Publication Type: Conference Paper/Unpublished Manuscript
Abstract: A graph G is H-decomposable if it can be expressed as an edge disjoint union of H-subgraphs. We say that G is randomly H-decomposable if every collection of edge disjoint H-subgraphs of G can be extended to an H-decomposition of G. In this paper we characteriz randomly $\$P\_k\$$-decomposable graphs for $\$2\backslash le\; k\; \backslash le11\$$. We also prove several structural results related to these graphs. Finally, suggestions for further research in this area are given.

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: For practicing and prospective secondary mathematics teachers, the role of mathematical reasoning and proof in their mathematical training is crucial for a number of reasons: (1) formal mathematical proof serves as a tool for teachers to develop a profound understanding of mathematics and as a means for communicating their understanding; (2) reasoning and proof are featured prominently in the secondary school curricula as envisioned in the NCTM Principles; and, (3) reasoning and proof can form the basis for the development and assessment of student learning and discourse. Following the scheme suggested by the Seldens (2003), we undertook a cross-sectional study of pre- and in-service secondary mathematics teachers’ abilities to validate purported proofs by mathematical induction with an eye toward determining what facets they attended to when reading such an argument. Of the 82 validation attempts only 9 correctly identified that the attempt was flawed.

The reviews of our article submission were mixed, including one reviewer who insisted that the proposition P(k+1) can be established by any means. This sparked an in-depth analysis of the mathematical induction argumentation style using Toulmin’s (1958) argumentation scheme. The concept of a warrant from Toulmin’s scheme is the logical connection between what is given in a proof and what is concluded. In this talk we will discuss the flawed arguments presented to the participants, how Toulmin’s scheme can be utilized to analyze students’ attempts at proof by mathematical induction, and how the scheme can be used as a pedagogical tool in the undergraduate mathematics classroom.

Publication Type: Poster
Abstract: The presentation will summarize findings and recommendations from a Title VI-funded study of the challenges and prospects for improving international exposure and options in the undergraduate training of prospective elementary and secondary school teachers. The research covered such topics as curriculum requirements, faculty development, advising, foreign language study, and governance issues related to international education. Because history courses are an important part of the training of K-12 teachers, the findings are relevant for those who teach their courses and for those who determine curriculum requirements.

The research data come from more than 400 interviews at 41 institutions (research and comprehensive universities and liberal arts colleges) across the United States and with current teachers, producing a daunting amount of information for an “exploratory” study. More than a third of the interviews were in Arts and Sciences, where prospective teachers actually take most of their courses (notwithstanding a perception that they are in “Education” programs). From the data on curriculum and course requirements we see that most teachers are required to have at least one and probably more history courses, indicating that history faculty are important players in the teacher training field, whether or not they think of themselves in those terms. The research findings point to mostly modest adjustments that could and should be made – university-wide, in Education, and in Arts and Sciences – to prepare prospective teachers for their work in an increasingly interconnected world. The teachers-in-training will, after all, also be preparing future students of history.

The recommendations that are most relevant for historians include suggestions about course revisions, overall curriculum for the declared teacher-in-training, advising, foreign language instruction, and the role of general education. Indeed, many of the research findings and recommendations can be relevant to undergraduate programs in other professional fields as well – and to Arts and Sciences majors themselves.

Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: In 1998, Oklahoma instituted a univeral pre-kindergarten program in order to improve educational and developmental outcomes of children. We analyze the short-term effects of pre-kindergarten on children in Tulsa Public Schools (TPS). The main difficulty with estimating the causal impact of a voluntary pre-K program on test scores is that certain parents are more likely to select pre-K for their children, and these parents might also have other unobservable characteristics that influence the test outcomes of their children. We rely on a quasi-experimental framework to address this selection bias. We find that the program increased cognitive/knowledge scores by 0.39 standard deviation, increased motor skills scores by 0.24 standard deviation, and increased language scores by 0.33 standard deviation. Also, we find that the impacts tend to be largest for Hispanics and for blacks, with little impact for whites. Children who qualify for the full free-lunch program also have much larger impacts than the population as a whole.

Publication Type: Proceeding
Abstract: Even though K-12 education policy has become an increasingly salient topic in the United States, few individuals understand the diverse arrangements states have devised to govern America's schools. Describing that variability and then using it to explain student academic success and state policy production is this paper’s empirical goal. That focus provides a new test of institutional theories of executive power in policy networks, which predict that more powerful executives in less fragmented networks are likely to produce desirable outputs and outcomes. The results strongly suggest that states perform better when governors are empowered to appoint leaders of state education agencies, but that performance wanes if governors can appoint agency leaders and members of state education boards. The results are more mixed regarding education finances, where fragmentation has inconsistent impacts on student academic success, but does appear to attenuate effective policy production.