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102

10 Rubrics and Formative Assessment: Feedback and Student Self-Assessment

Formative assessment is an active and intentional learning process that partners the teacher and students to continuously and systematically gather evidence of learning with the express goal of improving student achievement (Moss & Brookhart, 2009, p. 6). Formative assessment is about forming learning—that is, it is assessment that gives information that moves students forward. If no further learning occurred, then whatever the intention, an assessment was not formative.

Chapter 9 described how to use rubrics to help clarify learning targets for students—the foundational strategy of formative assessment. This chapter covers the use of rubrics for giving feedback that feeds forward, for supporting student self‑assessment and goal setting, and for helping

students ask effective questions about their work.

How to use rubrics for teacher and peer feedback

Because rubrics enumerate the criteria for learning and describe performance along a continuum for each one, they are a good framework for feedback. This section

Self-ReflectIon

How do you use rubrics for feedback and student

self-assessment in your classroom?

Brookhart, Susan M.. How to Create and Use Rubrics for Formative Assessment and Grading, Association for Supervision & Curriculum Development, 2013. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/amridge/detail.action?docID=1123215. Created from amridge on 2022-02-22 04:53:35.

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Feedback and Student Self-Assessment | 103

presents several strategies for using rubrics as the basis for teacher and peer feedback. Use one of them or design similar strategies that work in your context.

Teacher feedback on rubrics-based feedback sheets

If you are using well‑written, general, analytic rubrics (as I recommend for most purposes) for sharing with students and for feedback, you can photocopy the rubrics themselves, leaving space for comments. Provide feedback by circling the performance level for each criterion that best matches the student’s work in its current form. Then you will not have to rewrite the general description, which is already circled. Instead, use what time you have available for written feedback to write something specific to the student’s work.

For example, if the class is working on the ideas in their writing, the teacher may give feedback on writing using the Ideas rubric in the 6+1 Trait Writing rubrics (see Appendix A). If she has circled “Support for topic is incidental or confusing, not focused,” the specific comments might tell the student what she found confusing or why the supporting details did not seem, in fact, to support the topic. This combination of general feedback from the rubric and specific feedback in writing will be enough for many students to see the way forward and improve their work in revision. For a few students, if conferencing is needed—for example, if the teacher wants to ask a student about the logic of including some details or check for understanding of story details that seemed confusing—much of the preliminary information is already present in the circled portions of the general rubrics and in the specific written feedback.

Yellow and blue make green

Similar to the “highlighters or colored pencils” method presented in Chapter 9 for helping students understand the learning target and criteria they are aiming for, you can also use highlighters for teacher feedback on student work and student self‑assess‑ ment. Ask students to use the highlighters as before, highlighting a statement from the description of performance in the rubric and highlighting where they identify this quality, but this time in their own work instead of in sample work. They can then assess whether they are satisfied with the evidence they have highlighted or want to change, augment, or revise it.

Two‑color highlighting (Chappuis, 2009) can be used to compare teacher and self‑assessment perspectives on the same work. Students use yellow highlighters, and

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104 | How to Create and Use Rubrics

teachers use blue highlighters. Where there is agreement on what constitutes evidence for performance as described in the rubric, the resulting highlights will be green.

This is not just a coloring‑book exercise, however. Important information comes with the comparison. If most of the highlighted area is green, both the student and the teacher are interpreting the work in the same way and more or less agreeing on its quality. If most of the highlighted area is yellow, the student is seeing evidence that the teacher is not. It may be that the student is not clear on the meaning of the criterion, or the student may be overvaluing the work. If most of the highlighted area is blue, the teacher is seeing evidence that the student is not. The student may be not clear on the meaning of the criterion or undervaluing the work.

Any place where teacher and student perspectives vary on the worth of the stu‑ dent’s work relative to criteria can be fertile ground for written feedback from the teacher, student questioning, or conferencing. The feedback, questions, or conferences should address more than just understanding the highlighting or the description of current work. What should come next? Provide feedback on what the student can do to improve the work.

Paired-peer feedback

Peers can use rubrics to give each other feedback. The rubrics provide structure for peer discussions, making it easier for the students to focus on the criteria rather than personal reactions to the work. The rubrics also aid dialogue. As the students use the language of the rubrics to discuss each other’s work, they are developing their own con‑ ceptions of the meaning of the criteria while they are giving information to their peers.

The simplest form of peer feedback involves students working in pairs. The teacher should assign peers that are well matched in terms of interest, ability, or compatibility, depending on the particular assignment.

Peer feedback works best in a classroom where constructive criticism is viewed as an important part of learning. In a classroom characterized by a grading‑focused or eval‑ uative culture (“Whad‑ja‑get?”), peer feedback may not work well; students may hesitate to criticize their peers so as not to imply there is anything “wrong.” Try peer feedback only when you are sure that your students value opportunities to learn. If you try peer feedback and it doesn’t work very well, even after careful preparation, be prepared to ask yourself whether your students are telling you they are more focused on getting a good grade than improving their work.

