Understanding The Gap

See a gap in understanding? Mine it to move your students forward. How good are you at exploiting students’ mathematical mistakes? In this remarkable book, the authors remind us that student mistakes are not random, and when we take the time to “mine the gap,” we can dispel misunderstandings before they take root. Included are 180 downloadable high-quality tasks, aligned to the standards and big ideas of grades 6–8 mathematics. Each task includes sample student work, commentary on strengths and gaps, and next instructional steps. Whether you use this bank of tasks for instruction or assessment, you will love how it helps you easily identify students’ thinking and then follow up with instruction that brings clear, complete understanding.

The comprehensive analysis in this report describes the design of public programs for prescription drug coverage in Canada, and how their design in each province leads to widely varying out-of-pocket spending. Cette publication comprend un résumé en français, suivi d'une version anglaise du rapport intégral.

Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our young learners’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 160 high-quality tasks aligned to the standards and big ideas of grades K-2 mathematics, including counting and representing numbers, number relationships and comparison, addition and subtraction within 100 and 1000, money and time, and multiplication and division. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality taskwhat you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct “gap” commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see.

Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our students’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 180 high-quality tasks aligned to the standards and big ideas of Grades 3-5 mathematics, including addition and subtraction of multi-digit whole numbers, multiplication and division of single and multi-digit whole numbers, foundational fraction concepts, foundational decimal concepts, and operations with fractions and decimals. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality task what you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct “gap” commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see.

Closing the gender pay gap begins with awareness and understanding of the state of the gap. This hybrid book that serves as a resource for both the academic and corporate communities, builds the reader’s awareness of the gender pay gap, its magnitude and ramifications, and provides action plans to address the challenge. Much of the existing literature on the gender pay gap provides an excellent foundation in stating facts and inferences; yet, the reader is often left wondering "now what?" This book tells the story of the state of the gap by the numbers and then offers specific actions that can be taken to achieve equity. The authors combine backgrounds in statistics and management/HR to provide a unique perspective in painting a broader overview of the issue, examining the history of the gender pay gap, its global impact, and how nations are addressing the issue. The book shines a light on the wide-ranging effects of the gap, including women’s poverty rates, student loans, economic growth, childhood poverty, and corporate profits, and offers insights to help close it with best practices of select organizations. Upper-level undergraduate, postgraduate, and executive education students will appreciate the clarity and conciseness of this guide to understanding and solving an important human resources issue. The inclusion of a brief instructor’s manual and PowerPoint slides for each chapter differentiates this book and adds to the ease of adoption in both the academic and corporate setting.

The market for business knowledge is booming as companies looking to improve their performance pour millions of pounds into training programmes, consultants, and executive education. Why then, are there so many gaps between what firms know they should do and waht they actual do? This volume confronts the challenge of turning knowledge about how to improve performance into actions that produce measurable results. The authors identify the causes of this gap and explain how to close it.