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2014 ASCD Conference on Educational Leadership

2014 ASCD Conference on Educational Leadership

October 31–November 2, 2014, Orlando, Fla.

Learn the secrets to great leadership practices, and get immediate and practical solutions that address your needs.

 

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Art and Science of Teaching

by Robert J. Marzano

Table of Contents

Chapter 1. What will I do to establish and communicate learning goals, track student progress, and celebrate success?

Arguably the most basic issue a teacher can consider is what he or she will do to establish and communicate learning goals, track student progress, and celebrate success. In effect, this design question includes three distinct but highly related elements: (1) setting and communicating learning goals, (2) tracking student progress, and (3) celebrating success. These elements have a fairly straightforward relationship. Establishing and communicating learning goals are the starting place. After all, for learning to be effective, clear targets in terms of information and skill must be established. But establishing and communicating learning goals alone do not suffice to enhance student learning. Rather, once goals have been set it is natural and necessary to track progress. This assessment does not occur at the end of a unit only but throughout the unit. Finally, given that each student has made progress in one or more learning goals, the teacher and students can celebrate those successes.

In the Classroom

Let's start by looking at a classroom scenario as an example. Mr. Hutchins begins his unit on Hiroshima and Nagasaki by passing out a sheet of paper with the three learning goals for the unit:

  • Goal 1. Students will understand the major events leading up to the development of the atomic bomb, starting with Einstein's publication of the theory of special relativity in 1905 and ending with the development of the two bombs Little Boy and Fat Man in 1945.
  • Goal 2. Students will understand the major factors involved in making the decision to use atomic weapons on Hiroshima and Nagasaki.
  • Goal 3. Students will understand the effects that using atomic weapons had on the outcome of World War II and the Japanese people.

At the bottom of the page is a line on which students record their own goal for the unit. To facilitate this step, Mr. Hutchins has a brief whole-class discussion and asks students to identify aspects of the content about which they want to learn more. One student says: “By the end of the unit I want to know about the Japanese Samurai.” Mr. Hutchins explains that the Samurai were warriors centuries before World War II but that the Samurai spirit definitely was a part of the Japanese view of combat. He says that sounds like a great personal goal.

For each learning goal, Mr. Hutchins has created a rubric that spells out specific levels of understanding. He discusses each level with students and explains that these levels will become even more clear as the unit goes on. Throughout the unit, Mr. Hutchins assesses students' progress on the learning goals using quizzes, tests, and even informal assessments such as brief discussions with students. Each assessment is scored using the rubric distributed on the first day.

As formative information is collected regarding student progress on these goals, students chart their progress using graphs. At first some students are dismayed by the fact that their initial scores are quite low—1s and 2s on the rubric. But throughout the unit students see their scores gradually rise. They soon realize that even if you begin the unit with a score of 0 for a particular learning goal, you can end up with a score of 4.

By the end of the unit virtually all students have demonstrated that they have learned, even though everyone does not end up with the same final score. Progress is celebrated for each student. For each learning goal, Mr. Hutchins recognizes those students who gained one point on the scale, each student who gained two points on the scale, and so on. Virtually every student in class has a sense of accomplishment by the unit's end.

Research and Theory

As demonstrated by the scenario for Mr. Hutchins's class, this design question includes a number of components, one of which is goal setting. Figure 1.1 summarizes the findings from a number of synthesis studies on goal setting.


Figure 1.1. Research Results for Goal Setting


Synthesis Study

Focus

Number of Effect Sizes

Average Effect Size

Percentile Gain

Wise & Okey, 1983a

General effects of setting goals or objectives

3

25

1.37

0.48

41

18

Lipsey & Wilson, 1993b

General effects of setting goals or objectives

204

0.55

21

Walberg, 1999

General effects of setting goals or objectives

21

0.40

16

aTwo effect sizes are listed because of the manner in which effect sizes are reported. Readers should consult that study for more details.

bThe review includes a wide variety of ways and contexts in which goals might be used.


