EXISTENCE OF SOLUTIONS FOR A FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.

On moduli spaces of semistable sheaves on K3 surfaces

Ich untersuche die nicht bereits durch die Arbeit "Singular symplectic moduli spaces" von Kaledin, Lehn und Sorger (Invent. Math. 164 (2006), no. 3) abgedeckten Fälle von Modulräumen halbstabiler Garben auf projektiven K3-Flächen - die Fälle mit Mukai-Vektor (0,c,0) sowie die Modulräume zu nichtgenerischen amplen Divisoren - hinsichtlich der möglichen Konstruktion neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten. Ich stelle einen Zusammenhang zu den bereits untersuchten Modulräumen und Verallgemeinerungen derselben her und erweitere bekannte Ergebnisse auf alle offenen Fälle von Garben vom Rang 0 und viele Fälle von Garben von positivem Rang. Insbesondere kann in diesen Fällen die Existenz neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten, die birational über Komponenten des Modulraums liegen, ausgeschlossen werden.

Attempting to improve standardized test results using Study Islands' web-based mastery program

State standardized testing has always been a tool to measure a school’s performance and to help evaluate school curriculum. However, with the school of choice legislation in 1992, the MEAP test became a measuring stick to grade schools by and a major tool in attracting school of choice students. Now, declining enrollment and a state budget struggling to stay out of the red have made school of choice students more important than ever before. MEAP scores have become the deciding factor in some cases. For the past five years, the Hancock Middle School staff has been working hard to improve their students’ MEAP scores in accordance with President Bush's “No Child Left Behind” legislation. In 2005, the school was awarded a grant that enabled staff to work for two years on writing and working towards school goals that were based on the improvement of MEAP scores in writing and math. As part of this effort, the school purchased an internet-based program geared at giving students practice on state content standards. This study examined the results of efforts by Hancock Middle School to help improve student scores in mathematics on the MEAP test through the use of an online program called “Study Island.” In the past, the program was used to remediate students, and as a review with an incentive at the end of the year for students completing a certain number of objectives. It had also been used as a review before upcoming MEAP testing in the fall. All of these methods may have helped a few students perform at an increased level on their standardized test, but the question remained of whether a sustained use of the program in a classroom setting would increase an understanding of concepts and performance on the MEAP for the masses. This study addressed this question. Student MEAP scores and Study Island data from experimental and comparison groups of students were compared to understand how a sustained use of Study Island in the classroom would impact student test scores on the MEAP. In addition, these data were analyzed to determine whether Study Island results provide a good indicator of students’ MEAP performance. The results of the study suggest that there were limited benefits related to sustained use of Study Island and gave some indications about the effectiveness of the mathematics curriculum at Hancock Middle School. These results and implications for instruction are discussed.

SUPPORTING LEARNING FOR NAVAJO STUDENTS THROUGH ETHNOMATHEMATICS

The purpose of this research was to address how culturally informed ethnomathematical methods of teaching can be utilized to support the learning of Navajo students in mathematics. The study was conducted over the course of four years on the Navajo Reservations at Tohatchi Middle School in Tohatchi New Mexico. The students involved in the study were all in 8th grade and were enrolled either in Algebra 1 or a Response to Intervention, RTI, class. The data collected came in the form of a student survey, student observation and student assessment. The teacher written survey, a math textbook word problem, and two original math textbook problems along with their rewritten version were the sources of these three studies. The first year of the study consisted of a math attitude survey and how Navajo students perceived math as a subject of interest. The students answered four questions pertaining to their thoughts about mathematics. The students’ responses were positive according to their written answers. The second year of the study involved the observation of how students worked through a math word problem as a group. This method tested how the students culturally interacted in order to solve a math problem. Their questions and reasoning to solve the problem were shared with peers and the teacher. The teacher supported the students in understanding and solving the problem by asking questions that kept the students focused on the goal of solving the problem. The students worked collaboratively and openly in order to complete the activity. During the iv study, the teacher was more able to notice the students’ deficiencies individually or as a group, therefore was able to support them in a more specific manner. The last study was conducted over a period of two different years. This study was used to determine how textbook bias in the form of its sentence structure or word choice affects the performance of students who are not culturally familiar with one or both. It was found that the students performed better and took less time on the rewritten problem than on the original problem. The data suggests that focusing on the culture, language and education of Navajo students can affect how the students learn and understand math.

Open Tour of Poster Session

The campus community and your invited guests will have an hour and a half to tour your poster session. They will be able to hear you describe the problems you worked on this week and ask you questions about your work.

Panelist Presentations & Q&A

Immediately following lunch, our women panelists will speak about the mathematics courses they took and the role mathematics plays in their chosen career, followed by questions from the audience.

Warranty vs. Non-Warranty Road Construction

A project to show whether a Warranty or Non-Warranty option would end up cheaper in twenty years.

Healthcare Outlier Payment Costs

The purpose of this project is to determine the cost of healthcare per individual depending on the amount of care needed.

Warranty vs. Non-Warranty Road Options

Comparing the cost effectiveness of warranty vs. non-warranty road construction options for a 100 mile section of road over a 20 year period.

Social Networking Charts

This project resulted in a chart illustrating connections in Social Networks.

Healthcare Costs: How Much Could a Hospital Make on Outlier Patients in Montana?

This poster illustrates hospital cost for outlier patients in Montana.

Social Networking: How to Build Social Networks

This poster illustrates variables and connections in social networking.

What Makes Science Hard for Newcomers?

Part I What makes science hard for newcomers? 1) The background (briefly) of my research - (why the math anxiety model doesn’t fit) 2) The Tier analysis (a visual) – message: there are many types of science learners in your class than simply younger versions of yourself 3) Three approaches (bio, chem, physics) but only one Nature 4) The (different) vocabularies of the three Sciences 5) How mathematics is variously used in Science Part II Rules and rules-driven assignments- lQ vs OQ1) How to incorporate creativity into assignments and tests? 2) Tests- borrowing “thought questions" from other fields (If Columbus hadn't discovered the new World, when and under whose law would it have been discovered?) 3) Grading practices (partial credit, post-exam credit for finding and explaining nontrivial errors 4) Icing on the cake – applications, examples of science/engineering from Tuesdays NY Times Part III Making Change at the Departmental Level 1) Taking control of at least some portion of the curriculum 2) Varying style of presentation 3) Taking control of at least some portion of the exams 4) GRADING pros and cons of grading on a curve 5) Updating labs and lab reporting.