Graphical Approach to Teaching Compound Interest in High School Math Classes

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

A study of the relationship between educational placement and the achievement of urban low socioeconomic Hispanic middle school students with and without specific learning disabilities

Public schools traditionally have been held accountable for educating the majority of the nation’s school children, and through the years, these schools have been evaluated in a variety of ways. Currently, evaluation measures for accountability purposes consist solely of standardized test scores. In the past, only test scores of general education students were analyzed. Laws governing the education of students with disabilities, however, have extended accountability measures not only to include those students, but to report their scores in a disaggregated form (No Child Left Behind Act, 2001). The recent emphasis on accountability and compliance has resulted in the need for schools to carefully examine how programs, services, and policies impact student achievement (Bowers & Figgers, 2003). ^ Standard-based school reform and accountability systems have raised expectations about student learning outcomes for all students, including those with disabilities and minority students. Yet, overall, racial/ethnic minority students are performing well below their White non-Hispanic peers in most academic areas. Additionally, with respect to special education, there exists an enduring problem of disproportionate representation of racial/ethnic minority students (National Research Council, 2000). ^ This study examined classroom placement (inclusive versus non-inclusive) relative to academic performance of urban, low socioeconomic Hispanic students with and without disabilities in secondary content area classrooms. A mixed method research design was used to investigate this important issue using data from a local school district and results from field observations. The study compared performance levels of four middle school Hispanic student subgroups (students with disabilities in inclusive settings, students without disabilities in inclusive settings, students with disabilities in resource settings, and student without disabilities in general education settings) each in their respective placements for two consecutive years, exploring existing practices within authentic settings. ^ Significant differences were found in the relationship of educational placement and achievement between grade level and disability in the areas of math and reading. Additionally, clear and important differences were observed in student-teacher interactions. Recommendations for further researchers and stakeholders include soliciting responses from teams at the schools composed of general education and special education teachers, administrative personnel, and students as well as broadening the study across grade levels and exceptionalities. ^

The relationship between educational placement, instructional practices, and achievement gains of Black students with specific learning disabilities in secondary urban school settings

Black students, in general, are underserved academically (Darling-Hammond, 2000; Townsend, 2002) and overrepresented in special education (Donovan & Cross, 2002). Black students with disabilities are further overrepresented in more restrictive educational environments (Skiba, Poloni-Staudinger, Gallini, Simmons & Feggins-Azziz, 2006). Although the National Longitudinal Transition Study 2 (NLTS2) revealed that the academic performance of students with learning disabilities is positively related to the percentage of courses taken in the general education setting (Newman, 2006), the research specifically on placement of Black students with disabilities, particularly at the secondary level, as it relates to academic achievement is lacking. While previous studies have sought to determine which placement is better for students with disabilities, no study was found that specifically examined the impact of placement specific to Black students with specific learning disabilities (SLD) in urban settings (Fore, III, Hagan-Burke, Burke, Boon & Smith, 2008; Rea, McLaughlin & Walther-Thomas, 2002). This study examined educational placement, instructional best practices, and achievement gains of Black students with SLD in urban secondary settings using an ex post facto research design. Achievement, placement, and demographic data were collected and analyzed on approximately 314 Black eighth grade students with SLD. The Teacher Instructional Practices Survey was developed and used to collect and analyze data from the teachers of 78 of these students as it relates to instructional best practices. Results indicate no significant difference in reading but a significant difference in math gains of students served in inclusive settings as compared to resource settings with a small effect size. Also, no significant relationship was found between achievement gains and the reported use of instructional best practices. However, there was a relationship between educational placement and the use of instructional best practices. The results implied that there is a need for training with both general and special education teachers on instructional best practices for SWD and that there should be certain IEP team considerations when making placement decisions for this population of students with disabilities. It is recommended that future research in this area include classroom observations and factors other than test scores to measure growth in achievement.

Metacognitive Strategies and Learning

During the past decade, metacognition has been identified not only as a component of cognition but also as an important factor in learning. This practitioner proposes that educators and educational researchers should focus on the development and implementation of metacognitive learning strategies. The existing metacognitive studies have concentrated on several areas. One area centers on the continuing efforts to identify all the elements of metacognition. Another area concentrates on the roles that metacognition plays in specific learning behaviors that occur at various ages and levels of complexity. The third area investigates the relationships of metacognition to specific content areas of learning by focusing on the effects of metacognitive learning strategies. The most common areas of study have been reading comprehension, math skills, writing skills, and applying metacognitive strategies to learn various subjects using the computer. Directly or indirectly, the existing studies relate to the expanding applications of the relationships and relevancies of metacognition to learning. Considerable evidence confirms that when students use metacognitive strategies they often experience a higher level of learning. This practitioner believes that experiencing higher levels of learning gives students the confidence they need to construct knowledge which promotes lifelong learning.

