The framework shown below (Figure 1) illustrates the inter-connectedness of various types of curriculum - intended, written (textbook), assessed, implemented, and learned. It also illustrates forces that impact on each type of curriculum. CSMC scholars are investigating various research questions embedded within the framework (see "Research in Progress" for a listing of ongoing and completed studies).

The Center is committed to engaging in and promoting a program of research that assists curriculum developers, teacher leaders, school administrators, and policy makers to better understand the critical design and implementation factors that enable curriculum materials to support student learning.

A sample of research questions is noted below. They are organized around six broad and inter-related areas of curriculum: curriculum design and analysis; adoption and enactment; student learning; teacher knowledge and beliefs; history and status; and policy.

Curriculum Design and Analysis

• What are the critical design features of mathematics curriculum materials that support effective teaching and student learning (e.g., nature of tasks, range of tasks, sequence of tasks, presentation of tasks)?
• How can curriculum materials be designed to better serve the learning needs of all students, including reluctant learners and those from diverse cultural backgrounds?
• What are the developmental trajectories of major mathematical topics when considered from a mathematical structure perspective? From an algorithmic perspective? From a historical perspective? From a cognitive science perspective?
• How can curriculum materials be designed to capitalize on continued advances in the mathematical sciences? In computing technologies?
• What evaluation tools are most effective when studying and analyzing curriculum? What information do they yield for various purposes and what are their limitations?

Curriculum Adoption and Enactment

• To what extent and in what ways do teachers of mathematics use instructional materials such as the district-adopted textbook and/or district or state curriculum frameworks? How do teachers adjust/supplement curriculum materials? For what purposes?
• What processes do districts/schools/teachers use in selecting mathematics curriculum materials? Do the processes used in state-adoption states differ from those in states with open textbook adoption? If so, in what ways?
• How do various factors (e.g., contextual factors--such as length or organization of class periods or access to technologies; teacher attributes--such as, knowledge of content or beliefs about mathematics; external factors--such as parents or administrators) influence how mathematics curriculum materials are used?
• What influence does professional development based on curriculum investigation and implementation have on teachers use of particular types of mathematics curriculum materials?
• To what extent do mathematics instructional materials support or limit various facets of the work of teaching (e.g., planning, guiding student discussion, selecting tasks)?

Curriculum and Student Learning

• What are the patterns of student learning and continued study of mathematics associated with regular and sustained use of various kinds of instructional materials? How are those patterns related to fidelity of intended use?
• To what extent and in what ways do students utilize instructional materials (e.g., textbooks, technology) and how does this use impact student conceptions of, and dispositions toward, mathematics?
• To what extent do various kinds of curriculum materials differentially foster the mathematical development of all students, especially underserved populations? Do they widen/narrow existing achievement gaps in mathematics?

Curriculum and Teacher Knowledge and Beliefs

• To what extent and in what ways do adoption and enactment of new mathematics instructional materials impact teachers' conceptions of mathematics? Mathematical content knowledge? Pedagogical content knowledge? Teaching methods and instructional practice? Dispositions toward mathematics teaching?
• To what extent and in what ways do mathematics instructional materials influence the learning of teachers? What is the influence of teacher experience and/or teacher preparation in this process? What mathematics curriculum design features may be of most use to particular groups of teachers (e.g., novices, teachers with differing mathematics content backgrounds)?
• What is the impact of alignment (or misalignment) of teachers' beliefs (about mathematics and learning) and curriculum material implementation?

History and Status of Curricula

• To what extent is a common mathematics curriculum presented to students at particular grades in the U. S.? (As articulated in state curriculum frameworks? As measured on high-stakes assessments? As emphasized by teachers? As outlined in textbooks?)
• To what extent are mathematics instructional materials used in schools aligned with nationally developed standards (e.g., National Council of Teachers of Mathematics Principles and Standards for School Mathematics or Achieve's Foundations for Success)?
• How are mathematics curriculum materials developed, tested, revised, marketed? Is the process the same across K-12? If not, how does the process differ and for what reasons?
• To what extent and in what ways have mathematics curriculum materials changed in the past century? In what ways has the priority and presentation of particular mathematical topics changed/evolved over time? To what extent have topics been added or deleted from the curriculum? What factors drive mathematics curriculum changes?
• What mathematics textbooks and instructional materials are used in K-12 classrooms? Are there identifiable patterns of usage by states, by different types of schools or students?
• What factors affect public perceptions of mathematics curriculum materials?

Policy and Curriculum

• To what extent do national educational policies (e.g., NCLB) influence the content of state mathematics curriculum frameworks, statewide assessments, and textbooks and their selection?
• To what extent does high-stakes testing affect mathematics curriculum development, mathematics curriculum selection, and mathematics curriculum implementation?
• To what extent do state mathematics curriculum frameworks influence the content of commercially generated textbooks?
• What are the impediments to better articulation between pre-college and college mathematics curricula and how might they be addressed?