The Inner Corona Algebra of a C0(X)-Algebra

Date of Acceptance: 15/07/2015

Begreppens roll vid inlärning av algebra : En litteraturstudie om den roll begrepp och begreppsförmåga spelar vid inlärning av algebra för elever i årskurs 4-6

Svenska elever har presterat dåligt i internationella undersökningar en längre tid när det gäller algebraområdet i matematik. Elevernas begreppsförståelse har pekats ut som en faktor som spelar in i de dåliga resultaten för svenska elever del. Syftet med denna studie har därför varit att ta reda på den roll som begrepp och begreppsförmåga spelar vid inlärning av algebra samt vilken begreppsförståelse elever i årskurs 4-6 har. Genom en systematisk litteraturstudie har frågeställningarna besvarats. Resultaten visar att brister i begreppsförståelse i algebra också leder till brister i kunskap i algebra. Undervisning med fokus på begrepp leder till bättre förståelse för begrepp samtidigt som det även leder till procedurell kunskap. Elever i årskurs 4-6 kan hantera variabler och använda dem i matematiska uttryck. Fördelar med en tidig introduktion av variabelbegreppet är att elever bygger en bättre förståelse för begreppet.

Begreppens roll vid inlärning av algebra : En litteraturstudie om den roll begrepp och begreppsförmåga spelar vid inlärning av algebra för elever i årskurs 4-6

Svenska elever har presterat dåligt i internationella undersökningar en längre tid när det gäller algebraområdet i matematik. Elevernas begreppsförståelse har pekats ut som en faktor som spelar in i de dåliga resultaten för svenska elever del. Syftet med denna studie har därför varit att ta reda på den roll som begrepp och begreppsförmåga spelar vid inlärning av algebra samt vilken begreppsförståelse elever i årskurs 4-6 har. Genom en systematisk litteraturstudie har frågeställningarna besvarats. Resultaten visar att brister i begreppsförståelse i algebra också leder till brister i kunskap i algebra. Undervisning med fokus på begrepp leder till bättre förståelse för begrepp samtidigt som det även leder till procedurell kunskap. Elever i årskurs 4-6 kan hantera variabler och använda dem i matematiska uttryck. Fördelar med en tidig introduktion av variabelbegreppet är att elever bygger en bättre förståelse för begreppet.

Computer-aided tool for the teaching of relational algebra in data base courses

This article describes the design and implementation of computer-aided tool called Relational Algebra Translator (RAT) in data base courses, for the teaching of relational algebra. There was a problem when introducing the relational algebra topic in the course EIF 211 Design and Implementation of Databases, which belongs to the career of Engineering in Information Systems of the National University of Costa Rica, because students attending this course were lacking profound mathematical knowledge, which led to a learning problem, being this an important subject to understand what the data bases search and request do RAT comes along to enhance the teaching-learning process.It introduces the architectural and design principles required for its implementation, such as: the language symbol table, the gramatical rules and the basic algorithms that RAT uses to translate from relational algebra to SQL language. This tool has been used for one periods and has demonstrated to be effective in the learning-teaching process.  This urged investigators to publish it in the web site: www.slinfo.una.ac.cr in order for this tool to be used in other university courses.

A case study of a district's intended and unintended results connected to the implementation of a required ninth-grade algebra 1 strategic initiative

There is a long history of debate around mathematics standards, reform efforts, and accountability. This research identified ways that national expectations and context drive local implementation of mathematics reform efforts and identified the external and internal factors that impact teachers’ acceptance or resistance to policy implementation at the local level. This research also adds to the body of knowledge about acceptance and resistance to policy implementation efforts. This case study involved the analysis of documents to provide a chronological perspective, assess the current state of the District’s mathematics reform, and determine the District’s readiness to implement the Common Core Curriculum. The school system in question has continued to struggle with meeting the needs of all students in Algebra 1. Therefore, the results of this case study will be useful to the District’s leaders as they include the compilation and analysis of a decade’s worth of data specific to Algebra 1.

