Search

In 2000, Thomas Fink and Young Mao studied neck ties and, with certain assumptions, found 85 different ways to tie a neck tie. They gave a formal language which describes how a tie is made, giving a sequence of moves for each neck tie. The ends of a neck tie can be joined together, which gives a physical model of a mathematical knot that we call a tie knot. In this paper we classify the knot type of each of Fink and Mao's 85 tie knots. We describe how the unknot, left and right trefoil, twist knots and $(2,p)$ torus knots can be recognized from their sequence of moves. We also view tie knots as a family within the set of all knots. Among other results, we prove that any tie knot is prime and alternating., Comment: 22 pages, 17 figures, 3 tables. Some minor errors corrected

This descriptive study examined two aspects of teacher education (text materials and curricular methods) with respect to the question of how gay, lesbian, bisexual, and transsexual (GLBT) issues are presented and discussed. The first study focused on a content analysis of a variety of textbooks (lifespan development, adolescent development, and multicultural/social foundations) that are available for use in teacher education programs. Findings here indicated a general inclusion of GLBT issues in lifespan and adolescence texts, though there were some structural and content treatment considerations. The second study involved a set of interviews with 11 teacher educators from a variety of programs nationwide. Four main themes were derived from the data (curricular consistency, community/campus contexts, perceived administrative response, and perceived student response). Findings suggest that while GLBT issues are increasingly a part of teacher education programs, there is still inconsistency across and within programs. Implications for these studies include recommendations for incorporating GLBT issues into teacher preparation in a more formal manner as well as integrating the issues across the curriculum. (Contains 15 references.) (Author/SM)

A study investigated whether grade-level status affects learning through cross-age activities. Data were collected through unstructured and open-ended audiotaped interviews with 11 pairs of students in a combined third- and fifth-grade class. Coding and analysis of data revealed seven themes related to students' perceptions of their interactions as they worked in cross-age pairs. Three themes were elaborated upon: (1) "We both know different things"; (2) "Because they help us a lot"; and (3) "We work together." Interactions between these themes were investigated to see how and why status differences influence small group work. Status was defined by grade level/age, and therefore, knowledge. Results showed that fifth graders perceived the third graders as incapable and therefore did things for the third graders as opposed to trying to help them learn to do them on their own. Results suggest that the effects of differences in knowledge status in small groups can lead to interactions that do not foster learning on the part of either the high- or the low-status partner. Suggested ways to deal with this "Lady Bountiful syndrome" in classrooms include assigning lower status students to leadership positions and "preteaching" key elements to lower status students. (BAC)

A primary objective of this study was to examine the relations among students' perceptions of the classroom goal orientation as ability-focused goals and their own goals, as well as the relationships between these two components and other motivational factors such as subject-specific self-efficacy and task value. An additional purpose was to determine the role of students' prior beliefs about intelligence on their goals, sense of efficacy, and values. Subjects were 194 sixth graders who completed 2 instruments, the Patterns of Adaptive Learning Survey (Midgley and Maehr, 1990) and a second survey constructed to measure items regarding perceptions of classroom goal orientation. Results suggest that, while perceptions of classroom goal stresses may not have a strong direct effect on how much students value their subject, there is a strong indirect effect through personal goals and self-efficacy of classroom goal stresses on subject valuing. Causes of the positive relationships between relative ability goals, self-efficacy, and subject valuing are not clear, but it is clear that it is important to differentiate between extrinsic and relative ability goals in future research, because these two goals relate with other motivational constructs in very different ways. Support is also found for the notion that there are domain differences in motivation. Four tables and one figure present study findings. (Contains 32 references.) (SLD)

Recent studies have documented a decline in academic performance and motivation as students move from elementary to middle level schools. This paper expands these studies in three ways: (1) by examining the classroom-level differences among middle school students' motivation to see if motivational constructs vary by classroom; (2) by exploring the specific within-classroom factors that affect early adolescents' motivation in mathematics and science; and (3) by using Hierarchical Linear Modeling (HLM) which is a multilevel technique. The 673 students in the study came from two middle schools in a largely blue collar community--most of the students were white. Participants completed the Patterns of Adaptive Learning Survey as well as questionnaires pertaining to specific academic subjects. All teachers filled out questionnaires assessing their pedagogical beliefs, instructional practices, and perceptions of the school culture. Results indicate that math teachers had a significant effect on their students' self-concept of ability. Likewise, science teachers who used ability-focused instructional practices, had students with lower measures of "learning focus" toward science than teachers who did not publicly acknowledge test scores or grades. Similar investigations are advocated for the later middle school and high school levels. Eight tables provide statistical summaries. (RJM)

Students' motivation was studied within specific academic content areas using a goal theory framework. The relationships between motivational orientation and cognitive processes within and across content areas are also considered. Six-hundred sixth and seventh graders, approximately 90% white, from two suburban middle schools participated. Students completed general and four domain-specific surveys in mathematics, English, social studies, and science. Surveys, constructed for this study, assessed individual goal orientation (learning focus or ability focus) and cognitive strategy use (surface or deep level) within each domain. Findings suggest that students differentiated their goals and strategies within the four subject matter areas. There was a significant negative relationship between learning-focused goal orientation and ability-focused goal orientation. Most gender differences occurred with respect to the English content area. In English, boys were less likely than girls to hold a learning-focused goal orientation and to report using deeper level strategies, and were more likely to use surface level strategies. Results suggest that motivation is more effectively studied in a domain-specific paradigm. Addressing motivational and cognitive issues within subject areas has the potential to add to the understanding of student decision making. Eleven tables and 8 graphs present study data, and there is a 33-item list of references. (SLD)