Education Commons^™

Matching Functions And Graphs At Multiple Levels Of Bloom’S Revised Taxonomy, Kris H. Green

Mathematical and Computing Sciences Faculty/Staff Publications

This paper illustrates the power of Bloom's revised taxonomy for teaching, learning and assessing [3] in aligning our curriculum expectations and our assessment tools in multivariable calculus. The particular assessment tool considered involves a common matching problem to evaluate students' abilities to think about functions from graphical and formulaic representations. Through this analysis we gain additional understanding of why students may have difficulty in performing well on certain activities.

If Mowat And Davis Are Correct, Then Teaching Is Hard: A Response To Elizabeth Mowat & Brent Davis, Kris H. Green, Bernard P. Ricca

Mathematical and Computing Sciences Faculty/Staff Publications

In lieu of an abstract, below is the article's first paragraph.

Mowat & Davis (this issue) present a model of learning mathematics that relies heavily on ideas from network (or graph) theory. The important questions (to us, at least) concern the dynamics of the nodes and links. Answers – even tentative ones such as we present here – to these questions lead to a second set of questions concerning the implications of these answers to teachers and researchers.

Using Spreadsheets To Discover Meaning For Parameters In Nonlinear Models, Kris H. Green

Mathematical and Computing Sciences Faculty/Staff Publications

Using spreadsheets one can develop an exploratory environment where mathematics students can develop their own understanding of the relationship between the parameters of commonly encountered families of functions (linear, logarithmic, exponential and power) and a natural interpretation of “rate of change” for those functions. The key to this understanding involves expanding the concept of rate of change to include percent changes. Through the use of the spreadsheet model, students can explore and easily determine which type of change is most natural for a given family of functions. This, in turn, provides a mechanism for interpreting the parameters of the function …

Reorganizing Freshman Business Mathematics Ii: Authentic Assessment In Mathematics Through Professional Memos, Kris H. Green, W. Allen Emerson

Mathematical and Computing Sciences Faculty/Staff Publications

Part I of this paper described the development of a new Freshman Business Mathematics (FBM) course at our college. In this second part of the paper, we discuss our assessment tool, the business memo, as a venue for students to apply mathematical skills, via mathematical modeling, to realistic business problems. These memos have proven a crucial step in turning our FBM course around from a dreaded course with little connection to students’ intended careers into a course where students experience the power of mathematics for solving problems and informing decisions. Comments from students in the course throughout its six-year history …

Promoting Mathematical Communication And Community Via Blackboard, Kris H. Green, Erica L. Johnson

Mathematical and Computing Sciences Faculty/Staff Publications

Major changes in mathematics pedagogy include writing as pedagogy and the role of community in learning. The classroom community is naturally extended by the use of online discussion boards. In this paper several models for student use of online discussion boards that have been successfully used to promote mathematical discourse are presented. Structured and unstructured examples that are easily adaptable and transportable to a variety of mathematics classroom settings are offered. These assignments facilitate student engagement and interaction outside of the classroom. Assessment, utility, and transferability are offered. Although the authors use the discussion boards provided by Blackboard, this particular …

A New Framework For Grading, Kris H. Green, W. Allen Emerson

Mathematical and Computing Sciences Faculty/Staff Publications

Grading is one of the least liked, least understood and least considered aspects of teaching. After years of work, we have developed a grading system that is quite different from traditional and reformed approaches to grading and which meaningfully incorporates and integrates the collection of evidence, the evaluation of evidence, and the reporting of judgments about that evidence. This system satisfies the requirements of good grading system and answers many of the problems faced by more traditional methods by substantially changing the way in which grade information is aggregated, resulting in a final course grade that aligns qualitative evaluation with …

A Solution To Einstein’S Field Equations For A Tachyonic Gas: Possible Astrophysical Applications, Kris H. Green, W. John Cocke

Mathematical and Computing Sciences Faculty/Staff Publications

In this paper we show that a change in the signs of some of the metric components of the solution of the field equations for the classical cosmic string results in a solution which we interpret as a time-dependent wall composed of tachyons. We show that the walls have the property of focusing the paths of particles which pass through them. As an illustration of this focusing, we demonstrate the results of a simple simulation of the interaction between one such tachyon wall and a rotating disk of point masses. This interaction leads to the temporary formation of spiral structures. …

Creating Successful Calculus Writing Assignments, Kris H. Green

Mathematical and Computing Sciences Faculty/Staff Publications

I discuss three different writing assignments that I have used in my calculus courses. These assignments are introduced with a discussion of purpose and audience. Defining these qualities of an assignment will ensure that your writing assignments are more successful. The assignments discussed and explored here represent three different purposes: personal, informational and a blend of the two. The audiences for these assignments are diverse and force the students to incorporate particular modes of writing that demonstrate much of their thinking. Assessment of student learning as a result of these assignments is discussed. A fourth writing assignment is developed from …