
A mathematical function for measuring the congruence among the strand representation in the enacted curriculum, state assessments, and district pacing guides is presented. This method allows the enacted curriculum to be incorporated in alignment studies even when the analysis of student work is limited to short‐term collections.
Keywords: Manhattan distance, congruence, enacted curriculum, pacing calendar, pacing guide, Walberg productivity model, breadth of coverage, curriculum alignment, standards alignment
Read the PDFA mathematical algorithm is presented that relates student achievement with directly observable, quantifiable teacher and student behaviors, producing a modified form of the Walberg model. The measurable factors that comprise the quality of instruction are expanded in a linear basis of research-based teaching components and techniques. The quantity of instruction, related to the timing of classroom processes, is also included in the model. The role such a model can play in education reform and potential research is also discussed, as well as its potential use in classroom observation rubrics programmed on mobile devices.
To teach the rigorous skills and knowledge students need to succeed in future collegeentry courses and workforce training programs, education stakeholders have increasingly called for more rigorous curricula, instruction, and assessments. Identifying the critical attributes of rigor and measuring its appearance in curricular materials is therefore fundamental to progress in this area. By superposing two widely accepted models for describing rigor — Bloom's Taxonomy of Educational Objectives and Webb’s Depth-of- Knowledge (DOK) model — this article defines cognitive rigor (CR) and introduces the CR matrix for analyzing instruction and enhancing teacher lesson planning. Two large-scale collections of student work samples analyzed using the CR matrix are presented, illustrating the preponderance of curricular items aligned to each cell in the matrix. Educators should use the cognitive rigor matrix to align the content in their curricular materials to the instructional techniques used in classroom delivery.
Key words: Bloom's Taxonomy, Webb's depth of knowledge, cognitive rigor, critical thinking, enacted curriculum, delivered curriculum
This article discusses research in classroom time usage and the benefits and weaknesses of prior research in this area. The article addresses in particular how to precisely measure the use of time in classrooms and how to address the issue of partial engagement, in which only a portion of the class is academically engaged. The article defines three engagement indices that account for the range of attentiveness found in school children. A classroom observation instrument introduced in this article provides a means for education researchers and school staff to classroom timing measurements and display the results visually. Education researchers can use the tools provided in this article to measure the impact of various reform efforts on classroom effectiveness; school administrators can use these tools to monitor the efficiency of their teachers use of classroom time. Contains 7 references and 5 figures.
Key words: classroom observation, time on task, academic engagement time, allocated time, time on task
Depth of knowledge is a common measure of rigor used extensively at the state level to align assessments with state content standards. However, the use of depth of knowledge at the classroom level is just beginning. In this article, we establish a link between depth of knowledge and the questioning strategies teachers should consider employing during lessons. The result is a systematic strategy for employing peer?shares and group based activities based on the depth?of?knowledge level of the questions. Should use the strategies presented in this article to develop lesson plans that provide enhanced opportunities for students to engage in critical thinking. (Contains 2 tables and 30 references.)
Key words: depth of knowledge, questioning strategies, rigor, cognitive rigor