### Origin and Nature of Mathematics

Students understand and can describe the major approaches—cultural, philosophical, and psychological—to explaining the origin and nature of mathematics and its relation to understanding and modeling the physical world.

### Historical Periods and Contributions

Students understand and can describe the major historical periods of development of mathematical thought, as well as the contributions of various cultures and individuals within those periods.

### Historical Development of Concepts and Practices

Students understand and can describe the historical development of concepts and practices central to school mathematics, including numeration, arithmetic, algebra, geometry, calculus, and probability.

### Complexity of Human Mathematical Activity and Learning

Through understanding the complex relationship between mathematical practices and human experience, students appreciate the complexity of teaching and learning mathematics and the different approaches and experiences adolescents will bring to learning those practices.