Performance Tasks and Rubrics for Middle School Mathematics

Meeting Rigorous Standards and Assessments

Charlotte Danielson, Elizabeth Marquez

• Publisher: Taylor & Francis
• Year: 2016
• eBook ISBN: 9781317442516
• Edition: 2
• Topic: Education
• Subtopic: Education General

Performance tasks are highly effective tools to assist you in implementing rigorous standards. But how do you create, evaluate, and use such tools? In this bestselling book, educational experts Charlotte Danielson and Elizabeth Marquez explain how to construct and apply performance tasks to gauge students' deeper understanding of mathematical concepts at the middle school level. You'll learn how to:

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• Evaluate the quality of performance tasks, whether you've written them yourself or found them online;

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• Use performance tasks for instructional decision-making and to prepare students for summative assessments;

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• Create your own performance tasks, or adapt pre-made tasks to best suit students' needs;

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• Design and use scoring rubrics to evaluate complex performance tasks;

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• Use your students' results to communicate more effectively with parents.

This must-have second edition is fully aligned to the Common Core State Standards and assessments and includes a variety of new performance tasks and rubrics, along with samples of student work. Additionally, downloadable student handout versions of all the performance tasks are available as free eResources from our website (www.routledge.com/9781138906914), so you can easily distribute them to your class.

1

Introduction

What Is Performance Assessment?

This book concerns the classroom use of performance assessment, and the evaluation of student work in response to performance tasks. It contains a collection of performance tasks in middle school mathematics, but also includes guidance for educators to design or adapt performance tasks for their own use and to be a wise consumer of performance tasks that may be available to them.

While performance assessment is essential to a well-rounded assessment plan, it should not be used exclusively. Other item types associated with traditional testing have an important role to play, particularly in assessing a large domain or evaluating student knowledge. But in assessing student understanding, in order to ascertain how well students can apply their knowledge, some type of performance assessment is essential.

In this book, performance assessment means any assessment of student learning that requires the evaluation of student writing, products, or behavior. That is, it includes all assessment with the exception of multiple choice, matching, true/false testing, or problems with a single correct answer. Classroom-based performance assessment includes all such assessment that occurs in the classroom for formative or summative purposes and is evaluated by teachers as distinct from large-scale, state-wide testing programs.

Performance assessment is fundamentally criterion-referenced rather than norm-referenced. That is, teachers who adopt performance assessment are concerned with the degree to which students can demonstrate knowledge and skill in a certain field. They know what it means to demonstrate competence; the purpose of a performance assessment is to allow students to show what they can do. The criteria for evaluating performance are important; teachers use their professional judgment in establishing such criteria and defining levels of performance. And the standards they set for student performance are typically above those expected for minimal competency; they define accomplished performance.

Norm-referenced tests are less valuable to teachers than are performance assessments. True, teachers may learn what their students can do compared to other students of the same age. However, the items on the test may or may not reflect the curriculum of a given school or district; to the extent that these are different, the information provided may not be of value to the teacher. Moreover, the results of most standardized tests are not known for some time. Even for those items included in a school’s curriculum, it does not help a teacher to know in June that a student did not know, in April, a concept that was taught the previous November. Of what possible use is that information to the teacher in June? It may not even still be true. And even if true, the information comes too late to be useful.

In addition, the only way students demonstrate progress on a norm-referenced test is in comparison to other students. Progress per se is not shown as progress. That is, a student’s standing may move from the 48th percentile to the 53rd percentile. However, the student may not have learned much but other students may have learned less! So while norm-referenced tests have their value, for example for large-scale program evaluation, they are of limited use to teachers who want to know what each of their students have learned with respect to the Common Core State Standards or any set of standards that guides their curriculum. Performance assessment, then, is criterion-referenced. It reflects the curriculum goals of a teacher, school, or district with respect to the set of standards that guides their curriculum and when used in the context of classroom teaching, it informs instructional decisions.

The remaining sections of this chapter describe the different uses and types of performance assessment.

The Uses of Classroom-Based Performance Assessment

Assessment of student learning in the classroom is done for many purposes and can serve many ends. When teachers design or choose their assessment strategies, it is helpful to determine, at the outset, which of the many possible uses they have in mind. Some possibilities are described here.

Instructional Decision-Making

Many teachers discover, after they have taught a concept, that many students didn’t “get it”; that, while they may have had looks of understanding on their faces, and may have participated in the instructional activities, they are unable to demonstrate the knowledge or understanding on their own.

This is important information for teachers to have, as they determine what to do next with a class, or even with a few students. They may decide that they must re-teach the concept, or create a different type of instructional activity. Alternatively, if only a few students lack understanding, a teacher might decide to work with them separately, or to design an activity that can be used for peer tutoring.