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Assuming that you have a learning‑focused classroom culture, you still need to prepare students for peer feedback. Make sure that the students understand the rubrics they will be using and that they can apply them to anonymous work samples accurately. Make sure the students understand the assignments on which they will be using the rubrics for the peer feedback. Set a few important ground rules and have students explain, and even role‑play, what they mean. Use rules that make sense for your grade level, students, and content area. Here are examples of some common peer‑feedback ground rules:

When You Are Giving Peer Feedback 1. Read or view your peer’s work carefully. Talk about the work, not the

person who did the work. 2. Use terms from the rubrics to explain and describe what you see in

the work. 3. Give your own suggestions and ideas, and explain why you think these

suggestions would help improve the work. 4. Listen to your peer’s comments and questions.

When You Are Receiving Peer Feedback 1. Listen to your peer’s comments. Take time to think about them before

you respond. 2. Compare your peer’s comments to the rubrics, and decide what com‑

ments you will use in your revisions. 3. Thank your peer for the feedback.

Finally, peer feedback gets better with practice. When you use paired‑peer feedback, observe the pairs and give them feedback on their feedback, as it were. Look for, and comment on, how students use the rubrics, how clearly they describe the work, how use‑ ful their suggestions for improvement are, how supportive they are, and so on. Just as for any skill, giving and receiving peer feedback can (and should) be taught and learned.

How to use rubrics for student self-assessment and goal setting

Because rubrics encode the qualities of good work that students are shooting for, they are the appropriate reference point for students’ monitoring of their own work.

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106 | How to Create and Use Rubrics

This section presents some examples of how that might be done, and I encourage you to devise others that fit the students, content, and grade level you teach.

Strategic goal setting revisited

In Chapter 9 we talked about students using rubrics to plan a separate strategy for successful performance on each criterion and recording their strategies on their copies of the rubric. When work on the activity or assignment begins, have students use their rubrics, annotated with their personal strategies, to monitor and regulate their work. They can use any number of methods for this. Here are a couple of them.

Quick-check. Each time students work on their assignments or projects, set aside one minute at the end of work time. For each strategy students have identified, have them check the following:

• Did I do this today? • Did it help me?

For example, consider a student in a writing class that was using the 6+1 Trait Writing rubrics. One student’s strategy for improving his performance (and learning) under the Word Choice criterion was “I will check a thesaurus any time a word isn’t as powerful, precise, or engaging as I would like.” Thus the student would ask himself, “Did I use a thesaurus in my writing today? Did it help me choose more powerful, precise, or engag‑ ing words?” Students can make their own charts to record these checks, or they can make a mark next to where they have written their strategies on their rubrics.

Journaling. In classes where regular journaling is part of student self‑reflection, students can record their strategies and their reflections upon the use of those strategies as part of their regular self‑reflection. Here the questions are similar—Did I actually use the strategy I planned to and did it help me improve my work?—but there is room for reflecting on what specifically the strategy helped (or did not help) the student do and why that might be the case. Teachers may or may not read these reflections. The intent is for students to exercise metacognition, to think about their thinking.

Think-pair-don’t share. Give students five minutes at the end of a work session to work in pairs. Each partner will describe the strategies that were planned, whether the strategies were used, to what degree the strategies helped, and why this might be so. This activity is a sort of debriefing of the work session, strategy use, and perceptions of learning. Similar to the conventional think‑pair‑share activity, students work with partners for this self‑reflection session. Unlike a conventional think‑pair‑share activity,

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Feedback and Student Self-Assessment | 107

however, students do not share the results of their paired conversations with the whole class. The teacher may speak with one or more of the pairs as they are reflecting, to help them focus, as needed.

Charting progress

Charting progress means two different things. Students think of their progress toward completing individual assignments or projects, and they think of progress more broadly as learning. It is a good idea to have students chart at least the latter (learning progress) and sometimes the former.

Charting progress on an individual assignment, with rubrics. Give students the rubrics. Midway through the work, ask them to mark the rubrics at the level where they are for each criterion. Students can place a vertical line or a large dot at the appro‑ priate level on each criterion. This can be done individually or in pairs. When the assign‑ ment or project is finished but before students turn it in, ask them to self‑assess their finished product with the rubrics. Then have them draw an arrow from the first dot or line to the second, right on the rubrics, to make a graphic illustration of their progress.

Charting longer-term learning progress. General rubrics that are used across tasks can be used for longer‑term charting of progress during a report period, a semes‑ ter, or even a year. Depending on the purpose, students can use general rubrics for foundational skills (Chapter 4) or standards‑based grading rubrics (Chapter 6) to keep track of their learning of those skills or standards. Have students construct a histogram with time on the horizontal axis and performance levels on the vertical axis.

