Appendix A Appendix B

Assessment in a Middle-school Mathematics Teacher Preparation Program

 
Appendix C:  An Introduction to NCATE Accreditation Requirements

NCATE (National Council for Accreditation of Teacher Education) is in the process of adopting new standards, which can be found in the document, “NCATE/NCTM Program Standards (2003)” (at http://www.ncate.org/standard/programstds.htm, under Mathematics Education; the document can be obtained as a pdf (Acrobat Reader) file).  These standards are very detailed, and describe both content knowledge and skills that teacher candidates must demonstrate.  Some of the skills will be learned in their education courses, but “process standards” 1 – 6 (knowledge of “mathematical problem solving,” “reasoning and proof,” “mathematical communication,” “mathematical connections,” “mathematical representation,” and “technology”) as well as the “content standards” (there are also “pedagogy” and “field-based experiences” standards) are primarily learned in the mathematics courses.  For each standard, several indicators of what it would mean to meet that standard are listed.  The process standard indicators are the same for all levels (Elementary Mathematics Specialists, Middle Grades, and Secondary Level), but the content standard indicators become more elaborate the higher the grade level.  As an example of Process Standard indicators, for “Knowledge of Mathematical Problem Solving” the indicators are

1.1 Apply and adapt a variety of appropriate strategies to solve problems. 

1.2 Solve problems that arise in mathematics and those involving mathematics in other contexts.

1.3 Build new mathematical knowledge through problem solving.

1.4 Monitor and reflect on the process of mathematical problem solving.

For the middle level, the Content Standard “Knowledge of Discrete Mathematics:  Candidates apply the fundamental ideas of discrete mathematics in the formulation and solution of problems,” has as indicators

13.1 Demonstrate a conceptual understanding of the fundamental ideas of discrete mathematics such as finite graphs, trees and combinatorics.

13.2 Use technological tools to apply the fundamental concepts of discrete mathematics.

13.3 Demonstrate knowledge of the historical development of discrete mathematics including contributions from diverse cultures.

NCATE’s matrix for each of these indicators asks “How do our candidates acquire and demonstrate the knowledge addressed to this standard?” “What evidence supports candidates’ knowledge acquisition and performance?” and “What are our findings?”