To interpret these findings, it is important to understand the concept of an effect size. Briefly, in this text an effect size tells you how much larger (or smaller) you might expect the average score to be in a class where students use a particular strategy as compared to a class where the strategy is not used. In Figure 1.1 three studies are reported, and effect sizes are reported for each. Each of these studies is a synthesis study, in that it summarizes the results from a number of other studies. For example, the Lipsey and Wilson (1993) study synthesizes findings from 204 reports. Consider the average effect size of 0.55 from those 204 effect sizes. This means that in the 204 studies they examined, the average score in classes where goal setting was effectively employed was 0.55 standard deviations greater than the average score in classes where goal setting was not employed. Perhaps the easiest way to interpret this effect size is to examine the last column of Figure 1.1, which reports percentile gains. For the Lipsey and Wilson effect size of 0.55, the percentile gain is 21. This means that the average score in classes where goal setting was effectively employed would be 21 percentile points higher than the average score in classes where goal setting was not employed. (For a more detailed discussion of effect sizes and their interpretations, see Marzano, Waters, & McNulty, 2005.)

One additional point should be made about the effect sizes reported in this text. They are averages. Of the 204 effect sizes, some are much larger than the 0.55 average, and some are much lower. In fact, some are below zero, which indicates that the classrooms where goals were not set outperformed the classrooms where goals were set. This is almost always the case with research regarding instructional strategies. Seeing effect sizes like those reported in Figure 1.1 tells us that goal setting has a general tendency to enhance learning. However, educators must remember that the goal-setting strategy and every other strategy mentioned in this book must be done well and at the right time to produce positive effects on student learning.

As illustrated in Mr. Hutchins's scenario, feedback is intimately related to goal setting. Figure 1.2 reports the findings from synthesis studies on feedback.


Figure 1.2. Research Results for Feedback


Synthesis Study

Focus

Number of Effect Sizes

Average Effect Size

Percentile Gain

Bloom, 1976

General effects of feedback

8

1.47

43

Lysakowski & Walberg, 1981a

General effects of feedback

39

1.15

37

Lysakowski & Walberg, 1982

General effects of feedback

94

0.97

33

Haller, Child, & Walberg, 1988b

General effects of feedback

115

0.71

26

Tennenbaum & Goldring, 1989

General effects of feedback

16

0.66

25

Bangert-Drowns, Kulik, Kulik, & Morgan, 1991

General effects of feedback

58

0.26

10

Kumar, 1991c

General effects of feedback

5

1.35

41

Walberg, 1999

General effects of feedback

20

0.94

33

Haas, 2005

General effects of feedback

19

0.55

21

aReported in Fraser, Walberg, Welch, & Hattie, 1987.

bFeedback was embedded in general metacognitive strategies.

cThe dependent variable was engagement.


Notice that the effect sizes in Figure 1.2 tend to be a bit larger than those reported in Figure 1.1. This makes intuitive sense. Goal setting is the beginning step only in this design question. Clear goals establish an initial target. Feedback provides students with information regarding their progress toward that target. Goal setting and feedback used in tandem are probably more powerful than either one in isolation. In fact, without clear goals it might be difficult to provide effective feedback.

Formative assessment is another line of research related to the research on feedback. Teachers administer formative assessments while students are learning new information or new skills. In contrast, teachers administer summative assessments at the end of learning experiences, for example, at the end of the semester or the school year. Major reviews of research on the effects of formative assessment indicate that it might be one of the more powerful weapons in a teacher's arsenal. To illustrate, as a result of a synthesis of more than 250 studies, Black and Wiliam (1998) describe the impact of effective formative assessment in the following way:

The research reported here shows conclusively that formative assessment does improve learning. The gains in achievement appear to be quite considerable, and as noted earlier, amongst the largest ever reported for educational interventions. As an illustration of just how big these gains are, an effect size of 0.7, if it could be achieved on a nationwide scale, would be equivalent to raising the mathematics attainment score of an “average” country like England, New Zealand, or the United States into the “top five” after the Pacific rim countries of Singapore, Korea, Japan, and Hong Kong. (p. 61)

One strong finding from the research on formative assessment is that the frequency of assessments is related to student academic achievement. This is demonstrated in the meta-analysis by Bangert-Drowns, Kulik, and Kulik (1991). Figure 1.3 depicts their analysis of findings from 29 studies on the frequency of assessments.


