Formação de professores de matemática da educação superior e as tecnologias digitais: aspectos do conhecimento revelados no contexto de uma comunidade de prática online

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Formação continuada de professores como um projeto coletivo e de identidade profissional

This research is part of the field of teacher training, especially developed the topic of continuing education. There is, according to the literature, the importance of this training for teachers as a sort of continuum, trajectory in which the teacher will (re) building their knowledge throughout their lives, in order to provide knowledge and values that add to your practice teaching. However, often the training activities are designed for knowledge transmitter model forming agent for the teacher, disregarding the different contexts of school communities, this strategy which hardly reaches the real needs of teachers in their daily lives. It is evident, too, the need to provide, in training moments, spaces to engage in dialogue and reflect on the teachers profession today, (re) building thus their teacher identity. In this context, the objective of this research is to examine whether the continued formation is configured as a collective construction and as a space for reflection on what it means to be a teacher. The research is characterized by a qualitative approach, and to collect data, we used the semi-structured interview technique. Participants were five teachers in the areas of Physical Education, History, English, Portuguese and Mathematics, a state school Treble city education (SP). The results show the importance of continuing education for teachers, which provides reflections, discussions, acquisition of knowledge and skills that contribute to its performance, motivating and developing strategies to enable them to face the challenges of everyday life and reflect collectively on what it means to be a teacher. It was concluded that continuing education for this group of teachers is configured as a space for collective construction, which together with other teachers rethink, reflect and continuously reconstruct their practices and objectives, and enables reflection on the teaching profession constantly. It will be essential, therefore...

Math Anxiety: What can teachers do to help their students over come the feeling?

In this action research study of my classroom of 7th and 8th grade mathematics, I investigated how math anxiety relates to the student work and behavior in the classroom, and how this can affect the student’s overall relationship to mathematics. I discovered that the harder the work, the more math anxiety was displayed. The harder I pushed students to think more deeply, the fewer responses to my questions I received. I noticed difference in the students’ body language and overall behavior. As a result of this research, I plan to help my students try to overcome the feeling of math anxiety and try to teach them different methods to use when they are feeling anxious. The methods that I plan to use hopefully will help the students when they are feeling anxiety and help the students to understand the math being taught and how to apply the math they learn to everyday life.

Formação continuada de professores como um projeto coletivo e de identidade profissional

This research is part of the field of teacher training, especially developed the topic of continuing education. There is, according to the literature, the importance of this training for teachers as a sort of continuum, trajectory in which the teacher will (re) building their knowledge throughout their lives, in order to provide knowledge and values that add to your practice teaching. However, often the training activities are designed for knowledge transmitter model forming agent for the teacher, disregarding the different contexts of school communities, this strategy which hardly reaches the real needs of teachers in their daily lives. It is evident, too, the need to provide, in training moments, spaces to engage in dialogue and reflect on the teachers profession today, (re) building thus their teacher identity. In this context, the objective of this research is to examine whether the continued formation is configured as a collective construction and as a space for reflection on what it means to be a teacher. The research is characterized by a qualitative approach, and to collect data, we used the semi-structured interview technique. Participants were five teachers in the areas of Physical Education, History, English, Portuguese and Mathematics, a state school Treble city education (SP). The results show the importance of continuing education for teachers, which provides reflections, discussions, acquisition of knowledge and skills that contribute to its performance, motivating and developing strategies to enable them to face the challenges of everyday life and reflect collectively on what it means to be a teacher. It was concluded that continuing education for this group of teachers is configured as a space for collective construction, which together with other teachers rethink, reflect and continuously reconstruct their practices and objectives, and enables reflection on the teaching profession constantly. It will be essential, therefore...

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.

Geophysical and geological analysis of the Collingwood Member of the Trenton Formation

The Collingwood Member is a mid to late Ordovician self-sourced reservoir deposited across the northern Michigan Basin and parts of Ontario, Canada. Although it had been previously studied in Canada, there has been relatively little data available from the Michigan subsurface. Recent commercial interest in the Collingwood has resulted in the drilling and production of several wells in the state of Michigan. An analysis of core samples, measured laboratory data, and petrophysical logs has yielded both a quantitative and qualitative understanding of the formation in the Michigan Basin. The Collingwood is a low permeability and low porosity carbonate package that is very high in organic content. It is composed primarily of a uniformly fine grained carbonate matrix with lesser amounts of kerogen, silica, and clays. The kerogen content of the Collingwood is finely dispersed in the clay and carbonate mineral phases. Geochemical and production data show that both oil and gas phases are present based on regional thermal maturity. The deposit is richest in the north-central part of the basin with thickest deposition and highest organic content. The Collingwood is a fairly thin deposit and vertical fractures may very easily extend into the surrounding formations. Completion and treatment techniques should be designed around these parameters to enhance production.

