I am doing a correlational study on the relationship between teachers' sense of efficacy and school culture score( IV) and student achievement(DV). The new NJ Teacher's Evaluation system moderates/mediates the relationship.
In your study, you assume that school culture affect student achievement. Therefore, school culture score is an independent variable and student achievement is a dependent variable. Because school culture (your independent variable) will not affect the new NJ Teacher's Evaluation system, the new NJ Teacher's Evaluation system could not be a mediator.
However, the existence of the new NJ Teacher's Evaluation system has a potential to change the way that school culture affect student achievement, so it could be a moderator in your study.
The moderator or mediator relationship should be based on theory, primarily on early studies done in that context. Teacher evaluation system is primarily aimed at quality management, it may be affecting the teachers' perceived efficacy. Adding to the answers as already provided by other scholars, the ultimate decision would be based on theoretical support in favor of mediation or moderation. The following references may be helpful for futher reading:
Husbands, C. T., & Fosh, P. (1993). Students' evaluation of teaching in higher education: experiences from four European countries and some implications of the practice [1]. Assessment and evaluation in higher education, 18(2), 95-114.
Kupermintz, H. (2003). Teacher effects and teacher effectiveness: A validity investigation of the Tennessee Value Added Assessment System. Educational evaluation and policy analysis, 25(3), 287-298.
Sanders, W. L., Wright, S. P., & Horn, S. P. (1997). Teacher and classroom context effects on student achievement: Implications for teacher evaluation. Journal of personnel evaluation in education, 11(1), 57-67.
Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of personality and social psychology, 51(6), 1173.