This paper presents a visual representation of complex solutions of quadratic equations in the xy plane. Rather than moving to the complex plane, students are able to experience a geometric interpretation of the solutions in the xy plane. I am also working on these types of representations with higher order polynomials with some success.

Within statistics instruction, students are often requested to sketch the curve representing a normal distribution with a given mean and standard deviation. Unfortunately, these sketches are often notoriously imprecise. Poor sketches are usually the result of missing mathematical knowledge. This paper considers relationships which exist among…

One of the units of in a standard differential equations course is a discussion of the oscillatory motion of a spring and the associated material on forcing functions and resonance. During the presentation on practical resonance, the instructor may tell students that it is similar to when they take their siblings to the playground and help them on…

It is shown that the well-known Lorentz formula for time dilation can be derived from a distance-time graph plotted for a spaceship communicating with Earth.

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

This article examines a classroom discussion of multiple interpretations of the scales on two distance versus time graphs. The analysis describes how two students and a teacher used multiple meanings for phrases of the form "I went by" and coordinated these meanings with different views of the scales. Students' ambiguous and shifting meanings did…

The report describes the development and evaluation of an instructional program in tangible graph interpretation for braille readers. Because graphs frequently appear in textbooks and in other printed sources, lack of appropriate translation for blind persons can be a significant educational obstacle. Based on anlyses of typical graph reading…

Analyzes the commercial energy statistics of the world by dividing the nations into three groups: developed market economy, developed planned economy, and developing nations. (GS)

Experimentation with graphical methods for data presentation is important for improving graphical communication in science. Several graphical methods are discussed including full scale breaks, dot charts, and multibased logging. Full scale breaks are suggested as replacements for partial scale breaks since partial scale breaks can fail to provide…

Presented at the International Seminar on Experimental Research in Music Education (Reading, England, 1968). The full report will be published in "Journal of Research in Music Education, Summer 1969.

The Interaction Sequence Graph records the occurrence of events according to Flanders' 10 categories of verbal interaction, the duration of each behavioral event, and the relationship of each event to those which precede and follow it. Data obtained by observing classroom teaching are analyzed and converted from a long series of numbers to a…

Text and graphs describe the Dynamic Range Configuration audiogram developed at the Central Institute for the Deaf in St. Louis, Missouri. The audiogram displays the portion of the average speech spectrum audible to the child, with and without amplification, and can be effective in counseling parents and planning appropriate amplification.…

An expense account book report encourages students to be creative and doesn't penalize students with reading and writing disabilities. Pie graphs showing expenditures a character from a book might make reveal divergent thinking skills and with a minimum of words. A reproducible worksheet is included. (MT)

Graphical perception is the visual decoding of the quantitative and qualitative information encoded on graphs. Some recent theoretical/experimental investigations of graphical perception are described, identifying certain elementary graphical-perception tasks that are performed in the visual decoding of quantitative information from graphs.…