Nina Arshavsky – författare

Engaging in mathematical investigations yourself will help you be a better mathematics teacher! National, state, and local curriculum requirements and recommendations increasingly emphasize active student involvement in exploratory investigations. Teachers now face new demands when they field unexpected student discoveries, determine when some open-ended activity has played out its usefulness or is just on the verge of paying off in a major way, and judge which student-initiated directions are likely to lead to development of important mathematical ideas and which are dead ends. These pedagogical judgments depend heavily on deep mathematical knowledge. Ways to Think About Mathematics uses immersion experiences in algebra, geometry, and statistics to help mathematics teachers improve their knowledge and understanding of mathematical concepts. By experiencing open-ended problems, making and checking conjectures, and evaluating problem solving strategies, every math teacher can become better prepared to deal with day-to-day classroom decisions. Funded by the National Science Foundation and successfully field-tested in a wide variety of professional development and preservice settings, the materials in this book integrate mathematical thinking, effective teaching practices, and explicit connections to exemplary curricula. Because it is aligned with the principles and standards of the National Council of Teachers of Mathematics but is not fixed to any single curriculum, the materials in this book can be aligned with any state or district standards. Emphasizing all components of mathematical investigation, this accessible volume focuses on: Mathematical ways of thinking Discovering connections between mathematical ideas Posing and analyzing problems Making, modifying, testing, and proving conjectures Linking higher level mathematics to the content of grade 6-12 classrooms Ways to Think About Mathematics gives teachers the opportunity to grow as learners and teachers of mathematics by including problems for teachers to explore as well as selected "Problems for the Classroom" for the classes they teach.

Engaging in mathematical investigations yourself will help you be a better mathematics teacher! National, state, and local curriculum requirements and recommendations increasingly emphasize active student involvement in exploratory investigations. Teachers now face new demands when they field unexpected student discoveries, determine when some open-ended activity has played out its usefulness or is just on the verge of paying off in a major way, and judge which student-initiated directions are likely to lead to development of important mathematical ideas and which are dead ends. These pedagogical judgments depend heavily on deep mathematical knowledge. Ways to Think About Mathematics uses immersion experiences in algebra, geometry, and statistics to help mathematics teachers improve their knowledge and understanding of mathematical concepts. By experiencing open-ended problems, making and checking conjectures, and evaluating problem solving strategies, every math teacher can become better prepared to deal with day-to-day classroom decisions. Funded by the National Science Foundation and successfully field-tested in a wide variety of professional development and preservice settings, the materials in this book integrate mathematical thinking, effective teaching practices, and explicit connections to exemplary curricula. Because it is aligned with the principles and standards of the National Council of Teachers of Mathematics but is not fixed to any single curriculum, the materials in this book can be aligned with any state or district standards. Emphasizing all components of mathematical investigation, this accessible volume focuses on: Mathematical ways of thinking Discovering connections between mathematical ideas Posing and analyzing problems Making, modifying, testing, and proving conjectures Linking higher level mathematics to the content of grade 6-12 classrooms Ways to Think About Mathematics gives teachers the opportunity to grow as learners and teachers of mathematics by including problems for teachers to explore as well as selected "Problems for the Classroom" for the classes they teach.

Early Colleges as a Model for Schooling advocates for early college high schools as an effective means of reducing academic, cultural, and financial obstacles to postsecondary education.This perceptive work evaluates, both quantitatively and qualitatively, the impacts of early colleges—hybrids that blend elements of secondary and postsecondary education. It examines the strengths and challenges of early college models of different designs and explores their place in the greater education system.Julie A. Edmunds, Fatih Unlu, Elizabeth J. Glennie, and Nina Arshavsky craft their narrative around the findings of one of the most ambitious studies to date on early college high schools, a fifteen-year longitudinal study involving more than four thousand students across nineteen secondary schools that have adopted the model. They offer insight into the student experience within early college high schools and beyond.The authors demonstrate how the well-structured and supportive educational environment of early college not only prepares students academically for college-level coursework but also helps students navigate logistical challenges in applying for colleges and universities. They show how the positive outcomes of the early college experience can help tip the balance toward successful postsecondary educational experiences, especially for historically underserved students such as low-income students, minority students, and first-generation college students.As the authors point out, a shift in the way the transition between secondary and postsecondary education is implemented provides an achievable approach to improving college readiness and lowering educational barriers. They argue persuasively that wider adoption of this educational model in high schools has great potential to improve overall access to higher education.