UCSMP Grades 6-12 Curriculum Features

Wide scope. The UCSMP curriculum for grades 6-12 interweaves five strong strands: arithmetic, algebra, geometry, statistics, and discrete mathematics. This wide scope continues and builds on equivalent strands in the UCSMP Everyday Mathematics curriculum. And it reflects national recommendations over the past thirty years in mathematics education, including A Nation At Risk (1983), the NCTM Curriculum and Evaluation Standards (1989), Principles and Standards for School Mathematics (2000), the broad recommendations surrounding the more recent NCTM Focal Points (2006) and Focus in High School Mathematics (draft, 2008), the GAISE standards of the American Statistical Association (2005), and the recommendations of the College Board (2007) and Achieve (2008).

Real-world orientation. The power of mathematics lies in its abstractness, giving it the ability to be applied in many diverse situations. But we use mathematics because of its many real-world applications, which are important for every individual to learn in order to make wise decisions and to participate in a knowledgeable way in our democracy. Applications are essential because, except for the few students who will have a life in pure mathematics, being able to do mathematics is of little use unless the student can apply that content. We owe it to our students to teach them the applications of mathematics, for if a student does not learn to apply mathematics in a mathematics class, it is doubtful the student will learn applications somewhere else.

Technology use. Preparation for today’s workplaces requires that students be familiar with up-to-date technology. For the mathematics classroom, useful technology includes spreadsheets, graphing utilities, computer algebra systems, dynamic geometry drawing programs, statistical software, and applets. Students are gradually introduced to these technologies throughout the program. UCSMP and McGraw-Hill Education provide a wide assortment of electronic resources to help students learn key concepts and to assist teachers in instruction and assessment.

Four dimensions of understanding. To understand a mathematical concept means to be able to carry out algorithms related to that concept; to develop and use mathematical properties and relationships involving the concept; to apply the concept in problems, both real-world and theoretical; and to represent or picture the concept. Each dimension allows questions ranging from simple exercises to the invention of new ideas. We call this the SPUR approach: Skill, Properties, Uses, and Representations.

Student text organization. Each student book is designed to maximize the acquisition of both skills and concepts. The content of each book is carefully sequenced in 12-14 chapters, split into 6-10 lessons. Each lesson has reading followed by four types of questions, all of which should be covered: Covering the Ideas, Applying the Mathematics, Review, and Exploration. At the end of each chapter, a carefully-focused Self-Test and a Chapter Review, keyed to objectives in all the dimensions of understanding, are used to solidify performance of skills and concepts from the chapters so that they can be applied later with confidence.

Mastery and review. Lesson Masters in the CD with the teacher’s editions provide more practice on the objectives for each lesson. Ideas introduced in a lesson, as well as ideas from prior lessons and chapters, and from previous courses are reinforced through the Review questions. The Self-Test and Review are designed to enable the teacher and student to assess what work still needs to be done before a chapter test.

Reading and active learning. One of the most important goals for any mathematics course is to help a student learn to learn. The third edition has more activities than prior editions. These activities, all within lessons, enable students to be more participatory in their learning and development of concepts. Many examples are guided, with partially-completed solutions to encourage students to read with care and fill in the missing details. Mental mathematics exercises begin each lesson. Stopping points called Quiz Yourself (QY) ask students questions over material just read in order to check their understanding. There are also many more questions requiring writing because writing helps students clarify their thinking and is an important aspect of communicating mathematical ideas to others.

Learning to make choices. All UCSMP courses utilize a variety of tools and technologies in an activity-oriented approach. Students learn through guided activities, examples, and quiz-yourself questions within the text. Lessons present the student with explorations and optional projects to coincide with the material presented. Students are continually asked to make wise choices between mental mathematics, paper-and-pencil skills, and CAS and graphing technology.


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