Class Notes for Math 918: Local Cohomology, Instructor Tom Marley

Topics include: Injective Module, Basic Properties of Local Cohomology Modules, Local Cohomology as a Cech Complex, Long exact sequences on Local Cohomology, Arithmetic Rank, Change of Rings Principle, Local Cohomology as a direct limit of Ext modules, Local Duality, Chevelley’s Theorem, Hartshorne- Lichtenbaum Vanishing Theorem, Falting’s Theorem.

Class Notes for Math 871: General Topology, Instructor Jamie Radcliffe

Topics include: Topological space and continuous functions (bases, the product topology, the box topology, the subspace topology, the quotient topology, the metric topology), connectedness (path connected, locally connected), compactness, completeness, countability, filters, and the fundamental group.

Uma análise dos livros de André Perez Y Marin: um momento da história da matemática escolar brasileira no início do século XX

Pós-graduação em Educação Matemática - IGCE

Números Complexos: um estudo histórico sobre sua abordagem na coleção Matemática 2º ciclo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Avaliação na sala de aula de matemática: práticas e concepções

This research aims to understand the assessment practices used by teachers at a public state school in the city of Cunha, Sao Paulo. To this end, we interviewed five mathematics teachers, who answered a questionnaire with five questions. The responses were analyzed according to the rigor of phenomenological research. To understand the investigation region, that is to say, the meaning of evaluation, we proceeded to a review of studies on the subject in authors like Buriasco (2002), Pavanello (2006), Hoffmann (1994), expressive in Mathematics Education that allows us to explain the concept of prevailing interpretation in the area. The phenomenological analysis enabled the development of three categories open revealing the concept of evaluation of teachers investigated. The first shows the review As a way to measure the knowledge acquired by the student. His interpretation leads us to understand that for some teachers, the research subjects, the assessment becomes a method to ' measure ' the knowledge acquired by the student. The second category, expressed by As a way of understanding the student's behavior in class, shows that some of the interviewees understand the evaluation as a medium that reveals and appreciates the ways of the student behave in class. Finally, the third category refers to the evaluation by means of said instruments. On this subject the claim that the assessment is through instruments such that: evidence, exercise lists, among others. In summary, interviews and categories analyzed explain the ways in which the assessment reveals the concept of implicit learning the instruments used in the evaluation practices of teachers interviewed. However, the authors read, evaluation is a necessary and permanent teaching job in teaching, which must follow step by step the process of teaching and learning. It follows, ... (Complete abstract click electronic access below)

Alternative Tasks for the Teaching and the Learning of functions: analysis of an intervention in the High School

In this paper we focus on the application of two mathematical alternative tasks to the teaching and learning of functions with high school students. The tasks were elaborated according to the following methodological approach: (i) Problem Solving and/or mathematics investigation and (ii) a pedagogical proposal, which defends that mathematical knowledge is developed by means of a balance between logic and intuition. We employed a qualitative research approach (characterized as a case study) aimed at analyzing the didactic pedagogical potential of this type of methodology in high school. We found that tasks such as those presented and discussed in this paper provide a more significant learning for the students, allowing a better conceptual understanding, becoming still more powerful when one considers the social-cultural context of the students.

Describing some of the Dimensions that comprise the Profile of the Faculty Staff of Statistics Departments in Brazil

Statistics is a required course in virtually all undergraduate programs in Brazilian universities. In addition, undergraduate programs in Statistics are offered in many public universities. However, despite the importance of this science, there are no systematic studies in the national literature regarding the characterization of the faculty staff, which is responsible for the teaching of statistics in the country. In this context, this paper presents a description of the faculty members of undergraduate courses in Statistics. This description was based on a descriptive sample, related to aspects of their education and scientific production. A prediction of future demand for PhDs in Statistics to fill the vacancies is also provided based on the retirement of faculty members in undergraduate courses in Statistics in the country.

Changes in Preservice Teachers’ Self-Efficacy: From Science Methods to Student Teaching

The purpose of this research was to assess preservice teachers self-efficacy at different stages of their educational career in an attempt to determine the extent to which self-efficacy beliefs may change over time. In addition, the critical incidents, which may contribute to changes in self-efficacy, were also investigated. The instrument used in the study was the Teaching Science as Inquiry (TSI) Instrument. The TSI Instrument was administered to 38 preservice elementary teachers to measure the self-efficacy beliefs of the teacher participants in regard to the teaching of science as inquiry. Based on the results and the associated data analysis, mean and median values demonstrate positive change for self-efficacy and outcome expectancy throughout the data collection period.