Teaching and aligning upper level mathematics classes to Michigan high school content expectations in an alternative education setting : approaches and issues

After teaching regular education secondary mathematics for seven years, I accepted a position in an alternative education high school. Over the next four years, the State of Michigan adopted new graduation requirements phasing in a mandate for all students to complete Geometry and Algebra 2 courses. Since many of my students were already struggling in Algebra 1, getting them through Geometry and Algebra 2 seemed like a daunting task. To better instruct my students, I wanted to know how other teachers in similar situations were addressing the new High School Content Expectations (HSCEs) in upper level mathematics. This study examines how thoroughly alternative education teachers in Michigan are addressing the HSCEs in their courses, what approaches they have found most effective, and what issues are preventing teachers and schools from successfully implementing the HSCEs. Twenty-six alternative high school educators completed an online survey that included a variety of questions regarding school characteristics, curriculum alignment, implementation approaches and issues. Follow-up phone interviews were conducted with four of these participants. The survey responses were used to categorize schools as successful, unsuccessful, and neutral schools in terms of meeting the HSCEs. Responses from schools in each category were compared to identify common approaches and issues among them and to identify significant differences between school groups. Data analysis showed that successful schools taught more of the HSCEs through a variety of instructional approaches, with an emphasis on varying the ways students learned the material. Individualized instruction was frequently mentioned by successful schools and was strikingly absent from unsuccessful school responses. The main obstacle to successful implementation of the HSCEs identified in the study was gaps in student knowledge. This caused pace of instruction to also be a significant issue. School representatives were fairly united against the belief that the Algebra 2 graduation requirement was appropriate for all alternative education students. Possible implications of these findings are discussed.

FOSSIL PLANTS AND PALYNOMORPHS FROM THE LATE PALEOZOIC CUTLER FORMATION, EASTERN PARADOX BASIN

The late Paleozoic Cutler Formation, where exposed near the modern-day town of Gateway, Colorado, has traditionally been interpreted as the product of alluvial fan deposition within the easternmost portion of the Paradox Basin. The Paradox Basin formed between the western margin of the Uncompahgre Uplift segment of the Ancestral Rocky Mountains and the western paleoshoreline of the North American portion of Pangea. The Paradox Basin region is commonly thought to have experienced semi-arid to arid conditions and warm temperatures during the Pennsylvanian and Permian. Evidence described in this paper support prior interpretations regarding paleoclimate conditions and the inferred depositional environment for the Cutler Formation near Gateway, Colorado. Plant fossils collected from the late Paleozoic Cutler Formation in The Palisade Wilderness Study Area (managed by the U.S. Department of the Interior, Bureau of Land Management) of western Colorado include Calamites, Walchia, Pecopteris, and many calamitean fragments. The flora collected is interpreted to have lived in an arid or semi-arid environment that included wet areas of limited areal extent located near the apex of an alluvial fan system. Palynological analysis of samples collected revealed the presence of the common Pennsylvanian palynomorphs Thymospora pseudothiessenii and Lophotriletes microsaetosus. These fossils suggest that warm and at least seasonally and locally wet conditions existed in the area during the time that the plants were growing. All evidence of late Paleozoic plant life collected during this study was found along the western margin of the Uncompahgre Uplift segment of the Ancestral Rocky Mountains. During the late Paleozoic, sediment was eroded from the Uncompahgre Uplift and deposited in the adjacent Paradox Basin. The preservation of plant fossils in the most proximal parts of the Paradox Basin is remarkable due to the fact that much of the proximal Cutler Formation consists of conglomerates and sandstones deposited as debris flow and by fluvial systems. The plants must have grown in a protected setting, possibly an abandoned channel on the alluvial fan, and been rapidly buried in the subsiding Paradox Basin. It is likely that there was abundant vegetation in and adjacent to low-lying wet areas at the time the Cutler Formation was deposited.

Local Resources for Learning/Teaching CS for Pre-College Students/Teachers

Presentation by Dr. Frank Ackerman. Additional information can be found on Montana Tech's Department of Computer Sciences website.