Self -regulated learning: The role of a journal in the learning process for students and teachers

A fundamental goal of education is to equip students with self-regulatory capabilities that enable them to educate themselves. Self directedness not only contributes to success in formal instruction but also promotes lifelong learning (Bandura, 1997). The area of research on self-regulated learning is well grounded within the framework of psychological literature attributed to motivation, metacognition, strategy use and learning. This study explored past research and established the purpose of teaching students to self-regulate their learning and highlighted the fact that teachers are expected to assume a major role in the learning process. A student reflective writing journal activity was sustained for a period of two semesters in two fourth-grade mathematics classrooms. The reflective writing journal was analyzed in search of identifying strategies reported by students. Research questions were analyzed using descriptive statistics, frequency counts, cross-tabs and chi-square analyses. ^ Results based on student-use of the journals and teacher interviews indicated that the use of a reflective writing journal does promote self-regulated learning strategies to the extent which the student is engaged in the journaling process. Those students identified as highly self-regulated learners on the basis of their strategy use, were shown to consistently claim to learn math “as well or better than planned” on a weekly basis. Furthermore, good self-regulators were able to recognize specific strategies that helped them do well and change their strategies across time based on the planned learning objectives. The perspectives of the participating teachers were examined in order to establish the context in which the students were working. The effect of “planned change” and/or the resistance to change as established in previous research, from the teachers point of view, was also explored. The analysis of the journal data did establish a significant difference between students who utilized homework as a strategy. ^ Based on the journals and interviews, this study finds that the systematic use of metacognitive, motivational and/or learning strategies can have a positive effect on student's responsiveness to their learning environment. Furthermore, it reflects that teaching students “how to learn” can be a vital part of the effectiveness of any curriculum. ^

Math 412 - Topology with Applications

Highlights of Data Expedition: • Students explored daily observations of local climate data spanning the past 35 years. • Topological Data Analysis, or TDA for short, provides cutting-edge tools for studying the geometry of data in arbitrarily high dimensions. • Using TDA tools, students discovered intrinsic dynamical features of the data and learned how to quantify periodic phenomenon in a time-series. • Since nature invariably produces noisy data which rarely has exact periodicity, students also considered the theoretical basis of almost-periodicity and even invented and tested new mathematical definitions of almost-periodic functions. Summary The dataset we used for this data expedition comes from the Global Historical Climatology Network. “GHCN (Global Historical Climatology Network)-Daily is an integrated database of daily climate summaries from land surface stations across the globe.” Source: https://www.ncdc.noaa.gov/oa/climate/ghcn-daily/ We focused on the daily maximum and minimum temperatures from January 1, 1980 to April 1, 2015 collected from RDU International Airport. Through a guided series of exercises designed to be performed in Matlab, students explore these time-series, initially by direct visualization and basic statistical techniques. Then students are guided through a special sliding-window construction which transforms a time-series into a high-dimensional geometric curve. These high-dimensional curves can be visualized by projecting down to lower dimensions as in the figure below (Figure 1), however, our focus here was to use persistent homology to directly study the high-dimensional embedding. The shape of these curves has meaningful information but how one describes the “shape” of data depends on which scale the data is being considered. However, choosing the appropriate scale is rarely an obvious choice. Persistent homology overcomes this obstacle by allowing us to quantitatively study geometric features of the data across multiple-scales. Through this data expedition, students are introduced to numerically computing persistent homology using the rips collapse algorithm and interpreting the results. In the specific context of sliding-window constructions, 1-dimensional persistent homology can reveal the nature of periodic structure in the original data. I created a special technique to study how these high-dimensional sliding-window curves form loops in order to quantify the periodicity. Students are guided through this construction and learn how to visualize and interpret this information. Climate data is extremely complex (as anyone who has suffered from a bad weather prediction can attest) and numerous variables play a role in determining our daily weather and temperatures. This complexity coupled with imperfections of measuring devices results in very noisy data. This causes the annual seasonal periodicity to be far from exact. To this end, I have students explore existing theoretical notions of almost-periodicity and test it on the data. They find that some existing definitions are also inadequate in this context. Hence I challenged them to invent new mathematics by proposing and testing their own definition. These students rose to the challenge and suggested a number of creative definitions. While autocorrelation and spectral methods based on Fourier analysis are often used to explore periodicity, the construction here provides an alternative paradigm to quantify periodic structure in almost-periodic signals using tools from topological data analysis.

