Mathematics Curriculum and Instruction

The mathematics curriculum in K–12 schools is organized across four major areas, number systems, algebra, geometry and measurement, and statistics and probability. While emphasis varies, each grade level's curriculum will likely include experiences with topics in each area. During their study of mathematics, students are expected to learn concepts and procedures, and both are required for mathematical expertise.

The study of numbers begins early with whole numbers and the process of counting. As students age, the number systems they study increase to include integers, rational numbers, and real numbers. Students learn to represent numbers in a variety of ways. For example, the number 5 may be represented by 5 beans, as the difference between 12 and 7, as a product of 20 and ¼, and as the square root of 25. Students learn to write numbers as fractions, decimals, and percents and to complete computation problems with numbers written in various forms. Understanding that numbers can be represented in many different ways is key to developing common sense about numbers and being able to use them in various real-world settings.

The study of algebra begins with a study of patterns by young children. Some patterns involve counting; others involve computational relationships. Older students begin to write patterns using variables and then use variables as unknowns in equations and inequalities and when solving problems. Students learn to represent functions using a table of values, an equation, and a graph. The ability to describe patterns in different ways and to use a variety of different representations is key to developing algebraic thinking.

The study of geometry and measurement includes shapes, their properties and relationships. Students begin exploring common two- and three-dimensional shapes. As they study more complex shapes, they also analyze shapes for their properties, noting such characteristics as number of sides, sum of angle measures, and sides or angles of equal measure. Students learn that some shapes are congruent and some are similar. They also learn how sets of shapes are related, such as all squares are parallelograms. Students study perimeter, area, and volume and their use in the real world.

The study of statistics and probability centers on ways to display and analyze data. Young students create bar graphs of information about themselves and their surroundings. Older students learn other ways to display data and how to select the best representation for a particular set of data. Measures of central tendency (mean, median, and mode) are studied as well as measures of variability, such as the range and standard deviation. Concepts of chance and likelihood provide an introduction to probability; students then learn to calculate the probability of an event occurring and use concepts of probability to analyze information in the real world.

During the study of mathematics, students in all grades develop their problem-solving and reasoning processes. A primary purpose of studying mathematics is developing abilities useful in solving problems that arise in both real-world and mathematical settings. Systematic reasoning is a critical part of mathematics, so students need to engage in the process of making conjectures and developing sound deductive arguments. Problem solving and reasoning should be [Page 307]an integral part of the study of all content areas in mathematics.

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