Effectiveness of an Online Social Constructivist Mathematical Problem Solving Course for Malaysian Pre-Service Teachers

This study assessed the effectiveness of an online mathematical problem solving course designed using a social constructivist approach for pre-service teachers. Thirty-seven pre-service teachers at the Batu Lintang Teacher Institute, Sarawak, Malaysia were randomly selected to participate in the study. The participants were required to complete the course online without the typical face-to-face classes and they were also required to solve authentic mathematical problems in small groups of 4-5 participants based on the Polya’s Problem Solving Model via asynchronous online discussions. Quantitative and qualitative methods such as questionnaires and interviews were used to evaluate the effects of the online learning course. Findings showed that a majority of the participants were satisfied with their learning experiences in the course. There were no significant changes in the participants’ attitudes toward mathematics, while the participants’ skills in problem solving for “understand the problem” and “devise a plan” steps based on the Polya’s Model were significantly enhanced, though no improvement was apparent for “carry out the plan” and “review”. The results also showed that there were significant improvements in the participants’ critical thinking skills. Furthermore, participants with higher initial computer skills were also found to show higher performance in mathematical problem solving as compared to those with lower computer skills. However, there were no significant differences in the participants’ achievements in the course based on gender. Generally, the online social constructivist mathematical problem solving course is beneficial to the participants and ought to be given the attention it deserves as an alternative to traditional classes. Nonetheless, careful considerations need to be made in the designing and implementing of online courses to minimize problems that participants might encounter while participating in such courses.

Beyond questionnaires – Exploring adult education teachers' mathematical beliefs with pictures and interviews

Because of the impact that mathematical beliefs have on an individual’s behaviour, they are generally well researched. However, little mathematical belief research has taken place in the field of adult education. This paper presents preliminary results from a study conducted in this field in Switzerland. It is based on Ernest’s (1989) description of mathematics as an instrumental, Platonist or problem solving construct. The analysis uses pictures drawn by the participants and interviews conducted with them as data. Using a categorising scheme developed by Rolka and Halverscheid (2011), the author argues that adults’ mathematical beliefs are complex and especially personal aspects are difficult to capture with said scheme. Particularly the analysis of visual data requires a more refined method of analysis.

Explicit mathematics and operational set theory: some ontological comparisons

We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.

Theoretical models of planetary system formation II. Post-formation evolution

Aims. We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. Methods. We use the symplectic integrator SyMBA to numerically integrate the orbits of planets for 100 Myr, using populations from previous studies as initial conditions. Results. We show that within the populations studied, mass and semimajor axis distributions experience only minor changes from post-formation evolution. We also show that, depending upon their initial distribution, planetary eccentricities can statistically increase or decrease as a result of gravitational interactions. We find that planetary masses and orbital spacings provided by planet formation models do not result in eccentricity distributions comparable to observed exoplanet eccentricities, requiring other phenomena, such as stellar fly-bys, to account for observed eccentricities.

How Plankton Swim: An Interdisciplinary Approach for Using Mathematics & Physics to Understand the Biology of the Natural World

The authors have developed and field-tested high school-level curricular materials that guide students to use biology, mathematics, and physics to understand plankton and how these tiny organisms move in a world where their intuition does not apply. The authors chose plankton as the focus of their materials primarily because the challenges faced by plankton are novel problems to most students, forcing adoption of new perspectives and making the study of plankton exciting. Additional reasons that they chose plankton to focus on include their ecological importance, their availability to most teachers and students, the ease with which they can be collected and observed, and the current focus of some scientific researchers on their movement and behavior. These curricular materials include a series of inquiry-based, hands-on exercises designed to be accessible to students with a range of backgrounds. Many of these materials could be adapted for use by middle-school, and/or college-level students. In this article, the authors describe sample lessons, summarize what worked well, and flag obstacles they encountered while integrating mathematics and physics into the biology classroom.

Promoting Student Collaboration in a Detracked, Heterogeneous Secondary Mathematics Classroom

Detracking and heterogeneous groupwork are two educational practices that have been shown to have promise for affording all students needed learning opportunities to develop mathematical proficiency. However, teachers face significant pedagogical challenges in organizing productive groupwork in these settings. This study offers an analysis of one teacher’s role in creating a classroom system that supported student collaboration within groups in a detracked, heterogeneous geometry classroom. The analysis focuses on four categories of the teacher’s work that created a set of affordances to support within group collaborative practices and links the teacher’s work with principles of complex systems.