A visual approach to understanding the chain rule and related derivative formulae, for functions from R to R and from C to C, is presented. This apparently novel approach has been successfully used with several audiences: students first studying calculus, students with some background in linear algebra, students beginning study of functions of a…

Utilizing video study methodology where participants, as well as the researcher, analyzed their own video data, this research examined the nature of students talking aloud during peer collaborations in mathematics. The findings suggest that students engage in three types of talking aloud: (1) clarification of thinking (i.e. spontaneous utterances…

Problem statement: Although there is agreement on the potential of project based learning (PBL) and virtual manipulatives (VMs), their positive impact depends on how they are used. This study was based on supporting the use of online PBL environments and improving the efficacy of the instructional practices in PBL by combining the potentials of…

A study was conducted at a southern university in sophomore level production classes to assess skills such as the order of arithmetic operations, decimal and percent conversion, solving of algebraic expressions, and evaluation of formulas. The study was replicated using business statistics and quantitative analysis classes at a southeastern…

Solving problems in different ways is strongly advised for mathematics learning and teaching. There is, however, little data available on the examination of teachers' openness to and evaluation of different solutions to the problems. In this paper, the author examines classroom teachers' openness to different solutions (or to what extent they…

This article deals with a brief history of Fibonacci's life and career. It includes Fibonacci's major mathematical discoveries to establish that he was undoubtedly one of the most brilliant mathematicians of the Medieval Period. Special attention is given to the Fibonacci numbers, the golden number and the Lucas numbers and their fundamental…

This article portrays action research conducted in relation to students' faulty use of the equality sign in a Grade Four mathematics classroom in Sweden. Substantial background on teacher-researcher collaboration that prepares ground for the action research is offered. Drawing on cultural-historical and activity theory perspectives, the conduct of…

Proposition 209 banned the use of racial preferences in admissions at public colleges in California. We analyze unique data for all applicants and enrollees within the University of California (UC) system before and after Prop 209. After Prop 209, graduation rates increased by 4.4%. We present evidence that certain institutions are better at…

This study uses simulation techniques to examine the statistical power of the group- randomized design and the matched-pair (MP) randomized block design under various parameter combinations. Both nearest neighbor matching and random matching are used for the MP design. The power of each design for any parameter combination was calculated from…

An account is made of the relationship between the convergence behaviour of a sequence and the accumulation points of the underlying set of the sequence. The aim is to provide students with opportunities to contrast two types of mathematical entities through their commonalities and differences in structure. The more set-oriented perspective that…

Recommendations and standards from various stakeholders in the mathematical preparation of teachers, such as "The Mathematical Education of Teachers" (http://www.cbmsweb.org/MET_Document/chapter_2.htm) and "Beyond Crossroads" (http://beyondcrossroads.amatyc.org/doc/CH6.html), call for courses that emphasize connections within topics in…

In late October 1967, the USS Scorpion was lost at sea, somewhere between the Azores and Norfolk Virginia. Dr. Craven of the U.S. Navy's Special Projects Division is credited with using Bayesian Search Theory to locate the submarine. Bayesian Search Theory is a straightforward and interesting application of Bayes' theorem which involves searching…

Measuring quality of service in academic libraries traditionally includes quantifiable data such as collection size, staff counts, circulation numbers, reference service statistics, qualitative analyses of customer satisfaction, shelving accuracy, and building comfort. In the libraries of the third millennium, virtual worlds, Web content and…

We propose a laboratory learning pathway, suitable for secondary school up to introductory undergraduate level, employing the VnR dynamic modelling software. It is composed of three increasingly complex activities dealing with experimental work, model design and discussion. (Contains 4 footnotes, 1 table and 5 figures.)

The Lorentz velocity addition formula for one-dimensional motion presents a number of problems for beginning students of special relativity. In this paper we suggest a simple rewrite of the formula that is easier for students to memorize and manipulate, and furthermore is more intuitive in understanding the correction necessary when adding…