Figure 1.3. Achieved Gain Associated with Number of Assessments over 15 Weeks


Number of Assessments

Effect Size

Percentile Gain

0

0

0

1

0.34

13.5

5

0.53

20.0

10

0.60

22.5

15

0.66

24.5

20

0.71

26.0

25

0.78

28.5

30

0.82

29.0

Note: Effect sizes are from data reported by Bangert-Drowns, Kulik, & Kulik, 1991.


To interpret Figure 1.3, assume that we are examining the learning of a particular student who is involved in a 15-week course. (For a discussion of how this figure was constructed, see Marzano, 2006, Technical Note 2.2.) Figure 1.3 depicts the increase in learning one might expect when differing quantities of formative assessments are employed during that 15-week session. If five assessments are employed, a gain in student achievement of 20 percentile points is expected. If 25 assessments are administered, a gain in student achievement of 28.5 percentile points is expected, and so on. This same phenomenon is reported by Fuchs and Fuchs (1986) in their meta-analysis of 21 controlled studies. They report that providing two assessments per week results in an effect size of 0.85 or a percentile gain of 30 points.

A third critical component of this design question is the area of research on reinforcing effort and providing recognition for accomplishments. Reinforcing effort means that students see a direct link between how hard they try at a particular task and their success at that task. Over the years, research has provided evidence for this intuitively appealing notion, as summarized in Figure 1.4.


Figure 1.4. Research Results for Reinforcing Effort


Synthesis Study

Focus

Number of Effect Sizes

Average Effect Size

Percentile Gain

Stipek & Weisz, 1981

Reinforcing efforta

17

0.54

21

Schunk & Cox, 1986

Reinforcing effort

3

0.93

32

Kumar, 1991b

Reinforcing effort

6

1.72

46

Hattie, Biggs, & Purdie, 1996c

Reinforcing effort

8

2

2

2

1.42

0.57

2.14

0.97

42

22

48

33

aThese studies also dealt with students' sense of control.

bThe dependent variable was engagement.

cMultiple effect sizes are listed because of the manner in which effect sizes are reported. Readers should consult that study for more details.


Among other things, reinforcing effort means that students see a direct relationship between how hard they work and how much they learn. Quite obviously, formative assessments aid this dynamic in that students can observe the increase in their learning over time.

Providing recognition for student learning is a bit of a contentious issue—at least on the surface. Figure 1.5 reports the results of two synthesis studies on the effects of praise on student performance. The results reported by Wilkinson (1981) are not very compelling, in that praise does not seem to have much of an effect is student achievement. The 6 percentile point gain shown in those studies is not that large. On the other hand, the results reported by Bloom (1976) are noteworthy; a 21 percentile point gain is considerable. A plausible reason for the discrepancy is that these two studies were very general in nature, in that praise was defined in a wide variety of ways across studies.


Figure 1.5. Research Results on Praise


Synthesis Study

Focus

Number of Effect Sizes

Average Effect Size

Percentile Gain

Bloom, 1976

General effects of praise

12

0.54

21

Wilkinson, 1981a

General effects of praise

14

0.16

6

aReported in Fraser et al., 1987.


Other synthesis studies—particularly research on the effects of reward on intrinsic motivation—have been more focused in their analyses. Figure 1.6 summarizes findings from two major synthesis studies on the topic.


Figure 1.6. Research Results on Rewards


Synthesis Study

Measure Used to Assess Intrinsic Motivation

Number of Effect Sizes

Average Effect Size

Percentile Gain

Cameron & Pierce, 1994

Free-choice behavior

57

-0.06

-2

Interest/attitude

47

0.21

8

Deci, Koestner, & Ryan, 2001

Free-choice behavior

101

-0.24

-9

Interest/attitude

84

0.04

2


Among other things, both studies in Figure 1.6 examined the impact of what is commonly referred to as extrinsic rewards on what is referred to as intrinsic motivation. Both are somewhat fuzzy concepts that allow significant variation in how they are defined. (For a discussion, see Cameron & Pierce, 1994.) Considered at face value though, external reward is typically thought of as some type of token or payment for success. Intrinsic motivation is necessarily defined in contrast to extrinsic motivation. According to Cameron and Pierce (1994):

