Highly regarded by instructors in past editions for its sequencing of topics and extensive set of exercises, the latest edition of Abstract Algebra retains its concrete approach with its gentle introduction to basic background material and its gradual increase in the level of sophistication as the student progresses through the book. Abstract concepts are introduced only after a careful study of important examples. Beachy and Blair’s clear narrative presentation responds to the needs of inexperienced students who stumble over proof writing, who understand definitions and theorems but cannot do the problems, and who want more examples that tie into their previous experience. The authors introduce chapters by indicating why the material is important and, at the same time, relating the new material to things from the student’s background and linking the subject matter of the chapter to the broader picture. Building proficiency in learning mathematics by tailoring instruction to students’ specific misconceptions and learning needs is the backbone of this indispensable text, written for K–8 pre- and inservice teachers, as well tutors. An important theme is that long-term retention is based on a strong conceptual foundation of numeracy and on a well-designed learning environment. Each chapter deals with a different mathematics topic, including whole numbers, fractions, decimals, as well as time and money. Chapters also include examples of error patterns and specific, well-defined strategies and activities for diagnosis, prescription, and remediation. New to this edition is a chapter devoted to English language learners. The complexities of language barriers are delineated along with reasons that students struggle with learning English and mathematics at the same time. An audio file of common mathematics terms translated from English into most-often spoken languages by ELLs can be accessed at www.youareamathperson.com. Outstanding features: • Response to Intervention (RTI) model underpins discussions of differentiating instruction. • Mathematics content reflects components of the Common Core State Standards Initiative for Mathematics and the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics. • Case studies and student examples promote a sound understanding of learners’ varied cognitive, behavioral, and physical needs. • Discussion questions challenge readers to think more deeply about the application and utility of concepts related to the error patterns. • Step-by-step directions for interactive instructional classroom games and activities are provided to extend and enrich teaching and learning.
The goal of this book is to bring together the concept of self-efficacy theory with practical how-to strategies for both teachers and parents to use in heightening their students’ levels of self-efficacy. The book examines how self-efficacy theory relates to the acquisition of mathematical competence. The text also provides specific and practical how-to strategies for both teachers and parents in applying these principles to classroom mathematics instruction and activities. The self-efficacy practices and applications to mathematics are also suitable for families working with learners outside the school environment. Acquiring mathematical skills requires more than knowing arithmetic tables, memorizing rules, and knowing proofs. It requires a basic belief that one is capable of obtaining this information, making sense of it, and applying and generalizing it in mathematical problems. In addition, a student must believe that obtaining these skills leads to a positive outcome, whether it is perceived to be a good or passing grade, comfort-level in tackling mathematical problems, being able to advance to the next mathematics course, being able to score highly on the math section of the SAT and/or be competitive for a desired job. The ability of students to achieve and exceed grade level competence in mathematics is addressed through the lens of Albert Bandura’s Self-Efficacy Theory. This theoretical position states that one will persist in mastering a behavior (in this case, mastering mathematical principles and skills), in the face of obstacles or failures—to the extent that one believes he or she has the ability to do so, and that there is a desired outcome for doing so. The research literature on the role of self-efficacy in mathematic instruction is examined to demonstrate the validity of using this concept to increase student (and parent/teacher) confidence in learning and applying grade-appropriate math content. Specific teaching methodologies will be provided that infuse self-efficacy strategies for students. Lastly, teachers and parents are provided strategies to increase their own self-efficacy when it comes to conveying mathematics principles to their child or student, as well as strategies to assess their students’ level of self-efficacy over time. Teaching and learning mathematics so that students achieve success at their grade level or above can present a variety of challenges. One barrier that affects learners is the belief that one is not capable of learning mathematics or not naturally talented in the field, not a “math person.” As a result, learners may not believe they are capable of a positive outcome for achieving mathematics success. This book is an important resource for pre-service and in-service teachers, as well as families in applying the theory of self-efficacy to support learners in becoming confident and assured in their ability to understand and apply mathematical principles and procedures. Coupled with classroom ready mathematics instructional strategies, the book provides readers with the background, tools and strategies needed to carry content success and confidence forward to remain persistent in solving all future mathematical problems.
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