Inductive Theorem Proving and Computer Algebra in the Mathweb Software Bus

Reasoning systems have reached a high degree of maturity in the last decade. However, even the most successful systems are usually not general purpose problem solvers but are typically specialised on problems in a certain domain. The MathWeb SOftware Bus (Mathweb-SB) is a system for combining reasoning specialists via a common osftware bus. We described the integration of the lambda-clam systems, a reasoning specialist for proofs by induction, into the MathWeb-SB. Due to this integration, lambda-clam now offers its theorem proving expertise to other systems in the MathWeb-SB. On the other hand, lambda-clam can use the services of any reasoning specialist already integrated. We focus on the latter and describe first experimnents on proving theorems by induction using the computational power of the MAPLE system within lambda-clam.

El polinomio de Lagrange: un ejemplo de visualización

Este reporte es el resultado de un doble proceso. Por una parte de un interés surgido en el Seminario de Pensamiento Matemático y por otro de la inquietud por compartir una propuesta didáctica para la enseñanza de un tema en particular. En este enfoque alternativo, el profesor podría dejar de ser el emisor del conocimiento y el estudiante su receptor. Investigaciones recientes de la matemática educativa, ponen en evidencia que el proceso de enseñanza aprendizaje trasciende al mero acto de transmitir un saber. Desde el acercamiento teórico de la socio epistemología, consideramos que la visualización aplicada al tratamiento escolar de una noción juega un papel preponderante en la formación de conceptos y procesos matemáticos entre los alumnos. La intención del póster fue la de mostrar un ejemplo concreto de cómo puede enriquecerse un enfoque educativo si se incluye una situación de aprendizaje en la que se haga uso de la visualización del concepto. En este caso, presentamos una situación en la que el estudiante esté en condiciones de llegar, mediante sus propias nociones y de la movilización de habilidades de visualización, a una construcción del polinomio de Lagrange que pasa por n puntos.

A Retrospective-Longitudinal Examination of the Relationship between Apportionment of Seat Time in Community-College Algebra Courses and Student Academic Performance

During the past decade, there has been a dramatic increase by postsecondary institutions in providing academic programs and course offerings in a multitude of formats and venues (Biemiller, 2009; Kucsera & Zimmaro, 2010; Lang, 2009; Mangan, 2008). Strategies pertaining to reapportionment of course-delivery seat time have been a major facet of these institutional initiatives; most notably, within many open-door 2-year colleges. Often, these enrollment-management decisions are driven by the desire to increase market-share, optimize the usage of finite facility capacity, and contain costs, especially during these economically turbulent times. So, while enrollments have surged to the point where nearly one in three 18-to-24 year-old U.S. undergraduates are community college students (Pew Research Center, 2009), graduation rates, on average, still remain distressingly low (Complete College America, 2011). Among the learning-theory constructs related to seat-time reapportionment efforts is the cognitive phenomenon commonly referred to as the spacing effect, the degree to which learning is enhanced by a series of shorter, separated sessions as opposed to fewer, more massed episodes. This ex post facto study explored whether seat time in a postsecondary developmental-level algebra course is significantly related to: course success; course-enrollment persistence; and, longitudinally, the time to successfully complete a general-education-level mathematics course. Hierarchical logistic regression and discrete-time survival analysis were used to perform a multi-level, multivariable analysis of a student cohort (N = 3,284) enrolled at a large, multi-campus, urban community college. The subjects were retrospectively tracked over a 2-year longitudinal period. The study found that students in long seat-time classes tended to withdraw earlier and more often than did their peers in short seat-time classes (p < .05). Additionally, a model comprised of nine statistically significant covariates (all with p-values less than .01) was constructed. However, no longitudinal seat-time group differences were detected nor was there sufficient statistical evidence to conclude that seat time was predictive of developmental-level course success. A principal aim of this study was to demonstrate—to educational leaders, researchers, and institutional-research/business-intelligence professionals—the advantages and computational practicability of survival analysis, an underused but more powerful way to investigate changes in students over time.

