Foreword [to Digital literacy, technology and social inclusion: making sense of one-to-one computer programmes around the world]

(Excerto) In times past, learning to read, write and do arithmetic was to get on course to earn the “writ of emancipation” in society. These skills are still essential today, but are not enough to live in society. Reading and critically understanding the world we live in, with all its complexity, difficulties and challenges, require not only other skills (learning to search for and validate information, reading with new codes and grammar, etc) but, to a certain extent, also metaskills, matrixes and mechanisms that are transversal to the different and new literacies, are necessary. They are needed not just to interpret but equally to communicate and participate in the little worlds that make up our everyday activities as well as, in a broader sense, in the world of the polis, which today is a global world.

TOPSpro Data Dictionary, July 1, 2005–June 30, 2006

The passage of the Workforce Investment Act (WIA) of 1998 [Public Law 105-220] by the 105th Congress has ushered in a new era of collaboration, coordination, cooperation and accountability. The overall goal of the Act is “to increase the employability, retention, and earnings of participants, and increase occupational skill attainment by participants, and, as a result improve the quality of the workforce, reduce welfare dependency, and enhance the productivity and competitiveness of the Nation.” The key principles inculcated in the Act are: • Streamlining services; • Empowering individuals; • Universal access; • Increased accountability; • New roles for local boards; • State and local flexibility; • Improved youth programs. The purpose of Title II, The Adult Education and Family Literacy Act (AEFLA), of the Workforce Investment Act of 1998 is to create a partnership among the federal government, states, and localities to provide, on a voluntary basis, adult education and literacy services in order to: • Assist adults become literate and obtain the knowledge and skills necessary for employment and self-sufficiency; • Assist adults who are parents obtain the educational skills necessary to become full partners in the educational development of their children; • Assist adults in the completion of a secondary school education. Adult education is an important part of the workforce investment system. Title II restructures and improves programs previously authorized by the Adult Education Act. AEFLA focuses on strengthening program quality by requiring States to give priority in awarding funds to local programs that are based on a solid foundation of research, address the diverse needs of adult learners, and utilize other effective practices and strategies. To promote continuous program involvement and to ensure optimal return on the Federal investment, AEFLA also establishes a State performance accountability system. Under this system, the Secretary and each State must reach agreement on annual levels of performance for a number of “core indicators” specified in the law: • Demonstrated improvements in literacy skill levels in reading, writing, and speaking the English language, numeracy, problem solving, English language acquisition, and other literacy skills. • Placement in, retention in, or completion of postsecondary education, training, unsubsidized employment or career advancement. • Receipt of a secondary school diploma or its recognized equivalent. Iowa’s community college based adult basic education program has implemented a series of proactive strategies in order to effectively and systematically meet the challenges posed by WIA. The Iowa TOPSpro Data Dictionary is a direct result of Iowa’s pro-active efforts in this educational arena.

Mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Applied mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Numeracy activities : plenary, practical and problem solving.

Es un recurso didáctico para desarrollar en los alumnos de la etapa 3 (key stage 3) del curriculo nacional inglés la comprensión de las matemáticas y las habilidades para el cálculo. Incluye actividades, que pueden fotocopiarse, y que están diseñadas para trabajar de forma individual o en grupo y para que sus respuestas, resultados y objetivos se puedan mejorar mediante la repetición y la práctica. Además, son actividades flexibles, es decir, el profesor puede ampliar o modificar su contenido según las circunstancias de los alumnos. También, es vital el uso del lenguaje, tanto oral como escrito, por los alumnos para ayudarles a comprender y dominar estos conceptos matemáticos.

Resolução de problemas no ensino da matemática: uma experiência com base no rali matemático

Since the 1980s, problem solving has been recommended by international curriculum proposals for the teaching of mathematics. In Brazil, with the publication of the National Curriculum Guidelines in 1997, this trend was reinforced and became the central activity of the classroom. Troubleshooting is seen as an asset in the learning process of the student, providing a context for learning concepts, mathematical methods and attitudes. However, this methodological approach requires deeper research, especially for new teaches. This work aims at a further study in this subject and in the experiences with problem solving in the classroom of High School students. The ground basis for this was the Mathematical Transalpine Rally, a competition between classrooms that seeks to facilitate the problem solving within mathematics teaching, and through an autonomous and creative work, performed collectively. The results of this experience, as well as the contribuition for the student’s education are presented

Jogo Mega-Duque: uma proposta para o ensino de probabilidade

Pós-graduação em Matemática em Rede Nacional - IBILCE

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.

