The relationship between the secondary mathematics curriculum, college persistence, and success at an urban community college

According to Venezia, Kirst, and Antonio (2003) and Barth’s 2002 Thinking K16 Ticket to Nowhere report, the disconnect between K-12 and postsecondary education was a contributing factor to high attrition rates. Since mathematics emerged as a primary concern for college readiness, Barth (2002) called for improving student transitions from K-12 to postsecondary institutions through the use of state or local data. The purpose of the present study was to analyze mathematics course-taking patterns of secondary students in a local context and to evaluate high school characteristics in order to explore their relationships with Associate degree attainment or continuous enrollment at an urban community college. Also, this study extended a national study conducted by Clifford Adelman (The Toolbox Revisited, 2006) as it specifically focused on community college students that were not included his study. Furthermore, this study used the theoretical framework that human capital, social capital, and cultural capital influence habitus—an individual’s or a group’s learned inclination to behave within the parameters of the imposed prevailing culture and norms. Specifically, the school embedded culture as it relates to tracking worked as a reproduction tool of ultimate benefit for the privileged group (Oakes, 1994). ^ Using multilevel analysis, this ex post facto study examined non-causal relationships between math course-taking patterns and college persistence of public high school graduates who enrolled at the local community college for up to 6 years. One school-level variable (percent of racial/ethnic minorities) and 7 student-level variables (community college math proportion, remedial math attempts, race, gender, first-year credits earned, socioeconomic status, and summer credits earned) emerged as predictors for college persistence. Study results indicated that students who enter higher education at the community college may have had lower opportunities to learn and therefore needed higher levels of remediation, which was shown to detract students from degree completion. Community college leaders are called to partner with local high schools with high percentages of racial/ethnic minorities to design academic programs aimed at improving the academic preparation of high school students in mathematics and promote student engagement during the first year and summers of college. ^

The efficacy of an interactive computer system for teaching developmental mathematics to college students

Many students are entering colleges and universities in the United States underprepared in mathematics. National statistics indicate that only approximately one-third of students in developmental mathematics courses pass. When underprepared students repeatedly enroll in courses that do not count toward their degree, it costs them money and delays graduation. This study investigated a possible solution to this problem: Whether using a particular computer assisted learning strategy combined with using mastery learning techniques improved the overall performance of students in a developmental mathematics course. Participants received one of three teaching strategies: (a) group A was taught using traditional instruction with mastery learning supplemented with computer assisted instruction, (b) group B was taught using traditional instruction supplemented with computer assisted instruction in the absence of mastery learning and, (c) group C was taught using traditional instruction without mastery learning or computer assisted instruction. Participants were students in MAT1033, a developmental mathematics course at a large public 4-year college. An analysis of covariance using participants' pretest scores as the covariate tested the null hypothesis that there was no significant difference in the adjusted mean final examination scores among the three groups. Group A participants had significantly higher adjusted mean posttest score than did group C participants. A chi-square test tested the null hypothesis that there were no significant differences in the proportions of students who passed MAT1033 among the treatment groups. It was found that there was a significant difference in the proportion of students who passed among all three groups, with those in group A having the highest pass rate and those in group C the lowest. A discriminant factor analysis revealed that time on task correctly predicted the passing status of 89% of the participants. ^ It was concluded that the most efficacious strategy for teaching developmental mathematics was through the use of mastery learning supplemented by computer-assisted instruction. In addition, it was noted that time on task was a strong predictor of academic success over and above the predictive ability of a measure of previous knowledge of mathematics.^

Comparison of Linear Functions in Middle Grades Textbooks from Singapore and the United States

