This open textbook was created with the support of an ALG Textbook Transformation Grant. Topics include art integration, music integration, physical education / dance integration, and the theoretical foundations of arts integration in education
This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable exploring unfamiliar mathematical situations.
The primary goal of this book is to help you learn to think like a mathematician in some very specific ways. You will:
• Make sense of problems and persevere in solving them. You will develop and demonstrate this skill by working on difficult problems, making incremental progress, and revising solutions to problems as you learn more.
• Reason abstractly and quantitatively. You will demonstrate this skill by learning to represent situations using mathematical notation (abstraction) as well as creating and testing examples (making situations more concrete).
• Construct viable arguments and critique the reasoning of others. You will be expected to create both written and verbal explanations for your solutions to problems. The most important questions in this class are “Why?” and “How do you know you're right?” Practice asking these questions of yourself, of your professor, and of your fellow students.
Throughout the book, you will learn how to learn mathematics on you own by reading, working on problems, and making sense of new ideas on your own and in collaboration with other students in the class.
Children are inherently musical. They respond to music and learn through music. Music expresses children’s identity and heritage, teaches them to belong to a culture, and develops their cognitive well-being and inner self worth. As professional instructors, childcare workers, or students looking forward to a career working with children, we should continuously search for ways to tap into children’s natural reservoir of enthusiasm for singing, moving and experimenting with instruments. But how, you might ask? What music is appropriate for the children I’m working with? How can music help inspire a well-rounded child? How do I reach and teach children musically? Most importantly perhaps, how can I incorporate music into a curriculum that marginalizes the arts?
This book explores a holistic, artistic, and integrated approach to understanding the developmental connections between music and children. This book guides professionals to work through music, harnessing the processes that underlie music learning, and outlining developmentally appropriate methods to understand the role of music in children’s lives through play, games, creativity, and movement. Additionally, the book explores ways of applying music-making to benefit the whole child, i.e., socially, emotionally, physically, cognitively, and linguistically.
Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles and concepts that need to be borne in mind by all teachers and textbook authors—but which are little appreciated in the UK at present.
This study is aimed at anyone who would like to think more deeply about the discipline of ‘elementary mathematics’, in England and Wales and anywhere else. By analysing and supplementing the current curriculum, Teaching Mathematics provides food for thought for all those involved in school mathematics, whether as aspiring teachers or as experienced professionals. It challenges us all to reflect upon what it is that makes secondary school mathematics educationally, culturally, and socially important.
Table of Contents
I. Background: Why focus on Key Stage 3
II. The general advice in the Key Stage 3 programme of study
2. Working mathematically
III. The listed subject content for Key Stage 3
1. Number (and ratio and proportion)
3. Geometry and measures
4. Probability and Statistics
IV. A sample curriculum for all-written from a humane mathematical viewpoint
1. Very Brief version
2. Brief version