Intrinsically motivated behaviors are ones for which there is no apparent reward except the activity itself (Deci, 1971). Extrinsically motivated behaviors, on the other hand, refer to behaviors in which an external controlling variable [such as reward] can be readily identified. (p. 364)

The average effect sizes in Figure 1.6 show an uneven pattern—two effect sizes are below zero, and two effect sizes are above zero. However, the two effect sizes below zero are for studies that used free-choice behavior as the measure of intrinsic motivation. Typically these studies examine whether students (i.e., subjects) tend to engage in the task for which they are being rewarded even when they are not being asked to do the task. In both synthesis studies, the effect of extrinsic reward on free-choice behavior was negative. In contrast, positive effects (albeit small for the Deci, Koestner, & Ryan, 2001, study) are reported when the measure of intrinsic motivation is students' interest. Typically student interest is assessed by some form of self-report.

The contradictory findings for student interest versus student free-choice behavior do not provide any clear direction, but they do demonstrate the highly equivocal nature of the research on rewards and intrinsic motivation. A possible answer is found, however, by examining more carefully the distinction between free-time behavior and interest, as shown in Figure 1.7.


Figure 1.7. Influence of Abstract Versus Tangible Rewards


Synthesis Study

Measure Used to Assess Intrinsic Motivation

Number of Effect Sizes

Average Effect Size

Percentile Gain

Cameron & Pierce, 1994

Verbal on interest/attitude

15

0.45

17

Verbal on free time

15

0.42

16

Tangible on interest/attitude

37

0.09

4

Tangible on free time

51

-0.20

-8

Deci, Koestner, & Ryan, 2001

Verbal on interest/attitude

21

0.31

12

Verbal on free time

21

0.33

13

Tangible on interest/attitude

92

-0.34

-13

Tangible on free time

70

-0.07

-3


This research indicates that when verbal rewards are employed (e.g., positive comments about good performance, acknowledgments of knowledge gain) the trend is positive when intrinsic motivation is measured either by interest/attitude or by free-choice behavior. Even these results must be interpreted cautiously. Certainly, factors such as the age of students and the context in which rewards (verbal or otherwise) are given can influence their effect on students. It is safe to say, however, that when used appropriately verbal rewards and perhaps also tangible rewards can positively affect student achievement. Deci, Ryan, and Koestner (2001) share the following observations:

As our research and theory have always suggested, there are ways of using even tangible rewards that are less likely to have a negative effect and may, under limited circumstances, have a positive effect on intrinsic motivation. However, the use of rewards as a motivational strategy is clearly a risky proposition, so we continue to argue for thinking about educational practices that will engage students' interest and support the development of their self-regulation. We believe that it is an injustice to the integrity of our teachers and students to simply advocate that educators focus on the use of rewards to control behavior rather than grapple with the deeper issues of (a) why many students are not interested in learning within our educational system and (b) how intrinsic motivation and self-regulation can be promoted among these students. (p. 50)

Action Steps

Action Step 1. Make a Distinction Between Learning Goals and Learning Activities or Assignments

Even though the term learning goal is commonly used by practitioners, there appears to be some confusion as to its exact nature. For example, consider the following list, which typifies learning goals one might find in teachers' planning books:

  • Students will successfully complete the exercises in the back of Chapter 3.
  • Students will create a metaphor representing the food pyramid.
  • Students will be able to determine subject/verb agreement in a variety of simple, compound, and complete sentences.
  • Students will understand the defining characteristics of fables, fairy tales, and tall tales.
  • Students will investigate the relationship between speed of air flow and lift provided by an airplane wing.

Some of these statements—the first, second, and last—involve activities as opposed to learning goals. As the name implies, activities are things students do. As we will see in Design Questions 2, 3, and 4, activities are a critical part of effective teaching. They constitute the means by which the ends or learning goals are accomplished. However, they are not learning goals.

A learning goal is a statement of what students will know or be able to do. For example, Figure 1.8 lists learning goals for science, language arts, mathematics, and social studies, which differ from the related activities.


Figure 1.8. Learning Goals and Activities


Subject

Learning Goals

Activities

Science

Students will understand that

  • The sun is the largest body in the solar system.
  • The moon and earth rotate on their axes.
  • The moon orbits the earth while the earth orbits the sun.

