John Mason | The Open University (original) (raw)

Papers by John Mason

Constructing Knowledge for Teaching Secondary Mathematics, 2011

Mathematically, most theorems can be seen as classifying those mathematical objects which satisfy... more Mathematically, most theorems can be seen as classifying those mathematical objects which satisfy certain properties, in terms of other, usually more manageable, properties. Thus Pythagoras’ theorem classifies right-angled triangles as those triangles for which the sum of the squares on two sides is the square on the third, while the law of cosines defines a property which holds for all triangles. Whenever a method is devised for solving a particular problem, there is an immediate challenge (and value) to classify all those problems which succumb to the same method. This is a fundamental process in mathematics, and a key aspect of learning mathematics in order to appreciate each technique and the concepts on which it draws. Classifying and characterising are natural powers which children display long before they get to school. They are also a core component of mathematical pedagogy. For mathematical thinking, it is important that learners are provoked to use their own powers to classify and characterise so that these are developed explicitly throughout their mathematical schooling, which means teachers being aware of and drawing attention to their use, whether actual or potential. This chapter elaborates on these claims.

This thesis will explore the phenomenon of "travelling like a local". I position this a... more This thesis will explore the phenomenon of "travelling like a local". I position this as the outcome of cultural and societal trends in the consumption of European city breaks, where consumers seek unique and authentic experiences that tap into "local knowledge" and put them into contact with local people and cultures. This is believed to make for a more authentic and sustainable holiday. There are growing numbers of local organisa-tions who seek to promote "their" city to the tourist and who promise to share niche and hidden activities, and they are gaining in popularity. This trend is slowly being picked up by a variety of Destination Marketing Organ-isations, seeking to promote the "local" angle of their knowledge and offering. I will examine the campaigns of Visit Manchester, Visit Birmingham, and This is Antwerp, all of which claim to utilise local. I then contrast this information with that provided by local people and organisations. The...

This paper focuses on eight-year old students’ ways of approaching true/false number sentences. T... more This paper focuses on eight-year old students’ ways of approaching true/false number sentences. The data presented here belongs to a teaching experiment in which the use of relational thinking when solving number sentences was explicitly promoted. The study of the way of using this type of thinking and of students’ structure of attention, allow us to make distinctions and to provide a description of students’ different behaviours.Este artículo se centra en las formas en que alumnos de ocho años abordan la resolución de sentencias numéricas verdaderas y falsas. Los datos que se presentan pertenecen a un experimento de enseñanza en el cual se promovió explícitamente el uso del pensamiento relacional en la resolución de sentencias numéricas. El estudio del modo en que es usado este tipo de pensamiento y de la estructura de la atención de los alumnos, nos permite distinguir y aportar una descripción de los diferentes comportamientos de los alumnos.I want to thank the members of the CERM...

Learning Mathematics

... It lies behind the presentation of mathematical thinking in Mason, Burton and Stacey (1984), ... more ... It lies behind the presentation of mathematical thinking in Mason, Burton and Stacey (1984), and in the various courses and materials in mathematics education produced by the Open University Centre for Mathematics Education, not to say the experiential learning movement ...

Research in Mathematics Education, 2011

ABSTRACT

Teaching mathematics, 1994

Seeing comes before words. The child looks and recognises before it can speak... It is seeing whi... more Seeing comes before words. The child looks and recognises before it can speak... It is seeing which establishes our place in the surrounding world; we explain that world with words... We only see what we look at. To look is an act of choice. As a result of this act, ...

Mathematics Teaching Incorporating Micromath, Sep 1, 2008

Mathematics Teaching Practice, 2002

The Mathematical Gazette, 1984

The roots of any event are often hard to trace, but at some point some years ago now, some member... more The roots of any event are often hard to trace, but at some point some years ago now, some member of the Open University maths faculty was approached by a maths advisor and asked if we could arrange the programme for a one day mathematics outing for sixth form students. Since we have run all sorts of mathematical events for our own students, it seemed like a good opportunity to try out ideas on a different sort of student. This was the first of a burgeoning number of events we have planned and run, and the purpose of this note is to indicate as clearly as is possible in print what we do, with the thought that others might like to try something similar.

The SimCalc Vision and Contributions, 2013

Teaching “well” is seen here not as an engineering problem in which specific practices are locate... more Teaching “well” is seen here not as an engineering problem in which specific practices are located and demonstrated to “work,” but rather as a human endeavor calling upon the whole of the human psyche: behavior, cognition, affect and attention. The construct of different forms of attention as different ways of attending to something is used to analyze data from the chapter by Bishop, in order to shed light on what can happen when students are expected to explain, elaborate, and evaluate for themselves. Other constructs used include metaphor and metonymy, reflection and “taking a reflexive stance” as vital to learning effectively, the ways in which teachers, students and mathematics each mediate in interactions between the other two to form six modes of interaction, and a four-fold structure of activity based on motivational and resource axes.

Higher Combinatorics, 1977

Benefiting from economic globalization, China has stepped up its economy, which is especially sho... more Benefiting from economic globalization, China has stepped up its economy, which is especially shown by the continuous development of internet technology in the 20 century. The trend of informatization has seeped into every aspect of life, including financial accounting. It has broken the limitation of traditional accounting, bringing financial accounting new opportunities and challenges. This paper analyzesthe situation of financial accounting in China, explains the challenges from economic environment, production and business operation, organizational structures, and information processing and transferring, and provided suggested solutions accordingly.

MSOR Connections, 2002

... are two appendices: a representative collection of challenging explorations for first yearund... more ... are two appendices: a representative collection of challenging explorations for first yearundergraduate mathematics students in ... There are six main modes of interaction between student, content, and tutor: O Expounding, or ... What roles do they play in learning mathematics? ...

Traducción al español y edición: Cecilia Agudelo-Valderrama

International Handbook of Mathematics Education, 1996

Theory is seen as playing both a foreground role, in the sense that the enterprise of research in... more Theory is seen as playing both a foreground role, in the sense that the enterprise of research in mathematics education is to develop theory, and a background role, since all observation is theory laden. After considering different theoretical stances towards observation, data, and analysis, three broad approaches to research in mathematics education are identified and the role played by theory in each of these is discussed. The chapter concludes with some speculations concerning possible directions for development, moving from language as core domain of problematicity, to images, icons, and the impact of electronic media on interpretation in the future.