List Books » Using Technology and Problem Solving in Middle and High School Mathematics: Investigations Using Scientific and Graphing Calculators, Spreadsheets, and The Geometer's Sketchpad
Authors: Kenneth P. Goldberg
ISBN-13: 9780131181816, ISBN-10: 0131181815
Format: Paperback
Publisher: Prentice Hall
Date Published: May 2006
Edition: 1st Edition
Using Technology for Problem Solving in Middle and High School Mathematics: Investigations Using Scientific and Graphing Calculators, Spreadsheets, and The Geometer’s Sketchpad ©
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 © 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
Pt. 1 | The scientific calculator : research results on the classroom use of the scientific calculator | 1 |
Investigation 1 | Ancient Egyptian mathematics and unit fractions | 4 |
Investigation 2 | Recursively defined functions and the limit of an infinite sequence | 9 |
Investigation 3 | The effect of successive percentage increases and decreases on the price of an item | 19 |
Investigation 4 | Fixed points and converging sequences | 26 |
Pt. 2 | The graphing calculator : research results on the classroom use of the graphing calculator | 35 |
Investigation 5 | The formula for the sum of an infinite geometric series | 37 |
Investigation 6 | The units digits of perfect squares : histograms and relative frequency tables | 44 |
Investigation 7 | Probability and the concept of fairness : a simple program | 52 |
Investigation 8 | Examination the trajectory of an object in motion using graphs and tables of values | 60 |
Investigation 9 | A visual inspection of the real roots of a polynomial function | 66 |
Investigation 10 | The relationship between the coefficients of a first or second degree function and the behavior of its graph | 74 |
Investigation 11 | A visual discovery of trigonometric identities and formulas | 81 |
Investigation 12 | Exploring derivatives using both algebraic and visual representations | 88 |
Investigation 13 | Converging and diverging infinite series and special mathematical constants | 94 |
Investigation 14 | The use of linear and nonlinear regression for curve fitting and making predictions | 102 |
Investigation 15 | Exponential growth and exponential regression | 110 |
Investigation 16 | Generalized Fibonacci sequences using matrices | 117 |
Pt. 3 | Dynamic geometry software : research results and effective classroom practice | 125 |
Investigation 17 | Relating the properties of quadrilaterals to the properties of their diagonals and crating a book of shapes | 127 |
Investigation 18 | Inscribed quadrilaterals | 132 |
Investigation 19 | The sum of the perpendicular distances from and interior point of a regular polygon to its sides | 137 |
Investigation 20 | Perimeter and area relationships on a line segment | 142 |
Investigation 21 | Area relationship between inscribed and circumscribed circles of regular polygons | 147 |
Investigation 22 | The product of the segments of intersecting chords in a circle | 152 |
Investigation 23 | The geometric solution of a minimization problem using reflection of a point across a line segment | 155 |