Mathematics for Elementary School Teachers

Mathematics for Elementary School Teachers, 2/e, provides a unique opportunity for students to develop a clear understanding of mathematical concepts, procedures, and processes, to communicate these ideas to others, and to apply them to the real world. The goal is to achieve the optimum balance between presenting a thorough development of mathematical content and presenting it in a way that is understandable by students. The material has been revised so that it powerfully embodies the new Principles and Standards for School Mathematics of the National Council of Teachers of Mathematics.

Table of Contents:
1. Viewing Mathematics. Mathematics as Communication. Mathematics as Reasoning. Mathematics as Problem Solving. A Connected, Balanced View of Mathematics. 2. Sets and Whole Number Operations and Properties. Sets and Whole Numbers. Addition and Subtraction of Whole Numbers. Multiplication and Division of Whole Numbers. Numeration. 3. Estimation and Computation. Strategies and Procedures for Mental Computation. Strategies and Procedures for Estimation. Algorithms for Addition and Subtraction. Algorithms for Multiplication and Division. 4. Number Theory. Factors and Divisibility. Prime and Composite Numbers. 5. Understanding Integer Operations and Properties. Addition, Subtraction, and Order Properties of Integers. Integer Multiplication, Division, and Other Properties. 6. Rational Number Operations and Properties. Rational Number Ideas and Symbols. Adding and Subtracting Rational Numbers. Multiplying Rational Numbers. Dividing, Comparing, and Ordering Rational Numbers. 7. Proportional Reasoning. The Concept of Ratio. Proportional Variation and Solving Proportions. Solving Percent Problems. 8. Analyzing Data. Types of Data Displays. Data Displays that Show Relationships. Describing the Average and Spread of Data. Decision Making with Data. 9. Probability. Understanding Probability. Connecting Probability to Models and Counting. Simulations. Odds and Long-Term Behavior. Permutations and Combinations. 10. Introducing Geometry. Basic Ideas of Geometry. Solving Problems in Geometry. More About Angles. More About Triangles. More About Quadrilaterals. 11. Extending Geometry. Transformations. Geometric Patterns. Special Polygons. Three-Dimensional Figures. 12. Measurement. The Concept of Measurement. Measuring the Perimeter and Area of Polygons. Measuring the Surface Area and Volume of Solids. 13. Exploring Ideas of Algebra and Coordinate Geometry. Variables, Expressions, and Equations. Solving Equations. Exploring Graphs of Linear Equations. Connecting Algebra and Geometry. Appendices. A. Graphing Calculator. B. Geometry Exploration Software. C. Glossary of Geometric Terms. D. Constructions.

