What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades? How much do you know… and how much do you need to know? Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about rational numbers. It is organised around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to rational numbers, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

Understanding and Explanation clarifies the "explanation versus understanding" debate that has become central to the philosophy of the social sciences.

Books on abortion (other than collections of readings) typically express and defend a particular position. This book gives both sides, as evenly and objectively as possible; it gets to the heart of each position, the core idea which animates it. It then leaves the reader to make up his or her own mind. It is an introduction to the issue, not only to the basic positions on the issue. Despite being brief, it contains careful analyses and discussions of many topics often not found at all in other works. The treatment is thorough and detailed, but succinct. Understanding Abortion: From Mixed Feelings to Rational Thought is aimed at all people who want a better understanding of what the two sides on this issue are really saying, and what reasons they give for their position. Many people assume that this issue is an interminable one, with "no clear answers"; a purely emotional debate that cannot be addressed by the use of reasoned arguments. The book shows that this is not the case.

The selections are taken from chapters of Kuhn's books, including his Catholic Dogmatics, and from various articles that appeared in the Tübingen quarterly, Die theologische Quartalschrift. They are arranged according to the following topics: faith and reason; revelation and the personhood of God; responses to Protestant liberalism; theological topics, including grace and freedom, theology and the university; and Catholic fundamental theology. Though diverse in subject, when read together the essays yield a complete theological vision that derives from a carefully constructed theological foundation.

Psychological science now reveals much about the law's response to crime. This is the first text to bridge both fields as it presents psychological research and theory relevant to each phase of criminal justice processes. The materials are divided into three parts that follow a comprehensive introduction. The introduction analyses the major legal themes and values that guide criminal justice processes and points to the many psychological issues they raise. Part I examines how the legal system investigates and apprehends criminal suspects. Topics range from the identification, searching and seizing to the questioning of suspects. Part II focuses on how the legal system establishes guilt. To do so, it centres on the process of bargaining and pleading cases, assembling juries, providing expert witnesses, and considering defendants' mental states. Part III focuses on the disposition of cases. Namely, that part highlights the process of sentencing defendants, predicting criminal tendencies, treating and controlling offenders, and determining eligibility for such extreme punishments as the death penalty. The format seeks to give readers a feeling for the entire criminal justice process and for the role psychological science has and can play in it.

First Published in 1987. Routledge is an imprint of Taylor & Francis, an informa company.