Science and Mathematics Education | Open Access Articles

In recent years, research studies have shown that control decisions and processes, beliefs about the nature of mathematics, attitudes, and other affective variables have enormous impact on the mathematical performance of students. This paper gives an overview of the research on mathematical beliefs and reviews some work done in Christian education relating to theological beliefs. It then compares the two.

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Using Data To Develop Mathematical Methods, Philip R. Carlson Jun 1995

Using Data To Develop Mathematical Methods, Philip R. Carlson

ACMS Conference Proceedings 1995

An analysis of ordered pairs and their scatter plots leads to interesting questions related to mathematical modeling. Some statistical methods suggest ways to approach this analysis of the ordered pairs. Both high school and college methods are illustrated in this paper.

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The Intermediate Value Theorem, Dale Varberg Jun 1995

The Intermediate Value Theorem, Dale Varberg

ACMS Conference Proceedings 1995

The Intermediate Value Theorem (a continuous function on an interval assumes all values between any two of its values) is one of the big theorems of calculus. Yet the theorem is absent or briefly mentioned in most calculus textbooks. The theorem deserves better as we intend to show by listing ten picturesque consequences that we think could enliven any calculus course.

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What Does A Computer Program Mean? An Introduction To Denotational Semantics, Gene B. Chase Jun 1995

What Does A Computer Program Mean? An Introduction To Denotational Semantics, Gene B. Chase

ACMS Conference Proceedings 1995

This paper is for mathematicians who are curious about how topology is being used to prove computer programs correct. Those advanced parts have been limited to Sections III, V, and VI, and they are marked by a [clock symbol]. By contrast, sections II, IV, and VII are suitable as a companion to existing textbooks in a Computer Science course such as Organization of Programming Languages, the course CS 8 as described in Curriculum [1979]. Perhaps in a first reading you might read just those sections.

Among many books and articles on the semantics, or meaning, of computer languages, …

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Statistics, Mathematics, And Teaching, David S. Moore Jun 1995

Statistics, Mathematics, And Teaching, David S. Moore

ACMS Conference Proceedings 1995

In discussing our teaching, we may focus on content, what we want our students to learn, or on pedagogy, what we do to help them learn. These two topics are of course related. In particular, changes in pedagogy are often driven in part by changing priorities for what kinds of things we want students to learn. It is nonetheless convenient to address content and pedagogy separately. Pedagogy, certainly the less specific of the two, is the topic of my second paper. This paper concerns content, and in particular contains one side of a conversation between a statistician and mathematicians …

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Constructivism, Mathematics Education And Christianity, Ted Watanabe Jun 1995

Constructivism, Mathematics Education And Christianity, Ted Watanabe

ACMS Conference Proceedings 1995

In this paper, I briefly describe what constructivism is and its implications in the field of mathematics education. I will then discuss what this epistemology may mean to Christians who are in the field of mathematics education

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The 25 Greatest Mathematicians, Robert Brabenec Jun 1995

The 25 Greatest Mathematicians, Robert Brabenec

ACMS Conference Proceedings 1995

Many have tried to determine the greatest mathematicians in history. The purpose of this paper is to consider making such a list, along with some criteria to consider in making a rank order of these mathematicians.

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Experimenting With The Calculus Laboratory Setting, Glen Van Brummelen Jun 1995

Experimenting With The Calculus Laboratory Setting, Glen Van Brummelen

ACMS Conference Proceedings 1995

Reform of post-secondary mathematics education, particularly introductory calculus, is becoming commonplace across North America. Although there are many varieties of reform, most can be placed within the philosophical camp of social constructivism. According to this movement, mathematical knowledge is constructed in an interactive way through instructor-student and inter-student dialogue, rather than built in an axiomatic sense such as the "new math" of 20 years ago, or in the reductionistic, algorithmic sense dominant in secondary and introductory college mathematics. While I hold serious concerns about the relativizing of mathematical knowledge that occurs when social constructivism is adopted as a philosophy of …

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Improving The Teaching Of Mathematics, David S. Moore Jun 1995

Improving The Teaching Of Mathematics, David S. Moore

ACMS Conference Proceedings 1995

No one concerned about the teaching of college mathematics--and few mathematicians who are not concerned--can have missed the movement to reform teaching in the mathematical sciences at all levels. The teaching of any active branch of knowledge, like the church, is of course "reforming and ever to be reformed." Calls to modernize what we offer students are always with us. What is striking about the current reform movement is not only its momentum but the fact that it centers on pedagogy rather than on content. We ought, say the reformers, to radically alter our style of teaching. My purpose in …

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Introduction (1995), David L. Neuhouser Jun 1995