Studying Mathematics

Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.

This book is dedicated to preparing prospective college students for the study of mathematics. It can be used at the end of high school or during the first year of college, for personal study or for introductory courses. It aims to set a meeting between two relatives who rarely speak to each other: the Mathematics of Beauty, which shows up in some popular books and films, and the Mathematics of Toil, which is widely known. Toil can be overcome through an appropriate method of work. Beauty will be found in the achievement of a way of thinking. The first part concerns the mathematical language: the expressions “for all”, “there exists”, “implies”, “is false”, ...; what is a proof by contradiction; how to use indices, sums, induction. The second part tackles specific difficulties: to study a definition, to understand an idea and apply it, to fix a slightly wrong argument, to discuss suggestions, to explain a proof. The third part presents customary techniques and points of view in college mathematics. The reader can choose one of three difficulty levels (A, B, C).

As students of mathematics or its applications progress, courses focus increasingly on mathematical theories and applications themselves, and less on how to study these complex ideas. Studying Mathematics and its Applications aims to bridge this gap by focusing on the essential skills needed by students, helping them to study more effectively and successfully. The book leads the student through tasks, demonstrating how to use examples and cope with symbols and encouraging them to use these tools to apply mathematics and construct proofs. Offering practical advice on assessment and modes of study, this book is an invaluable companion to any Mathematics or Applications of Mathematics course.

Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.

Math Study Skills outlines good study habits and provides students with study strategies and tips to improve in areas such as time management, organization, and test-taking skills. With a friendly and relatable voice, Alan Bass addresses the misgivings and challenges many students face in a math class, and offers techniques to improve their study skills, as well as opportunities to practice and assess these techniques. This math study skills workbook is short enough to be used as a supplement in a math course, but can also be used as a main text in a study skills class.

"This book is a game changer! Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K- 6 goes beyond simply providing information by sharing a pathway for changing practice. . . Focusing on our students’ strengths should be routine and can be lost in the day-to-day teaching demands. A teacher using these approaches can change the trajectory of students’ lives forever. All teachers need this resource! Connie S. Schrock Emporia State University National Council of Supervisors of Mathematics President, 2017-2019 NEW COVID RESOURCES ADDED: A Parent’s Toolkit to Strengths-Based Learning in Math is now available on the book’s companion website to support families engaged in math learning at home. This toolkit provides a variety of home-based activities and games for families to engage in together. Your game plan for unlocking mathematics by focusing on students’ strengths. We often evaluate student thinking and their work from a deficit point of view, particularly in mathematics, where many teachers have been taught that their role is to diagnose and eradicate students’ misconceptions. But what if instead of focusing on what students don’t know or haven’t mastered, we identify their mathematical strengths and build next instructional steps on students’ points of power? Beth McCord Kobett and Karen S. Karp answer this question and others by highlighting five key teaching turnarounds for improving students’ mathematics learning: identify teaching strengths, discover and leverage students’ strengths, design instruction from a strengths-based perspective, help students identify their points of power, and promote strengths in the school community and at home. Each chapter provides opportunities to stop and consider current practice, reflect, and transfer practice while also sharing · Downloadable resources, activities, and tools · Examples of student work within Grades K–6 · Real teachers’ notes and reflections for discussion It’s time to turn around our approach to mathematics instruction, end deficit thinking, and nurture each student’s mathematical strengths by emphasizing what makes them each unique and powerful.

' The book has been written by an international group of very active researchers and scholars who have a passion for the study of Chinese mathematics education. It aims to provide readers with a comprehensive and updated picture of the teaching and learning of mathematics involving Chinese students from various perspectives, including the ways in which Chinese students learn mathematics in classrooms, schools and homes, the influence of the cultural and social environment on Chinese students' mathematics learning, and the strengths and weaknesses of the ways in which Chinese learn mathematics. Furthermore, based on the relevant research findings, the book explores the implications for mathematics education and offers sound suggestions for reform and improvement. This book is a must for anyone who is interested in the teaching and learning of mathematics concerning Chinese learners. Contents:Overview and International Perspectives:How Have Chinese Students Performed in Mathematics? A Perspective from Large-Scale International Comparisons (L-H Fan & Y Zhu)The Mathematics Curriculum: Toward Globalization or Westernization? (N-Y Wong et al.)Thinking Mathematically by Chinese Learners: A Cross-National Comparative Perspective (J-F Cai & V Cifarelli)An Examination of Coherence in a Chinese Mathematics Classroom (T Wang & J Murphy)A Chinese Cultural Model of Learning (J Li)Official Curriculum in Mathematics in Ancient China: How Did Candidates Study for the Examination? (M K Siu)Context and Teaching Materials:The “Two Basics”: Mathematics Teaching and Learning in Mainland China (D-Z Zhang et al.)A Comparative Study on Composite Difficulty between New and Old Chinese Mathematics Textbooks (J-S Bao)Textbook Use Within and Beyond Chinese Mathematics Classrooms: A Study of 12 Secondary Schools in Kunming and Fuzhou of China (L-H Fan et al.)Thorough Understanding of the Textbook: A Significant Feature of Chinese Teacher Manuals (J-H Li)Effects of Cram Schools on Children's Mathematics Learning (H M Huang)Pedagogy and Learning Processes:Teaching with Variation: A Chinese Way of Promoting Effective Mathematics Learning (L-Y Gu et al.)Cracking the Paradox of Chinese Learners: Looking into the Mathematics Classrooms in Hong Kong and Shanghai (R-J Huang & K S Leung)Identifying a Pattern of Teaching: An Analysis of a Shanghai Teacher's Lessons (F Lopez-Real et al.)Differences Within Communalities: How Is Mathematics Taught in Rural and Urban Regions in Mainland China? (Y-P Ma et al.)Teaching Approach: Theoretical or Experimental? (J Li)Capturing the Chinese Way of Teaching: The Learning-Questioning and Learning-Reviewing Instructional Model (S-H An)The Effects of Different Representations on Mathematics Learning of Chinese Children (B-Y Xu)Inspiration and Future Directions:The CHC Learner's Phenomenon: Its Implications on Mathematics Education (N-Y Wong)How Do Chinese Learn Mathematics? Some Evidence-Based Insights and Needed Directions (J-F Cai et al.) Readership: Researchers, educators, lecturers, and graduate students in mathematics and education. Keywords:Chinese Education;Chinese Learners;Mathematics Education;Cultural Influence;Teaching and Learning;Chinese ClassroomsKey Features:Represents a concerted research effort in mathematics education of Chinese learners, the first of its kindContains contributions from the world's leading scholars and most active researchers in this area and beyondProvides comprehensive coverage and insiders' perspectives on relevant issuesReviews: “A noteworthy feature of the book is that eleven of the chapter authors work in mainland China … The edited collection is a significant contribution to the research literature and provides an important resource in the field.” Research in Mathematics Education “In a context of revolving reforms of the mathematical curricula in the West, the research presented in How Chinese Learn Mathematics certainly gives a lot of food for thought about effectively combining a problem-oriented approach to basic mathematical knowledge and skills with a conceptual and abstract representation of mathematical objects.”EASTM “The book copes with the issue of mathematics education in a culturally attentive way and offer hints to reconsider policies on mathematics education in the Western world. Hence, it should be present in the library of each education department.”EMS Newsletter '