The LOGO programing of 30 ninth graders was analyzed from 3 theoretical perspectives: the van Hiele levels, the Structure of Observed Learning Outcomes taxonomy, and Skemp's model of mathematical understanding. Results indicate that success in LOGO programing appears necessary but insufficient for success with the geometric aspects of the analyzed…

Ninety-six eighth and ninth grade algebra students were asked to judge the equivalence of pairs of equations and to justify their responses on the basis of transformations or calculations. Students who gave justifications based upon transformation schemes had a significantly higher rate of correct responses than students who calculated solutions.…

Twelve middle school students, working in pairs, used a computer microworld to explore introductory geometric transformational concepts. Despite a tendency for symbolic overgeneralization, the students were able to use visual feedback from the microworld and discussions with partners to correct their own mistakes. (Author/JJK)

Participants in a fast-paced mathematics course and qualified nonparticipants were surveyed 10 years later with respect to undergraduate record, graduate experience, attitudes toward mathematics/science, and self-esteem. In general, participation was associated with stronger undergraduate records for all students and with more advanced graduate…

A study compared the performance of two groups of university students. One group (n=40) was taught calculus using a computer algebra system whereas the other (n=41) used paper-and-pencil computations. The computer group scored significantly higher than their counterparts on both a conceptual knowledge test and a calculus computational exam. (JJK)

This paper theoretically characterizes number sense as a set of cognitive capabilities for constructing and reasoning within mental models. This perspective provides support for viewing various aspects of number sense as features of students' general condition of knowing about numbers and magnitude, rather than as skills needing specific…

A study documented 10 college students' understanding of the limit concept and the factors affecting changes in that understanding. Encouragement by the researchers for the students to change their common informal models of limit to more formal conceptions were met with extreme resistance. (Author/JJK)

Presented is an alternative method for analyzing the van Hiele level of students' geometrical reasoning. The accuracy of students' answers may afford a description of acquisition and/or expertise for each of the van Hiele levels simultaneously rather than the traditional assignment and evaluation of one level at a time. (JJK)

Analyzes a classroom lesson in which a student teacher was unsuccessful in providing a conceptually based justification for the standard division-of-fractions algorithms, focusing on the student teacher's beliefs about good mathematics teaching and learning to teach. Attempts to understand why the lesson failed, what it reveals about learning to…

Reports case studies using personal construct psychology and the logic of fuzzy sets to elucidate the content and organization of two elementary school teachers' knowledge of fractions and mathematical pedagogy. Results identified four personal constructions that affected classroom events; knowledge of fractions, general pedagogical knowledge,…

Argues that many existing methods for teaching English diction for choral performance are ineffective. Describes a study of the Articulatory Diction Development Method (ADDM), focusing on kinesthetic awareness and speech articulator control. Concludes through research involving three high school choirs that the ADDM can improve choral tone and…

Presents results of a study of the relationship between the diagnostic skills of string music teachers and the performance competencies of their students. Reports no significant relationship between teacher skills and student competencies. Presents teacher ratings of the influence of 22 factors on students' musical achievement. (SG)

Discusses a study of how music education majors and nonmusic education majors evaluated a fifth grade music teacher. Reports that nonmusic majors gave significantly higher ratings than majors for three of four teacher characteristics analyzed. Recommends research to determine variables that affect observation and evaluation processes related to…

Describes two studies of young children's ability to identify single and combined elements in response to music activities. Reports that children were better able to identify single than multiple elements. Concludes that children's ability to identify elements in their singing develops sooner than the ability to focus on elements in music they…

Presents findings of research concerning the relationship between listener response to music and personality variables. Reports that correlations were found among undergraduate music appreciation students between the Music Listener Response Scale and sensing intuition for the entire group and between judgment perception and the scale among…