The Effect of Prior Experiences and Sequence of Instruction Upon Preservice Teachers\u27 Pedagogical Beliefs and Mathematical Knowledge for Teaching

This study investigated the effects of sequence of instruction in a laboratory-based mathematics content course for elementary teachers on preservice teachers\u27 (PSTs\u27) pedagogical beliefs and Mathematical Knowledge for Teaching (MKT) through a quasi-experimental design in which the order of laboratory tasks and explanations of content was altered between sections for a given unit and between units within a given section. This study also investigated the prior experiences a group of preservice elementary teachers shared as students of mathematics and examined how these experiences related to their beliefs regarding effective pedagogy through a phenomenology. Additionally, the perspective of an experienced instructor, who was new to facilitating a sequence of instruction in which PSTs explored mathematical before a formal explanation of content was delivered, was examined through a case study. Data were collected through mathematical autobiographies written by PSTs, pre- and post-assessments of MKT, classroom observations, exit surveys completed by PSTs, and interviews with the instructor and six PSTs. Results from these data revealed that most PSTs experienced a traditional school mathematics characterized by review, delivery of content, worked examples, and practice, and many PSTs also framed their interpretations of effective pedagogy within this traditional context. No significant differences were found in mean gains between those sections that explored content through laboratory tasks before an explanation was given and those that confirmed content through laboratories that followed an explanation of the content. Although the instructor did not initially identify differences between sequence groups, as the semester progressed, she found the discourse richer and PSTs more independent in their problem solving in the exploratory section, and these benefits came with no drop off in MKT

Problems Faced by Early Space Transportation Planners

The problems faced by early planners of U.S. space boosters up to Saturn are described beginning with early space flight proposals, extending through the golden age of rocket technology during the 1950\u27s, and following the reactions to Soviet space accomplishments. The problems a mixture of sorting out futuristic conceptions, settling differences over what was technically feasible, and gaining political and public acceptancecould have their counterparts today