Toolkit98
Can There Really Be Assessments That Promote Learning?
Mention the word "assessment" to most students and teachers and they will immediately respond with the concept of "tests"—the kind used to monitor and track student performance. TESTS—the type given to produce grades, select students for special programs, and report to the Board of Education. Wouldn't it be exciting, however, if the word "assessment" was associated not with traditional testing, but with a different process—one that not only provides an opportunity for teachers and students to thoughtfully examine what has been learned, how we know it has been learned, and what needs to happen next to reach a new level of learning, but also is an episode of learning in and of itself?
The following performance assessment in mathematics is an example of such an assessment. It illustrates how assessment and instruction can be integrated as a "tool for learning."
Performance Assessment: Mathematics
Performance assessment is "assessment based on observation and judgment" (Stiggins, 1994); we observe a behavior or examine a work product and judge its quality. This is frequently done in the classroom by teachers, and is a common occurrence in daily life as well—just think of the Olympics, job performance reviews, and the driver's test. These kinds of judgments can be very subjective. The goal is to make these essentially subjective judgments as objective as possible. This is done through the development of performance criteria that clearly define characteristics and indicators of quality student work.
The criteria developed to judge the quality of student work are also critical to making performance assessment a powerful tool for learning because the criteria clearly communicate what is valued in the work—what it takes to be successful. These criteria for quality are teachable to students, allowing them access to the "secrets" of success. (In fact, students can be full partners in the development of the criteria for success.)
Thoughtfully written and teachable criteria support standards-based teaching. When students and teachers begin to share the same vision of success, they quickly develop a vocabulary for discussing this vision. All are working toward the same clear and identifiable standard. This improves student achievement.
| & Reference Box
Richard Stiggins, Student Centered Classroom Assessment, 2nd Ed., 1997, Columbus, OH: Macmillan. |
To see how this works, we'll use a mathematics assessment example. Let's begin with analyzing samples of student work. Look at the two student solutions in Figure 2.4 and take a moment to jot down your reactions to them. What did you notice? Are there any obvious strengths? Weaknesses? What features did you respond to? Which solution did you think was the best? Why?
| Figure 2.4
Mathematics Applications—Grade 4 |
Most teachers and students examining solutions such as these tend to like and dislike the same sorts of things. Typical comments for the first solution include: vague, may not have understood the problem fully, and had to read a lot into the solution in order to understand what the student did. Typical comments for the second solution include: understood the problem fully, clear solution, communicated well in pictures and words, logical, detailed, organized, insightful, correct answer, explained thinking, used all relevant information, distinguished relevant information from irrelevant information, used data accurately, correct process, on topic, creative, focused, showed process, used pictures correctly, good explanation, and went beyond the minimum. How did your list of comments compare to these?
| Û Related Toolkit98 Activities and Chapters
Appendix A—Sampler contains several other rubrics/criteria for judging solutions to math problems. Compare them. Do the same sets of features tend to recur? Activities 2.1—Sorting Student Work, 2.2—How Can We Know They're Learning? involve sorting student work, generating lists of desirable features, and beginning the process of developing performance criteria. |
Comparing solutions to mathematics problems helps us all sort through the complexity of features that make solutions successful. Such exercises can help teachers and students explore what makes a solution work. In fact, the same sets of features recur on brainstormed lists from teachers across the country. They form the basis for performance criteria for mathematics applications problems in many places. For example, Sample A.18—Mathematics Problem Solving (in the Sampler in Appendix A) shows a "four-trait" model for assessing such problems. There are four traits because teachers in Oregon felt that their list of comments tended to fall into four major areas: conceptual understanding, procedural knowledge, problem-solving strategies, and communication. Look at the features other teachers tend to place under each trait (Figure 2.5). Do the comments you made on the work in Figure 2.4 fit in the same way?
The four-trait model for analyzing mathematics applications is, thus, basically an attempt to systematically write down what we, as educators, already value so we can be consistent in our vision of success across students, across assignments, and across time. And, equally importantly, so students can share in the vision of success and not have it constantly shifting in unknown ways between teachers or assignments.
| Figure 2.5
What Teachers of Mathematics Value |
| Conceptual Understanding
Distinguished irrelevant information
|
Procedural Knowledge
Used pictures correctly
|
| Problem-Solving Strategies
Logical
|
Communication
Detailed
|
Value of Criteria to Teachers. Have you ever been nervous grading students' open-ended mathematics problems? Those who have rated or scored mathematics during a direct mathematics assessment using criteria such as the four traits unanimously agree that the very process of assessing teaches a great deal about what makes mathematics solutions successful. Raters have to internalize a set of criteria so thoroughly that they can be consistent both with themselves over time and with other raters. During the process of scoring hundreds of papers, raters get to see lots of examples of what good and poor mathematics actually looks like and to analyze it systematically to determine why it is good or poor. These teachers return to the classroom much more confident in commenting on student work and helping students understand what it takes to produce sound, efficient, and understandable solutions to mathematics problems.
Great! As teachers become more consistent in their analysis of student math work, they gain the confidence to share their insights with students. If assessing brings about a shared vocabulary and a deeper sense of what it takes to solve mathematics problems well, then wouldn't students also benefit from the same process? The answer is YES.
Value of Criteria to Students. Students can also learn to analyze sample work and develop a systematic vocabulary for describing quality so they can develop their own sense of what it means to present a good solution. Consider the following quotes from the area of writing assessment and think of how they might also apply to mathematics problem solving, science process skills, group collaboration skills, and other complex goals we have for students.