Whatever course of action a teacher decides upon, however, it is decided on the basis of information regarding student understanding. That implies that the assessment strategies used will reveal student understanding, or lack of it. When used for instructional decision-making, it is the teacher alone who uses the information to determine whether the instructional activities achieved their intended purpose.

Feedback to Students

Performance assessment, like any assessment, may also be used to provide feedback to students regarding their progress. Depending on how it is constructed, a performance task can let students know in which dimensions of performance they excel, and in which they need to devote additional energy. Such feedback is, by its nature, individualized; the feedback provided to one student will be very different from that provided to another if their performances are different. It is efficient for the teacher, however, since the important dimensions of performance have been identified beforehand.

Communication with Families

Actual student performance on well-designed tasks can provide families with authentic evidence of their child’s level of functioning. Many parents are skeptical of tests that they don’t understand, and are not sure of the meaning of numbers, percentiles and scaled scores. But student answers to an open-ended question or to other performance assessments are easy to understand and can serve to demonstrate to families the level of understanding of their child. These samples of student work are highly beneficial for open house or parent conferences, serving to educate parents and to validate the judgments of the teacher.

Such indication of student performance is of particular importance if a teacher is concerned about a child and wants to persuade a parent/guardian that action is needed. It is impossible for parents, when confronted with the work of their own child, to question the commitment of the teacher in meeting that child’s needs. Whether the work is exemplary and the teacher is recommending a more advanced placement, or the work reveals little understanding, the actual samples of student performance are invaluable to a teacher in making a case for action.

Summative Evaluation of Student Learning

In addition to having formative purposes, a performance assessment may be used to evaluate student learning and may contribute to decisions regarding grades. The issue of grading is complex and will be addressed more fully on page 17 of this book, but the results from performance tasks, like any assessment, can serve to substantiate a teacher’s judgment in assigning a grade.

Different Types of Classroom-Based Assessment

Assessment takes many forms, depending on the types of instructional goals being assessed, and the use to which the assessment will be put. The major types are presented in table form (Table 1.1), and are described in the following sections.

Summative Assessments

Summative assessments have always been (and will continue to be) an important method for ascertaining what students know and can do.

When teachers decide to move to more authentic aspects of performance in order to evaluate student learning, they do not necessarily abandon traditional types of summative assessments. On the contrary, they may use traditional tests or item types for that which they are well suited (for example, for sampling knowledge), recognizing their substantial strengths as a methodology. However, when teachers want to measure the depth, rigor, and complexity of comprehension they may use summative assessments which include performance tasks or technology-enhanced items or extended constructed-response items. Of course, summative as well as formative assessments may include both traditional and non-traditional item types.

Summative assessments are generally given to students under what we call “testing conditions,” that is, conditions that ensure that we are actually getting the authentic work of individuals and that the experience is the same for all students. Testing conditions are:

Limited time. Generally speaking, time for a test is strictly limited. Students must complete the test within a certain amount of time (frequently a class period, but sometimes more or less than that). This provision ensures that some students don’t devote far greater time to the assignments than others.

Limited (or no) resources. Although there are exceptions to this rule (such as open-book tests and the use of calculators), students taking a test are usually not permitted to consult materials as they work. An insistence on no additional resources rules out, of course, trips to the library while taking a test. This provision ensures that what students produce on the test reflects only their own understanding.

No talking with peers or looking at others’ papers. When taking a test, it is important that students produce their own work. Unless teachers adhere to this condition, they are never sure whether what they receive from an individual student reflects that student’s understanding, or that of his or her friends.

Table 1.1 Forms of Classroom-Based Assessment

Note: *For the purposes of this book, extended constructed response and all non-traditional assessment is considered performance assessment.

In addition, summative assessments are traditionally of two basic types: selected response and constructed response.

Selected response. In a selected-response test, students select the best answer from those given. True/false and matching tests may also be included in this category. Short-answer items are technically constructed-response items (since the student supplies the answer), but since there is generally a single right answer, such items are a special case, and share more characteristics in their scoring with multipl...

Table of contents

• Cover Page
• Performance Tasks and Rubrics for Middle School Mathematics
• Math Performance Tasks
• Title
• Copyright
• Dedication
• Contents
• eResources
• Meet the Authors
• Foreword
• Preface
• Acknowledgments
• 1 Introduction: What Is Performance Assessment?
• 2 Why Use Performance Assessment?
• 3 Making an Evaluation Plan
• 4 Understanding Quality Performance Tasks
• 5 Creating and Adapting Performance Tasks
• 6 Using Rubrics to Evaluate Complex Performance
• 7 Creating and Adapting Rubrics
• 8 Middle School Mathematics Performance Tasks