Learning About Assessment, Learning Through Assessment (1998) / Chapter Skim
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II. Learning Challenges
II. Learning Challenges
Pages 5-22
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From page 5... ...
1 Figure 1. The Assessment Process /~sin~ `~_ evidence _J _ ~ `' planning the ~ ~ evidence J ~gathering: ~ evidenced Adapted with permission from Assessment Standards for School Mathematics, NCTM, 1995, p.
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The assessment process has a simple message about teaching and learning: that a teacher's classroom actions should be based on a thoughtful analysis of student understanding. Since the introduction of the first set of standards in mathematics in 1989, it has become increasingly evident that, in order to help teachers transform their practice in accordance with standards, professional development must reach levels of need much deeper than the need for information.
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These multiple purposes necessitate more complexity in the design and facilitation of the teachers' learning opportunities, so that they can exercise the judgment and develop the inferencing skills necessary to follow the cycle of the assessment process, from planning to gathering evidence to interpreting evidence to using evidence, and back to further planning. In many assessment work groups, teachers adopt, adapt, and create tasks.
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3 Leadership for Urban Mathematics Reform Project, Education Development Center, 1994-1997, supported as a Teacher Enhancement project by the National Science Foundation, ESI-9353449 8 Driscoll and Bryant
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1 Figure 2. One solution to the Postage Stamp problem ok.'` _ O ~i~ l 1@,1 7 32 Zip 37 3143~BG7 Z I 3 2' Voel ~' 4G Sl As I)
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Opportunities to discuss beauty also arise from surprising mathematical results. Groups working on this problem are usually surprised and excited when their evidence leads them to infer that the following statement is true: "For relatively prime stamp denominations p and q, the largest postage amount that carrot be made with combinations of p-stamps and q-stamps is (p - l)
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An overarching purpose of teacher assessment groups is to help teachers become more knowledgeable about how to select one form of assessment over another. In this case, if a group of teachers is keen to see how well students understand the concepts of ratio and proportion, then they need to consider the following question: Would the problem-solving demands of the second taske.g., requiring students to make plans and organizing information-provide less valuable evidence of student learning of the Learning About Assessment, Learning Through Assessment 11
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, a team of teachers decided to experiment with relevance of context as a dimension in tasks, on the supposition that students are more likely to engage in relevant tasks. Their experiment 4Classroom Assessment in Mathematics Network Project, Education Development Center, 1991-1993, supported by the Department of Education as a National Eisenhower Project, R168C10098-92.
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You brave been offered a job waiting on tables at these Our deferent restaur~uts. A recent study shows secondband smoke Bow restaurant patrons dramatically increases the risk of lung cancer in restaurant workers.
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For example, teachers in one projects have used versions of the so-called Consecutive Sums task in a range of middle-grades and 5 Leadership for Urban Mathematics Reform Project, Education Development Center, 1994-1997, supported as a Teacher Enhancement project by the National Science Foundation, ESI-9353449. 14 Driscoll arid Bryant
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Often, students offer generalizations sometimes drawing from apparently thoughtful work with little explanation or convincing argument. (See, e.g., Figure 5.)
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In various groups of teachers, we have found it advantageous to build a discussion around a question: Though it doesn't look like the "algebraic" response you may have used in doing the task, in what ways is this response still reflective of algebraic thinking? The learning challenges related to judging the quality of student responses suggest the critical importance of two points of emphasis in discussion: purpose and criteria.
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In professional-development settings, teachers can hone their skills in making inferences about student thinking, strategize on how to tale with students about standards and their progress toward standards, and discuss how to design instruction to move students' understanding forward. In so doing, they can increase the likelihood that assessment will be used to improve teaching and learning and lessen the chances of individual Figure 7.
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From page 18... ...
This goal, often referred to as "inter-rater reliability" when the assessment's purpose is evaluation of student achievement, can be accomplished by structuring teacher discussions so that there are frequent opportunities to share, compare, and revise judgments rendered. judgment about consequent actions As mentioned earlier, assessments can be carried out for different purposes.
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From page 19... ...
This student started to use a helpful mathematical procedure but didn't carry it through. Even though this student has an understanding of the concept of 6, and verbally stated this while using the models provided, The did not represent this in the diagram and was unable to get close to a solution.
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From page 20... ...
7t~o~t~t 5am~ ~,tsc~ Suez, ~ ~ =~ /(~_ I+315t ~ ~ ~ Id. Reprinted with permission from Assessment Standards for School Mathematics, NCTM, 1995, p.
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Discussions about such items can motivate teachers' use of diagnostic questions to uncover patterns of student thinking. For example, the Third National Assessment of Educational Progress presented the following multiple choice item (NAEP, 19831: An army bus holds 36 soldiers.
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For one, teachers f ind that assessment and instruction can blend together as mutually supportive endeavors. Second, in embracing the various challenges to judgment around the topic of assessment, teacher groups not only build assessment skills; they can integrate the assessment process into other areas of their professional development, as well.
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