Teaching and learning mathematics:
Gespeichert in:
| Format: | Buch |
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| Sprache: | Undetermined |
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Exeter
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| Schriftenreihe: | Perspectives
... |
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| Online-Zugang: | Inhaltsverzeichnis |
| ISBN: | 0850680948 |
Internformat
MARC
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| 245 | 1 | 0 | |a Teaching and learning mathematics |c School of Education, Univ. of Exeter. Ed. Paul Ernest |
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Datensatz im Suchindex
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| adam_text | Contents
Preface, xi
An Introduction to Mathematics Education 1
The Objectives of Mathematics Teacher Education 2
Mathematical content. Applications of mathematics. Uses of computers
in mathematics education. The modern mathematics curriculum. Learn¬
ing theories. Models for teaching mathematics. Managing a learning
environment. Personal and professional growth.
Acquiring Mathematics Teaching Competencies 13
Preservice education. Inservice education.
Models for Educating Teachers 15
Experience based education. Competency based education.
Things to Do 19
Selected Bibliography 19
1 The Nature of Mathematics 23
Philosophy of Mathematics 23
Structure of Mathematical Systems 27
Modern Approaches to Mathematics 33
Modern arithmetic. Modern algebra. Modern geometries. Analysis.
Things to Do 58
Selected Bibliography 60
f The School Mathematics Curriculum 67
Influences on School Mathematics 68
Changes in society and education. Curriculum projects.
The New Mathematics Curricula 74
Algebra. Geometry. Trigonometry. The Secondary School Mathematics
Curriculum Improvement Study.
The New Math Curriculum: Success or Failure? 83
Things to Do 90
Selected Bibliography 91
3 Using Learning and Instructional Theories
in Teaching Mathematics 97
Piaget s Theory of Intellectual Development 98
Sensory motor stage. Preoperational stage. Concrete operational stage.
Formal operational stage. Factors in intellectual development. Piaget s
theory and teaching mathematics.
J. P. Guilford s Structure of Intellect Model 104
Intellectual variables.
Robert Gagne s Theory of Learning 108
The objects of mathematics learning. The phases of a learning se¬
quence. Types of learning. Learning hierarchies. AfinalnoteonGagne.
Dienes on Learning Mathematics 123
Mathematical concepts. Stages in learning mathematical concepts.
Games. Principles of concept learning. Applying Dienes theory in a
lesson.
Ausubel s Theory of Meaningful Verbal Learning 130
Reception and discovery learning, meaningful and rote learning. Pre¬
conditions for meaningful reception learning. Strategies for meaningful
verbal learning. An advance organizer lesson.
Jerome Bruner on Learning and Instruction 138
Bruner s theory of instruction. Theorems on learning mathematics.
Applications of Bruner s work.
B. F. Skinner on Teaching and Learning 147
Types of behavior and learning. Promoting learning and changing be¬
havior. General conditions of learning. The art of teaching.
Summary 157
Things to Do 158
Selected Bibliography 160
A Preparing to Teach Mathematics Lessons 167
Selecting and Classifying Educational Objectives 168
Cognitive objectives. Using cognitive objectives in the classroom.
Affective objectives. Summary.
Planning Mathematics Lessons 190
Mathematics content. Learning objectives. Learning resources. Pre
assessment and postassessment strategies. Teaching/learning strategies.
Summary.
Things to Do 215
Selected Bibliography 217
5 Models for Teaching and Learning the
Direct Objects of Mathematics 221
Expository Teaching/Learning Model 224
Advance Organizer Teaching/Learning Model 231
Assumptions underlying the model. Developing advance organizers.
Presenting advance organizers. Activities following the organizer.
Summary.
Learning by Discovery 241
Discovery learning defined. Purposes of discovery strategies. The
nature of discovery strategies. Conducting discovery lessons. Out¬
comes of discovery lessons. A discovery lesson plan.
The Use of Games to Learn Mathematics 251
Educational objectives and limitations of games. Strategies for using
games. Evaluating games. Types of games. Sources of mathematical
games. A lesson plan for a generalizable game.
The Individualized Teaching/Learning Model 272
A general model for individualizing instruction. Specific programs for
individualizing instruction. Classroom techniques for individualizing
instruction. Summary.
The Spiral Teaching/Learning Model 277
Spiral teaching and learning defined. Examples of the spiral approach
in learning mathematics.
Summary 283
Things to Do 283
Selected Bibliography 285
6 Models for Teaching and Learning the
Indirect Objects of Mathematics 289
A Teaching/Learning Model for Proving Theorems 289
What is a proof? Why should proofs be done in school? Teaching
students how to prove theorems.