Many U.S. students do not perform well on mathematics assessments with respect to algebra topics such as linear functions, a building-block for other functions. Poor achievement of U.S. middle school students in this topic is a problem. U.S. eighth graders have had average mathematics scores on international comparison tests such as Third International Mathematics Science Study, later known as Trends in Mathematics and Science Study, (TIMSS)-1995, -99, -03, while Singapore students have had highest average scores. U.S. eighth grade average mathematics scores improved on TIMMS-2007 and held steady onTIMMS-2011. Results from national assessments, PISA 2009 and 2012 and National Assessment of Educational Progress of 2007, 2009, and 2013, showed a lack of proficiency in algebra. Results of curriculum studies involving nations in TIMSS suggest that elementary textbooks in high-scoring countries were different than elementary textbooks and middle grades texts were different with respect to general features in the U.S. The purpose of this study was to compare treatments of linear functions in Singapore and U.S. middle grades mathematics textbooks. Results revealed features currently in textbooks. Findings should be valuable to constituencies who wish to improve U.S. mathematics achievement. Portions of eight Singapore and nine U.S. middle school student texts pertaining to linear functions were compared with respect to 22 features in three categories: (a) background features, (b) general features of problems, and (c) specific characterizations of problem practices, problem-solving competency types, and transfer of representation. Features were coded using a codebook developed by the researcher. Tallies and percentages were reported. Welch's t-tests and chi-square tests were used, respectively, to determine whether texts differed significantly for the features and if codes were independent of country. U.S. and Singapore textbooks differed in page appearance and number of pages, problems, and images. Texts were similar in problem appearance. Differences in problems related to assessment of conceptual learning. U.S. texts contained more problems requiring (a) use of definitions, (b) single computation, (c) interpreting, and (d) multiple responses. These differences may stem from cultural differences seen in attitudes toward education. Future studies should focus on density of page, spiral approach, and multiple response problems.

Dificultades del profesorado para planificar, coordinar y evaluar competencias claves. Un análisis desde la Inspección de Educación.

Este artículo presenta una investigación en la que se analizan las dificultades del profesorado para planificar, coordinar y evaluar competencias claves en una muestra de 23 centros educativos. El tema tiene hondas repercusiones ya que una mala praxis educativa de las competencias claves puede conculcar uno de los derechos fundamentales del alumnado a ser evaluado de forma objetiva (LODE: Art.6b y RD 732/1995: Art. 13.1) y poder superar las pruebas de evaluación consideradas necesarias para la obtención del título académico mínimo que otorga el estado español. La investigación se ha desarrollado desde una doble perspectiva metodológica; en primer lugar, es una investigación descriptiva en la que presentamos las características fundamentales de las competencias claves y la normativa básica para su desarrollo y evaluación. En segundo lugar,  aplicamos un procedimiento de análisis con una doble vertiente cualitativa mediante el empleo del programa Atlas-Ti y del enfoque reticular-categorial del análisis de redes sociales con la aplicación de UCINET y el visor yED Graph Editor para abordar el análisis de las principales dificultades y obstáculos detectados. Los resultados muestran que existen serias dificultades en las tres dimensiones analizadas: "planificación", "coordinación" y "evaluación" de competencias clave; especialmente en la necesidad de formación del profesorado, en la evaluación de las competencias, en la metodología para su desarrollo y en los procesos de coordinación interna para su consecución en los centros educativos.

Using blogs to enhance the capacity of mathematical communication in High School

The aim of this investigation is to analyze the use of the blog as an educational resource for the development of the mathematical communication in secondary education. With this aim, four aspects are analyzed: organization of mathematical thinking through communication; communication of mathematical thinking; analysis and evaluation of the strategies and mathematical thought of others; and expression of mathematical ideas using mathematical language. The research was conducted from a qualitative approach on an exploratory level, with the case study method of 4 classrooms of second grade of secondary education in a private school in Lima. The observational technique of 20 publications in the blog of the math class was applied; a study of a focal group with a sample of 9 students with different levels of academic performance; and an interview with the academic coordinator of the school was conducted. The results show that the organization of mathematical thinking through communication is carried out in the blog in a written, graphical and oral way through explanations, schemes and videos. Regarding communication of mathematical thinking, the blog is used to describe concepts, arguments and mathematical procedures with words and examples of the students. The analysis and evaluation of the strategies and mathematical thinking is performed through comments and debates about the publications. It was also noted that the blog does not facilitate the use of mathematical language to express mathematical ideas, since it does not allow direct writing of symbols nor graphic representation.

