Indicator C.1.4. Analyze the Mathematical Content of Curriculum

The alignment of standards, instructional materials, and assessment is critical in designing a cohesive, well-articulated curriculum. Well-prepared beginning teachers of mathematics are aware that the mathematics they teach is based on a variety of, often nested, documents. They know that connections exist among standards, curriculum documents, instructional materials, and assessment frameworks and have dispositions and commitment to analyze these guides to inform their teaching. They have the content preparation and the dispositions to analyze instructional resources, including those provided by textbook publishers and those available from sources online, to determine whether these resources fully address the content expectations described in standards and curriculum documents. When the materials fall short of the standards or expectations, well-prepared beginners are able to decide whether to replace or adapt the materials to better address the content and process expectations.

Well-prepared beginners realize that in addition to the curriculum and standards that they are accountable to teach, other resources can support their efforts to design rigorous, coherent mathematics instruction. Such resources include learning or standards progressions (cf. Generating Increased Science and Mathematics Opportunities, 2012; Institute for Mathematics and Education, n.d.) that describe relationships among standards within and across grades. Note that in addition to content progressions, other types of progressions to be considered are developmental progressions or learning trajectories. Well-prepared beginners understand the content within these materials and can discuss them with colleagues, administrators, and families of their students in ways that make sense to these audiences.

Through analyzing available resources, well-prepared beginners are able to make decisions about the sequencing and time required to teach the content in depth as well as to make important connections among the mathematics taught in the grades or units before and after what they are teaching.