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Mathematics, Education, and Other Endangered Species

Part of the Mathematics in Mind Book Series

DOI: 10.1007/978-3-319-90035-3

ISBN: 978-3-319-90034-6

Publisher: Springer International Publishing - Springer Journals

Apr 27, 2019

1 - 10 of 17 Chapters

LitStream

Chapter 1Is Mathematics Required in Real-life Situations?

Vinner, Shlomo

Pages: 1 –5

[In this chapter I argue against the common claim that mathematics is required in real-life situations.]
LitStream

Chapter 2What Is Mathematics for?

Vinner, Shlomo

Pages: 7 –8

[In this chapter I discuss the rationale of teaching mathematics to the entire school population. The intention is to develop the mind of the student. However, the way it is commonly taught fails to achieve that. The way it is commonly taught prepares the students to pass various exams. Moreover,...
LitStream

Chapter 3Can Scientific Thinking Help Us Cope with Our Existential Problems? Can Religious Thinking Help Us Cope with Our Existential Problems?

Vinner, Shlomo

Pages: 9 –18

[In this chapter I discuss the contribution of mathematical thinking, as part of scientific thinking, to coping with our existential problems. I also discuss the contribution of religious thinking to coping with our existential problems. In my opinion, our main existential problems are mortality...
LitStream

Chapter 4Concept Formation in Mathematics: Concept Definition and Concept Image

Vinner, Shlomo

Pages: 19 –21

[In this chapter I discuss concept formation in mathematics. On one hand, mathematical concepts (in case they are not primary concepts) should be formed by their mathematical definitions. However, the practice shows that, generally, with the majority of people, this is not true; concepts are...
LitStream

Chapter 5The Misconception Fallacy, the Pseudo-conceptual and the Pseudo-analytical Behaviors in Mathematical Contexts

Vinner, Shlomo

Pages: 23 –52

[In this chapter I examine the commonly accepted claim that each mistake people make is a result of a misconception. My claim is that there are other modes of thinking that form mistakes. The names I give them are the pseudo-conceptual and the pseudo-analytical modes of thinking. People who are...
LitStream

Chapter 6The Pseudo-conceptual Behavior in Contexts Outside the Mathematics Classroom

Vinner, Shlomo

Pages: 53 –57

[In this chapter I show that the pseudo-conceptualthinking/mode of thinkingpseudo-conceptual mode of thinking also occurs in situations in philosophy and social sciences. Thus, we see that it is wrong to restrict certain modes of thinking to mathematical situations. Mathematical thinking is not...
LitStream

Chapter 7Can E-learning (Computer-based Learning) Replace Teacher–Student Individual Communication?

Vinner, Shlomo

Pages: 59 –62

[My answer to the above question is negative. In order to establish my claim I am relying on a well-known work by Erlwanger (1973), which shows that without intensive interaction with a teacher the pupil can reach huge misconceptions about the topic under consideration.]
LitStream

Chapter 8What Is Mathematics?

Vinner, Shlomo

Pages: 63 –68

[This chapter has a reflective-philosophical nature. Usually people do not ask themselves what mathematics is. However, they have implicit ideas about it. The most common idea, in my opinion, is that mathematics is a collection of procedures (algorithms, formulas, etc.) intended to be used in...
LitStream

Chapter 9The Role of Examples in the Learning of Mathematics and in Everyday Thought Processes

Vinner, Shlomo

Pages: 69 –86

[In this chapter I discuss the role of examples in the learning of mathematics and in everyday thought processes. I discussconcept formationrole of examplesthought processes, everyday conjecture formation, and conjecture verification in mathematics and in everyday thought processes. Thus, I...
LitStream

Chapter 10Imagination Acts

Vinner, Shlomo

Pages: 87 –87

[In this chapter I discuss what I suggest calling “imagination acts.” These acts are strongly needed in mathematical thinking, which requires us to imagine things that do not exist in our real life. For instance: In Euclidean geometry we are required to think of points that have no dimensions,...

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