Sherman Alexie’s "The Toughest Indian in the World": Amalgamating the Oral and the Written Traditions

This article argues that The Toughest Indian in the World (2000) by Native-American author Sherman Alexie combines elements of his tribal (oral) tradition with others coming from the Western (literary) short-story form. Like other Native writers — such as Momaday, Silko or Vizenor — , Alexie is seen to bring into his short fiction characteristics of his people’s oral storytelling that make it much more dialogical and participatory. Among the author’s narrative techniques reminiscent of the oral tradition, aggregative repetitions of patterned thoughts and strategically-placed indeterminacies play a major role in encouraging his readers to engage in intellectual and emotional exchanges with the stories. Assisted by the ideas of theorists such as Ong (1988), Evers and Toelken (2001), and Teuton (2008), this article shows how Alexie’s short fiction is enriched and revitalized by the incorporation of oral elements. The essay also claims that new methods of analysis and assessment may be needed for this type of bicultural artistic forms. Despite the differences between the two modes of communication, Alexie succeeds in blending features and techniques from both traditions, thus creating a new hybrid short-story form that suitably conveys the trying experiences faced by his characters.

Committing Curricular Time to Science Literacy: The Benefits from Science-based Media Resources

Science reported in the media is an authentic source material to explore science research and innovation, to learn how science works and to consolidate science literacy skills.

Media reports intended to communicate science research and innovation provide opportunities for teachers to develop among their pupils the critical reading skills that are essential for promoting literacy in science.

This study focuses on a curricular intervention with upper primary pupils (age 11 years) and uses science reported in the media to facilitate science directed learning in the primary curriculum.

The study suggests that the use of science based media reports can be a positive learning experience for pupils. Strategies and teaching approaches can be used to boost pupils’ confidence and competence to adopt critical reading strategies when they encounter science-based media.

Critical reading and reasoning strategies vary in their degree of difficulty. This study would suggest that, when using media-based resources, teachers need approaches that systematically address the different levels of cognative challenge presented by media resources and create opportunities within the curriculum to revisit, consolidate and develop pupils’ critical reasoning skills.

Avaliação de literacia financeira da nova geração portuguesa

A educação financeira deve ser entendida como um conjunto amplo de orientações e esclarecimentos sobre comportamentos e atitudes adequados na gestão e no uso dos recursos financeiros pessoais. É a capacidade de saber utilizar o dinheiro como ferramenta para tornar a vida melhor, mais produtiva e mais equilibrada. Saber lidar com o dinheiro é indispensável para o bem estar de cada pessoa. Ter acesso à educação financeira possibilita-nos consumir com inteligência e sem exageros, ensina-nos a prever despesas e a investir adequadamente. Dada a importância deste tema, é essencial que as crianças tenham, desde cedo, contacto com o assunto, introduzindo a Educação Financeira nos currículos das Escolas. O presente trabalho pretende contribuir para averiguar qual o nível de literacia financeira de um grupo da nova geração portuguesa, traçando um perfil no que se refere ao conhecimento de conceitos financeiros e aos fatores que o influenciam. Utilizando os resultados desta avaliação, foi possível elaborar um programa de Educação Financeira, indo ao encontro das necessidades específicas dos alunos em questão. Numa análise global, os resultados obtidos mostram um cenário um pouco preocupante no que respeita aos níveis de literacia financeira do grupo em análise, relativamente a alguns aspetos, como o crédito. Os resultados sugerem a existência de alguns fatores que poderão influenciar o nível de literacia, tais como a discussão de assuntos no domínio das finanças pessoais, tanto em casa, como na escola e a participação em atividades lúdicas ligadas à matemática, entre outros. A análise de clusters realizada possibilitou a identificação de quatro grupos de inquiridos, com diferentes conhecimentos sobre literacia financeira e diferentes estratégias de gestão das suas finanças pessoais.

Series representations of the remainders in the expansions for certain functions with applications

We present a summary of the series representations of the remainders in the expansions in ascending powers of t of 2/(et+1)2/(et+1) , sech t and coth t and establish simple bounds for these remainders when t>0t>0 . Several applications of these expansions are given which enable us to deduce some inequalities and completely monotonic functions associated with the ratio of two gamma functions. In addition, we derive a (presumably new) quadratic recurrence relation for the Bernoulli numbers Bn.

