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This book is intended to assist trade and industrial education teachers in teaching mathematical trade topics in a way that will increase students' conceptual understanding of them. The first chapter provides an overview of the book's contents and suggests ways of using it. The next five chapters address the following aspects of using principles and methods to increase students' conceptual understanding of the material at hand: mathematical methods (the mathematical and conceptual approaches); the topic plan (learning in context; modeling, solving, and interpreting; identifying facts, skills, strategies, and concepts; using prior knowledge; choosing an example, and lesson planning); teaching the facts and skills; teaching the strategies; and teaching the concepts (method for teaching concepts; development of a concept; workshop experience; discussion and analysis; generalization, representation, and reinforcement of a concept; application, and recording procedures). Chapters 7 through 9 contain examples specific to the teaching of roofing, electrical, and foundry applications. Each of these chapters contains sections addressing some or all of the following: context; analysis of the task; modeling, solving, and interpreting techniques; analysis of the mathematics; lesson planning procedures; review; facts and skills; concepts; and strategies. A resource wedge that groups resource types in a hierarchy based on their degree of concreteness or abstraction is appended. (MN)