Using linear algebra for protein structural comparison and classification.

In this article, we describe a novel methodology to extract semantic characteristics from protein structures using linear algebra in order to compose structural signature vectors which may be used efficiently to compare and classify protein structures into fold families. These signatures are built from the pattern of hydrophobic intrachain interactions using Singular Value Decomposition (SVD) and Latent Semantic Indexing (LSI) techniques. Considering proteins as documents and contacts as terms, we have built a retrieval system which is able to find conserved contacts in samples of myoglobin fold family and to retrieve these proteins among proteins of varied folds with precision of up to 80%. The classifier is a web tool available at our laboratory website. Users can search for similar chains from a specific PDB, view and compare their contact maps and browse their structures using a JMol plug-in.

Flow of a micropolar fluid bounded by a stretching sheet

We consider boundary layer flow of a micropolar fluid driven by a porous stretching sheet. A similarity solution is defined, and numerical solutions using Runge-Kutta and quasilinearisation schemes are obtained. A perturbation analysis is also used to derive analytic solutions to first order in the perturbing parameter. The resulting closed form solutions involve relatively complex expressions, and the analysis is made more tractable by a combination of offline and online work using a computational algebra system (CAS). For this combined numerical and analytic approach, the perturbation analysis yields a number of benefits with regard to the numerical work. The existence of a closed form solution helps to discriminate between acceptable and spurious numerical solutions. Also, the expressions obtained from the perturbation work can provide an accurate description of the solution for ranges of parameters where the numerical approaches considered here prove computationally more difficult.

Implementation of an integrated, technology-based, discovery mode assessment item involving an incubation period to enhance learning outcomes for engineering maths students

In this paper we discuss our current efforts to develop and implement an exploratory, discovery mode assessment item into the total learning and assessment profile for a target group of about 100 second level engineering mathematics students. The assessment item under development is composed of 2 parts, namely, a set of "pre-lab" homework problems (which focus on relevant prior mathematical knowledge, concepts and skills), and complementary computing laboratory exercises which are undertaken within a fixed (1 hour) time frame. In particular, the computing exercises exploit the algebraic manipulation and visualisation capabilities of the symbolic algebra package MAPLE, with the aim of promoting understanding of certain mathematical concepts and skills via visual and intuitive reasoning, rather than a formal or rigorous approach. The assessment task we are developing is aimed at providing students with a significant learning experience, in addition to providing feedback on their individual knowledge and skills. To this end, a noteworthy feature of the scheme is that marks awarded for the laboratory work are primarily based on the extent to which reflective, critical thinking is demonstrated, rather than the amount of CBE-style tasks completed by the student within the allowed time. With regard to student learning outcomes, a novel and potentially critical feature of our scheme is that the assessment task is designed to be intimately linked to the overall course content, in that it aims to introduce important concepts and skills (via individual student exploration) which will be revisited somewhat later in the pedagogically more restrictive formal lecture component of the course (typically a large group plenary format). Furthermore, the time delay involved, or "incubation period", is also a deliberate design feature: it is intended to allow students the opportunity to undergo potentially important internal re-adjustments in their understanding, before being exposed to lectures on related course content which are invariably delivered in a more condensed, formal and mathematically rigorous manner. In our presentation, we will discuss in more detail our motivation and rationale for trailing such a scheme for the targeted student group. Some of the advantages and disadvantages of our approach (as we perceived them at the initial stages) will also be enumerated. In a companion paper, the theoretical framework for our approach will be more fully elaborated, and measures of student learning outcomes (as obtained from eg. student provided feedback) will be discussed.

Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Investigating functional thinking in the elementary classroom : foundations of early algebraic reasoning

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers. These lessons were designed to enable students to build mental representations in order to explore the use of function tables by focusing on the relationship between input and output numbers with the intention of extracting the algebraic nature of the arithmetic involved. All lessons were videotaped. The results indicate that elementary students are not only capable of developing functional thinking but also of communicating their thinking both verbally and symbolically.