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

Cooperative Learning Groups in the Middle School Mathematics Classroom

In this action research study of my classroom of 8th grade mathematics, I investigated the inclusion of cooperative learning groups. Data was collected to see how cooperative learning groups affected oral and written communication, math scores, and attitudes toward mathematics. On the one hand, I discovered that many students enjoyed the opportunity to work within a group. On the other hand, there continues to be a handful of students who would rather work alone. The benefits outweigh the demands. Overall, students benefitted from the inclusion of cooperative learning groups. Oral explanations of solutions and methods improved during the study. Written expression also improved over this time period. As a result of this research, I plan to continue with the incorporation of cooperative learning groups in the middle school math classroom.

Movimentos discursivos nas vozes dos sujeitos da Prova Rio

A partir de 2009, a Prefeitura Municipal do Rio de Janeiro inicia a aplicação sistemática de provas bimestrais de Língua Portuguesa e Matemática formuladas Por órgãos especializados em avaliações padronizadas. Tais avaliações, com efeito, materializam camadas de um discurso educacional que vincula qualidade à mensuração de conhecimento em determinados componentes curriculares. Assumindo um modelo de reprodução das avaliações em Larga Escala, a prefeitura enfatiza os resultados mensuráveis nas avaliações sistemáticas, legitimando-os como verdadeiros paradigmas metonímicos da qualidade da educação carioca, enfatizados pela SME em seu discurso virtual disponível em sua página oficial na internet. A partir da constatação de que o discurso é uma prática social, ancorado nas contribuições de Teun A. Van Dijk, Norman Fairclough, Boaventura Sousa de santos entre outros, é traçado nesta pesquisa um percurso de investigação que dialoga com a Análise Crítica do Discurso na busca por elementos discursivos nos textos de professores e alunos acerca dessa cultura de testes padronizados que possam apontar a fluidez dos discursos de protestos que atravessam o cotidiano escolar.

John N. Jackson papers, 1960-1989, n.d.

John N. Jackson was born in Nottingham, England in 1926. He developed a passion for landforms and geography from his father, a high school math and science teacher who had studied geology. During the Second World War, he served in the British Navy. He received his BA from the University of Birmingham, and a PhD from the University of Manchester. After spending a year as a visiting professor at the University of British Columbia, he was hired in 1965 as the founding head of the Geography Department at Brock University. He taught at Brock for more than 25 years, immersing himself in the geography and history of the Niagara area. He became particularly interested in the history of the Welland Canals. He authored 20 books on various topics, including land use in Niagara, the history of St. Catharines, the Welland Canal, and railways in the Niagara Peninsula. He died in 2010, at the age of 84.

L’évolution de la motivation pour les mathématiques au second cycle du secondaire selon la séquence scolaire et le sexe

De nombreuses études sur l’évolution de la motivation pour les mathématiques sont disponibles et il existe également plusieurs recherches qui se sont penchées sur la question de la différence motivationnelle entre les filles et les garçons. Cependant, aucune étude n’a tenu compte de la séquence scolaire des élèves en mathématiques pour comprendre le changement motivationnel vécu pendant le second cycle du secondaire, alors que le classement en différentes séquences est subi par tous au secondaire au Québec. Le but principal de cette étude est de documenter l’évolution de la motivation pour les mathématiques des élèves du second cycle du secondaire en considérant leur séquence de formation scolaire et leur sexe. Les élèves ont été classés dans deux séquences, soit celle des mathématiques de niveau de base (416-514) et une autre de niveau de mathématiques avancé (436-536). Trois mille quatre cent quarante élèves (1864 filles et 1576 garçons) provenant de 30 écoles secondaires publiques francophones de la grande région de Montréal ont répondu à cinq reprises à un questionnaire à items auto-révélés portant sur les variables motivationnelles suivantes : le sentiment de compétence, l’anxiété de performance, la perception de l’utilité des mathématiques, l’intérêt pour les mathématiques et les buts d’accomplissement. Ces élèves étaient inscrits en 3e année du secondaire à la première année de l’étude. Ils ont ensuite été suivis en 4e et 5e année du secondaire. Les résultats des analyses à niveaux multiples indiquent que la motivation scolaire des élèves est généralement en baisse au second cycle du secondaire. Cependant, cette diminution est particulièrement criante pour les élèves inscrits dans les séquences de mathématiques avancées. En somme, les résultats indiquent que les élèves inscrits dans les séquences avancées montrent des diminutions importantes de leur sentiment de compétence au second cycle du secondaire. Leur anxiété de performance est en hausse à la fin du secondaire et l’intérêt et la perception de l’utilité des mathématiques chutent pour l’ensemble des élèves. Les buts de maîtrise-approche sont également en baisse pour tous et les élèves des séquences de base maintiennent généralement des niveaux plus faibles. Une diminution des buts de performance-approche est aussi retrouvée, mais cette dernière n’atteint que les élèves dans les séquences de formation avancées. Des hausses importantes des buts d’évitement du travail sont retrouvées pour les élèves des séquences de mathématiques avancées à la fin du secondaire. Ainsi, les élèves des séquences de mathématiques avancées enregistrent la plus forte baisse motivationnelle pendant le second cycle du secondaire bien qu’ils obtiennent généralement des scores supérieurs aux élèves des séquences de base. Ces derniers maintiennent généralement leur niveau motivationnel. La différence motivationnelle entre les filles et les garçons ne sont pas souvent significatives, malgré le fait que les filles maintiennent généralement un niveau motivationnel inférieur à celui des garçons, et ce, par rapport à leur séquence de formation respective. En somme, les résultats de la présente étude indiquent que la diminution de la motivation au second cycle du secondaire pour les mathématiques touche principalement les élèves des séquences avancées. Il paraît ainsi pertinent de considérer la séquence scolaire dans les études sur l’évolution de la motivation, du moins en mathématiques. Il semble particulièrement important d’ajuster les interventions pédagogiques proposées aux élèves des séquences avancées afin de faciliter leur transition en mathématiques de quatrième secondaire.

