Teaching and learning mathematics with robotics in middle-years of schooling

Engaging and motivating students in mathematics lessons can be challenging. The traditional approach of chalk and talk can sometimes be problematic. The new generation of educational robotics has the potential to not only motivate students but also enable teachers to demonstrate concepts in mathematics by connecting concepts with the real world. Robotics hardware and the software are becoming increasing more user-friendly and as a consequence they can be blended in with classroom activities with greater ease. Using robotics in suitably designed activities promotes a constructivist learning environment and enables students to engage in higher order thinking through hands-on problem solving. Teamwork and collaborative learning are also enhanced through the use of this technology. This paper discusses a model for teaching concepts in mathematics in middle year classrooms. It will also highlight some of the benefits and challenges of using robotics in the learning environment.

Theories of learning mathematics

According to Karl Popper, widely regarded as one of the greatest philosophers of science in the 20th century, falsifiability is the primary characteristic that distinguishes scientific theories from ideologies – or dogma. For example, for people who argue that schools should treat creationism as a scientific theory, comparable to modern theories of evolution, advocates of creationism would need to become engaged in the generation of falsifiable hypothesis, and would need to abandon the practice of discouraging questioning and inquiry. Ironically, scientific theories themselves are accepted or rejected based on a principle that might be called survival of the fittest. So, for healthy theories on development to occur, four Darwinian functions should function: (a) variation – avoid orthodoxy and encourage divergent thinking, (b) selection – submit all assumptions and innovations to rigorous testing, (c) diffusion – encourage the shareability of new and/or viable ways of thinking, and (d) accumulation – encourage the reuseability of viable aspects of productive innovations.

Teaching and learning mathematics : a guide to research and its applications. 'Enseñando y aprendiendo matemáticas : una guía para el estudio y sus aplicaciones'.

El objetivo de esta obra es ofrecer una revisión de algunas de las investigaciones sobre la enseñanza de las matemáticas. En esta edición, se sintetizan las conclusiones de las investigaciones más recientes en diferentes partes del mundo. Abarca cuestiones tan diversas como el número y el cálculo; la forma y el espacio; probabilidad y estadística; investigación en el aula. Se han añadido dos nuevos capítulos, uno sobre el uso de la tecnología en la enseñanza de las matemáticas y otro en la solución de problemas. Cada capítulo ofrece una visión general de las investigaciones más recientes y un análisis detallado de los hallazgos más importantes. La investigación está relacionada con cuestiones del progreso de los alumnos, la diferenciación de la enseñanza y el rol de género. Tiene una extensa bibliografía.

Learning mathematics : issues, theory and classroom practice.

Recurso para profesores de matemáticas de primaria y secundaria. El texto considera las cuestiones relativas a cómo los estudiantes aprenden matemáticas. Cada uno de los once capítulos trata un tema particular que ilustra la interacción entre la teoría y la práctica. Esta edición cuenta con dos nuevos capítulos: uno relacionado con la cognición y la transferencia del aprendizaje, y otro que examina la importancia del modelo de aprendizaje en las matemáticas.

Inclusive approaches to teaching and learning mathematics

This chapter explores the role of mentors in supporting pre-service teachers to include all children in mathematics teaching, no matter what their individual needs.

Students' conflicting attitudes towards games as a vehicle for learning mathematics : a methodological dilemma

Mathematics games are widely employed in school classrooms for such reasons as a reward for early finishers or to enhance students' attitude towards mathematics. During a four week period, a total of 222 Grade 5 and 6 (9 to 12 years old) children from Melbourne, Australia, were taught multiplication and division of decimal numbers using calculator games or rich mathematical activities. Likert scale surveys of the children's attitudes towards games as a vehicle for learning mathematics revealed unexpectedly high proportions of negative attitudes at the conclusion of the research. In contrast, student interview data revealed positive associations between games and mathematical learning. This article reports on the methodological dilemma of resultant conflicting attitudinal data related to game- playing. Concerns arising from the divergence in the results are raised in this article. Implications based on the experience of this study may inform educational researchers about future methodological choices involving attitudinal research.