Figure 10.1 gives an example of one student tracking her progress on the criterion “Writing an Explanation” in the Math Problem‑Solving Rubric in Figure 4.1. Additional charts would be needed for the other criteria in the rubric. Each performance is listed, and then the student colors the bars in the graph to the height corresponding to her developing ability to show mathematical knowledge.

I want to make several very important points right away, because such a chart is prone to misinterpretation in classrooms that are grade oriented rather than learning oriented. First, this chart is for formative assessment and represents the student’s practice and learning. It does not represent final outcomes, except perhaps that the last entry recorded shows the answer to the question “Where am I now?” The entries would not be averaged or otherwise summarized into a grade. This chart is the student’s way of keeping track of her progress as she is learning. She will eventually receive a grade from a summative assessment of mathematical knowledge.

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108 | How to Create and Use Rubrics

figure 10.1 example of charting Progress with Rubrics

WRItInG An eXPlAnAtIon

5 • I write what I did

and why I did it. • I explain each step

of my work. • I use math words

and strategy names.

• I write the answer in a complete sen- tence at the end of my explanation.

4 • I write what I did

and a little about why I did it.

• I explain most of my work.

3 • I write a little

about what I did or why I did it, but not both.

• I explain some of my work.

2 • I write something

that doesn’t make sense.

• I write an unclear answer.

1 • I don’t write

anything to explain how I solved the problem.

oct. 7 Problem set #1

oct. 14 Problem set #2

oct. 21 Problem set #3

oct. 28 Problem set #4

nov. 4 Problem set #5

nov. 11 Problem set #6

Note: This example uses the Math Problem-Solving Rubric shown in Figure 4.1.

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Feedback and Student Self-Assessment | 109

Second, the assessments or learning opportunities themselves are not “equal,” and it is therefore mathematically inappropriate to summarize this chart by averaging. What is constant is the existence of the descriptions of performance for the various levels of Writing an Explanation, which are shown on the vertical axis. These performance levels describe the student’s “steps” in learning. The assessments are simply opportunities for the student to practice, learn, and show what she knows. The purpose of the chart is for the student to see a learning curve. Bars that rise indicate progress. Bars that stay the same or fall indicate lack of progress. The graphic representation helps students focus on the performance levels and plan their next steps.

How to use rubrics to help students ask effective questions about their work

The genius of rubrics lies in their two main features: the criteria and descriptions of performance across a range of quality levels. The “main ideas” students need in order to understand quality are named by the criteria themselves. The elements in the descriptions flesh out these criteria with “supporting ideas” or aspects of the work that contribute to overall quality. Both of these help students ask effective questions about their work.

Simple self-reflection with rubrics

For experienced, self‑regulated learners, simply give students dedicated time for self‑reflection at designated points during their work, and ask them to use the rubrics to do it. Appropriate points in the work will vary. For writing, they come after the first draft and after subsequent revisions. For multipart projects, they come as different compo‑ nents of the project are drafted. For term papers, they come after each phase has been attempted (draft thesis or research question, library/Internet research, outline, writing of sections of the paper, and so on). Effective, self‑regulated students can use rubrics to ask themselves whether their work contains the qualities they are shooting for. Many, if not most, students need more scaffolding and structure in order to use rubrics to ask effective questions about their work.

Scaffolded self-reflection with rubrics

Rubrics with structure like the Math Problem‑Solving Rubric in Figure 4.1 make asking effective questions about work very straightforward. Ask students to focus first

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110 | How to Create and Use Rubrics

on the top category (or the category they are shooting for, if not the top one), and turn the elements into questions:

• Do I figure out the correct answer? • Do I solve the problem with no mistakes? • Do I use all the important information from the problem? [and so on]

For rubrics that do not use such straightforward, student‑friendly terms, you can do one of two things. You can construct student‑friendly rubrics with the students, with the constraint that the descriptions have to be “I” statements that can be turned into “Do I” questions. That exercise in itself is good for helping students learn exactly what their target is (see Chapter 9).

Alternatively, you can have students use the criteria and descriptive elements in rubrics to pose their own questions. For example, Level 4 of the Content category in the rubric for written projects in Figure 4.2 says:

The thesis is clear. A large amount and variety of material and evidence support the thesis. All material is relevant. This material includes details. Information is accurate. Appropriate sources were consulted.

Brainstorm with students how questions can be written from these statements. If you start with “The thesis is clear,” students might suggest questions such as these:

• Is my thesis clear? • How clear is my thesis? • How do I know my thesis is clear? • How can I make my thesis more clear?

You can continue with each element in the description until you have a set of reflection questions for students to use. Or if your students get the hang of this quickly, you can use a few rounds of question generating to demonstrate how to turn descriptions into questions about work, and then have students write their own questions as they reflect.

