Early Mathematical Explorations

This book presents teachers with a sound theoretical framework for encouraging children to explore mathematical concepts and become numerate in the 21st century. It shows that mathematical learning can occur in a variety of ways, including when children explore ideas through play, problem solving and problem posing, engage in a rich variety of multimodal learning experiences, pursue self-directed activities and cooperate with others, and make connections between ideas and experiences in their everyday worlds. - Back cover

This book emanated primarily from concerns that the mathematical capabilities of young children continue to receive inadequate attention in both the research and instructional arenas. Research over many years has revealed that young children have sophisticated mathematical minds and a natural eagerness to engage in a range of mathematical activities. As the chapters in this book attest, current research is showing that young children are developing complex mathematical knowledge and abstract reasoning a good deal earlier than previously thought. A range of studies in prior to school and early school settings indicate that young learners do possess cognitive capacities which, with appropriately designed and implemented learning experiences, can enable forms of reasoning not typically seen in the early years. Although there is a large and coherent body of research on individual content domains such as counting and arithmetic, there have been remarkably few studies that have attempted to describe characteristics of structural development in young students’ mathematics. Collectively, the chapters highlight the importance of providing more exciting, relevant, and challenging 21st century mathematics learning for our young students. The chapters provide a broad scope in their topics and approaches to advancing young children’s mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualising the professional learning of teachers in promoting young children’s mathematics, including a consideration of the role of play, is also addressed.

"Much of the content in this book is adapted from Teaching Young Children (TYC), NAEYC's award-winning magazine ..."--Page [104]

An assistant examiner and teacher explains to students in simple, practical steps how to earn full marks on their individual exploration for HL or SL Mathematics. This book is intended for students taking either "Applications and Interpretation" or "Analysis and Approaches." Please note: if you are graduating in 2020 or before, you should buy the previous edition of this book. This edition is for the new courses--"Applications and Interpretation" and "Analysis and Approaches"--which will be taught beginning in August 2019 with first exams in May 2021.

This book presents a carefully curated selection of mathematical problems suitable for young minds aged 12 and beyond. Most of these problems have been adapted from the Dürer Competition, a venerable mathematics competition in Hungary renowned for fostering teamwork and encouraging creative thinking in the realm of mathematical problem-solving. Within the pages of this book, readers are invited to accompany Albrecht, Tarkal, and Zsordi on 14 captivating journeys to the enigmatic Island of Oxisz, where they will encounter a total of 84 thought-provoking problems. Some of these challenges are intricately interconnected, elevating the level of difficulty. The concluding section provides comprehensive solutions and helpful hints, illuminating the paths taken by the three friends to tackle the problems. No specialized prior knowledge is required beyond a solid foundation in mathematics from the first seven years of school. Nevertheless, many problems in the book demand original ideas or clever combinations of elementary principles. This book offers students, mathematics educators, and trainers alike a captivating glimpse into a distinctive competition, making it a valuable resource for cultivating problem-solving skills at an early age.

Gain confidence in your ability to incorporate math into all aspects of your early learning program.