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In secondary school, all students should learn an ambitious common foundation of mathematical ideas and applications. This shared mathematical understanding is as important for students who will enter the workplace as it is for those who will pursue further study in mathematics and science. All students should study mathematics in each of the four years that they are enrolled in high school.

Because students' interests and aspirations may change during and after high school, their mathematics education should guarantee access to a broad spectrum of career and educational options. They should experience the interplay of algebra, geometry, statistics, probability, and discrete mathematics. They need to understand the fundamental mathematical concepts of function and relation, invariance, and transformation. They should be adept at visualizing, describing, and analyzing situations in mathematical terms. And they need to be able to justify and prove mathematically based ideas.

High school mathematics builds on the skills and understandings developed in the lower grades. For example, students should enter high school with extensive experience in modeling various patterns and relationships. High school students might explore the following problem:

A student strained her knee in an intramural volleyball game, and her doctor prescribed an anti-inflammatory drug to reduce the swelling. She is to take two 220-milligram tablets every 8 hours for 10 days. If her kidneys filtered 60% of this drug from her body every 8 hours, how much of the drug was in her system after 10 days? How much of the drug would have been in her system if she had continued to take the drug for a year?

 Fig. 3. A spreadsheet computation of the "drug dosage" problem

Students might represent the equation informally as NEXT = 0.4(NOW) + 440, start at 440. Entering this relationship in a spreadsheet (see fig. 3), they could note that an "equilibrium" value of about 733 1/3 milligrams is reached. This investigation might lead to explorations of finite sequences and series.

High school students can study mathematics that extends beyond the material expected of all students in at least three ways. One is to include in the curriculum material that extends the foundational material in depth or sophistication. Two other approaches make use of supplementary courses. In the first, students enroll in additional courses concurrent with those expected of all students. In the second, students complete a three-year version of the shared material and then take other mathematics courses. In both situations, students can choose from such courses as computer science, technical mathematics, statistics, and calculus. Each of these approaches has the essential property that all students learn the same foundation of mathematics but some, if they wish, can study additional mathematics.

The Standards for high school students are ambitious. The demands made on high school teachers in achieving the Standards will require extended and sustained professional development and a large degree of administrative support.

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