Feedback on student self-reflection

Asking effective questions about their own work is the first key to supporting students’ effective self‑reflection. The second, of course, is answering those questions. As students are learning to self‑reflect, give them feedback on how well they answer the questions. Feedback on student self‑reflection is generally oral, but it can be written

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Feedback and Student Self-Assessment | 111

if students use a formal self‑reflection format. Feedback on student self‑reflection need not be given to all students all the time. Feedback on student self‑reflection is not used for grades.

Parker and Breyfogle (2011) describe a process of self‑reflection that began with Ms. Parker’s students using the Math Problem‑ Solving Rubric to evaluate three anonymous pieces of student work. Later in the project, the class evaluated anonymous work samples from a student’s Week 1 and Week 4 work and talked about how the rubric described the change. Then Ms. Parker used small‑group time to elicit more details about the students’ observations of the work by asking probing questions herself. Finally, she used individual conferences to ask students to apply the rubric to their own work. The follow‑up ques‑ tions she used (for example, “You wrote what you did, but did you say why you did it?”) functioned as feedback for the students, feeding them forward into their next steps in observation (“No, I just wrote what I did”), and finally to an action plan (writing why).

Summing up

One of the advantages of rubrics is their usefulness for formative assessment. Chapter 9 explored ways to use rubrics to share learning targets and criteria for success with students. Chapter 10 explored ways to use rubrics to develop student work and to give evidence of learning that students can use for further improvement. When students have written, drafted, practiced, honed, and polished, eventually it is time for a grade to certify the level of achievement or accomplishment the students have reached. Chapter 11 discusses ways to use rubrics in grading.

Self-ReflectIon

How can you involve students more in self-

reflection in your classroom?

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112

11 How to Use Rubrics for Grading

Most of this book has been about how to write or select high‑quality rubrics and how to use them formatively with students, as an aid to learning. I include this chapter on grading to complete the picture. Sometimes teachers use rubrics well until they get to grading, and then meaning falls apart because rubric levels are not the same kind of

numbers as the test scores and percentages most teachers grew up with. Note that this chapter is not a complete treatise on grading, just a discussion of how using rubrics plays out in the grading process. Readers who would like a more complete treatment of grading should consult Brookhart (2011) or O’Connor (2011).

What is grading?

We commonly use the term grading to mean two different things. We say, “I graded that assignment” or “I graded that test,” meaning a grade was assigned to an individual assessment. We also use grading to refer to the process of summarizing a set of individ‑ ual grades to arrive at a grade for a report card. Report card grades are usually assigned either to a standard or to a subject area, depending on whether the report cards are standards based or traditional. In this chapter, I talk about using rubrics for grading individual assessments and also about summarizing a set of grades that includes rubrics.

Self-ReflectIon

How have you handled using rubrics in grading?

What questions or issues have arisen for you?

How did you resolve them?

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How to Use Rubrics for Grading | 113

Rubric-based grades and percentages—An important difference

Rubrics typically use short scales, often three to six levels. The meaning of the distance between the levels is not the same as for a test, where one point usually means one tiny increment on a scale, either from a right‑wrong question or one point on a multipoint question. Rubrics use ordered categories—descriptions of performance along a continuum of quality—for each criterion. For this reason, turning rubrics into percentages, which many people do out of habit or out of the expectations of gradebook software, changes the meaning. For example, a 3 on a four‑point rubric typically means “Proficient.” Three out of four, however, is 75 percent, which in most grading scales is a C and sometimes even a D. Neither of those grades means “Proficient.”

The goal for all the grading recommendations in this chapter is to have the final grade end up representing, with as much fidelity as possible, the information about student learning contained in individual grades or in the set of grades being combined for a report card grade. Those who are interested in more of the quantitative reasoning behind these recommendations should consult Nitko and Brookhart (2011).

How to use rubrics to grade individual assessments

Use the same rubrics to grade the assignment that students have been using for‑ matively as part of their understanding of their learning target and for monitoring and improving their work. I hope for most readers this is a foregone conclusion.

If students have used rubrics formatively, as they worked, the main “grade” for their assignment should communicate what level they finally achieved on each criterion. This is the information that should be most meaningful to them because it will include descrip‑ tions of their work. One good way to do this is to circle the performance‑level descrip‑ tion that applies to the final work, for each criterion. You don’t need to take the time to write that general description, because it is already printed in the rubrics. With the time you save, you can make a few comments specific to the student’s particular work—not a lot, as the most effective time for feedback is before work is graded, not after.

If you need an overall grade for a performance assessment graded with analytic rubrics, you can combine the levels achieved for each criterion. Whether you summarize the per‑ formance for each criterion into a total‑performance description or not, students should see how they scored on each criterion. Criterion‑level results provide more useful information for students than one amalgamated score. However, sometimes you need to summarize an overall grade for one assessment for later use in a final grade. Sometimes you don’t, as when each criterion is recorded as a grade under a different standard. For

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114 | How to Create and Use Rubrics

example, one rubric score might be recorded under the standard for science content, one for inquiry skills, and one for communication.

