The title Connected Mathematics Project (CMP) reflects the author team's interest in developing student knowledge of mathematics that is rich in connections--connections among the various topic strands of the subject, connections between mathematics and its applications in other disciplines, connections between the planned teaching/learning activities and the special aptitudes and interests of middle school students, and connections between the preparation developed by elementary school mathematics and the goals of secondary school mathematics.

The developers were guided by five fundamental mathematical and instructional themes:

• The curriculum is organized around a selected number of important mathematical concepts and process goals. Each concept is studied in depth within a general theme.
  
  
• The curriculum emphasizes significant connections among various mathematical topics that are presented and connections between mathematics and problems in disciplines that are meaningful to students.
  
  
• Instruction emphasizes inquiry and discovery of mathematical ideas through investigation of structurally rich problem situations.
  
  
• Students grow in their ability to reason effectively with information represented in graphic, numeric, symbolic, and verbal forms and in their ability to move flexibly among these representations.
  
  
• Selection of mathematical goals and teaching approaches will reflect the information processing capabilities of calculators and computers and the fundamental changes such tools are making in the ways people learn mathematics and apply their knowledge to problem solving tasks.

The selection of mathematical content and process goals reflect the answers to two related questions:

What Mathematics Is Developed?

• NUMBER-Number sense; number theory; properties and operations of number systems, with focus on integers and rational numbers; estimation; ratio, proportion, and percent; representation of numbers in concrete, graphic, and symbolic forms.
  
  
• GEOMETRY-Spatial sense; two and three­dimensional shapes and their properties; relations among shapes (congruence, similarity, parallelism, perpendicularity, symmetry); coordinate systems; procedures for exact, approximate, and derived measurements; estimation.
  
  
• MEASUREMENT-Concepts of length, area, volume, mass: common properties of measurement systems; procedures for exact, approximate, and derived measurements; estimation.
  
  
• ALGEBRA-Variables, functions, relations; representation by symbolic expressions, numerical tables, and graphs; equations and inequalities; rates of change.
  
  
• STATISTICS and PROBABILITY-Collection, display, and analysis of data; sampling; decision­making under uncertainty; random events and probability; expected value; simulation.

In each strand the fundamental concern is to make sure students have a confident understanding of the most important concepts, principles, and techniques required to apply mathematics to the solution of significant problems. Themes and situations are used to develop mathematics and to engage the interest of students. That is, the mathematics and processes are motivated by the applied situation. Skilled performance of routine procedures is not useful unless those skills are accompanied by a clear sense of when and how they should be applied. While the previous topics have just been listed in separate strands, the intention is to make maximum use of relations and connections between strands and between grade levels.

In setting mathematical goals for a school curriculum, the choice of content topics must always be accompanied by analysis of the kinds of thinking that students will be able to demonstrate on completion of the curriculum. The answer to a second important curricular question is outlined below in eight key mathematical processes that will be developed throughout the main content strands. Each process goal is accompanied by some of its important component thinking skills.

What Will Students Be Able To Do?

• COUNT-Determine the number of elements in finite data sets, trees, graphs, networks, permutations, or combinations by applications of mental computation, estimation, counting principles, calculators and computers, and formal algorithms.
  
  
• VISUALIZE-Recognize and describe shape, size, and position of one, two, and three-dimensional objects and their images under transformations; interpret graphical representations of functions, relations, and symbolic expressions.
  
  
• COMPARE-Describe relations among quantities and shapes using concepts such as equal, less than, greater than, more or less likely, congruence, similarity, parallelism, perpendicularity, symmetry, and rates of growth or change.
  
  
• MEASURE-Assign numbers as measures of geometric objects, probabilities of events, and choices in a decision-making problem. Choose appropriate units or scales and make measurements by successive approximation and by the application of formal rules.
  
  
• MODEL-Construct, make inferences from, and interpret concrete, symbolic, graphic, verbal, and algorithmic models of quantitative, visual, statistical, probabilistic, and algebraic relations in problem situations. Translate information from one model form to another.
• REASON-Bring to any problem situation the disposition and ability to observe, experiment, analyze, abstract, induce, deduce, extend, generalize, relate, manipulate, and prove interesting and important patterns.
  
  
• PLAY-Have the disposition and imagination to inquire, investigate, tinker, dream, conjecture, invent, and communicate with others about mathematical ideas.
  
  
• USE TOOLS-Select and intelligently use calculators, computers, drawing tools, and physical models to represent, simulate, and manipulate patterns and relations in problem settings.