For anyone planning to teach K-12 mathematics in the era of the Common Core Standards, this report from the Conference Board of the Mathematical Sciences is a must read. Although the intended audience is those who teach mathematics to current and future teachers, the report is a valuable resource to teachers in describing K-12 school mathematics and the expectations for teachers in elementary, middle, and high school.
Here’s an excerpt:
At every grade level—elementary, middle, and high school—there is important mathematics that is both intellectually demanding to learn and widely used, such as reasoning strategies that rely on base-ten algorithms in elementary school; ratio, proportion, and exploratory statistics in middle school; algebra, geometry, and data analysis in high school. Teachers need to have more than a student’s understanding of the mathematics in these grades. To support curricular coherence, teachers need to know how the mathematics they teach is connected with that of prior and later grades. For example, an elementary teacher needs to know how the associative, commutative, and distributive properties are used together with place value in algorithms for addition and multiplication of whole numbers, and the significance of these algorithms for decimal arithmetic in later grades. In the middle grades, a teacher needs to know how to build on this foundation; for instance, how to help students to extend these algorithms correctly to decimals and to use the distributive and other properties when adding and subtracting linear expressions. A high school teacher builds on the same ideas in teaching students about calculations with polynomials and other symbolic expressions.