If you do need one overall grade (for example, “Science”) and must summarize an assessment with one overall score, use the median or mode, not the mean, of the scores for each criterion. Figure 11.1 summarizes how to calculate mean, median, and mode, the three most common ways to combine more than one score into a typical score. The figure summarizes all three, even though the median is recommended, so you can see how all three summarize “typical” performance but do so in different ways.

figure 11.1 three Ways to Summarize a Set of Scores: Mean, Median, and Mode

Measure of Central Tendency Example

On a six-point analytic rubric with four criteria, a student scores 6, 5, 3, 3.

Mean

• The sum of all scores divided by the number of scores

• Also known as the arithmetic average

Mean = 4.25

(6 + 5 + 3 + 3)/4 = 4.25

Median

• The score that has half of the scores above and half below it (even if it’s between two scores)

• Also known as the 50th percentile

Median = 4

(line scores up in order first) 6 5 3 3 ^ 4

Mode

• The most frequently occurring score in the set of scores

• Sometimes helpful to think of it as the “most popular” score

Mode = 3

(line scores up in order first)

6 5 3 3

Figure 11.1 uses as an example a performance that was scored with a six‑point analytic rubric with four criteria, on which one student scored 6, 5, 3, and 3, respectively. The example assumes all four criteria were of equal weight, which will not always be the case. To weight a criterion more heavily than others to calculate the mean, multiply the weight times the score. For example, to double the weight of the criterion on which

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How to Use Rubrics for Grading | 115

a student scored 6, for the mean, use 12 instead of 6, changing the mean to 5.75. To weight a criterion more heavily than others to calculate the median, repeat it. That is, use two 6s in the lineup, changing the median to 5.

I recommend the median for most summarizing purposes. The median is less prone to being pulled by extreme scores than is the mean, as the examples in Figure 11.1 show. And the median is more stable than the mode, as the examples also show. Sup‑ pose one of the 3s in the example had been a 5? One change in one criterion, probably not representing a hugely different performance overall, would change the overall score by two points—a lot on a six‑point scale. Plus the median is easy to calculate—for most analytical rubrics you can just count in your head. In the next section, when I will recom‑ mend using the median for summarizing sets of grades on individual assessments, you can let a spreadsheet do your median calculations.

How to combine individual rubric-based grades for a report card grade

The method you choose for combining grades should depend on two things: what types of grades you need to combine and what meaning you want your report card grade to convey. Ask yourself these questions:

• What kinds of individual grades am I going to summarize for the report card grade? Are all your individual grades on scales from rubrics, or are your individual grades a mixture of rubrics and percentages? If all your grades are from rubrics, are they all on the same scale? Or were some four‑point rubrics, some six‑point, and so on? This makes a difference in how you combine them. It’s the familiar “apples and oranges” logic. Before you combine numbers meaningfully, they should be on the same scale.

• How must I report the students’ grades on the report card? Does your report card use letter grades (for example, A, B, C, D, F) or percentages or standards‑based performance categories? This distinction makes a difference in how you combine individual grades as well.

• What is my report card grade supposed to mean? I’ll take it as a given that your report card grade is supposed to reflect achievement (as opposed to effort, attendance, and so on). Is achievement reported by subject or by standard on your report cards? The reason this makes a difference for combining grades is that if achieve‑ ment is separated by standard, you can privilege the most recent evidence; as the student improves on the standard, the grade will go up, even if it started low, because it represents learning in the same domain. If achievement is reported

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116 | How to Create and Use Rubrics

by subject, then the order of the evidence makes less difference, because differ‑ ent standards are covered in different units. Doing poorly on one standard at the beginning of the report period is not subject to revision because of doing well on a different standard toward the end of the report period.

You can use Figure 11.2 to help you decide on a method to use for summarizing your students’ individual grades into their report card grades. You will notice in Figure 11.2 that the methods follow three general steps. Each of these steps is worked out in different ways depending on the answers you gave to the three questions (what kinds of grades, how must you report, and what the reported grade is supposed to mean).

The figure lists each question in turn, and then displays two flow charts that start with the answer to the first question. All the recommended methods accomplish these objectives:

• Identify the set of individual grades you are going to summarize, based on what the report card grade is supposed to mean.

• Make sure the individual grades to be summarized are on the same scale. • Use a summarizing method that expresses in one grade the “typical” achievement

level shown in the set of individual grades.

The following sections discusses each of these points in greater detail. Identify the set of individual grades you are going to summarize, based on

what the report card grade is supposed to mean. Usually report card grades are supposed to reflect achievement of a standard or achievement in a subject. It is impor‑ tant to make sure you have recorded grades organized by standard or subject, respec‑ tively. That sounds obvious; in fact, it sounds like something you shouldn’t need advice about. However, it’s worth mentioning, especially in a book on rubrics.