O conceito de saber escolar clássico em Dermeval Saviani: Implicações para a Educação Matemática

The aim of this paper is initially to consider some issues related to the relationship between humanization and alienation in the process of historical social development of human gender. These considerations are fundamental for understanding the concept of classical in Dermeval Saviani and the consequences for research about the historical development of Mathematics currently found in school curriculums. The intention is to value the appropriation of school mathematics as a humanizing element that becomes accessible through the activity of teaching.

Resolução de problemas de dedução lógica na promoção da comunicação matemática na oralidade

Relatório de Estágio apresentado à Escola Superior de Educação do Instituto Politécnico de Castelo Branco para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico.

Texto guía para docentes enfocado en el bloque de matemáticas discretas en el primero B.G.U.

El presente trabajo de titulación denominado Texto Guía para Docentes enfocado en el bloque de Matemáticas Discretas del Primero B.G.U, ha sido desarrollado con la finalidad de presentar un aporte significativoy de ayuda al docente de Matemáticas de Primero de Bachillerato, anhelando un mejor desenvolvimiento dentro del aula de clase. Este documento está elaborado en base a la legislación educativa ecuatoriana vigente y de los documentos oficiales del Ministerio de Educación, el tema propuesto corresponde al tercer bloque curricular del primer año de Bachillerato General Unificado en la asignatura de Matemáticas. Nuestro trabajo de titulación se compone de tres capítulos. En el capítulo uno, se presenta una síntesis de temas como la evolución de la educación ecuatoriana, los modelos pedagógicos, los métodos de enseñanza, didáctica de la matemática y programación lineal, considerados como base para el desarrollo de la propuesta. En el capítulo dos, se detalla la investigación estadística realizada mediante una encuesta aplicada a docentes de Matemáticas de Primer año de Bachillerato, pertenecientes a la Coordinación Zonal 6 de Educación, Distrito Norte. Los resultados encontrados cimentaron la propuesta de la implementación del texto guía para el aprendizaje de Matemáticas Discretas. En el capítulo tres se elabora la propuesta del texto guía, estructurado en seis guías didácticas, cada una corresponde al desarrollo de una destreza con criterio de desempeñopara el tema planteado. Al final de este capítulo, se detallan conclusiones y recomendaciones dirigidas para el docente de matemáticas.

Measuring math anxiety in Italian college and high school students: Validity, reliability and gender invariance of the Abbreviated Math Anxiety Scale (AMAS)

Given that the ability to manage numbers is essential in a modern society, mathematics anxiety – which has been demonstrated to have unfortunate consequences in terms of mastery of math – has become a subject of increasing interest, and the need to accurately measure it has arisen. One of the widely employed scales to measure math anxiety is the Abbreviated Math Anxiety Scale (AMAS) (Hopko, Mahadevan, Bare & Hunt, 2003). The first aim of the present paper was to confirm the factor structure of the AMAS when administered to Italian high school and college students, and to test the invariance of the scale across educational levels. Additionally, we assessed the reliability and validity of the Italian version of the scale. Finally, we tested the invariance of the AMAS across genders. The overall findings provide evidence for the validity and reliability of the AMAS when administered to Italian students.