The background impact in HEI math lectures: an experience in math in the 1st year of Accounting and Management Degree

It is a fact, and far from being a new one, that students have been entering Higher Education courses with many different backgrounds in terms of secondary school programs they attended. The impact of these basic skills is a general and worldwide challenge, fundamentally when facing some specific “constructive” subjects like foreign languages and Mathematics. Working with students with an extensive variety of Math qualifications is an outrageous challenge when they enter an advanced Math course, leading to an almost generalized expectations’ failure - from students enrolled in course and from their teachers, who feel powerless in trying to monitor knowledge construction from completely different “starting points”. If teachers’ "haste" is average, more than half of the students do not “go along” and give up, even before experiencing any kind of evaluation procedure. On the contrary, if the “speed” is too low, others are discouraged (feeling not progressing at all) and the teacher runs the risk of not meeting the minimum objectives (general and specific) of its course, which may have a negative impact on students’ future training development. Failure in Mathematics, despite being a recurrent and global issue, does not have any “magical solution”, however, in general, teachers in this area seem untiring, searching, investigating, trying and implementing new and old “recipes” to tackle and demystify this subject. In this article we describe a project developed in a Math course, with the first year students from an Accounting and Management bachelor degree, and its outcomes since it was brought to practice, revealing its impact in students’ success, from approval to dropout rates, in this course. We will shortly describe students’ differentiated Math backgrounds, their results in a pre-assessment analysis and how we try to deal with these differences and level them up, having in mind the same “finish line”. One should never forget that all these students where officially accepted in higher education institutions, so they are ones’ reality, the reality of institutions whose name one should value and strive to defend.

The development of an eBook for teaching and learning mathematics

Mobile devices, smartphones, phablets and tablets, are widely avail‐ able. This is a generation of digital natives. We cannot ignore that they are no longer the same students for which the education system was designed tradition‐ ally. Studying math is many times a cumbersome task. But this can be changed if the teacher takes advantage of the technology that is currently available. We are working in the use of different tools to extend the classroom in a blended learning model. In this paper, it is presented the development of an eBook for teaching mathematics to secondary students. It is developed with the free and open standard EPUB 3 that is available for Android and iOS platforms. This specification supports video embedded in the eBook. In this paper it is shown how to take advantage of this feature, making videos available about lectures and problems resolutions, which is especially interesting for learning mathematics.

Ecological Literacy And Beyond: Problem-based Learning For Future Professionals.

Ecological science contributes to solving a broad range of environmental problems. However, lack of ecological literacy in practice often limits application of this knowledge. In this paper, we highlight a critical but often overlooked demand on ecological literacy: to enable professionals of various careers to apply scientific knowledge when faced with environmental problems. Current university courses on ecology often fail to persuade students that ecological science provides important tools for environmental problem solving. We propose problem-based learning to improve the understanding of ecological science and its usefulness for real-world environmental issues that professionals in careers as diverse as engineering, public health, architecture, social sciences, or management will address. Courses should set clear learning objectives for cognitive skills they expect students to acquire. Thus, professionals in different fields will be enabled to improve environmental decision-making processes and to participate effectively in multidisciplinary work groups charged with tackling environmental issues.

Flicker perimetry in healthy subjects: influence of age and gender, learning effect and short-term fluctuation

PURPOSE: To determine the mean critical fusion frequency and the short-term fluctuation, to analyze the influence of age, gender, and the learning effect in healthy subjects undergoing flicker perimetry. METHODS: Study 1 - 95 healthy subjects underwent flicker perimetry once in one eye. Mean critical fusion frequency values were compared between genders, and the influence of age was evaluated using linear regression analysis. Study 2 - 20 healthy subjects underwent flicker perimetry 5 times in one eye. The first 3 sessions were separated by an interval of 1 to 30 days, whereas the last 3 sessions were performed within the same day. The first 3 sessions were used to investigate the presence of a learning effect, whereas the last 3 tests were used to calculate short-term fluctuation. RESULTS: Study 1 - Linear regression analysis demonstrated that mean global, foveal, central, and critical fusion frequency per quadrant significantly decreased with age (p<0.05).There were no statistically significant differences in mean critical fusion frequency values between males and females (p>0.05), with the exception of the central area and inferonasal quadrant (p=0.049 and p=0.011, respectively), where the values were lower in females. Study 2 - Mean global (p=0.014), central (p=0.008), and peripheral (p=0.03) critical fusion frequency were significantly lower in the first session compared to the second and third sessions. The mean global short-term fluctuation was 5.06±1.13 Hz, the mean interindividual and intraindividual variabilities were 11.2±2.8% and 6.4±1.5%, respectively. CONCLUSION: This study suggests that, in healthy subjects, critical fusion frequency decreases with age, that flicker perimetry is associated with a learning effect, and that a moderately high short-term fluctuation is expected.