Students will watch the video on the relationship between the earth and the moon and the place of these bodies in the solar system.

Language Arts

Students will be able to

  • Sound out words that are not in their sight vocabulary but are known to them.

Students will observe the teacher sounding and blending a word.

Mathematics

Students will be able to

  • Solve equations with one variable.

Students will practice solving 10 equations in cooperative groups.

Social Studies

Students will understand

  • The defining characteristics of the barter system.

Students will describe what the United Sates might be like if it were based on the barter system as opposed to a monetary system.


The learning goals presented in Figure 1.8 have a distinct format that emphasizes the knowledge students would potentially gain. Teachers provide the related activities to help students attain those learning goals. I will explain how some activities are designed to introduce students to new content in Chapter 2 how some activities are designed to help students practice and deepen their understanding of new content in Chapter 3, and how some activities are designed to help students generate and test hypotheses about content in Chapter 4.

Teachers would most likely use the science and language arts activities in Figure 1.8 to introduce new content to students. The mathematics activity would most likely serve as a practice activity. The social studies activity would most likely promote generating and testing hypotheses.

In general, I recommend that learning goals be stated in one of the following formats:

Students will be able to______________________.
or
Students will understand____________________.
These formats represent different types of knowledge and have been suggested by those who have constructed taxonomies of learning (Anderson et al., 2001; Marzano & Kendall, 2007). The reason for the two formats is that content knowledge can be organized into two broad categories: declarative knowledge and procedural knowledge. Chapter 4 addresses these two types of knowledge in some depth. Briefly, though, declarative knowledge is informational in nature. Procedural knowledge involves strategies, skills, and processes. In Figure 1.8, the learning goals for science and social studies are declarative or informational in nature. Hence they employ the stem “students will understand. . . .” The mathematics and language arts goals are procedural or strategy oriented. Hence they employ the stem “students will be able to. . . .” Occasionally a learning goal involves a substantial amount of declarative and procedural knowledge. In such cases, the following format can be useful:
Students will understand ___________ and be able to ___________.
To illustrate, the following 3rd grade learning goal for number sense includes both declarative and procedural knowledge: “Students will understand the defining characteristics of whole numbers, decimals, and fractions with like denominators, and will be able to convert between equivalent forms as well as represent factors and multiples of whole numbers through 100.”

Action Step 2. Write a Rubric or Scale for Each Learning Goal

Once learning goals have been established, the next step is to state them in rubric format. There are many different approaches to designing rubrics. The one presented here is explained in depth in the book Classroom Assessment and Grading That Work (Marzano, 2006) and has some research supporting its utility (see Flicek, 2005a, 2005b; Marzano, 2002). For reasons articulated in Classroom Assessment and Grading That Work, I prefer to use the term scale as opposed to the term rubric. Figure 1.9 shows what I refer to as the simplified scale.


Figure 1.9. Simplified Scale


Score 4.0: In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught.

Score 3.0: No major errors or omissions regarding any of the information and/or processes (simple or complex) that were explicitly taught.

Score 2.0: No major errors or omissions regarding the simpler details and processes but major errors or omissions regarding the more complex ideas and processes.

Score 1.0: With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.

Score 0.0: Even with help, no understanding or skill demonstrated.

© 2004 by Marzano & Associates. All rights reserved.


The simplified scale contains five whole-point values only—4.0, 3.0, 2.0, 1.0, and 0.0—as contrasted with a more detailed scale that has half-point scores—3.5, 2.5, 1.5, and 0.5. Although the simplified scale is generally less precise than the complete scale, I have found it a good starting place for teachers who are not familiar with using scales of this design. Additionally, in some situations half-point scores are difficult to discern or simply do not make much sense.