Developing guidelines for teachers helping students experiencing difficulty in learning mathematics

As part of an ongoing project, we have developed a model of planning and teaching that is designed to assist teachers to help students overcome barriers they might experience in learning mathematics. The following is a discussion of one aspect of the model that we term “enabling prompts”. These refer to the directions, invitations, or questions that a teacher offers when interacting one-on-one with students experiencing difficulties. We argue that teachers should plan to pose subsidiary questions in the first instance, rather than, for example, offering further explanations. We outline our overall planning and teaching model, we present some examples of enabling prompts used by our project teachers, and we propose some considerations for teachers when structuring their own enabling prompts.

Young children learning mathematics: a guide for educators and families

Can young children learn mathematics before school? What ideas and concepts are they capable of learning? How can adults develop a child's mathematical thinking from birth to five years? Early learning plays a critical role in laying a foundation for later success in schooling. This book explores the possibilities and potential for early childhood educators, parents and carers to stimulate young children's mathematical thinking. Drawing on the authors' significant research, it answers frequently asked questions about early childhood mathematics, discusses the experiences, activities and conversations that could lead to mathematics learning, and provides simple, easy-to-follow guidelines on introducing and building on the mathematical concepts underpinning play and activity in young children aged from birth to five.

Beyond deficit models of learning mathematics : Socio-cultural directions for change and research

Major paradigmatic changes in mathematics education research are drawing attention to new perspectives on learning. Whereas deficit models were previously in the foreground of research designs, these have been replaced by a wide variety of theoretical directions for studying diverse approaches to learning mathematics. There is now an acceptance of the need for richness and variety in research practices so that approaches can be studied, compared and mutually applied and improved. Psychological and quantitative approaches and methods are now increasingly complemented, or even replaced, by new directions that rely on social and anthropological theories and methods. Rather than reviving ideas about deficit research in mathematics education, the aim of this chapter is to present some socio-cultural perspectives of mathematics learning, and to show how these perspectives go beyond the deficit model of learning. Framing the main traditional markers of discrimination in school mathematics—gender, social class and ethnicity—in a perspective of social justice, the chapter concludes with a reflection on equality in terms of the democratic principle of meritocracy in mathematics education.

Teaching and learning mathematics and science in a second or third language

 This study investigates the interaction between languages used for particular purposes in mathematics and science classrooms and the accompanying multimodal resources that support teachers’ strategies. The dual investigation sets this study apart, and produces its originality and contribution to the field. It develops a novel multimodal description of pedagogic strategies in multilingual mathematics and science classrooms in Malaysia.

The Effects Improving Student Discourse Has on Learning Mathematics

In this action research study of my 8th grade mathematics classroom, I investigated how improving student discourse affects learning mathematics. I conducted this study because I wanted to give students more opportunities to develop and share their ideas with their peers as well as with me. My idea was to create a learning environment that encouraged students to voice their opinions. In order to do so, I needed to reassure and model with my students that they were in a classroom where it was safe to take risks, and they should feel comfortable sharing their ideas. By facilitating activities for students to complete in groups, asking students to prepare work to share with the class, and offering more opportunities for students to work with each other on discovering and exploring math skills being presented, I set the tone for abundant student discourse to take place in the mathematics classroom. I discovered that students became more comfortable with math skills the more opportunities they had to discuss the ideas in various settings. I also found that as the study went on, students discovered the importance of being able to share their mathematical ideas and valued the ability to verbalize their thoughts with others. As a result of this study, I plan to continue offering many opportunities for students to work in groups as well as to share their ideas with the class.

A Simple Computer Game for Learning Mathematics

It is sometimes unquantifiable how hard it is for most people to deal with game addiction. Several articles have equally been published to address this subject, some suggesting the concept of Educational and serious games. Similarly, researchers have revealed that it does not come easy learning a subject like math. This is where the illusive world of computer games comes in. It is amazing how much people learn from games. In this paper, we have designed and programmed a simple PC math game that teaches rudimentary topics in mathematics.