If you used analytic rubrics for a project and are grading by subject, typically you will summarize the set of analytic rubrics for the project into one overall score, as discussed in the previous section of this chapter. However, if you used analytic rubrics for a project and are grading by standard, you may need to keep one or more of the criteria separate. For example, if students wrote a report on an event in history and its effects, and you graded it with the General Rubric for Written Projects in Figure 4.2, the “Content” and “Reasoning & Evidence” scores might be put together to be indicators of a standard about understanding and analyzing historical events, and the “Clarity” score might be an indicator of a standard about communicating about historical events or a standard about expository writing.

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How to Use Rubrics for Grading | 117 fi

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Therefore, it’s very important to know what specific set of information you will need for your report card grade before you record your individual grades. If you have recorded individual grades by standard or subject, as needed, you can easily calculate meaning‑ ful report card grades. If you have not, or if you have made overall grades out of rubric results that should have been kept separate, you will not have the right information at hand when it’s time to calculate final grades. Even worse, if you recorded improperly orga‑ nized grades into gradebook software that calculates final grades automatically, you may not even be aware that your final grades do not mean what you intended them to mean.

Begin the report period by selecting the right organization method for your grade records. It’s not hard to organize ahead of time. It’s very difficult, and sometimes impos‑ sible, to reorganize mixed‑up results.

Make sure the individual grades to be summarized are on the same scale. Here, the term scale means the numbers or levels in which the individual grade is expressed. There might be several different kinds of scales within the set of grades you identified as the set to be summarized for one report card grade. For example, you might have percentages, some four‑point rubrics, some six‑point rubrics, and so on. Obviously a 4 conveys very different information about achievement on those different scales, and yet if you were to average them, those different meanings would become muddled.

If you have used rubrics with the same proficiency scale for every graded assessment, whether it was a test or performance assessment or project or assignment of any type, your individual grades are already on the same scale for grading purposes. Chapter 6 described how to create this kind of rubric.

If all your recorded grades for individual assignments are from rubrics, but the rubrics have not been designed such that the levels have the same meaning, or if the rubrics do not all have the same number of levels, or both, you need to put them all on the same scale before you combine them. This follows the “comparing apples and oranges” principle. You need to make sure all your rubrics are apples (or oranges, or bananas for that mat‑ ter); that is, that they are all comparable and can be meaningfully combined.

Whether your set of individual grades is by subject or by standard, if you are report- ing in letter grades (for example, A, B, C, D, F) or performance categories (for example, Advanced, Proficient, Nearing Proficiency, Not Yet), or in any other short scale that is really a list of ordered categories of achievement, the easiest thing to do is to transform each individual grade into a category on that scale. Then when you combine the grades, your result will already be on the scale you need, and you’ll save yourself having to do a

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second transformation. I recommend you do this at the time you record each individual grade, but if you haven’t, do the transformation before calculating the report card grade.

For example, consider Figure 11.3. The top section lists the grades for five assess‑ ments for four students. These grades illustrate a common situation that occurs when teachers have used a mixture of tests or quizzes graded with percentages and perfor‑ mance assessments graded with rubrics. Using multiple, different measures is a good practice. It allows for assessing different aspects of a content domain, at different cogni‑ tive levels, and with different performance modalities. It does, however, create a grading situation with incompatible scales, as illustrated in Figure 11.3. Take a moment to verify for yourself that if you simply “averaged” the numbers (added them up and divided by 5), you would get uninterpretable results.

figure 11.3 example of Summarizing by converting Individual Grades

to the Scale Used for Reporting

Original Grades for Individual Assessments

Student Assessment

#1 Assessment

#2 Assessment

#3 Assessment

#4 Assessment

Aiden 79 2 74 3 4

Brittney 68 2 69 2 3

Carlos 93 4 98 5 6

Daniela 88 3 92 5 5

Transformed Grades, with Report Card Grade (median)

Student Assessment

#1 Assessment

#2 Assessment

#3 Assessment

#4 Assessment

#5 Report

Card Grade

Aiden C C C C B C

Brittney D C D D C D

Carlos A A A A- A A

Daniela B B A A- A- A-

Note: The original grades for Assessments #1 and #3 were in percentages. The original grades for Assessment #2 were on four-point rubrics with 3 indicating Proficient. The original grades for Assessments #4 and #5 were on six-point rubrics with 4 and above indicating Proficient. The transformed grades were put on a letter-grade scale (A, B, C, D, F ) because they were to be summarized into a letter grade for the report card.

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The solution to this problem is to discern the meaning of each individual grade in terms of the grading scale you must use for reporting so that you can meaningfully combine the results. In this illustration, the report card requires letter grades. If the report card required reporting proficiency levels (Advanced, Proficient, and so on), the procedure would be the same but instead of converting to letters, you would convert to proficiency levels.

