Educational Notes

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Essays and reports, some related to the Mathematics Emporium at Virginia Tech; Reverse chronological order.

Multidimensional grading scales , 6 page pdf file Januray 2007. A proposal for boosting skill levels among strong students without increasing failure rates. Elaborates "New grade scales for the new age?" (1998).

Communication between the mathematical and math-education communities , 11 page pdf file June 2006. An analysis of difficulties in even addressing problems in K-12 education, and a proposal for avoiding them.

Integral calculus outcomes, Spring 2006 , 12 page pdf file May 2006. Technical report on analysis of performance on common-time final and class tests, including comparisons of computer-tested and traditional sections.

Evaluation of methods in math education , 13 page pdf file March 2006. Problems in K-12 education not addressed by math education research.

The K-12 math test conundrum , 2 page pdf file January 2005. Problems with high-stakes testing; article for the Notices of the American Mathematical Society.

Course definitions in K-12 math education , 16 page pdf file December 2004. Organizational suggestions for structuring K-12 education, motivated by work with state standards documents and computer-based courses.

Lessons from the Emporium 1: Goals and economics , With Michael Williams, 6 page pdf file November 2003. The Math Emporium at Virginia Tech is an undergraduate math learning facility with over 500 computers and a large help staff. This is the first of three articles on "lessons": things we initially did not fully appreciate but over the last six years have learned are vital for success. This installment deals with economic constraints and how they influence educational methods and goals.

Lessons from the Emporium 2: Help for computer-based learning , With Michael Williams, 4 page pdf file November 2003. This installment describes the one-on-one help system we have evolved to support the learning process.

A paper "Lessons from the Emporium 3: Testing and course design" has been removed for revision.

Software-generated test questions , Mathematica notebook, April 2001. Computer-based testing has the potential to lighten faculty workloads and improve learning and the classroom atmosphere. Much work has been done on the mechanics of testing usually assuming that questions will be drawn from a database constructed by hand. The point here is that the educational wisdom used in making up questions can sometimes be encoded in software to provide large numbers of high-quality questions quickly and accurately.

Faculty interview assessment of student group work , 4 page pdf file, August 2000. Interviews by faculty are a potentially valuable way to encourage and assess work by groups of students. An analysis of problems with current practice, and how they might be avoided.

Assessing costs and benefits in NSF educational grants , 2 page pdf file, January 2000. Lack of cost assessment in NSF educational grants may be pushing development in wrong directions.

New grade scales for the new age? or, Educational goals are no longer one-dimensional; how can we adapt? , 2 page pdf file, revised September 1998. There is a big disjunction between what society expects (educate everybody) and what educators think they should be doing (educate some well). Educators will "lose" if they don't come to terms with new realities.

On-line help , 6 pages, March 1998. A grant proposal funded by the Center for Innovation in Learning, for development of on-line help facilities for use in the Emporium and with off-site math courses. The model is the student-initiated session at the student work area, as evolved in the Emporium, rather than a class or tutoring situation. Cost is a major constraint since equipment has to be provided at each student work area. This requires a careful analysis of what is really essential to a help session.

Emporium supervisor's manual , 9 page pdf file, February 1998. A guide to supervising the help staff on the Emporium floor. Topics are floor management (basic procedures); assignments and training (use people for what they can do well); and assessment (orient toward improvement, keep it internal).