Beyond hope: Rhetorics of mobility, possibility, and literacy

When writing teachers enter the classroom, they often bring with them a deep faith in the power of literacy to rectify social inequalities and improve their students’ social and economic standing. It is this faith—this hope for change—that draws some writing teachers to locations of social and economic hardship. I am interested in how teachers and theorists construct their own narratives of social mobility, possibility, and literacy. My dissertation analyzes the production and expression of beliefs about literacy in the narratives of a diverse group of writing teachers and theorists, from those beginning their careers to those who are published and widely read. The central questions guiding this study are: How do teachers’ and theorists’ narratives of becoming literate intersect with literacy theories? and How do such literacy narratives intersect with beliefs in the power of literacy to improve individuals’ lives socially, economically, and personally? I contend that the professional literature needs to address more fully how teachers’ and theorists’ personal histories with literacy shape what they see as possible (and desirable) for students, especially those from marginalized communities. A central focus of the dissertation is on how teachers and theorists attempt to resolve a paradox they are likely to encounter in narratives about literacy. On one hand, they are immersed in a popular culture that cherishes narrative links between literacy and economic advancement (and, further, between such advancement and a “good life”). On the other hand, in professional discourse and in teacher preparation courses, they are likely to encounter narratives that complicate an assumed causal relationship between literacy and economic progress. Understanding, through literacy narratives, how teachers and theorists chart a practical path through or around this paradox can be beneficial to literacy education in three ways. First, it can offer direction in professional development and teacher education, addressing how teachers negotiate the boundaries between personal experience, theory, and pedagogy. Second, it can help teachers create spaces wherein students can explore the impact of paradoxical views about the role of literacy on their own lives. Finally, it can offer direction in public policy discourse, extending awareness of what we want—and need—from English language arts education in the twenty-first century. To explore these issues, I draw on case studies and ethnographic observation as well as narrative inquiry into teachers’ and theorists’ published literacy narratives. I situate my findings within three interrelated frames: 1) the narratives of new teachers, 2) the published works of literacy educators and theorists, and 3) my own literacy narrative. My first chapter, “Beyond Hope,” explores the tenuous connections between hope and critique in literacy studies and provides a methodological overview of the study. I argue that scholarship must move beyond a singular focus on either hope or critique in order to identify the transformative potential of literacy in particular circumstances. Analyzing literacy narratives provides a way of locating a critically informed sense of possibility. My second chapter, “Making Teachers, Making Literacy,” explores the intersection between teachers’ lives and the theories they study, based on qualitative analysis of a preservice course for secondary education English teachers. I examine how these preservice English teachers understood literacy, how their narratives of becoming literate and teaching English connected—and did not connect—with theoretical and pedagogical positions, and how these stories might inform their future work as practitioners. Centering primarily on preservice teachers who resisted Nancie Atwell’s pedagogy of possibility because they found it too good to be true, this research concentrates on moments of disjuncture, as expressed in class discussion and in one-on-one interviews, when literacy theories failed to align with aspiring teachers’ understandings of their own experiences and also with what they imagined as possible in disadvantaged educational settings. In my third and fourth chapters, I analyze the narratives of celebrated teachers and theorists who put forth an agenda that emphasizes possibilities through literacy, examining how they negotiate the relationship between their own literacy stories and literacy theories. Specifically, I investigate the narratives of three proponents of critical literacy: Mike Rose, Paulo Freire, and Myles Horton, all highly respected literacy teachers whose working-class backgrounds influenced their commitment to teaching in disenfranchised communities. In chapter 3, “Reading Lives on the Boundary,” I demonstrate how Mike Rose’s 1989 autobiographical text, Lives on the Boundary, juxtaposes rhetorics of mobility with critiques of such possibility. Through an analysis of work published in professional journals, I offer a reception history of Rose’s narrative, focusing specifically on how teachers have negotiated the tension between hope and critique. I follow this analysis with three case studies, drawn from a larger sampling, that inquire into the personal connections that writing teachers make with Lives on the Boundary. The teachers in this study, who provided written responses and participated in audio-recorded follow-up interviews, were asked to compare Rose’s story to their own stories, considering how their personal literacy histories influenced their teaching. My findings illustrate how a group of teachers and theorists have projected their own assessments of what literacy and higher education can and cannot accomplish onto this influential text. In my fourth chapter, “Horton and Freire’s Road as Literacy Narrative,” I concentrate on Myles Horton and Paulo Freire’s 1990 collaborative spoken book, We Make the Road by Walking. Central to my analysis are the educators’ stories about their formative years, including their own primary and secondary education experiences. I argue that We Make the Road by Walking demonstrates how theories of literacy cannot be divorced from personal histories. I begin by examining the spoken book as a literacy narrative that fuses personal and theoretical knowledge, focusing specifically on its authors’ ideas on theory. Drawing on Bakhtin’s notion of the chronotope—the intersection of time and space within narrative—I then explore the literacy narratives emerging from the production process of the book, in a video production about Horton and Freire’s meeting, and ultimately in the two men’s reflections on their childhood years (Dialogic). Interspersed with these accounts is archival material on the book’s editorial production that illustrates the value of increased dialogue between personal history and theories of literacy. My fifth chapter is both a reflective analysis and a qualitative study of my work at a men’s medium-high security prison in Illinois, where I conducted research and served as the instructor of an upper-level writing course, “Writing for a Change,” in the spring of 2009. Entitled “Doing Time with Literacy Narratives,” this chapter explores the complex ways in which literacy and incarceration are configured in students’ narratives as well as my own. With and against students’ stories, I juxtapose my own experiences with literacy, particularly in relation to being the son of an imprisoned father. In exploring the intersections between such stories, I demonstrate how literacy narratives can function as a heuristic for exploring beliefs about literacy between teachers and students both inside and outside of the prison-industrial complex. My conclusion pulls together the various themes that emerged in the three frames, from the making of new teachers to the published literacy narratives of teachers and theorists to my own literacy narrative. Writing teachers encounter considerable pressure to align their curricula with one or another theory of literacy, which has the effect of negating the authority of knowledge about literacy gleaned from experience as readers and writers. My dissertation contends that there is much to be gained by finding ways of articulating theories of literacy that encompass teachers’ knowledge of reading and writing as expressed in personal narratives of literacy. While powerful cultural rhetorics of upward social mobility often neutralize the critical potential of teachers’ own narratives of literacy—potential that has been documented by scholars in writing studies and allied disciplines—this is not always the case. The chapters in this dissertation offer evidence that hopeful and critical positions on the transformational possibilities of literacy are not mutually exclusive.

