Correlation with NCMT and AMATYC Standards Standards for Intellectual Development Dugopolski's Algebra for College Students I-1 Problem Solving Students will engage in substantial mathematical problem solving. Real-life problems are integrated into nearly every section. Problem solving strategies are given and graphs are used frequently to illustrate relationships between real-life variables. I-2 Modeling Students will learn mathematics through modeling real-world situations. The text includes problems involving a wide variety of real-world situations. See the Index of Applications. I-3 Reasoning: Students will expand their mathematical reasoning skills as they develop convincing mathematical arguments. Students are encouraged to reason with the Getting More Involved Exercises, which include open-ended questions that request written answers. I-4 Connecting with Other Disciplines: Students will develop the view that mathematics is a growing discipline, interrelated with human culture, and understand its connections to other disciplines. Every chapter has a Chapter Opener and a Math at Work feature, which show how mathematics is used by real people in a variety of human endeavors. The exercises also include problems directly related to these features. I-5 Communicating: Students will acquire the ability to read, write, listen to, and to speak mathematics. The exercises in every section of the text begin with some simple writing exercises that can only be answered by reading the text. The Getting More Involved Exercises include numerous discussion and writing exercises. Also, Enriching Your Mathematical Word Power encourages students to learn the vocabulary of algebra. I-6 Using Technology: Students will use appropriate technology to enhance their mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of their results. Exercises that require a scientific calculator as well as exercises that require a graphing calculator are included. The Calculator Close-ups give tips for using a graphing calculator and show how a graphing calculator can be used to enhance our understanding of algebra. I-7 Developing Mathematical Power: Students will engage in rich experiences that encourage independent, nontrivial exploration in mathematics, develop and reinforce tenacity and confidence in their abilities to use mathematics, and inspire them to pursue the study of mathematics and related disciplines. The exercises involve mathematics in a wide variety of disciplines. However, these exercises are chosen and written so they can be understood by students who may not be very familiar with the terms and principles of these disciplines. This technique encourages students to do the exercises and to develop confidence in using mathematics in other disciplines.   Standards for Content Dugopolski's Algebra for College Students C-1: Number Sense Students will perform arithmetic operations, as well as reason and draw conclusions from numerical information. Fractions, decimals, and percents are used throughout the text. Many multiple-part questions not only ask for numerical answers, but also ask students to make decisions or draw conclusions. C-2: Symbolism and Algebra Students will translate problem situations into their symbolic representations and use those representations to solve problems. Symbolic representation of problem situations occurs in nearly every section of the text. Symbolic representation of real-world situations is introduced in Chapter 1. In Chapter 2 students are taught to translate problem situations into algebra. C-3: Geometry Students will develop a spatial and measurement sense. The text contains numerous problems involving common geometric shapes. Much emphasis is placed on units and reconciling the units in an answer. For example, in work problems we find the amount of work by multiplying the rate and the time: . C-4: Function Students will demonstrate understanding of the concept of function by several means (verbally, numerically, graphically, and symbolically) and incorporate it as a central theme into their use of mathematics. Linear functions are introduced in Section 3.3, after the discussion of linear equations in two variables and their graphs. An early introduction to functions in general is found in Sections 3.5 and 3.6, with emphasis on verbal rules, formulas, tables, and graphs. Additional topics on functions are included in Chapter 9. C-5: Discrete Mathematics Students will use discrete mathematical algorithms and develop combinatorial abilities in order to solve problems of finite character and enumerate sets without direct counting. The basic facts about permutations, combinations, labeling, and probability are introduced in Chapter 14. C-6: Probability and Statistics Students will analyze data and use probability and statistical models to make inferences about real-world situations. Numerous problems involve real data taken from web sites such as the U.S. Census Bureau. Web addresses are given in the problems. C-7: Deductive Proof Students will appreciate the deductive nature of mathematics as an identifying characteristic of the discipline, recognize the roles of definitions, axioms, and theorems, and identify and construct valid deductive arguments. This text is a mathematics text. Definitions are given and explanations are provided as to why the rules or theorems follow from the definitions. In the Getting More Involved Exercises students are often asked to draw conclusions and give explanations.   Standards for Pedagogy Dugopolski's Algebra for College Students P-1: Teaching with Technology Mathematics faculty will model the use of appropriate technology in the teaching of mathematics so students can benefit from the opportunities it presents as a medium of instruction. The Calculator Close-ups will help both students and teachers to see how a graphing calculator can be used to enhance understanding. For example, one can easily see the importance of parentheses when calculating and on a graphing calculator. P-2: Interactive and Collaborative Learning Mathematics faculty will foster interactive learning through student writing, reading, speaking, and collaborative activities so students can learn to work effectively in groups and communicate about mathematics both orally and in writing. The true-false Warm-up Exercises can be used to stimulate discussion and communication. The Getting More Involved Exercises contain Writing, Exploration, Discussion, and Cooperative Learning Exercises. A detailed Collaborative Activity is included at the end of each chapter P-3: Connecting with Other Experiences Mathematics faculty will actively involve students in meaningful mathematics problems that build upon their experiences, focus on broad mathematical themes, and build connections within branches of mathematics and between mathematics and other disciplines so that students will view mathematics as a connected whole relevant to their lives. As shown in the Index of Applications, the text has relevant applications that come from areas such as sports, business, health, finance, and chemistry, to name a few. All applications are written so that in one or two sentences the student can understand the problem. These applications do not require any advanced knowledge in these areas. P-4: Multiple Approaches Mathematics faculty will model the use of multiple approaches - numerical, graphical, symbolic, and verbal - to help students learn a variety of techniques for solving problems. Reading graphs in two variables is introduced in Chapter 1, while graphing in two variables is covered in Chapter 3. Graphs are often used to enhance understanding, even though a graph may not be necessary to solve the problem. P-5: Experiencing Mathematics Mathematics faculty will provide learning activities, including projects and apprenticeships, that promote independent thinking and require sustained effort and time so that students will have the confidence to access and use needed mathematics and other technical information independently, to form conjectures from an array of specific examples, and to draw conclusions form general principles. Making Connections Exercises at the ends of Chapters 2 through 13 incorporate ideas from previous chapters. They also include multiple part application problems, which require ideas from more than one chapter. These exercises encourage students to see the whole picture rather than view the subject as a collection of independent ideas. The Getting More Involved Exercises ask students to dig a bit deeper, make conjectures, and draw conclusions.

Back To Homepage