In this example, Assessments #1 and #3 were tests, and their results were in per‑ centages. The percentages were transformed to letter grades using the scale 90–100=A, 80–89=B, and so on, for ease of illustration. You would, of course, use whatever scale was in place in your district or school to do this transformation.

Assessment #2 was a performance assessment scored with four‑point rubrics, where 3 was Proficient. These rubric results were transformed to letter grades by a judgment call, that 3 (Proficient) represented B‑level work, 4 (Advanced) represented A‑level work, and 2 (Nearing Proficiency) represented C‑level work. Assessments #4 and #5 were performance assessments scored with six‑point rubrics, similar to the 6+1 Trait Writing rubrics, where 4 and above meant Proficient. In this example, to be consistent with the decision to use a B to represent Proficient, the six‑point rubric was transformed as follows: 6=A, 5=A‑, 4=B, 3=C, 2=D, 1=F. As for the percentage transfor‑ mations, you would use the conventions in your school or district to transform the rubric results into letters, which would not have to match the transformations in this example.

If you are using rubrics but your report card grades must be expressed in percentages, that’s a stickier wicket. Technically you can’t add precision (more distinctions or gra‑ dations in the scale) that wasn’t there in the first place. So mapping a small number of performance categories from rubrics onto a scale with 101 possible points (0 to 100) is not mathematically an appropriate thing to do. If you have to end up with percentages, however, it won’t help you much if I just say don’t use percentages with rubrics. You would be technically correct but left with no way to report students’ grades.

Therefore, I suggest that if you have to report in percentages you work to change your district’s reporting system and in the meantime know that you are compromising for the sake of following required policy. If you have to report final grades in percent‑ ages, it’s better to use judgments about student learning than mathematics that distorts the meaning about student learning. Whether all your recorded grades for individual assignments are from rubrics or some are from rubrics and others are expressed in per‑ centages, you need to put them all on the percentage scale before you combine them.

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The purpose is to make sure that they are all comparable and can be combined to yield a meaningful result on the percentage scale.

If you know you need percentages, you can get such scores from rubrics in one of two ways. You can calculate percentages mathematically from your rubrics, or you can use a conversion chart based on judgment.

To calculate percentages from rubrics (I cringe even writing that! What a horrible position to be in!), make sure all the rubrics you use for assignments have at least 20 total points. Thirty is even better. Using at least 20 total points helps address the prob‑ lem of percentage meanings not coinciding with rubric meanings, which was explained in the introduction to this chapter. (Recall the example that three out of four is 75 per‑ cent, which is not “Proficient” on most percentage grading scales).

You won’t be able to avoid this problem entirely, but you can improve it a bit by using larger numbers. Five 3s, on five 4‑point rubrics, still yields 75 percent (15 out of 20 possible points). However, in the three‑out‑of‑four case, the scale jumped from 75 percent to 100 percent; it was impossible to score anything in between. With five 4‑point rubrics for a total of 20 points, there are possible scores in between (80 percent for four 3s and a 4, 85 percent for three 3s and two 4s, and so on). The bottom line is, if you have to convert rubrics to percentages—kicking and screaming at compromising information about student learning—at least do it with total points of 20 or more.

I once had a question from a teacher during a workshop on grading. She asked about rubrics in which the lowest category is a 1. Often the description of performance in the low category includes things like “Answer was unreadable” or even “No answer was given.” She was concerned that students would, in effect, be “getting points” for doing no work. That was an interesting question, but it rests on the assumption that the grades are for doing work. Grades are supposed to be measures of achievement, and they are always on arbitrary scales invented by educators. If a student scores 25 percent because of getting five 1s on an assignment scored with five 4‑point rubrics, the student still fails. In fact, that 25 percent is exactly the same as the chance (guessing) score for a multiple‑choice test with four‑option questions scored right/wrong and then converted to a percentage.

Using a conversion chart based on judgment to transform rubric scores into percentages is a bit more defensible than calculating percentages from rubric scores because the judgments are about what the scores say about student learning. It is still mathematically impossible to make scores more precise than they were in the first

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place, but at least the judgments can be thoughtful. Figure 11.4 is an example of a con‑ version chart constructed by using teacher judgment.

figure 11.4 A Judgment-Based conversion chart for Recording

Rubric Results as Percentages

Median of Scores for All Criteria on One Assessment

Judgment-Based “Percentage” Grade for That Assessment

4.0 99

3.5 92

3.0 85

2.5 79

2.0 75

1.5 67

1.0 59

The chart in Figure 11.4 reflects judgments about learning. The reasoning flowed from the premise that the 3 was supposed to reflect proficiency and should therefore end up being a “middle B” on the percentage scale used in the school. In this example, for ease of illustration we are representing percentages on a scale where 90 to 100 is an A, 80 to 89 is a B, and so on. Thus, in this conversion chart, a student with performance at the bottom level of the rubric fails but is at the top of the F range on the percentage scale. A conversion chart in a school with a different scale would have different num‑ bers. A conversion chart based on different judgments about what the four levels of performance should represent on the scale would also have different numbers.

