Mathematics teacher education, mathematical habits of mind, assessment tasks, teacher reflection.
||September 03, 2018
||The Author(s) 2018. This article is published with open access at www.chitkara.edu.in/publications
As schools and teachers in the U.S. fine-tune their implementation of mathematics standards promoting college and career readiness, the number of support resources continues to expand. One resource focus experiencing significant growth involves sample items and tasks asserting alignment with the college and career ready mathematical content and practice standards. Such samples regularly identify both the content standards addressed and the mathematical habits of mind that students have the potential to engage in. Consistently absent are evaluation criteria articulating how engagement and demonstration of associated mathematical practices can be assessed, concurrent with content. The authors discuss the development of rubrics that attempt to faithfully assess the integration of mathematical content and practice standards and highlight the benefits to mathematics teachers, coaches, professional developers, and mathematics teacher educators of engaging in such reflective rubric-creating activities.
As schools and teachers in the U.S. refine and enhance implementation of college and career readiness standards (Common Core State Standards for Mathematics, Nebraska’s College and Career Ready Standards for Mathematics), the number of resources supporting enactment continues to expand in both breadth and depth. One resource focus experiencing significant growth involves sample items, tasks, and assessments proclaiming alignment with such standards. Summative assessment resources typically provide stakeholders with practice tests, open access sample assessment tasks, or ‘released’ items (Partnership for the Assessment of Readiness for College and Careers, Smarter Balanced Assessment Consortium, Minnesota Department of Education). In addition, a variety of organizational and individual entities, not to mention the plethora of mathematics textbook publishers, continue to add to the inventory of available items and tasks (Dan Meyer’s Three-Act Math Tasks, Illustrative Mathematics, Achieve the Core’s Mathematics Tasks and Assessments). Such sample tasks regularly identify both the content standards addressed and the mathematical habits of mind that students have the potential to engage in (Common Core’s Standards for Mathematical Practice, Virginia Department of Education’s Mathematical Process Goals for Students). Frequently accompanying these tasks are instructional recommendations, implementation guidelines, or evaluation criteria, such as rubrics or point systems. Unfortunately, with few exceptions (Education Development Center’s Implementing the Mathematical Practice Standards; New York City Department of Education’s WeTeachNYC Library), such resources fail to explicate how students might actually engage in the indicated mathematical processes and proficiencies or what such engagement might look like. By ‘what engagement might look like’, the authors mean “to articulate what a student would need to say or write (communicate) to establish her engagement in particular mathematical habits of mind”. Finally, such resources fail to make explicit how demonstrating specific mathematical habits of mind, or lack of such demonstration, impacts student assessment. In this report, the authors put forth and discuss the development of three rubrics that attempt to coherently assess the integration of mathematics content and mathematical habits of mind. Rubric development involved a small sample of prospective and practicing secondary school mathematics teachers (teachers of students ages 14-18 years), referred to as ‘participating teachers’. Although the rubrics themselves might appear of limited value, due to their non-generic nature (their connection to specific content), the rubrics should be considered as secondary to their development—a very cognitive process for everyone involved in their construction.
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