Introduction to geodesics in sub-Riemannian geometry

International audience

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.

“Varopoulos paradigm”: Mackey property versus metrizability in topological groups.

The class of all locally quasi-convex (lqc) abelian groups contains all locally convex vector spaces (lcs) considered as topological groups. Therefore it is natural to extend classical properties of locally convex spaces to this larger class of abelian topological groups. In the present paper we consider the following well known property of lcs: “A metrizable locally convex space carries its Mackey topology ”. This claim cannot be extended to lqc-groups in the natural way, as we have recently proved with other coauthors (Außenhofer and de la Barrera Mayoral in J Pure Appl Algebra 216(6):1340–1347, 2012; Díaz Nieto and Martín Peinador in Descriptive Topology and Functional Analysis, Springer Proceedings in Mathematics and Statistics, Vol 80 doi:10.1007/978-3-319-05224-3_7, 2014; Dikranjan et al. in Forum Math 26:723–757, 2014). We say that an abelian group G satisfies the Varopoulos paradigm (VP) if any metrizable locally quasi-convex topology on G is the Mackey topology. In the present paper we prove that in any unbounded group there exists a lqc metrizable topology that is not Mackey. This statement (Theorem C) allows us to show that the class of groups satisfying VP coincides with the class of finite exponent groups. Thus, a property of topological nature characterizes an algebraic feature of abelian groups.

Some misspecfication problems in long-memory time series models

Doctor of Philosophy in Mathematics