A Teaching/Learning Model for Problem Solving 308
What is problem solving? Why solve problems in school mathematics?
Strategies for teaching and learning problem solving.
The Laboratory Teaching/Learning Model 323
Objectives in using mathematics laboratories. Teaching/Learning
strategies for mathematics laboratories. Facilities and resources for
mathematics laboratories.
The Inquiry Teaching/Learning Model 340
Stages in the inquiry process. Teaching and learning inquiry methods.
An inquiry lesson.
The Group Processes Model 351
Objectives of the group processes model. Characteristics of the group processes
model. Teaching students to work in groups. Special problems encountered in
group activities.
The Computer Augmented Teaching/Learning Model 362
Why use computers in teaching and learning mathematics? Ways in
which computers are used in mathematics education. An approach to
computer augmented learning. Computer augmented learning re¬
sources. The future of computers in mathematics education.
Things to Do 372
Selected Bibliograpy 374
7 Developing and Maintaining an
Effective Learning Environment 379
Evaluating, Selecting, and Using Mathematics Textbooks 379
Purposes of mathematics textbooks. What to look for in a mathematics
textbook. Using mathematics textbooks effectively.
Obtaining and Using Teaching/Learning Resources 387
Assigning and Evaluating Homework 390
Planning and preparing assignments. Giving homework assignments
to students. Evaluating and grading assignments.
Classroom Questioning Strategies 396
Objectives of classroom questioning strategies. Types of questions.
Developing effective questioning strategies.
Diagnosing and Resolving Learning Difficulties 401
The causes of learning difficulties. Techniques for diagnosing learning
difficulties. Procedures for resolving learning difficulties.
Maintaining Discipline in the Classroom 413
Approaches to discipline. Causes of discipline problems. Preventing
discipline problems. How to deal with discipline problems.
Testing and Grading Students 424
Reasons for testing students. Types of tests and test items. Selecting
and constructing tests. Giving tests to students. Marking tests and as¬
signing grades. Evaluating tests and using test results.
Evaluating the Effectiveness of Instruction 436
A general model for evaluating instruction. Techniques for evaluating
instruction.
Things to Do 445
Selected Bibliography 448
8 Professional Considerations
Outside the Classroom 453
Working with Other Teachers, School Administrators, and Parents 453
Rights and Responsibilities of Teachers 459
Dealing with Changes in Educational Systems 463
Changes within a school or school system. General changes in the
educational system.
Working with Students Outside the Classroom 467
Supervising groups of students. Tutoring students. Advising and coun¬
seling students. Helping students prepare for standardized tests. Direct¬
ing extracurricular activities.
Continuing Education and Professional Development 471
Independent study. School workshops and college courses. Participa¬
tion in professional organizations.
The Changing Nature of Education 475
Social and economic influences upon education. Implications of
societal changes for schools. Educational objectives for the future.
Changing roles for school teachers.
The Future of Mathematics Education 484
Factors influencing mathematics education. The future content of
school mathematics. Teaching in the future. Recommendations for
mathematics education. A final note.
Things to Do 495
Selected Bibliography 497
r Teaching Exceptional Students 501
Teaching Mathematics to Slow Learners 501
Characteristics and needs of slow learners. Teaching/Learning strate¬
gies for slow learners. Reading ability in learning mathematics.
Teaching Mathematically Gifted Students 531
Characteristics of gifted students. The needs of gifted students. Teach¬
ing/Learning activities for gifted students. Programs and resources for
teaching the gifted.
Things to Do 547
Selected Bibliography 548
Index, 555
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| spelling | Teaching and learning mathematics School of Education, Univ. of Exeter. Ed. Paul Ernest Exeter txt rdacontent n rdamedia nc rdacarrier Perspectives ... Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 s DE-604 Ernest, Paul Sonstige oth University of Exeter School of Education Sonstige (DE-588)3064162-7 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012516762&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Teaching and learning mathematics Mathematikunterricht (DE-588)4037949-8 gnd |
| subject_GND | (DE-588)4037949-8 |
| title | Teaching and learning mathematics |
| title_auth | Teaching and learning mathematics |
| title_exact_search | Teaching and learning mathematics |
| title_full | Teaching and learning mathematics School of Education, Univ. of Exeter. Ed. Paul Ernest |
| title_fullStr | Teaching and learning mathematics School of Education, Univ. of Exeter. Ed. Paul Ernest |
| title_full_unstemmed | Teaching and learning mathematics School of Education, Univ. of Exeter. Ed. Paul Ernest |
| title_short | Teaching and learning mathematics |
| title_sort | teaching and learning mathematics |
| topic | Mathematikunterricht (DE-588)4037949-8 gnd |
| topic_facet | Mathematikunterricht |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012516762&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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