### Mathematics

Students have a deep understanding of select central concepts in middle school mathematics as well as core representations, canonical examples, and alternative algorithms germane to teaching these select concepts.

### Mathematical Exploration

Students can engage in meaningful mathematical exploration, are willing and able to approach and solve challenging mathematics problems, and can reflect on their own learning to make inferences about how adolescents learn mathematics.

### Mathematical Understanding

Students know and can describe what it means to understand mathematics relationally, can demonstrate mathematical understanding by creating and evaluating conceptually-oriented mathematical explanations, and can explain why conceptually-oriented mathematics instruction is essential for supporting adolescents' learning of mathematics.

### Mathematics Instruction

Students recognize that mathematics instruction that does not build relational understanding has failed a majority of adolescents, even themselves, and that they have a moral obligation to seek the necessary knowledge and expertise to teach mathematics in ways that enable all adolescents to develop conceptual understanding, procedural fluency, and facility with authentic mathematical practices.