Precise Mathematical Language: Exploring the Relationship Between Student Vocabulary Understanding and Student Achievement

In this action research study of my classroom of fifth grade mathematics, I investigate the relationship between student understanding of precise mathematics vocabulary and student achievement in mathematics. Specifically, I focused on students’ understanding of written mathematics problems and on their ability to use precise mathematical language in their written solutions of critical thinking problems. I discovered that students are resistant to change; they prefer to do what comes naturally to them. Since they have not been previously taught to use precise mathematical language in their communication about math, they have great difficulty in adapting to this new requirement. However, with teaching modeling and ample opportunities to use the language of mathematics, students’ understanding and use of specific mathematical vocabulary is increased.

Strategies and Precise Vocabulary Knowledge: Exploring the Relationships Among Mathematics Vocabulary, Problem Solving, and Confidence

In this action research study I focused on my eighth grade pre-algebra students’ abilities to attack problems with enthusiasm and self confidence whether they completely understand the concepts or not. I wanted to teach them specific strategies and introduce and use precise vocabulary as a part of the problem solving process in hopes that I would see students’ confidence improve as they worked with mathematics. I used non-routine problems and concept-related open-ended problems to teach and model problem solving strategies. I introduced and practiced communication with specific and precise vocabulary with the goal of increasing student confidence and lowering student anxiety when they were faced with mathematics problem solving. I discovered that although students were working more willingly on problem solving and more inclined to attempt word problems using the strategies introduced in class, they were still reluctant to use specific vocabulary as they communicated to solve problems. As a result of this research, my style of teaching problem solving will evolve so that I focus more specifically on strategies and use precise vocabulary. I will spend more time introducing strategies and necessary vocabulary at the beginning of the year and continue to focus on strategies and process in order to lower my students’ anxiety and thus increase their self confidence when it comes to doing mathematics, especially problem solving.

Increasing Student Confidence and Knowledge through Student Presentations

In this action research study of a 9th grade Algebra classroom, I investigated the influence of having students present homework solutions and what effect it had on student learning and student confidence. Students were asked to present solutions to homework problems each day and were rated on how well they did. The students were also surveyed about their confidence and feelings about mathematics. Students were also observed for information about who they asked questions of when presented with a math problem they did not understand. In this classroom, two teachers were involved in instruction and this study examines what affect this had on student learning and who was asked for help. As a result of presentations, students’ confidence increased and students reacted positively to both the presentations and their own mathematical learning. The students felt the presentations were a benefit to the class and watching their peers solve mathematical equations helped them to better understand the mathematics.

Written Solutions of Mathematical Word Problems

In this action research study of my classroom of ten ninth grade algebra students, I investigated how my students expressed written solutions of mathematical word problems. I discovered that my students writing and performance improved as they experienced different strategies to attack problem solving. These experiences helped improve the confidence of my students in their problem solving skills and in their mathematical writing. I also discovered that my teaching style changed, as my students took on more responsibility for their learning. As a result of this research, I plan to implement problem solving activities in all my classrooms next year. I also plan to have my students develop their written communication skills by presenting their solutions to their problem solving activities in writing.

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

A construção da ideia de número na educação infantil

This paper seeks to understand-the process by which the child in kindergarten builds the idea of number. Therefore we developed a qualitative study of phenomenological approach that involved field work in the classroom with children of four and five years. Starting from their real-world contexts, their experiences and using the natural language tasks are designed to help the student to go beyond the already known, analyzing how they thinks and what knowledge they bring their lived experience. By interference carried expanded mathematical ideas acquired. The analysis and interpretation of research data shows that the idea of number is built by children from all kinds of relationships created between objects and the world around them, and the more diverse are these experiences, the greater the understanding opportunities and development of mathematical skills and competencies. It showed also that, in kindergarten, children tread just a few ways to build the idea of number

Educational intervention regarding hypothermia: a teaching strategy for education in the Surgery Department

This is a quasi-experimental study performed using a short-term educational intervention involving nursing aides working in a Surgery Department, with the objective to identify the social and professional characteristics of the nursing aides, identify the differences in their knowledge regarding hypothermia following the educational intervention, and relate the nursing actions to the studied variables. It was found that the educational intervention was effective, considering that the difference in the mean nursing actions was 5.35 following the intervention. However, no significant difference was found regarding the nursing actions related to the studied variables. Further studies should be performed to investigate the education of nursing professionals considering their significant learning requirements in different units.

