan

10.7560/708815-002

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Citations (0)

Tools and Mathematics in the Real World

Mathematics education library (2016)

John Monaghan

Section (typography)

10.1007/978-3-319-02396-0_14

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Citations (2)

Towards a Socio-Cultural Framework for the Analysis of Joint Student-Teacher Development over Technology-Based Mathematics Lessons.

International Journal for Technology in Mathematics Education (2013)

John Monaghan

This paper offers a framework, an extension of Valsiner's theory, for the analysis of joint student-teacher development over a series of technology-based mathematics lessons. The framework is suitable for developing research studies over a moderately long period of time and considers interrelated student-teacher development as well as the influence of significant others on teacher development. After a short introduction, the paper sketches the need for a framework that can capture student and teacher development over technology-based mathematics lessons. It then outlines Valsiner's zone theory and the extension of this theory. The paper ends with a consideration of theoretical, methodological and practical issues in researching innovative mathematics classroom work with technology.

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Citations (1)

A cultural-historical perspective on mathematics teaching and learning

Research in Mathematics Education (2012)

John Monaghan

10.1080/14794802.2012.657443

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Citations (3)