M any years ago, an interesting problem that had been implemented in a primary-grade classroom sparked a conversation among the three authors of this article. The problem was a classic both-addends-unknown story problem, one of twelve distinct types of Both-Addends-Unknown word problems that kindergarten, first-grade, and second-grade students are expected to solve, according to the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) Operations and Algebra domain (see fig. 1). Student thinking processes and the relative problem difficulty of the other eleven types
The successful development and implementation of this assessment involved many experts in mathematics education and many more students. Some of the key people involved with the development of the test are listed here along with their roles in the endeavor. Robert Schoen designed the content and format of the test, coordinated the feasibility study, created the scoring criteria, interpreted the results, and coordinated the writing of this report. Daniel Anderson performed the data analysis for the item calibration, exploratory factor analysis, item-response theorybased models, and vertical linking between grade levels, and he also contributed to writing the report. Claire Riddell assisted with the development and production of the test and the scoring criteria. Charity Bauduin reviewed the alignment of items with the Mathematics Florida Standards, managed the reportwriting process, and assisted with editing the style and format of the report. Amanda Tazaz coordinated the dissemination and collection of the tests and corresponding consent forms. She also provided editing and conceptual feedback for the report. Kristy Farina designed and managed the data-entry system, trained data-entry personnel on the system, verified the accuracy of the data, and assisted with description of the data-entry process and sample descriptives for the present report. Alexandra Utecht, Shelby McCrackin, Senai Tazaz, and Claire Riddell served as data-entry personnel. Claire Riddell, Mark McClure, and Monica Hurdal served as reviewers of the test items, response options, and scoring. Xiaotong Yang, Ahmet Guven, and Lanrong Li provided assistance with calculating the ICCs and R 2 estimates based on the field-test data. Anne Thistle provided valuable assistance with copy editing. We would like to acknowledge the important contributions made by the reviewers of the early drafts of the test and express our gratitude for their contributions of expertise. These reviewers include Charity
Students will engage in a both-addends-unknown problem to explore the different ways that seven mice can be arranged in two cages. Students will work with combinations of seven and have the opportunity to justify and reason about the total number of combinations possible. Students will also make generalizations about the relationship between the number of mice and the total number of combinations possible. Each month, elementary school teachers are presented with a problem along with suggested instructional notes; asked to use the problem in their own classrooms; and encouraged to report solutions, strategies, reflections, and misconceptions to the journal audience.
This article introduces a task designed around SMP 7: Look for and make use of structure, and it encourages students to explore structure through multiple representations. Each month, elementary school teachers are presented with a problem along with suggested instructional notes and asked to use the problem in their own classrooms and report solutions, strategies, reflections, and misconceptions to the journal audience.
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