Mathematics as Liberal Education: Whitehead and the Rhythm of Life

In several of his works, Alfred North Whitehead (1861–1947) presents mathematics as a way of learning about general ideas that increase our understanding of the universe. The danger is that students get bogged down in its technical operations. He argues that mathematics should be an integral part of a new kind of liberal education, incorporating science, the humanities, and “technical education” (making things with one’s hands), thereby integrating “head-work and hand-work.” In order to appreciate the role mathematics plays in modern science, students should understand its diverse history which is capable of bringing abstract ideas to life. Moreover, mathematics can discern the alternating rhythms of repetition and difference in nature constituting the periodicity of life. Since these same rhythms are to be found in his theory of learning as growth, there appears to be a pattern linking Whitehead’s approach to mathematics and his educational philosophy.     

The occurrence of assimilation and accommodation in learning high school physics

The Piagetian model of intelligence consists of the elements of content, mental structures and mental functioning. While the first two elements are said to be variants, the third element is described as invariant. Mental functioning begins with a process called assimilation which promotes disequilibrium and, in reestablishing equilibrium, the learner accommodates to what was assimilated. The assimilation-disequilibrium-accommodation process has been labeled adaptation which Piaget described as the accord of thought with things. The newly-acquired ideas (or concepts) are next organized with other knowledge; Piaget described that organization process as the accord of thought with thought. While the Piagetian mental functioning model has been available for some time, empirical evidence that the model actually did or did not function was not found. Teaching and curriculum development procedures were extracted from the mental functioning model and a twelfth-grade physics course was so organized and taught. Naturalistic data collected from individual student interviews and in-class discussions were used to evaluate the hypothesis that mental functioning and the factors which compose it are integral parts of the learning process.     

When Is It Acceptable to Lie? Interpersonal and Intergroup Perspectives on Deception

While deception is generally viewed as an undesirable and unethical action, people evaluate some lies as more detrimental than others. This study examined factors influencing deception assessments, including the seriousness of the lie and whom it benefits. The effect of an intergroup versus an interpersonal context for the lie was examined. Utilizing 24 vignettes varying in terms of these conditions, 259 participants evaluated a lie’s appropriateness, deceptiveness, and complexity. Altruistic and white lies were viewed as less deceptive and more acceptable than self-serving and more consequential lies. Lies evaluated as least acceptable were interpersonal, serious, and self-serving compared to altruistic lies and those embedded in an intergroup context. Intergroup and interpersonal deceptions are recognized as distinct forms of lying and are evaluated differently.     

Student self-evaluation,teacher evaluation,and learner performance

A total of 341 Latvian students and eight teachers participated in this study of student self-evaluation and teacher evaluation. Students completed a 12-lesson teacher-directed instructional program on conducting and writing a report of their own experimental research. Sixteen classes were randomly assigned to one of four treatment conditions: (1) no in-program evaluation, (2) self-evaluation and revision at the research design and draft final report stages, (3) teacher evaluation and student revision at both stages, (4) self-plus-teacher evaluation and student revision at both stages. Students in the teacher-evaluation and self-plus-teacher evaluation conditions received significantly higher ratings from an independent rater on their final research reports. However, students under the self-evaluation conditions had greater confidence in their ability to conduct future experiments. This research is based on Dr. Olina's dissertation at Arizona State University, and was supported by grants from the Arizona State University Graduate Research Support Program and the Assessment Training Institute Foundaton in Portland, Oregon. We gratefully acknowledge their support.     

Teacher, self and peer evaluation of lesson plans written by preservice teachers

The study investigated the effects of three types of evaluation on preservice teachers’ performance, knowledge and attitudes related to writing lesson plans that incorporate technology. Subjects were randomly assigned to one of the three treatment conditions: teacher-evaluation, self-evaluation or peer-evaluation. All groups completed three class periods of instruction on writing lesson plans, then each subject submitted his/her draft lesson plan. The drafts were evaluated by assigned evaluators (teacher, self or peer), who provided scores and written feedback on a 15-item rubric. Students then revised their lesson plans into final form. All three treatment groups improved their lesson plans significantly from draft version to final version, with the teacher-evaluation group showing significantly greater improvement and writing significantly better final lesson plans than each of the other two groups. Teacher-evaluation and self-evaluation groups had significantly higher scores on a knowledge-based posttest than the peer-evaluation group. Several suggestions are discussed for making further improvements in the self-evaluation and peer-evaluation processes.     

Use of Writing with Symbols 2000 Software to Facilitate Emergent Literacy Development

This paper outlines the use of the Writing with Symbols 2000 software to facilitate emergent literacy development. The program’s use of pictures incorporated with text has great potential to help young children with and without disabilities acquire fundamental literacy concepts about print, phonemic awareness, alphabetic principle, vocabulary development, and comprehension. The flexibility and features of the software allow early childhood professionals to create a variety of early literacy tools for the classroom, including worksheets, storybooks, and interactive activities.     

Linking extreme precocity and adult eminence: a study of eight prodigies at international chess

Do prodigies have extraordinary innate talent or do they just start very early and get much practice? Why do relatively few become eminent as adults? Is it because early and later success often need somewhat different abilities and gatekeepers rule? International chess is a good test domain for both issues because it has objective longitudinal data, unvarying task requirements, and no glass ceiling. Eight prodigies were studied. Some did not start chess particularly young but quickly reached high performance levels. Five already are very eminent, one becoming the youngest‐ever world champion at age 18. Chess prodigies probably do have great natural talent. Prodigies in domains with certain characteristics may tend to become eminent if they persist.     

Student performance and attitudes using personalized mathematics instruction

This study investigated the effects of personalized instruction on the achievement and attitudes of Taiwanese students on two-step mathematics word problems. A total of 136 fourth-graders in a Taiwanese public school participated in the study. Subjects initially completed a Student Survey on which they chose their favorite foods, sports, stores, classmates, and other selections. The most popular items were then used to create personalized math word problems for the pretest, personalized instructional program, and posttest. Subjects were blocked by ability based on their pretest scores and were randomly assigned within ability levels to either a personalized or nonpersonalized version of the print-based instructional program. After finishing the program, subjects completed a student attitude survey and the posttest. A repeated-measures univariate analysis of variance revealed that subjects in the personalized treatment made significantly greater pretest-to-posttest gains than those in the nonpersonalized treatment. Subjects also performed significantly better on the personalized pretest and posttest problems than on the nonpersonalized problems. Personalized subjects and higher-ability students both had significantly more positive attitudes toward the instructional program than did their nonpersonalized and lower-ability counterparts. This research was conducted while he was a doctoral student at Arizona State University.     

Effect of early experience and age on initial responsiveness ofTilapia mossambica fry to a maternal model

Fry of the maternal mouth brooding fishTilapia mossambica were tested for the effects of (1) rearing and (2) increasing age on initial responsiveness to a gray disk covered with small black pits that served as a maternal model. In the first experiment, the eggs were removed from their mother’s mouth shortly after spawning, hatched, and the fry raised in groups, singly in complete visual isolation, or by the mother (control) until testing. When free swimming, the fry were tested individually for responsiveness to the model. High levels of responsiveness were exhibited by all fry regardless of rearing experience, indicating that responsiveness to the mother’s mouth is fully developed at birth and needs no previous social experience for its expression. In the second experiment, naive group-reared fry were tested individually for initial responsiveness to the model at 13, 16, 20, or 26 days postspawning. It was found that naive fry were strongly attracted to the model at 13 and 16 days of age but were neutral or actively avoiding it at 26 days of age. This decline is almost identical to the decline in responsiveness of normally reared fry toward their actual mother.