Using technology for problem solving in middle and high school mathematics : investigations using scientific and graphing calculators, spreadsheets, and the Geometer's Sketchpad

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Using technology for problem solving in middle and high school mathematics : investigations using scientific and graphing calculators, spreadsheets, and the Geometer's Sketchpad

Kenneth P. Goldberg

Pearson Merrill Prentice Hall, c2007

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Includes bibliographical references and index

内容説明・目次

内容説明

Using Technology for Problem Solving in Middle and High School Mathematics: Investigations Using Scientific and Graphing Calculators, Spreadsheets, and The Geometer's Sketchpad (c) Firmly rooted in the NCTM Principles and Standards, Using Technology for Problem Solving in Middle and High School Mathematics examines why technology is essential to today's mathematics classroom, and illustrates how using technology can encourage and enhance your students' study and understanding of mathematics. Inquiry-based, this book provides both a five-step model and 23 sample investigations that demonstrate how to help students become better problem solvers through the use of four types of instructional technology: the scientific calculator, the graphing calculator, spreadsheet software, and The Geometer's Sketchpad (c) software. Here's what reviewers say about this book: "The five-step model provided here is excellent, giving teachers a rich mathematical perspective to draw upon. This process moves students from inductive explorations to deductive justifications of the results, which is aligned with current theories on how students best learn." Dr. Robert M. Horton, Clemson University "I like the organization of the investigations; they include a nice variety of topics and tend to avoid the `already known' examples. The level of technology used moves from simple to more complex, and the reader is exposed to potentially new uses of the technology beyond commonly used (novice) features." Dr. Linda Bolte, Eastern Washington University "I really like the idea of the research summaries. In all cases, I think bringing mathematics research into the practice arena is extremely useful and productive." Dr. Janet Bowers, San Diego State University

目次

Preface Recommendations and Guidelines for Using Technology in the Mathematics Classroom PART I The Scientific Calculator Research Results on the Classroom Use of the Scientific Calculator Investigation #1--An Investigation into Ancient Egyptian Mathematics and Unit Fractions Investigation #2--An Investigation into Recursively Defined Functions and the Limit of an Infinite Sequence Investigation #3--An Investigation into the Effect of Successive Percentage Increases and Decreases on the Price of an Item Investigation #4--An Investigation into Fixed Points and Converging Sequences PART II The Graphing Calculator Research Results on the Classroom Use of the Graphing Calculator Investigation #5--An Investigation into the Formula for the Sum of an Infinite Geometric Series Investigation #6--An Investigation into the Units Digits of Perfect Squares Using Histograms and Frequency Tables Investigation #7--An Investigation into Probability and the Concept of Fairness Through a Simple Program Investigation #8--An Investigation into the Trajectory of an Object in Motion Using Graphs and Tables of Values Investigation #9--A Visual Investigation into the Number of Real Roots of a Polynomial Equation with Real Coefficients Investigation #10--An Investigation into the Relationship between the Coefficients of a First or Second Degree Function and the Behavior of Its Graph Investigation #11--An Investigation into a Visual Discovery of Trigonometric Identities and Relationships Investigation #12--An Investigation into the Derivative Using Both Algebraic and Visual Representations Investigation #13--An Investigation into Converging and Diverging Infinite Series, and Special Mathematical Constants Investigation #14--An Investigation into the Use of Linear and Non-Linear Regression for Curve Fitting and Making Predictions Investigation #15--An Investigation into Exponential Growth and Exponential Regression Investigation #16--An Investigation into Generalized Fibonacci Sequences Using Matrices PART III Dynamic Geometry Using the Geometer's Sketchpad Research Results on the Classroom Use of the Geometer's Sketchpad Software Investigation #17--An Investigation Relating the Properties of Quadrilaterals to the Properties of Their Diagonals and Creating a Book of Shapes Investigation #18--An Investigation into Inscribed Quadrilaterals and Triangles Investigation #19--An Investigation of the Sum of the Perpendicular Distances From a Point Inside a Regular Polygon to its Sides Investigation #20--An Investigation into Perimeter and Area Relationships on a Line Segment Investigation #21--An Investigation into Area Relationships Between Inscribed and Circumscribed Circles of Regular Polygons Investigation #22--An Investigation into the Product of the Segments of Intersecting Chords of a Circle Investigation #23--An Investigation into the Geometric Solution of a Minimization Problem Using Reflection of a Point Across a Line Segment

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