The Importance of Teaching Students How to Read to Comprehend Mathematical Language

In this action research study of my classroom of 8th and 9th grade Algebra I students, I investigated if there are any benefits for the students in my class to learn how to read, translate, use, and understand the mathematical language found daily in their math lessons. I discovered that daily use and practice of the mathematical language in both written and verbal form, by not only me but by my students as well, improved their understanding of the textbook instructions, increased their vocabulary and also increased their understanding of their math lessons. I also found that my students remembered the mathematical material better with constant use of mathematical language and terms. As a result of this research, I plan to continue stressing the use of mathematical language and vocabulary in my classroom and will try to develop new ways to help students to read, understand, and remember mathematical language they find daily in their textbooks.

Understanding the Mathematical Language

In this action research study of my calculus classroom consisting of only 12th grade students, I investigated activities that would affect a student’s understanding of mathematical language. The goal in examining these activities in a systematic way was to see if a student’s deeper understanding of math terms and symbols resulted in a better understanding of the mathematical concepts being taught. I discovered that some students will rise to the challenge of understanding mathematics more deeply, and some will not. In the process of expecting more from students, the frustration level of both the students and the teacher increased. As a result of this research, I plan to see what other activities will enhance the understanding of mathematical language.

Daily Problem-Solving Warm-Ups: Harboring Mathematical Thinking In The Middle School Classroom

In this action research study of my classroom of 8th grade mathematics, I investigated the use of daily warm-ups written in problem-solving format. Data was collected to determine if use of such warm-ups would have an effect on students’ abilities to problem solve, their overall attitudes regarding problem solving and whether such an activity could also enhance their readiness each day to learn new mathematics concepts. It was also my hope that this practice would have some positive impact on maximizing the amount of time I have with my students for math instruction. I discovered that daily exposure to problem-solving practices did impact the students’ overall abilities and achievement (though sometimes not positively) and similarly the students’ attitudes showed slight changes as well. It certainly seemed to improve their readiness for the day’s lesson as class started in a more timely manner and students were more actively involved in learning mathematics (or perhaps working on mathematics) than other classes not involved in the research. As a result of this study, I plan to continue using daily warm-ups and problem-solving (perhaps on a less formal or regimented level) and continue gathering data to further determine if this methodology can be useful in improving students’ overall mathematical skills, abilities and achievement.

Modelling Mathematical Reasoning in Physics Education

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Effectiveness of an Online Social Constructivist Mathematical Problem Solving Course for Malaysian Pre-Service Teachers

This study assessed the effectiveness of an online mathematical problem solving course designed using a social constructivist approach for pre-service teachers. Thirty-seven pre-service teachers at the Batu Lintang Teacher Institute, Sarawak, Malaysia were randomly selected to participate in the study. The participants were required to complete the course online without the typical face-to-face classes and they were also required to solve authentic mathematical problems in small groups of 4-5 participants based on the Polya’s Problem Solving Model via asynchronous online discussions. Quantitative and qualitative methods such as questionnaires and interviews were used to evaluate the effects of the online learning course. Findings showed that a majority of the participants were satisfied with their learning experiences in the course. There were no significant changes in the participants’ attitudes toward mathematics, while the participants’ skills in problem solving for “understand the problem” and “devise a plan” steps based on the Polya’s Model were significantly enhanced, though no improvement was apparent for “carry out the plan” and “review”. The results also showed that there were significant improvements in the participants’ critical thinking skills. Furthermore, participants with higher initial computer skills were also found to show higher performance in mathematical problem solving as compared to those with lower computer skills. However, there were no significant differences in the participants’ achievements in the course based on gender. Generally, the online social constructivist mathematical problem solving course is beneficial to the participants and ought to be given the attention it deserves as an alternative to traditional classes. Nonetheless, careful considerations need to be made in the designing and implementing of online courses to minimize problems that participants might encounter while participating in such courses.

The mathematical solution of engineering problems

"Evolved from ... lecture notes used ... in the School of Engineering of Columbia University."