GRADE 3 AND GRADE 6 MATHEMATICS: A COMPARISON OF ONTARIO’S 2005 CURRICULUM POLICY DOCUMENT, CURRICULUM SUPPORT MATERIALS, AND LARGE-SCALE ASSESSMENT TO COMPARABLE ELEMENTS IN FLORIDA
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A high-quality, challenging, and accessible mathematics education provides students in elementary or middle school with a foundation for future understanding of mathematics (NCTM, 2007). As such, influential curriculum documents have changed over the years to emphasize the importance of mathematics−more emphasis has been placed on problem-solving, reasoning, and communicating (specifically: proposing and defending mathematical ideas and conjectures and responding thoughtfully to mathematical ideas) than ever before (Goos, 2004, p. 260). Research has also documented the importance of alignment among curriculum, textbooks, and large-scale assessments. This study documented curriculum alignment among Ontario’s and Florida’s mathematics curriculum, curriculum support materials for Grades 3 and 6, and large-scale assessment questions for Grades 3 and 6; the latter two focussing specifically on the Measurement strand and the Geometry and Spatial Sense strand. Curriculum alignment was then compared between the two jurisdictions. The documents were examined and analyzed to compare the language used (action verbs) in the abovementioned documents with the six hierarchical thinking levels in Benjamin Bloom’s taxonomy in the cognitive domain (under the headings of: knowledge, comprehension, application, analysis, synthesis, and evaluation) using Bloom-based assessment blueprints. The findings from this analysis using the weighted Bloom-based assessment blueprints showed that: (a) a high cognitive demand was generated by the action verbs included in Ontario’s Grades 3 and 6 mathematics curriculum expectations; (b) a low cognitive demand, was generated by the actions verbs included in Florida’s Grade 3 and 6 mathematics curriculum standards, benchmarks, and grade level expectations; and, (c) a low cognitive demand was generated by the action verbs included in the questions in Ontario’s and Florida’s curriculum support materials and large-scale assessments. Therefore, there are gaps in curriculum alignment for both jurisdictions which could have a significant impact on teacher practice and student achievement. Four main ideas emerged through this document analysis, including the value of exploring a curriculum in depth, the importance of using an educational taxonomy to determine the cognitive demand generated by the action verbs used in documents, and the significance of curriculum alignment. The significance and implications of this study suggest that the research conducted for this project has made an initial contribution to growing work on how actions verbs imply different levels of thinking skills needed to meet an objective, complete a task or question, solve a problem, and/or follow a direction.