About the Author :
Phares O'Daffer was born and raised in Weldon, Illinois. He received his B.S.(1955) and M.S.(1956) from Illinois State University, studied at the University of Iowa(1958) and the University of Michigan(1962), and received his PhD in Mathematics Education from the University of Illinois(1968). His teaching experience spans ages from grade 3 to college, and includes early involvement with the University of Illinois Committee on School Mathematics (UICSM) and the Ball State Expermental Program. Phares has taught at Ball State University (1960-64) and was Professor of Mathematics at Illinois State University (1968-1988). Phares has co-authored six major K-8 Elementary School Mathematics textbook series, used extensively in elementary schools in the United States and other countries. He has authored or co-authored over 140 mathematics books ranging from a kindergarten text to a college text for elementary teachers, and a number of articles in professional journals. He has also served as Chairman of the Editorial Panel for the Arithmetic Teacher, a major journal of the National Council of Teachers of Mathematics. Phares has had a long time interest in genealogy, and you can get acquainted with his involvement by visiting his genealogy website, www.Odaffer.com. His other activities include golf, tennis, and service on the board of directors of a local hospital and on a community college foundation board. He is married to Harriet Gove O'Daffer, and has three children and seven grandchildren. Randy Charles received his bachelor's degree from Indiana University of Pennsylvania in 1971. He was a high school mathematics teacher in Maryland from 1971 to 1974 during which time he simultaneously attended the University of Maryland. He received his master's degree from the University of Maryland in 1974. He attended Indiana University from 1974 to 1977 where he worked on a federally-funded research and curriculum development project on problem solving. He was a K-12 mathematics supervisor in a school district of about 30,000 students in West Virginia from 1977 to 1982 and then moved on to Illinois State University. He was a Professor in the Department of Mathematics and Computer Science at San Jose State University, California, from 1987 until January 2001 when he decided to pursue writing full time. Randy started writing textbooks for elementary and secondary school mathematics in 1978. He has written more than 75 textbooks for children and teachers. He has been involved in numerous activities with NCTM and has authored several NCTM publications, mostly in the area of problem solving. Randy has been a speaker at hundreds of state, national, and international mathematics education conferences and was a national speaker for the Learning magazine for many years. He is past vice-president of the National Council of Supervisors of Mathematics. Tom Cooney was born and raised in Toledo, Ohio. He received his B.Ed. and M.Ed. Degrees from the University of Toledo with majors in mathematics and mathematics education respectively and his Ph.D. in Mathematics Education from the University of Illinois in 1969. He taught middle and secondary school mathematics in Rossford, Ohio from 1960-1966 while completing his doctorate. Upon completion of his Ph.D., he went to the University of Georgia's Department of Mathematics Education where, after 30 years, he became Professor Emeritus. His research on teaching and teacher education has been internationally recognized through his publications and his lectures in more than 20 countries. Tom was awarded the Gladys Thomason Award for outstanding service to the Georgia Council of Teachers of Mathematics and has received the Distinguished Alumni Award from the University of Illinois College of Education. He was the initial editor of the international Journal of Mathematics Teacher Education. His most recent work involves developing assessment items for elementary, middle, and secondary school teachers. John Dossey grew up in East Peoria, Illinois in the shadow of the Caterpillar Tractor plant where his father worked. Interested in how things work and go and wanting to be able to explain these actions and motions, he gravitated toward mathematics and teaching with B.S. and M.S. degrees from Illinois State University in 1965 and 1968 respectively. Along with the first degree, John began his teaching career at the junior high school level, later moving to the high school level and a position as a K-12 mathematics coordinator. John completed his Ph.D. in mathematics education at the University of Illinois at Urbana-Champaign in 1971. By this time, he was already teaching mathematics and mathematics education classes in the Department of Mathematics at Illinois State University. At Illinois State he moved through the ranks from Instructor to the position of Distinguished University Professor of Mathematics. Here he became involved in a variety of activities involving state, national (NAEP), and international (SIMS, TIMSS, & PISA) student assessments. These experiences lead to his authoring or co-authoring over 80 books ranging from middle-school through collegiate mathematics to methods texts for prospective teachers of mathematics to professional works on national and international assessments and curriculum. Along the way, John served as President of the National Council of Teachers of Mathematics, leading them to the development of the initial NCTM Standards; as Chair of the Conference Board for the Mathematical Sciences in Washington, DC; as Visiting Professor of Mathematics at the U.S. Military Academy at West Point, NY; and as a member of many national and international committees and boards dealing with mathematics and mathematics education issues. Away from this professional life, John and his wife, Anne, enjoy living in the country, traveling, and getting together with friends. Jane Faith Schielack discovered her love of mathematics in elementary school in Tulsa, Oklahoma and it continued through high school in Houston, Texas. She received her BS in Education from Texas A&M University in 1975, with certification in Mathematics and English, Grades 1-12. After teaching third grade in Victoria, Texas, Janie earned an MA in Mathematics Education from the University of Texas at Austin in 1979 and became the elementary mathematics consultant at the Texas Education Agency. In 1982, she returned to Texas A&M University and received her Ph.D. in Mathematics Education in 1988 while working as a lecturer in the Department of Mathematics teaching the mathematics courses for elementary and secondary education majors. Now an Associate Professor in Mathematics and Education at Texas A&M University, Janie has continued her involvement with the Texas Education Agency's development of the state-mandated curriculum in mathematics; made hundreds of presentations at mathematics conferences for teachers; written and presented a variety of professional development institutes for in-service teachers; and authored articles and textbooks focusing on helping children understand mathematics, with special attention to the effective instructional uses of calculators. For the past 18 years, she has spent her free time enjoying her family as her children grew into young adults while she unabashedly used them as guinea pigs and handy sources of data on learning.