In a recent article, Inglis and Alcock (2012) contended that their data challenge the claim that when mathematicians validate proofs, they initially skim a proof to grasp its main idea before reading individual parts of the proof more carefully. This result is based on the fact that when mathematicians read proofs in their study, on average their initial reading of a proof took half as long as their total time spent reading that proof. Authors Keith Weber and Juan Pablo Mejía-Ramos present an analysis of Inglis and Alcock's data that suggests that mathematicians frequently used an initial skimming strategy when engaging in proof validation tasks.
Keith Weber and Juan Pablo Mejía-Ramos
Kristen Lew and Juan Pablo Mejía-Ramos
This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First, mathematicians believed that mathematical language should obey the conventions of academic language, whereas students were either unaware of these conventions or unaware that these conventions applied to proof writing. Second, students did not fully understand the nuances involved in how mathematicians introduce objects in proofs. Third, mathematicians focused on the context of the proof to decide how formal a proof should be, whereas students did not seem to be aware of the importance of this factor.
Leone Burton and Candia Morgan
In this article we report on part of a study of the epistemological perspectives of practicing research mathematicians. We explore the identities that mathematicians present to the world in their writing and the ways in which they represent the nature of mathematical activity. Analysis of 53 published research papers reveals substantial variations in these aspects of mathematicians' writing. The interpretation of these variations is supported by extracts from interviews with the mathematicians. We discuss the implications for students and for novice researchers beginning to write about their mathematical activity.
Sabrina R. Goldberg
Introduce mixed-ability classes to a project exploring famous mathematicians and scientists and ignite students' math interest.
Michael K. Weiss and Deborah Moore-Russo
The moves that mathematicians use to generate new questions can also be used by teachers and students to tie content together and spur exploration.
James E. Lightner
WE OFTEN STUDY THE PUBLISHED WORKS of the great mathematicians, accept them, and use them gratefully as we solve our problems and delve into the abstractions of our chosen field of mathematics. But rarely do we realize that all these developments were the products of human minds. Mathematicians, indeed, are quite human, and they are not always serious! Their lives are full of interesting twists, turns, and quirks that make them all the more human.
James Byrnie Shaw
It is of interest to those who study mathematics and also to those who teach it to note what mathematicians have had to say as to the manner of arriving at their results. Mathematics is a constantly growing part of human knowledge, and has the unique quality that its results are permanent, and form a synthetic unity which is not paralleled by any other part of human knowledge. The text for this paper is found in an inquiry instituted in 1905-6 by the journal “L’Enseignment mathéma-tique” as to the method of mathematicians, and which was discussed by Flournoy, Professor of Psychology, and Claparéde, Director of the psychological laboratory, in Geneva. While one must not over-value the results of such a questionnaire, yet they have their place, and may at least suggest some things to reflect over. This summary and discussion was published in 1905 and 1906, and in 1908 as a pamphlet, by Gauthier-Villars, Paris.
Thomas F. Banchoff
A mathematician reflects on his experiences as a young mathematician in grade school and describes his experiences working with K–6 teachers and students.
Robert W. Prielipp
Edited by Howard Eves
How many of the three famous mathematicians whose lives are described briefly below can you identify?
Robert L. Stright
Millions of children and adults are acquainted with the book, Alice in Wonderland, and its author, Lewis Carroll (Charles Lutwidge Dodgson). It is also a fairly well-known fact that Carroll was some sort of a mathematician. Few people realize, however, the amount of mathematics contained in this seemingly simple book and others like it. Nor do most people realize the effect of Carroll's mathematical mind upon his work. “Alice in Wonder land owes its unique place in our literature to the fact that it was the work of a genius, that of a mathematician and logician who was also a humorist and a poet.”1 In fact, the “Alice” books (Alice in Wonderland and Through the Looking Glass) have been described as the “original work of a mathematician and logician, interested in the precise meaning of words, who was at the same time a genius of invention and poetic imagination with a love for children and a gift for entertaining them.”2