Breastfeeding: knowledge and practice

The objective of this study was to characterize the practices of breastfeeding promotion developed by nursing professionals of the Family Health Strategy and analyze the correlation between their knowledge of breastfeeding and how often they provided teaching regarding this topic. This cross-sectional, descriptive study was performed at the Family Health Strategy units of Uberaba, Minas Gerais with 85 nursing professionals, using two questionnaires. Data analysis was performed using frequency distribution and Spearman's correlation analysis. Most professionals said that they often addressed breastfeeding in the investigated practices. However, a poor correlation was observed between the frequency of this approach and the mean score on knowledge test. The nursing professionals' statements indicate that breastfeeding recommendations were provided regardless of their knowledge on the topic.

Evaluation of a multimedia online tool for teaching bronchial hygiene to physical therapy students

Background: Advances in information technology have been widely used in teaching health care professionals. The use of multimedia resources may be important for clinical learning and we are not aware of previous reports using such technology in respiratory physical therapy education. Objectives: Our approach was to evaluate a conventional bronchial hygiene techniques (BHTs) course with an interactive online environment, including multimedia resources. Methods: Previous developed audiovisual support material comprised: physiology, physiopathology and BHTs, accessible to students through the Internet in conjunction with BHTs classes. Two groups of students were compared and both attended regular classes: the on-line group (n=8) received access to online resources, while the control group (n=8) received conventional written material. Student's performance was evaluated before and after the course. Results: A preliminary test (score 0 to 10) was applied before the beginning of the course, showing that the initial knowledge of both groups was comparable [online, 6.75 (SD=0.88) vs. control, 6.125 (SD=1.35); p>0.05]. Two weeks after the end of the course, a second test showed that the online group performed significantly better than the control group [respectively, 7.75 (SD=1.28) vs. 5.93 (SD=0.72); p>0.05]. Conclusions: The use of a multimedia online resource had a positive impact on student's learning in respiratory therapy field in which instrumental and manual resources are often used and can be explored using this technology.

Computer game-based and traditional learning method: a comparison regarding students’ knowledge retention

Abstract Background Educational computer games are examples of computer-assisted learning objects, representing an educational strategy of growing interest. Given the changes in the digital world over the last decades, students of the current generation expect technology to be used in advancing their learning requiring a need to change traditional passive learning methodologies to an active multisensory experimental learning methodology. The objective of this study was to compare a computer game-based learning method with a traditional learning method, regarding learning gains and knowledge retention, as means of teaching head and neck Anatomy and Physiology to Speech-Language and Hearing pathology undergraduate students. Methods Students were randomized to participate to one of the learning methods and the data analyst was blinded to which method of learning the students had received. Students’ prior knowledge (i.e. before undergoing the learning method), short-term knowledge retention and long-term knowledge retention (i.e. six months after undergoing the learning method) were assessed with a multiple choice questionnaire. Students’ performance was compared considering the three moments of assessment for both for the mean total score and for separated mean scores for Anatomy questions and for Physiology questions. Results Students that received the game-based method performed better in the pos-test assessment only when considering the Anatomy questions section. Students that received the traditional lecture performed better in both post-test and long-term post-test when considering the Anatomy and Physiology questions. Conclusions The game-based learning method is comparable to the traditional learning method in general and in short-term gains, while the traditional lecture still seems to be more effective to improve students’ short and long-term knowledge retention.

