Paul Ernest
Biographic Data
| ID | 1041482 |
|---|---|
| NAME | Paul Ernest |
| GIVEN NAMES | Paul |
| FAMILY NAME | Ernest |
| SIGNATURE | ERNEST P |
| AFFILIATIONS | University of Exeter |
| ORCID | 0000-0001-7985-2852 |
| VERIFIED | Yes |
| TOTAL WORKS | 11 |
| TOTAL CITATIONS | 3 |
| AUTHOR COUNT | 10 |
| EDITOR COUNT | 1 |
| FIRST PUBLICATION YEAR | 1975 |
| LATEST PUBLICATION YEAR | 2021 |
| H-INDEX | 1 |
Mathematics, ethics and purism
A traditional problem of ethics in mathematics is the denial of social responsibility. Pure mathematics is viewed as neutral and value free, and therefore free of ethical responsibility. Applications of mathematics are seen as employing a neutral set of tools which, of themselves, are free from social responsibility. However, mathematicians are convinced they know what constitutes good mathematics. Furthermore many pure mathematicians are committ…
The Philosophy of Mathematics Education
Mathematics Education, Philosophy of Education, Educational Philosophy
Mathematics Education and Philosophy
Reconceptualizing the Philosophy of Mathematics: Fresh Winds in the Philosophy of Mathematics, Reuben Hersh What can the Sociologist of Knowledge Say About 2+2=4?, DavidBloor. Post-Modernist and Post- Structuralist Approaches: Reasoning in a Post-Modern Age, Valerie Walkerdine Mathematical Writing, Thinking, and Virtual Reality, Brian Rotman. The Human Face of Mathematics: Mathematics and Art: Cold Calipers against Warm Flesh?, Philip J. Davis Di…
Mathematics, Education, And Philosophy
Mathematics Teacher Education and Quality
‘Quality’ in mathematics teaching does not relate solely to pupil achievement, to teaching approaches or to deeply held beliefs about the nature of mathematics and its teaching and learning, but to all of these. A model of a teacher's mathematics‐related belief‐system is presented, and the issue of the contrast between espoused and enacted beliefs is discussed. ‘Quality’ in mathematics teacher education raises all of these issues, as well as the …
The Philosophy of Mathematics Education
Brief analysis of the philosophy of mathematics education including multiple ways of interpreting it and some of its central questions and problems.• The varying roles of philosophy in mathematics education research including applications of concepts from branches of philosophy and philosophical styles of analysis and thinking.• Introduction to critical mathematics education, an area of research concerned with critical and social justice issues t…
The Meaning of Mathematical Expressions
Mathematicians and physical scientists depend heavily on the formal symbolism of mathematics in order to express and develop their theories. For this and other reasons the last hundred years has seen a growing interest in the nature of formal language and the way it expresses meaning; particularly the objective, shared aspect of meaning as opposed to subjective, personal aspects.This dichotomy suggests the question: do the objective philosophical…
The Knowledge, Beliefs and Attitudes of the Mathematics Teacher
Official pressure for reforms in the teaching of mathematics overlooks a key factor: the psychological foundations of the practice of teaching mathematics, including the teacher's knowledge, beliefs and attitudes. Research on teaching and teacher education also under‐emphasises this area, which Shulman terms the ‘missing program’ in research on teacher cognitions. The present paper addresses this lack by proposing an analytic model of the differe…
Piaget's Epistemology and the Social Practice of Mathematics
A Model of the Cognitive Meaning of Mathematical Expressions
S ummary . The central focus of the paper is the nature of the mental representations of the meaning of the linguistic expressions of mathematics. An information‐processing model for the construction of mental representations is presented. The model provides syntactical tree structures as meaning representations. It is argued that the major function of written mathematical language in school mathematics is in the initial presentations of pupil ta…
A Critique of some Formal Theories of Meaning
A Model of the Cognitive Meaning of Mathematical Expressions
S ummary . The central focus of the paper is the nature of the mental representations of the meaning of the linguistic expressions of mathematics. An information‐processing model for the construction of mental representations is presented. The model provides syntactical tree structures as meaning representations. It is argued that the major function of written mathematical language in school mathematics is in the initial presentations of pupil ta…
A Critique of some Formal Theories of Meaning
A Critique of some Formal Theories of Meaning
A Model of the Cognitive Meaning of Mathematical Expressions
S ummary . The central focus of the paper is the nature of the mental representations of the meaning of the linguistic expressions of mathematics. An information‐processing model for the construction of mental representations is presented. The model provides syntactical tree structures as meaning representations. It is argued that the major function of written mathematical language in school mathematics is in the initial presentations of pupil ta…
The Knowledge, Beliefs and Attitudes of the Mathematics Teacher
Official pressure for reforms in the teaching of mathematics overlooks a key factor: the psychological foundations of the practice of teaching mathematics, including the teacher's knowledge, beliefs and attitudes. Research on teaching and teacher education also under‐emphasises this area, which Shulman terms the ‘missing program’ in research on teacher cognitions. The present paper addresses this lack by proposing an analytic model of the differe…
Piaget's Epistemology and the Social Practice of Mathematics
The Meaning of Mathematical Expressions
Mathematicians and physical scientists depend heavily on the formal symbolism of mathematics in order to express and develop their theories. For this and other reasons the last hundred years has seen a growing interest in the nature of formal language and the way it expresses meaning; particularly the objective, shared aspect of meaning as opposed to subjective, personal aspects.This dichotomy suggests the question: do the objective philosophical…
Mathematics Teacher Education and Quality
‘Quality’ in mathematics teaching does not relate solely to pupil achievement, to teaching approaches or to deeply held beliefs about the nature of mathematics and its teaching and learning, but to all of these. A model of a teacher's mathematics‐related belief‐system is presented, and the issue of the contrast between espoused and enacted beliefs is discussed. ‘Quality’ in mathematics teacher education raises all of these issues, as well as the …
The Philosophy of Mathematics Education
Brief analysis of the philosophy of mathematics education including multiple ways of interpreting it and some of its central questions and problems.• The varying roles of philosophy in mathematics education research including applications of concepts from branches of philosophy and philosophical styles of analysis and thinking.• Introduction to critical mathematics education, an area of research concerned with critical and social justice issues t…
Mathematics Education and Philosophy
Reconceptualizing the Philosophy of Mathematics: Fresh Winds in the Philosophy of Mathematics, Reuben Hersh What can the Sociologist of Knowledge Say About 2+2=4?, DavidBloor. Post-Modernist and Post- Structuralist Approaches: Reasoning in a Post-Modern Age, Valerie Walkerdine Mathematical Writing, Thinking, and Virtual Reality, Brian Rotman. The Human Face of Mathematics: Mathematics and Art: Cold Calipers against Warm Flesh?, Philip J. Davis Di…
Mathematics, Education, And Philosophy
The Philosophy of Mathematics Education
Mathematics Education, Philosophy of Education, Educational Philosophy
Mathematics, ethics and purism
A traditional problem of ethics in mathematics is the denial of social responsibility. Pure mathematics is viewed as neutral and value free, and therefore free of ethical responsibility. Applications of mathematics are seen as employing a neutral set of tools which, of themselves, are free from social responsibility. However, mathematicians are convinced they know what constitutes good mathematics. Furthermore many pure mathematicians are committ…
Epistemology (7 works) · Mathematics education (7 works) · Philosophy (6 works) · Psychology (5 works) · Connected Mathematics (4 works) · Mathematics Education and Teaching Techniques (4 works) · Cognition (3 works) · Computer Science (3 works) · Mathematics (3 works) · Meaning (existential) (3 works)