Different aspects in designing mathematics education: Three examples from the Freudenthal Institute

Three teaching designs are offered. They were developed for 12 to 16 year old pupils taking into account their personal differences in terms of gender (in Making Up the Cube), culture (in Mecca), knowledge, and use of calculators in The integrating calculator. The designs concern the representation of three-dimensional objects in the plane, directions and great circles on the sphere, and exploration of the integrating calculator.     

Community‐Based Educational Planning for Severely Handicapped Students: An Expanding Role for Teachers∗

The emphasis on deinstitutionalization in recent years has resulted in a substantial increase in the use of small community-based residential facilities for disabled students; concomitantry there has been a shift towards a developmental or functional model for instructing these students. These initiatives have resulted in changes in the educational system and in the roles of teachers. Instructional planning for disabled students can no longer be viewed simply within the constraints of the classroom; rather a functional curriculum must be developed which provides for the learning and practising of skills across environments, including residences. Educators must fully participate with parents and residential staff to ensure the coordination of children's habilitation programs; without this involvement, crucial elements may be overlooked. In this paper a model is presented which describes how educators can participate in the planning of programs for severely disabled students in community-based residences. Steps in the process involve assessment of current skills and deficits, evaluation of the type and quality of services children are currently receiving, development of goals, identification and analysis of community resources, specification of individual objectives, monitoring of progress, and evaluation of overall service provision.

     

A treatment program for failure to thrive: A cost/effectiveness analysis

Failure to thrive (FTT) is a frequent cause for the admission of infants to the hospital. Such hospitalizations are often lengthy and expensive, and usually do not contribute to an understanding of the etiology of FTT. Generally, organic causes of FTT can be ruled out by a thorough history and physical examination. In this study two groups were examined: 17 infants who were admitted to foster medical placement homes (MPH), private homes with specially trained parents; and a comparison group of 18 infants who were treated in a more traditional way with diagnostic hospitalization. The groups were similar in all regards prior to admission. All infants were less than a year of age. Family disruption was a prominent feature in both groups, but socio-demographic analysis showed them to be similar in all areas studied. The comparison group gained an average of 276 grams in the hospital over 8.6 days. The MPH group gained 362 grams in the hospital over 8.7 days, with an additional 1270 grams in the medical placement home over 31.1 days. Five children were admitted to the medical placement home without hospitalization. After correcting for an expected weight gain of 15 grams per day (normal growth), the comparison group showed a catch-up growth of 16 gms/day, while the MPH group gained 29 gms/day in excess of expectation, almost twice the comparison group. A 100-gram weight gain cost +308 in the MPH program and +1,635 in the traditional approach. This five-fold difference was felt to be a significant deterrent to the continuing approach of admitting children to the hospital for for the workup of FTT.(ABSTRACT TRUNCATED AT 250 WORDS)     

The significance of discrepancies between the verbal and non-verbal intelligence scores of a group of first year university students

The object of the study was to investigate the significance of the differences between verbal and non-verbal scores on the New South African Group Intelligence Test (NSAGT).The experimental subjects were first year university students. They were subdivided into three groups: one group whose non-verbal scores were higher than their verbal scores, a second group whose verbal scores were higher than their nonverbal scores and a third group, acting as a control group, whose verbal and nonverbal scores were approximately equal.The three groups were compared with regard to such features as visual and auditory acuity, personal adjustment and academic achievement. The raw data were arranged in three-dimensional contingency tables and interrelationships between variables were computed by means of the G² test.A positive correlation was found between temperamental personality features and high non-verbal scores on the NSAGT.This article is based on the MA dissertation of the second author under the supervision of the first author. The study was partly sponsored by a grant from the Human Sciences Research Council. Republic of South Africa, to which body grateful acknowledgement is made. However, the opinions expressed and the conclusions drawn are the absolute responsibility of the authors     

Developing Mentors: An Analysis of Shared Mentoring Practices

Understanding how experienced teachers share and articulate effective mentoring practices can guide efforts to prepare quality mentors. This qualitative study focused on mentoring practices within a teacher-designed student-teaching program conceptualized while the mentor teachers within the program were students in a graduate-level mentoring course and implemented upon the mentors’ completion of their graduate studies. Data sources included interviews and field notes from meetings with mentors and student teachers. The results detail specific mentoring practices: explicit instruction through scaffolding, developing the whole teacher, student-teacher-directed learning, fostering student teachers’ individual practice, explicit mentoring of one another, and reflecting on mentoring. These practices were enabled by program structures such as mentor meetings, an online forum, and mentors’ observation of all student teachers in the program.     

The Role of Reform Curricular Materials in an Internship: The Case of Alice and Gregory

This report describes a case study of asecondary school mathematics internship wheremost of the elements of the internship ecologywere aligned with calls by the National Councilof Teachers of Mathematics [NCTM] for reform.Much research has been done on the lack ofimpact of teacher education programs on teacherclassroom behavior. Often this results fromdissonance between the philosophy and goals ofuniversity teacher education programs and thoseof schools. The case documented here offers aninstance of alignment between the universityprogram and the school internship site. Thefindings showed that within this supportiveatmosphere the reform curricular materialsbeing used in the classroom had a strong andlargely positive influence on the character ofthe internship experience, and on the intern'slearning. The form and content of the materials– Core-Plus Mathematics Project'sContemporary Mathematics in Context –supported reform-oriented development for theintern by providing particular foci to theplanning discussions between the intern and thementor. These areas of focus were: (a) themathematics content itself, (b) conceptualunderstanding as a main goal for instruction,and (c) the use of questioning as the bestmeans of guiding students to thatunderstanding. The findings highlight theimportance of developing reform-supportiveenvironments for intern teaching placements.     

Computer-managed instruction in Naval technical training

Based on the success reported by the behaviorally oriented programmed instruction movement in the 1960s, the Navy in the late 1960s and early 1970s began to individualize and self-pace a number of their high student throughput apprentice training courses. To facilitate self-pacing the Navy set up a centralized computer-managed instruction (CMI) system to manage self-paced courses. This paper describes the evolution of that CMI system, reviews a number of studies done on the system over 10 years (many of which were published as internal technical reports with restricted distribution), describes the demise of the system, and discusses future directions of self-paced and individualized instruction.     

Word processing in dyslexics

Dyslexic children (n=21, mean age=10.2 years) were compared with normal readers of the same age, normal readers of the same reading-age, and poor readers of the same reading-age on measures of phonological decoding and automatic word processing. Three different tasks, varying in phonological demand, were used: a naming task, an auditory-visual matching task, and a lexical decision task. On each task, word-pseudoword profiles were obtained to test phonological decoding skills and unspeeded-speeded profiles were assessed to test automaticity in word processing. Main results indicated that dyslexics have a deficit in automatic phonological decoding skills. The results are discussed within the framework of the phonological deficit and the automatization deficit hypothesis.