Level 4

All students should be able to reason and communicate proficiently in mathematics. They should have knowledge of and skill in the use of the vocabulary, forms of representation, materials, tools, techniques, and intellectual methods of the discipline of mathematics, including the ability to define and solve problems with reason, insight, inventiveness and proficiency.

In Connected Mathematics, students develop understanding of algorithms and strategies for computing and estimating in a variety of ways. They learn to recognize when an algorithm or strategy applies to a new context, and when they can build on the skills and strategies they know in order to develop new strategies. In these processes, students practice skills as an ongoing activity throughout the curriculum.

Students need to know how and when to use paper-and pencil algorithms, mental computation, calculator procedures, and estimation strategies. They need to recognize when an exact answer is required and when an approximate answer is sufficient, and they need a variety of methods for finding an answer. In some situations an approximate answer is sufficient and in these situations a paper-and-pencil algorithm may not be the most efficient (or practical) method.

Traditionally, an Algebra 1 course focuses on rules or specific strategies for solving standard types of symbolic manipulation problems-usually to simplify or combine expressions or solve equations. For many students, symbolic rules for manipulation are memorized with little attempt to make sense of why they work. They retain the ideas for only a short time. There is little evidence that traditional experiences with algebra help students develop the ability to "read" information from symbolic expression or equations, to write symbolic statements to represent their thinking about relationships in a problem, or to meaningfully manipulate symbolic expressions to solve problems.

In the United States, algebra is generally taught as a stand-alone course rather than as a strand integrated and supported by other strands. This practice is contrary to curriculum practices in most of the rest of the world. Today, there is a growing body of research that leads many United States educators to believe that the development of algebraic ideas can and should take place over a long period of time and well before the first year of high school. Developing algebra across the grades and integrating it with other strands helps students become proficient with algebraic reasoning in a variety of contexts and gives them a sense of the coherence of mathematics.