Mathematical models of cognitive processes

The research activity carried out during the PhD course was focused on the development of mathematical models of some cognitive processes and their validation by means of data present in literature, with a double aim: i) to achieve a better interpretation and explanation of the great amount of data obtained on these processes from different methodologies (electrophysiological recordings on animals, neuropsychological, psychophysical and neuroimaging studies in humans), ii) to exploit model predictions and results to guide future research and experiments. In particular, the research activity has been focused on two different projects: 1) the first one concerns the development of neural oscillators networks, in order to investigate the mechanisms of synchronization of the neural oscillatory activity during cognitive processes, such as object recognition, memory, language, attention; 2) the second one concerns the mathematical modelling of multisensory integration processes (e.g. visual-acoustic), which occur in several cortical and subcortical regions (in particular in a subcortical structure named Superior Colliculus (SC)), and which are fundamental for orienting motor and attentive responses to external world stimuli. This activity has been realized in collaboration with the Center for Studies and Researches in Cognitive Neuroscience of the University of Bologna (in Cesena) and the Department of Neurobiology and Anatomy of the Wake Forest University School of Medicine (NC, USA). PART 1. Objects representation in a number of cognitive functions, like perception and recognition, foresees distribute processes in different cortical areas. One of the main neurophysiological question concerns how the correlation between these disparate areas is realized, in order to succeed in grouping together the characteristics of the same object (binding problem) and in maintaining segregated the properties belonging to different objects simultaneously present (segmentation problem). Different theories have been proposed to address these questions (Barlow, 1972). One of the most influential theory is the so called “assembly coding”, postulated by Singer (2003), according to which 1) an object is well described by a few fundamental properties, processing in different and distributed cortical areas; 2) the recognition of the object would be realized by means of the simultaneously activation of the cortical areas representing its different features; 3) groups of properties belonging to different objects would be kept separated in the time domain. In Chapter 1.1 and in Chapter 1.2 we present two neural network models for object recognition, based on the “assembly coding” hypothesis. These models are networks of Wilson-Cowan oscillators which exploit: i) two high-level “Gestalt Rules” (the similarity and previous knowledge rules), to realize the functional link between elements of different cortical areas representing properties of the same object (binding problem); 2) the synchronization of the neural oscillatory activity in the γ-band (30-100Hz), to segregate in time the representations of different objects simultaneously present (segmentation problem). These models are able to recognize and reconstruct multiple simultaneous external objects, even in difficult case (some wrong or lacking features, shared features, superimposed noise). In Chapter 1.3 the previous models are extended to realize a semantic memory, in which sensory-motor representations of objects are linked with words. To this aim, the network, previously developed, devoted to the representation of objects as a collection of sensory-motor features, is reciprocally linked with a second network devoted to the representation of words (lexical network) Synapses linking the two networks are trained via a time-dependent Hebbian rule, during a training period in which individual objects are presented together with the corresponding words. Simulation results demonstrate that, during the retrieval phase, the network can deal with the simultaneous presence of objects (from sensory-motor inputs) and words (from linguistic inputs), can correctly associate objects with words and segment objects even in the presence of incomplete information. Moreover, the network can realize some semantic links among words representing objects with some shared features. These results support the idea that semantic memory can be described as an integrated process, whose content is retrieved by the co-activation of different multimodal regions. In perspective, extended versions of this model may be used to test conceptual theories, and to provide a quantitative assessment of existing data (for instance concerning patients with neural deficits). PART 2. The ability of the brain to integrate information from different sensory channels is fundamental to perception of the external world (Stein et al, 1993). It is well documented that a number of extraprimary areas have neurons capable of such a task; one of the best known of these is the superior colliculus (SC). This midbrain structure receives auditory, visual and somatosensory inputs from different subcortical and cortical areas, and is involved in the control of orientation to external events (Wallace et al, 1993). SC neurons respond to each of these sensory inputs separately, but is also capable of integrating them (Stein et al, 1993) so that the response to the combined multisensory stimuli is greater than that to the individual component stimuli (enhancement). This enhancement is proportionately greater if the modality-specific paired stimuli are weaker (the principle of inverse effectiveness). Several studies have shown that the capability of SC neurons to engage in multisensory integration requires inputs from cortex; primarily the anterior ectosylvian sulcus (AES), but also the rostral lateral suprasylvian sulcus (rLS). If these cortical inputs are deactivated the response of SC neurons to cross-modal stimulation is no different from that evoked by the most effective of its individual component stimuli (Jiang et al 2001). This phenomenon can be better understood through mathematical models. The use of mathematical models and neural networks can place the mass of data that has been accumulated about this phenomenon and its underlying circuitry into a coherent theoretical structure. In Chapter 2.1 a simple neural network model of this structure is presented; this model is able to reproduce a large number of SC behaviours like multisensory enhancement, multisensory and unisensory depression, inverse effectiveness. In Chapter 2.2 this model was improved by incorporating more neurophysiological knowledge about the neural circuitry underlying SC multisensory integration, in order to suggest possible physiological mechanisms through which it is effected. This endeavour was realized in collaboration with Professor B.E. Stein and Doctor B. Rowland during the 6 months-period spent at the Department of Neurobiology and Anatomy of the Wake Forest University School of Medicine (NC, USA), within the Marco Polo Project. The model includes four distinct unisensory areas that are devoted to a topological representation of external stimuli. Two of them represent subregions of the AES (i.e., FAES, an auditory area, and AEV, a visual area) and send descending inputs to the ipsilateral SC; the other two represent subcortical areas (one auditory and one visual) projecting ascending inputs to the same SC. Different competitive mechanisms, realized by means of population of interneurons, are used in the model to reproduce the different behaviour of SC neurons in conditions of cortical activation and deactivation. The model, with a single set of parameters, is able to mimic the behaviour of SC multisensory neurons in response to very different stimulus conditions (multisensory enhancement, inverse effectiveness, within- and cross-modal suppression of spatially disparate stimuli), with cortex functional and cortex deactivated, and with a particular type of membrane receptors (NMDA receptors) active or inhibited. All these results agree with the data reported in Jiang et al. (2001) and in Binns and Salt (1996). The model suggests that non-linearities in neural responses and synaptic (excitatory and inhibitory) connections can explain the fundamental aspects of multisensory integration, and provides a biologically plausible hypothesis about the underlying circuitry.

