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.

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.

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.

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.

The identification of gaps from systematic reviews is essential to the practice of ''evidence-based research.'' Health care research should begin and end with a systematic review. A comprehensive and explicit consideration of the existing evidence is necessary for the identification and development of an unanswered and answerable question, for the design of a study most likely to answer that question, and for the interpretation of the results of the study. In a systematic review, the consideration of existing evidence often highlights important areas where deficiencies in information limit our ability to make decisions. We define a research gap as a topic or area for which missing or inadequate information limits the ability of reviewers to reach a conclusion for a given question. A research gap may be further developed, such as through stakeholder engagement in prioritization, into research needs. Research needs are those areas where the gaps in the evidence limit decision making by patients, clinicians, and policy makers. A research gap may not be a research need if filling the gap would not be of use to stakeholders that make decisions in health care. The clear and explicit identification of research gaps is a necessary step in developing a research agenda. Evidence reports produced by Evidence-based Practice Centers (EPCs) have always included a future research section. However, in contrast to the explicit and transparent steps taken in the completion of a systematic review, there has not been a systematic process for the identification of research gaps. We developed a framework to systematically identify research gaps from systematic reviews. This framework facilitates the classification of where the current evidence falls short and why the evidence falls short. The framework included two elements: (1) the characterization the gaps and (2) the identification and classification of the reason(s) for the research gap. The PICOS structure (Population, Intervention, Comparison, Outcome and Setting) was used in this framework to describe questions or parts of questions inadequately addressed by the evidence synthesized in the systematic review. The issue of timing, sometimes included as PICOTS, was considered separately for Intervention, Comparison, and Outcome. The PICOS elements were the only sort of framework we had identified in an audit of existing methods for the identification of gaps used by EPCs and other related organizations (i.e., health technology assessment organizations). We chose to use this structure as it is one familiar to EPCs, and others, in developing questions. It is not only important to identify research gaps but also to determine how the evidence falls short, in order to maximally inform researchers, policy makers, and funders on the types of questions that need to be addressed and the types of studies needed to address these questions. Thus, the second element of the framework was the classification of the reasons for the existence of a research gap. For each research gap, the reason(s) that most preclude conclusions from being made in the systematic review is chosen by the review team completing the framework. To leverage work already being completed by review teams, we mapped the reasons for research gaps to concepts from commonly used evidence grading systems. Our objective in this project was to complete two types of further evaluation: (1) application of the framework across a larger sample of existing systematic reviews in different topic areas, and (2) implementation of the framework by EPCs. These two objectives were used to evaluate the framework and instructions for usability and to evaluate the application of the framework by others, outside of our EPC, including as part of the process of completing an EPC report. Our overall goal was to produce a revised framework with guidance that could be used by EPCs to explicitly identify research gaps from systematic reviews.

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.

Women have entered the labor market in unprecedented numbers. Yet these critically needed workers still earn less than men and have fewer opportunities for advancement. This study traces the evolution of the female labor force in America, addressing the issue of gender distinction in the workplace and refuting the notion that women's employment advances were a response to social revolution rather than long-run economic progress. Employing innovative quantitative history methods and new data series on employment, earnings, work experience, discrimination, and hours of work, this study establishes that the present economic status of women evolved gradually over the last two centuries and that past conceptions of women workers persist.