Sensitivity and specificity of machine learning classifiers for glaucoma diagnosis using Spectral Domain OCT and standard automated perimetry

PURPOSE: To evaluate the sensitivity and specificity of machine learning classifiers (MLCs) for glaucoma diagnosis using Spectral Domain OCT (SD-OCT) and standard automated perimetry (SAP). METHODS: Observational cross-sectional study. Sixty two glaucoma patients and 48 healthy individuals were included. All patients underwent a complete ophthalmologic examination, achromatic standard automated perimetry (SAP) and retinal nerve fiber layer (RNFL) imaging with SD-OCT (Cirrus HD-OCT; Carl Zeiss Meditec Inc., Dublin, California). Receiver operating characteristic (ROC) curves were obtained for all SD-OCT parameters and global indices of SAP. Subsequently, the following MLCs were tested using parameters from the SD-OCT and SAP: Bagging (BAG), Naive-Bayes (NB), Multilayer Perceptron (MLP), Radial Basis Function (RBF), Random Forest (RAN), Ensemble Selection (ENS), Classification Tree (CTREE), Ada Boost M1(ADA),Support Vector Machine Linear (SVML) and Support Vector Machine Gaussian (SVMG). Areas under the receiver operating characteristic curves (aROC) obtained for isolated SAP and OCT parameters were compared with MLCs using OCT+SAP data. RESULTS: Combining OCT and SAP data, MLCs' aROCs varied from 0.777(CTREE) to 0.946 (RAN).The best OCT+SAP aROC obtained with RAN (0.946) was significantly larger the best single OCT parameter (p<0.05), but was not significantly different from the aROC obtained with the best single SAP parameter (p=0.19). CONCLUSION: Machine learning classifiers trained on OCT and SAP data can successfully discriminate between healthy and glaucomatous eyes. The combination of OCT and SAP measurements improved the diagnostic accuracy compared with OCT data alone.

Pedagogia do esporte : pressupostos para uma teoria da avaliação da aprendizagem = Sport pedagogy: presuppositions for a learning assessment theory

Universidade Estadual de Campinas . Faculdade de Educação Física

Learning processes and the neural analysis of conditioning

Classical and operant conditioning principles, such as the behavioral discrepancy-derived assumption that reinforcement always selects antecedent stimulus and response relations, have been studied at the neural level, mainly by observing the strengthening of neuronal responses or synaptic connections. A review of the literature on the neural basis of behavior provided extensive scientific data that indicate a synthesis between the two conditioning processes based mainly on stimulus control in learning tasks. The resulting analysis revealed the following aspects. Dopamine acts as a behavioral discrepancy signal in the midbrain pathway of positive reinforcement, leading toward the nucleus accumbens. Dopamine modulates both types of conditioning in the Aplysia mollusk and in mammals. In vivo and in vitro mollusk preparations show convergence of both types of conditioning in the same motor neuron. Frontal cortical neurons are involved in behavioral discrimination in reversal and extinction procedures, and these neurons preferentially deliver glutamate through conditioned stimulus or discriminative stimulus pathways. Discriminative neural responses can reliably precede operant movements and can also be common to stimuli that share complex symbolic relations. The present article discusses convergent and divergent points between conditioning paradigms at the neural level of analysis to advance our knowledge on reinforcement.

The Process of Simulation Authoring/Creation by Chemistry Teachers: A Service Learning Experience

Two case studies are presented to describe the process of public school teachers authoring and creating chemistry simulations. They are part of the Virtual Didactic Laboratory for Chemistry, a project developed by the School of the Future of the University of Sao Paulo. the documental analysis of the material produced by two groups of teachers reflects different selection process for both themes and problem-situations when creating simulations. The study demonstrates the potential for chemistry learning with an approach that takes students' everyday lives into account and is based on collaborative work among teachers and researches. Also, from the teachers' perspectives, the possibilities of interaction that a simulation offers for classroom activities are considered.

Students' collective knowledge construction in the virtual learning environment ""ToLigado - your school interactive newspaper""

Introduction. The ToLigado Project - Your School Interactive Newspaper is an interactive virtual learning environment conceived, developed, implemented and supported by researchers at the School of the Future Research Laboratory of the University of Sao Paulo, Brazil. Method. This virtual learning environment aims to motivate trans-disciplinary research among public school students and teachers in 2,931 schools equipped with Internet-access computer rooms. Within this virtual community, students produce collective multimedia research documents that are immediately published in the portal. The project also aims to increase students' autonomy for research, collaborative work and Web authorship. Main sections of the portal are presented and described. Results. Partial results of the first two years' implementation are presented and indicate a strong motivation among students to produce knowledge despite the fragile hardware and software infrastructure at the time. Discussion. In this new environment, students should be seen as 'knowledge architects' and teachers as facilitators, or 'curiosity managers'. The ToLigado portal may constitute a repository for future studies regarding student attitudes in virtual learning environments, students' behaviour as 'authors', Web authorship involving collective knowledge production, teachers' behaviour as facilitators, and virtual learning environments as digital repositories of students' knowledge construction and social capital in virtual learning communities.