Problem solving for the 21st century

Mathematical problem solving has been the subject of substantial and often controversial research for several decades. We use the term, problem solving, here in a broad sense to cover a range of activities that challenge and extend one’s thinking. In this chapter, we initially present a sketch of past decades of research on mathematical problem solving and its impact on the mathematics curriculum. We then consider some of the factors that have limited previous research on problem solving. In the remainder of the chapter we address some ways in which we might advance the fields of problem-solving research and curriculum development.

Re-reading the reading lesson : episodes in the history of reading pedagogy

Reading pedagogy is constantly an object of discussion and debate in contemporary policy and practice but is rarely a matter for historical inquiry. This paper reports from a recent study of the history of reading pedagogy in Australia and beyond. It focuses on a recurring figure in the historical record—the ‘reading lesson’. Presented as a distinctive trope, the reading lesson is traced in its regularity in and through the discourse of reading pedagogy, starting in 1930s Australia and moving back into 19th-century Europe, and with specific reference to the UK and the USA. Teaching reading is expressly identified as a moral project—something that, it can be argued, clearly continues into the present.

The building blocks of digital media literacy: Socio-material participation and the production of media knowledge

This article outlines the knowledge and skills students develop when they engage in digital media production and analysis in school settings. The metaphor of ‘digital building blocks’ is used to describe the material practices, conceptual understandings and production of knowledge that lead to the development of digital media literacy. The article argues that the two established approaches to media literacy education, critical reading and media production, do not adequately explain how students develop media knowledge. It suggests there has been too little focus on material practices and how these relate to the development of conceptual understanding in media learning. The article explores empirical evidence from a four-year investigation in a primary school in Queensland, Australia using actor–network theory to explore ‘moments of translation’ as students deploy technologies and concepts to materially participate in digital culture. A generative model of media learning is presented with four categories of building blocks that isolate the specific skills and knowledge that can be taught and learnt to promote participation in digital media contexts: digital materials, conceptual understandings, media production and media analysis. The final section of the article makes initial comments on how the model might become the basis for curriculum development in schools and argues that further empirical research needs to occur to confirm the model’s utility.

Math-Towers: Online Interactive Collaborative Mathematics Explorations & Problem-Solving for Students Ages 11 to 15 years (Grades 6 to 10)

Math-Towers (www.math-towers.ca) is an online resource for students in grades 6 to 10 that supports collaborative problem-solving and investigations. This paper presents the philosophical position motivating the development of Math-Towers and describes how the site presents and motivates the mathematical challenges and supports participants' exploration and collaboration.

How does Oyster work? The simple interpretation of Oyster mathematics

Oyster® is a surface-piercing flap-type device designed to harvest wave energy in the nearshore environment. Established mathematical theories of wave energy conversion, such as 3D point-absorber and 2D terminator theory, are inadequate to accurately describe the behaviour of Oyster, historically resulting in distorted conclusions regarding the potential of such a concept to harness the power of ocean waves. Accurately reproducing the dynamics of Oyster requires the introduction of a new reference mathematical model, the “flap-type absorber”. A flap-type absorber is a large thin device which extracts energy by pitching about a horizontal axis parallel to the ocean bottom. This paper unravels the mathematics of Oyster as a flap-type absorber. The main goals of this work are to provide a simple–yet accurate–physical interpretation of the laws governing the mechanism of wave power absorption by Oyster and to emphasise why some other, more established, mathematical theories cannot be expected to accurately describe its behaviour.

Práticas de ensino supervisionadas do 1º e 2º ciclo do ensino básico: a prática de resolução de problemas na aquisição do conceito de comprimento e de perímetro no 3.º ano de escolaridade

Relatório final apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e 2.º Ciclos do Ensino Básico

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.