To demonstrate how the scale shown in Figure 1.9 can be used, assume that a health teacher wishes to score an assessment on the topic of obesity. The lowest score value on the scale is a 0.0, representing no knowledge of the topic—even with help the student demonstrates no understanding. A score of 1.0 indicates that with help the student shows partial knowledge of the simpler details and processes as well as the more complex ideas and processes regarding obesity. To be assigned a score of 2.0, the student independently demonstrates understanding and skill related to the simpler details and processes but not the more complex ideas and processes regarding obesity. For example, the student knows the general definition of obesity and some of the more obvious causes. A score of 3.0 indicates that the student demonstrates understanding of the simple and complex content that was taught in class. For example, the student understands the relationship between obesity and the chances of developing diseases such as heart disease as an adult. Additionally, the student understands risk factors for becoming obese as an adult even if you are not obese as a child. Finally, a score of 4.0 indicates that the student demonstrates inferences and applications that go beyond what was taught in class. For example, the student is able to identify his or her risk for becoming obese and personal actions necessary to avoid obesity, even though those actions were not specifically addressed in class.

The simplified scale has intuitive appeal and is easy to use. However, measurement theory tells us that the more values a scale has, the more precise the measurement (Embretson & Reise, 2000). To illustrate, assume that a teacher used a scale with only two values—pass and fail—to score a test. Also assume that to pass the test students had to answer 60 percent of the items correctly. In this scenario, the student who answered all items correctly would receive the same score (pass) as the student who answered 60 percent of the items correctly. Similarly, the student who answered no items correctly would receive the same score (fail) as the student who answered 59 percent of the items correctly. In general, the more score points on a scale, the more precise that scale can be. Figure 1.10 presents the complete scale.


Figure 1.10. Complete Scale


Score 4.0:In addition to Score 3.0 performance, in-depth inferences and applications that go beyond what was taught.

Score 3.5: In addition to Score 3.0 performance, partial success at inferences and applications that go beyond what was taught.

Score 3.0:No major errors or omissions regarding any of the information and/or processes (simple or complex) that were explicitly taught.

Score 2.5: No major errors or omissions regarding the simpler details and processes and partial knowledge of the more complex ideas and processes.

Score 2.0:No major errors or omissions regarding the simpler details and processes but major errors or omissions regarding the more complex ideas and processes.

Score 1.5: Partial knowledge of the simpler details and processes but major errors or omissions regarding the more complex ideas and processes.

Score 1.0:With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.

Score 0.5: With help, a partial understanding of some of the simpler details and processes but not the more complex ideas and processes.

Score 0.0:Even with help, no understanding or skill demonstrated.

© 2004 by Marzano & Associates. All rights reserved.


The scale in Figure 1.10 has half-point scores, whereas the scale in Figure 1.9 does not. The half-point scores are set off to the right to signify that they describe student response patterns between the whole-point scores and therefore allow for more precision in scoring an assessment. The half-point scores allow for partial credit to be assigned to items. To illustrate, a score of 3.0 indicates that a student has answered all items or tasks correctly that involve simpler details and processes as well as all items or tasks that involve more complex ideas and processes. A score of 2.0 indicates that the student has answered all items or tasks correctly that involve simpler details and processes but has missed all items or tasks that involve more complex ideas and processes. However, what score should be assigned if a student has answered all items or tasks correctly regarding simpler details and processes and some items or tasks correctly involving more complex ideas and processes or has received partial credit on those items or tasks? Using the simplified scale a teacher would have to assign a score of 2.0. Using the complete scale a teacher would assign a score value of 2.5. The second option allows for much more precision of measurement.

The complete scale, then, is a logical extension of the simplified scale. Teachers can use them interchangeably. When the type of assessment allows for determining partial credit, the teacher uses the complete scale. When the type of assessment does not allow for determining partial credit, the simplified scale is used.

The generic scales depicted in Figures 1.9 and 1.10 are easily translated into scales for specific learning goals. To illustrate, consider Figure 1.11, which shows a scale for the previously mentioned 3rd grade learning goal for number sense. The scale in Figure 1.11 is basically identical to the generic form of the complete scale in Figure 1.10 except that the score values 3.0 and 2.0 identify specific elements. Although it is also possible to fill in specific elements for the score value of 4.0, I have found that many school and district leaders wish to leave this up to individual teachers. For a more detailed discussion, the reader should consult Classroom Assessment and Grading That Work (Marzano, 2006). When learner goals have been articulated in scale format as in Figure 1.11, the teacher and students have clear direction about instructional targets as well as descriptions of levels of understanding and performance for those targets.


Figure 1.11. Scale for Number Sense in 3rd Grade


Score 4.0

In addition to Score 3.0 performance, in-depth inferences and applications that go beyond what was taught.