The Investigation of the Ways in Which Gender Stereotypes are Perpetuated through Questioning and Assessment Strategies in Inquiry-Based Science Classroom

The purpose of this study was to investigate the questioning strategies of preservice teachers whenteaching science as inquiry. The guiding questions for this research were: In what ways do the questioning strategies of preservice teachers differ for male and female elementary students when teaching science as inquiry and how is Bloom’s Taxonomy evident within the questioning strategies of preservice teachers? Examination of the data indicated that participants asked a total of 4,158 questions to their elementary aged students. Of these questions, 974 (23%) were asked to boys, and 991 (24%) were asked to girls. The remaining questions (53%) were asked to the class as a whole, therefore no gender could be assigned to these questions. In relation to Bloom’s Taxonomy, 74% of the questions were basic knowledge, 15% were secondary comprehension, 2% were application, 4% were analysis, 1% were synthesis, and 3% were evaluation.

Is virtuality close enough to reality? A comparison of the effectiveness of simulations with traditional laboratory activities in a high school biology class

Some schools do not have ideal access to laboratory space and supplies. Computer simulations of laboratory activities can be a cost-effective way of presenting experiences to students, but are those simulations as effective at supplementing content concepts? This study compared the use of traditional lab activities illustrating the principles of cell respiration and photosynthesis in an introductory high school biology class with virtual simulations of the same activities. Additionally student results were analyzed to assess if student conceptual understanding was affected by the complexity of the simulation. Although all student groups posted average gain increases between the pre and post-tests coupled with positive effect sizes, students who completed the wet lab version of the activity consistently outperformed the students who completed the virtual simulation of the same activity. There was no significant difference between the use of more or less complex simulations. Students also tended to rate the wet lab experience higher on a motivation and interest inventory.

Clean water in the classroom : understanding the importance of water quality

This study’s objective was to answer three research questions related to students’ knowledge and attitudes about water quality and availability issues. It is important to understand what knowledge students have about environmental problems such as these, because today’s students will become the problem solvers of the future. If environmental problems, such as those related to water quality, are ever going to be solved, students must be environmentally literate. Several methods of data collection were used. Surveys were given to both Bolivian and Jackson High School students in order to comparison their initial knowledge and attitudes about water quality issues. To study the effects of instruction, a unit of instruction about water quality issues was then taught to the Jackson High School students to see what impact it would have on their knowledge. In addition, the learning of two different groups of Jackson High School students was compared—one group of general education students and a second group of students that were learning in an inclusion classroom and included special education students and struggling learners form the general education population. Student and teacher journals, a unit test, and postsurvey responses were included in the data set. Results suggested that when comparing Bolivian students and Jackson High School students, Jackson High School students were more knowledgeable concerning clean water infrastructure and its importance, despite the fact that these issues were less relevant to their lives than for their Bolivian counterparts. Although overall, the data suggested that all the Jackson High students showed evidence that the instruction impacted their knowledge, the advanced Biology students appeared to show stronger gains than their peers in an inclusion classroom.

Assessment of a high school geological field course

Fieldwork is supportive of students’ natural inquiry abilities. Educational research findings suggest that instructors can foster the growth of thinking skills and promote science literacy by incorporating active learning strategies (McConnel et al, 2003). Huntoon (2001) states that there is a need to determine optimal learning strategies and to document the procedure of assessing those optimal geoscience curricula. This study seeks to determine if Earth Space II, a high school geological field course, can increase students’ knowledge of selected educational objectives. This research also seeks to measure any impact Earth Space II has on students’ attitude towards science. Assessment of the Earth Space II course objectives provided data on the impact of field courses on high school students’ scientific literacy, scientific inquiry skills, and understanding of selected course objectives. Knowledge assessment was done using a multiple choice format test, the Geoscience Concept Inventory, and an open-ended format essay test. Attitude assessment occurred by utilizing a preexisting science attitude survey. Both knowledge assessments items showed a positive effect size from the pretest to the posttest. The essay exam effect size was 17 and the Geoscience Concept Inventory effect size was 0.18. A positive impact on students’ attitude toward science was observed by an increase in the overall mean Likert value from the pre-survey to the post-survey.