Effective Learning & Teaching in Mathematics & Its Applications

By Peter Kahn; Joseph Kyle | Go to book overview
Save to active project

2

The genesis of mathematical structures

Robert Burn


Introduction

The lecturer's strength

When a lecturer in mathematics is appointed, this is normally on the strength of his or her research; not just on the fertility of his or her ideas, but also on the proven capacity to present them for publication according to the accepted norms. In mathematics itself the accepted norms generally have a deductive structure: definition, theorem, proof, corollary. This sequence has some degree of necessity about it. One needs terms from a definition in order to articulate a theorem, a proof to justify it and then corollaries to show its significance. Expounding mathematics according to this deductive sequence makes it as easy as can be for the logic to be checked. And where applications of mathematics are concerned the focus typically will be on a systematic presentation of the finished mathematical theory. Because these are the kinds of format in which the lecturer has established his or her expertise, it is not surprising that when lecturing or when writing a textbook, these are the formats a lecturer commonly uses. These formats are needed for convincing one's peers; they are rarely the most helpful for a student beginning to learn the subject.


The phenomena of learning mathematics and didactical inversion

In his Didactical Phenomenology of Mathematical Structures Hans Freudenthal (1983) distinguished between different phenomena in mathematics education:

-20-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
Loading One moment ...
Project items
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

Cited page

Bookmark this page
Effective Learning & Teaching in Mathematics & Its Applications
Settings

Settings

Typeface
Text size Smaller Larger
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

While we understand printed pages are helpful to our users, this limitation is necessary to help protect our publishers' copyrighted material and prevent its unlawful distribution. We are sorry for any inconvenience.
Full screen
/ 220

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

Cited passage

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.

Are you sure you want to delete this highlight?