Closed-loop investigation of the dynamical properties of cardiomyocyte electrophysiology by means of Dynamic clamp and Mathematical modelling

The research field of my PhD concerns mathematical modeling and numerical simulation, applied to the cardiac electrophysiology analysis at a single cell level. This is possible thanks to the development of mathematical descriptions of single cellular components, ionic channels, pumps, exchangers and subcellular compartments. Due to the difficulties of vivo experiments on human cells, most of the measurements are acquired in vitro using animal models (e.g. guinea pig, dog, rabbit). Moreover, to study the cardiac action potential and all its features, it is necessary to acquire more specific knowledge about single ionic currents that contribute to the cardiac activity. Electrophysiological models of the heart have become very accurate in recent years giving rise to extremely complicated systems of differential equations. Although describing the behavior of cardiac cells quite well, the models are computationally demanding for numerical simulations and are very difficult to analyze from a mathematical (dynamical-systems) viewpoint. Simplified mathematical models that capture the underlying dynamics to a certain extent are therefore frequently used. The results presented in this thesis have confirmed that a close integration of computational modeling and experimental recordings in real myocytes, as performed by dynamic clamp, is a useful tool in enhancing our understanding of various components of normal cardiac electrophysiology, but also arrhythmogenic mechanisms in a pathological condition, especially when fully integrated with experimental data.

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.

Teaching and assessment of implant dentistry in undergraduate and postgraduate education: a European consensus

This paper constitutes a summary of the consensus documents agreed at the First European Workshop on Implant Dentistry University Education held in Prague on 19-22 June 2008. Implant dentistry is becoming increasingly important treatment alternative for the restoration of missing teeth, as patients expectations and demands increase. Furthermore, implant related complications such as peri-implantitis are presenting more frequently in the dental surgery. This consensus paper recommends that implant dentistry should be an integral part of the undergraduate curriculum. Whilst few schools will achieve student competence in the surgical placement of implants this should not preclude the inclusion of the fundamental principles of implant dentistry in the undergraduate curriculum such as the evidence base for their use, indications and contraindications and treatment of the complications that may arise. The consensus paper sets out the rationale for the introduction of implant dentistry in the dental curriculum and the knowledge base for an undergraduate programme in the subject. It lists the competencies that might be sought without expectations of surgical placement of implants at this stage and the assessment methods that might be employed. The paper also addresses the competencies and educational pathways for postgraduate education in implant dentistry.

SNNAP: A Tool for Teaching Neuroscience

Simulation tools aid in learning neuroscience by providing the student with an interactive environment to carry out simulated experiments and test hypotheses. The field of neuroscience is well suited for the use of simulation tools since nerve cell signaling can be described by mathematical equations and solved by computer. Neural signaling entails the propagation of electrical current along nerve membrane and transmission to neighboring neurons through synaptic connections. Action potentials and synaptic transmission can be simulated and results displayed for visualization and analysis. The neurosimulator SNNAP (Simulator for Neural Networks and Action Potentials) is a simulation environment that provides users with editors for model building, simulator engine and visual display editor. This paper presents several modeling examples that illustrate some of the capabilities and features of SNNAP. First, the Hodgkin-Huxley (HH) model is presented and the threshold phenomenon is illustrated. Second, small neural networks are described with HH models using various synaptic connections available with SNNAP. Synaptic connections may be modulated through facilitation or depression with SNNAP. A study of vesicle pool dynamics is presented using an AMPA receptor model. Finally, a central pattern generator model of the Aplysia feeding circuit is illustrated as an example of a complex network that may be studied with SNNAP. Simulation code is provided for each case study described and tasks are suggested for further investigation.