I want (students) to see evaluation in its best sense—a source to inform teaching and learning. To that end we develop a vocabulary for commenting on the admirable and problematic aspects of writing....The more we examine samples, the richer and more helpful this language of evaluation becomes. (Erikson, 1992)
Winning points may be the final goal of classroom work as it is of the sports endeavor, but the grade, like the final score of the game, never taught anyone how to win again, or why they lost. For the truly successful contenders, playing the game is always about learning the game...however often it seems to be about scoring more wins than losses. (Lucas, 1992)
| & Reference Box
G. Hillocks, Jr., 1986. Research on Written Composition. National Council of Teachers of English, (800) 369-6283. C. Lucas, 1992. "Introduction: Writing Portfolios—Changes and Challenges," in K. Yancey (Ed.). Portfolios in the Writing Classroom, pp. 1-11. National Council of Teachers of Mathematics, (703) 620-9840. M. Erikson, 1992. "Developing Student Confidence to Evaluate Writing," in Quarterly of the National Writing Project & The Center for the Study of Writing and Literacy, Vol.14, pp. 7-9. |
Scales, criteria, and specific questions which students apply to their own or others' writing also have a powerful effect on enhancing quality. Through using the criteria systematically, students appear to internalize them and bring them to bear in generating new material even when they do not have the criteria in front of them. (Hillocks, 1986)
The goal of assessment should not be only to earn grades. The goal of assessment should be to help students know "how to win again." Clear performance criteria have this effect.
This is instructional assessment. Students learn something in the process of assessing and being assessed. They learn about mathematics problem solving and how to apply this knowledge to their own and others' works. They learn what effective mathematics solutions look like and what to do to make their own mathematics skills stronger.
Beyond Mathematics Assessment
The point here is that good performance criteria can be more than just a tool for teachers (or districts or states) to monitor student ability to write, problem solve, be good collaborators, or be critical thinkers. They also help both teachers and students conceptualize and define standards, especially in hard-to-define areas such as critical thinking, problem solving, collaborative learning, and communication. They provide a vocabulary for discussing features of work or behavior that have, in the past, been subtle and ill-defined.
Good performance criteria help teachers answer such questions as: What is expected? What are our standards? What does good performance look like? What do I want to accomplish? What kind of feedback do I give to improve student work next time? They help students to answer similar questions: What is expected? What does good performance look like? How will I know when I'm successful? Why did I win? How can I win again?
There are three essential features to make it work: (1) having a clear picture in our own heads of the criteria for success, (2) making sure the criteria are right—they really do describe the important features of quality, and (3) letting students "in on it."
In many discussions of integrating assessment and instruction, criteria are left out. There is a lot of talk about the tasks that should be given to students and how one must watch performance on these tasks to monitor where students are. But the question is: "What, exactly, do you watch for?" to determine progress, know when students are ready to move on to the next topic, or determine when mastery has occurred? Criteria tell us what to look for. Overt and public criteria—arrived at through discussion and collaborative learning and accessible to teachers, students, and parents—bring judgmental assessment from the realm of individualistic impressions to the realm of systematic and generalizable documentation of learning. They also result in assessment that promotes learning.
How does one know when criteria are clear enough?
These are the types of decisions that have to be made when developing criteria. The criteria have to describe what everyone really means by quality or they won’t help anybody. If a teacher or student believes that an essential component of quality has been left out or that an unimportant component of quality is prominently in the criteria, there will be no buy-in. If criteria leave out an important feature of quality, like voice in writing, teachers might not teach voice. What they see is what you’ll get, so criteria have to embody the real indicators of a sound performance and leave out that which is not important.
How does one know when criteria are the right ones?
| Û Related Toolkit98 Activities and Chapters
Not all performance criteria are created equally—they may not all be able to have the instructional effect described in this section. There may be certain design features that make them more or less useful as instructional tools. These features are outlined in Chapter 2 and Activities 3.3—Performance Criteria—Keys to Success and 1.9—Going to School. |
By encouraging students to engage in self- and peer evaluation teachers empower students to take control of their own learning. When students help determine the criteria for assessment they can make reasonable decisions about the quality of their own work. By engaging in self-assessments, students learn they are ultimately responsible for their own learning. It is in this area that portfolios are so powerful. (Tierney, et al. 1991, p.59)
| & Reference Box
J. Penick, J., 1989, "Issues-Based Education—A Need and Rationale," in Education and Urban Society, 22(1), pp. 3-8. Robert Tierney, M. Carter, & L. Desai, 1991, Portfolio Assessment in the Reading-Writing Classroom, Christopher Gordon, Publishers, Inc., (617) 762-5577. |
To be successful, students must learn how to evaluate rather than how to be evaluated....Evaluation is routine, something to be done at every step of the way as they examine decisions, observations, data, ideas and outcomes....[When] evaluation is a key process, and one over which students have considerable control, they are truly critical thinkers. (Penick, 1989)
| Û Related Toolkit98 Activities and Chapters
Appendix A—Sampler contains many other examples of performance criteria and rubrics. Activities 2.1—Sorting Student Work, 2.2—How Can We Know They're Learning? involve sorting student work, generating lists of desirable features, and beginning the process of developing performance criteria. Activity 2.5—How Knowledge of Performance Criteria Affect Performance illustrates the power of rubrics in assisting students to understand the requirements of a task. |
Relationship Between Classroom Performance Assessment and Large-Scale Assessment
So far, it may seem that we are only discussing classroom performance assessment. But, in reality, the whole enterprise is much more powerful if large-scale and classroom assessment are considered together as a unit. Consider the following points:
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