It is best if conversion charts like this one are constructed by several teachers or a whole department or school. The more perspectives reflected in the judgments, the better. And the more agreement there is about the judgments, the easier it will be to use them and explain them to students and parents.

Finally, to end this section I want to repeat that making percentages out of rubrics is a compromise, and one I’m not happy about. Do it only if your grading policies require it.

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Use a summarizing method that expresses in one grade the “typical” achievement level shown in the set of individual grades. Once you have your set of individual grades on the same scale—“apples to apples,” if you will—you are ready to combine them. For most purposes, I recommend the median. It’s an appropriate mea‑ sure of “typical” performance when the performance measures are ordered categories. Weighting more important grades is easy when you calculate a median (for example, to double, just count the same grade twice; to triple, count it three times). The median does not give any more weight to an extreme low or high score than to any other low or high score.

If you are reporting in letter grades (for example, A, B, C, D, F) or performance catego- ries (for example, Advanced, Proficient, Nearing Proficiency, Not Yet), or in any other short scale that is really a list of ordered categories of achievement, use the median letter grade or performance category. You have already transformed each of your individual grades to the reporting scale. Before you take the median, decide if you need to weight any individual grades more than others.

If you are reporting grades by subject, with the individual assignment grades measur- ing learning on different standards, consider doubling individual grades that reflect more important standards. Or you might consider doubling individual grades that reflect more complex thinking or extended work compared with individual grades that reflect recall and literal comprehension. After you are satisfied that the weights of your indi‑ vidual grades make them contribute their due to the whole set of information, then take the median, as described above and in Figure 11.1. In the example in Figure 11.3, the decision was not to weight any one assessment more heavily than another. Each indi‑ vidual assessment counted the same. The median was used to summarize the set of five grades, and the results are shown in the column labeled “Report Card Grade.”

If you are reporting grades by standard instead of subject, with all the assignments representing learning within the same domain, you should still weight individual grades in proportion to the contribution you want them to make to the report card grade. Once you have done that, however, pause before you calculate the median and look for patterns in the individual grades over time. If the pattern looks like a learning curve— that is, it starts low, then rises, and then levels off—those later individual grades in the leveling‑off period represent current student achievement of that standard. Take the median of those.

If the pattern is the opposite of that, decreasing over time (rarer, but it happens), you might still take the median of the recent evidence, or you might take the median of

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all the individual grades to give the student the benefit of the doubt. However, you also need to find out the reason why a student went into a slump. In fact, it’s better if you notice the slump before report card time and can do something about it.

If there is no discernible pattern, take the median of all the individual grades. The case of Cort in Figure 6.4 illustrates this scenario.

If you are using rubrics but your report card grades must be expressed in percentages, you have already transformed each of your individual grades into percentages. Give more weight to assessments of more important standards and assessments that measure complex and extended thinking, and less weight to assess‑ ments of less important standards and assess‑ ments of recall of information. I still recommend that you use the median percentage as your summary grade. That way you minimize the drastic effect of extreme scores and still report a defensible average grade. (Actually, I recommend the median even for summarizing grades that all began as percentages, not rubrics, for that same reason.) However, you could use the mean percentage as your summary grade as well.

Summing up

This chapter explained how to use rubrics for grading individual assessments and then how to combine them with other individual assessment results for report card grades. In my opinion, the most important aspect of rubrics is how they can be used to describe, develop, and support learning. The grading recommendations in this chapter, for both individual assessments and report cards, are aimed at handling the results of using rubrics for learning in a way that preserves the intended meaning about learning. Because scores from rubrics look like any other numbers, teachers often unknowingly total or average them in ways that are not appropriate for short, ordered‑category scales. I hope this chapter has helped you think through the meaning of grades resulting from rubrics.

The chapter recommended report card grading practices based on a series of deci‑ sions about grading that depend on the kinds of individual grades you have, the manner in which you must express your report card grade, and the meaning your report card

Self-ReflectIon

Which branches of the decision tree in Figure 11.2

are most relevant to your school and classroom

grading policies and needs? How do your grading

practices match with the recommendations made

in this chapter?

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grade is intended to have. That’s why there are different recommendations. The chap‑ ter, of course, could not cover every possible answer to those three questions. If your situation was not covered, you can still follow the general plan: (1) identify the set of individual grades you need to summarize, (2) put them all on the same scale, and (3) use a summarizing method that is appropriate to the kind of scores you have and that results in the most appropriate message about student achievement.

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