The modern math movement(s): an essay on how elementary school teachers in Brazil gave meaning to it

The main goal of this paper is to discuss the production of meaning of the Modern Math Movement. The main sources were data available in school archives and interviews with former teachers that we use in order to focus on the diversity of perspectives -that complement it or oppose it-, which comes up when teachers refer to the Movement. Using this process of signification, teachers whether accept it, invalidate it or adapt it to guidelines imposed to them in their teaching activities. We establish a methodology by following the premises of Oral History to gather oral testimonies. The theoretical foundations in which this article is written are the guidelines of Paul Ricoeur's Hermeneutics, John Thompson's Depth Hermeneutics and Bolivar's narrative analysis.

‘Wanna do more math’: engaging underachieving Indigenous learners the YuMi Deadly way.

The Accelerating Indigenous Mathematics (AIM) Program offered by the YuMi Deadly Centre from QUT accelerates the mathematics learning of underperforming students in Years 8 - 10 by a) apportioning Years 2-10 Australian Curriculum: Mathematics content into three years, and b) provides a teaching approach that accelerates the mathematical learning. The philosophy of the YuMi Deadly teaching approach for mathematics is one that requires a ‘body’, ‘hand’, ‘mind’ pedagogy. This presentation will provide examples of the “‘body’, ‘hand’, ‘mind’” mathematics pedagogy. In AIM classrooms, mathematics is presented this approach is having a positive impact. Students are willing ‘to have a go’ without shame; and they develop the desire to learn and improve their numeracy.

Problem solving in the primary school (K-2)

This article focuses on problem solving activities in a first grade classroom in a typical small community and school in Indiana. But, the teacher and the activities in this class were not at all typical of what goes on in most comparable classrooms; and, the issues that will be addressed are relevant and important for students from kindergarten through college. Can children really solve problems that involve concepts (or skills) that they have not yet been taught? Can children really create important mathematical concepts on their own – without a lot of guidance from teachers? What is the relationship between problem solving abilities and the mastery of skills that are widely regarded as being “prerequisites” to such tasks?Can primary school children (whose toolkits of skills are limited) engage productively in authentic simulations of “real life” problem solving situations? Can three-person teams of primary school children really work together collaboratively, and remain intensely engaged, on problem solving activities that require more than an hour to complete? Are the kinds of learning and problem solving experiences that are recommended (for example) in the USA’s Common Core State Curriculum Standards really representative of the kind that even young children encounter beyond school in the 21st century? … This article offers an existence proof showing why our answers to these questions are: Yes. Yes. Yes. Yes. Yes. Yes. And: No. … Even though the evidence we present is only intended to demonstrate what’s possible, not what’s likely to occur under any circumstances, there is no reason to expect that the things that our children accomplished could not be accomplished by average ability children in other schools and classrooms.

The effect of employment while in high school on educational attainment : a conditional difference-in-differences approach

Using American panel data from the National Education Longitudinal Study of 1988, this article investigates the effect of working during grade 12 on attainment.We employ, for the first time in the related literature, a semiparametric propensity score matching approach combined with difference-in-differences. We address selection on both observables and unobservables associated with part-time work decisions, without the need for instrumental variable. Once such factors are controlled for, little to no effects on reading and math scores are found. Overall, our results therefore suggest a negligible academic cost from part-time working by the end of high school.

Discovering Math APIs by Mining Unit Tests

In today's API-rich world, programmer productivity depends heavily on the programmer's ability to discover the required APIs. In this paper, we present a technique and tool, called MATHFINDER, to discover APIs for mathematical computations by mining unit tests of API methods. Given a math expression, MATHFINDER synthesizes pseudo-code to compute the expression by mapping its subexpressions to API method calls. For each subexpression, MATHFINDER searches for a method such that there is a mapping between method inputs and variables of the subexpression. The subexpression, when evaluated on the test inputs of the method under this mapping, should produce results that match the method output on a large number of tests. We implemented MATHFINDER as an Eclipse plugin for discovery of third-party Java APIs and performed a user study to evaluate its effectiveness. In the study, the use of MATHFINDER resulted in a 2x improvement in programmer productivity. In 96% of the subexpressions queried for in the study, MATHFINDER retrieved the desired API methods as the top-most result. The top-most pseudo-code snippet to implement the entire expression was correct in 93% of the cases. Since the number of methods and unit tests to mine could be large in practice, we also implement MATHFINDER in a MapReduce framework and evaluate its scalability and response time.