Using strengths-based approaches to support development in mathematics It’s time to re-imagine what’s possible and celebrate the brilliance multilingual learners bring to today’s classrooms. Innovative teaching strategies can position these learners as leaders in mathematics. Yet, as the number of multilingual learners in North American schools grows, many teachers have not had opportunities to gain the competencies required to teach these learners effectively, especially in disciplines such as mathematics. Multilingual learners—historically called English Language Learners—are expected to interpret the meaning of problems, analyze, make conjectures, evaluate their progress, and discuss and understand their own approaches and the approaches of their peers in mathematics classrooms. Thus, language plays a vital role in mathematics learning, and demonstrating these competencies in a second (or third) language is a challenging endeavor. Based on best practices and the authors’ years of research, this guide offers practical approaches that equip grades K-8 teachers to draw on the strengths of multilingual learners, partner with their families, and position these learners for success. Readers will find: • A focus on multilingual students as leaders • A strength-based approach that draws on students’ life experiences and cultural backgrounds • An emphasis on maintaining high expectations for learners’ capacity for mastering rigorous content • Strategies for representing concepts in different formats • Stop and Think questions throughout and reflection questions at the end of each chapter • Try It! Implementation activities, student work examples, and classroom transcripts With case studies and activities that provide a solid foundation for teachers’ growth and exploration, this groundbreaking book will help teachers and teacher educators engage in meaningful, humanized mathematics instruction.

Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom

This volume contains two review articles: "Stochastic Pro gramming" by Vo V. Kolbin, and "Application of Queueing-Theoretic Methods in Operations Research, " by N. Po Buslenko and A. P. Cherenkovo The first article covers almost all aspects of stochastic programming. Many of the results presented in it have not pre viously been surveyed in the Soviet literature and are of interest to both mathematicians and economists. The second article com prises an exhaustive treatise on the present state of the art of the statistical methods of queueing theory and the statistical modeling of queueing systems as applied to the analysis of complex systems. Contents STOCHASTIC PROGRAMMING V. V. Kolbin Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 § 1. The Geometry of Stochastic Linear Programming Problems. . . . . . . . . . . . . . . . . . . . 5 § 2. Chance-Constrained Problems . . . . . . . . . 8 § 3. Rigorous Statement of stochastic Linear Programming Problems . . . . . . . . . . 16 § 4. Game-Theoretic Statement of Stochastic Linear Programming Problems. . . . . . . . 18 § 5. Nonrigorous Statement of SLP Problems . . . 19 § 6. Existence of Domains of Stability of the Solutions of SLP Problems . . . . . . . . . 29 § 7. Stability of a Solution in the Mean. . . . . . . . . . . . 30 § 8. Dual Stochastic Linear Programming Problems. . . 37 § 9. Some Algorithms for the Solution of Stochastic Linear Programming Problems . . . . . . . . . . 40 § 10. Stochastic Nonlinear Programming: Some First Results . . . . . . . . . . . . . . . . . . . . . . 42 § 11. The Two-Stage SNLP Problem. . . . . . . . . . . . 47 § 12. Optimality and Existence of a Plan in Stochastic Nonlinear Programming Problems. 58 Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . .

The starting point of this volume was a conference entitled "Progress in Mathematical Programming," held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarkar's algorithm. There were thirty presentations and approximately fifty people attended. Presentations included new algorithms, new analyses of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming. Interestingly, most of the progress reported at the conference was on the theoretical side. Several new polynomial algorithms for linear program ming were presented (Barnes-Chopra-Jensen, Goldfarb-Mehrotra, Gonzaga, Kojima-Mizuno-Yoshise, Renegar, Todd, Vaidya, and Ye). Other algorithms presented were by Betke-Gritzmann, Blum, Gill-Murray-Saunders-Wright, Nazareth, Vial, and Zikan-Cottle. Efforts in the theoretical analysis of algo rithms were also reported (Anstreicher, Bayer-Lagarias, Imai, Lagarias, Megiddo-Shub, Lagarias, Smale, and Vanderbei). Computational experiences were reported by Lustig, Tomlin, Todd, Tone, Ye, and Zikan-Cottle. Of special interest, although not in the main direction discussed at the conference, was the report by Rinaldi on the practical solution of some large traveling salesman problems. At the time of the conference, it was still not clear whether the new algorithms developed since Karmarkar's algorithm would replace the simplex method in practice. Alan Hoffman presented results on conditions under which linear programming problems can be solved by greedy algorithms."