Score 3.5

In addition to Score 3.0 performance, partial success at inferences and applications that go beyond what was taught.

Score 3.0

The student demonstrates number sense by

  • ordering and comparing whole numbers (millions), decimals (thousandths), and fractions with like denominators
  • converting between equivalent forms of fractions, decimals, and whole numbers
  • finding and representing factors and multiples of whole numbers through 100

The student exhibits no major errors or omissions.

Score 2.5

No major errors or omissions regarding the simpler details and processes and partial knowledge of the more complex ideas and processes.

Score 2.0

The student exhibits no major errors or omissions regarding the simpler details and processes:

  • basic terminology, for example—
    • millions
    • thousandths
    • like denominator
    • factor
    • multiple
  • basic solutions, for example—
    • 5.15 is greater than 5.005
    • 3/4 is the same as 0.75
    • 4 is a factor of 12

However, the student exhibits major errors or omissions regarding the more complex ideas and processes stated in score 3.0.

Score 1.5

Partial knowledge of the simpler details and processes but major errors or omissions regarding the more complex ideas and processes.

Score 1.0

With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.

Score 0.5

With help, a partial understanding of some of the simpler details and processes but not the more complex ideas and processes.

Score 0.0

Even with help, no understanding or skill demonstrated.

Source: Adapted from Marzano & Haystead, in press.


Action Step 3. Have Students Identify Their Own Learning Goals

One way to enhance student involvement in an instructional unit's subject matter is to ask students to identify something that interests them beyond the teacher-identified learning goals. During a unit on habitats, for example, a particular student might decide that she wants to find out about a particular animal—the falcons she sometimes sees flying over the field next to her bedroom. Even though personal applications might not seem obvious to students at first, a little guidance can go a long way in demonstrating to students that they can relate their own interests to the content addressed in class. To illustrate, a teacher once shared with me a personal goal a student had identified during a mathematics unit on polynomials. The student wanted to know what types of polynomials were used when rating quarterbacks in football. As a result of some Internet research, the student identified and could explain three formulas for rating quarterbacks:

National Football League Quarterback Rating Formula
a = (((Comp/Att) × 100) - 30) / 20
b = ((TDs/Att) × 100) / 5
c = (9.5 - ((Int/Att) × 100)) / 4
d = ((Yards/Att) - 3) / 4
a, b, c, and d cannot be greater than 2.375 or less than 0.
QB Rating = (a + b + c + d) / 0.06
Arena Football League Quarterback Rating Formula
a = (((Comp/Att) × 100) - 30) / 20
b = ((TDs/Att) × 100) / (20/3)
c = (9.5 - ((Int/Att) × 100)) / 4
d = ((Yards/Att) - 3) / 4
a, b, c, and d cannot be greater than 2.375 or less than 0.
QB Rating = (a + b + c + d) / 0.06
National Collegiate Athletic League Quarterback Rating Formula
a = (Comp/Att) × 100
b = (TDs/Att) × 100
c = (Int/Att) × 100
d = Yards/Att
QB Rating = a + (3.3 × b) - (2 × c) + (8.4 × d)
Key: Comp = pass completions, Att = pass attempts, TDs = completed touchdown passes, Int = interceptions thrown, Yards = passing yards.

Once students have identified their personal goals, they should write them in a format similar to the one used by the teacher:

When this unit is completed I will better understand_________.
or
When this unit is completed I will be able to________________.
Students might also use a simplified version of the scale to keep track of their progress:
4. I did better than I thought I would do.
3. I accomplished my goal.
2. I didn't accomplish everything I want to, but I learned quite a bit.
1. I tried but didn't really learn much.
0. I didn't really try to accomplish my goal.

Action Step 4. Assess Students Using a Formative Approach

As described in the research and theory section, formative assessment is not only a powerful measurement tool but also a powerful instructional tool because it allows students to observe their own progress. As I explained, formative assessments are used while students are learning new content. In the case of a unit of instruction, formative assessments are used from the beginning to the end. The scale discussed in Action Step 2 is designed specifically for formative assessment because each score on the scale describes specific progress toward a specific learning goal. That is, a score of 4.0 indicates that the student has gone beyond the information and skill taught by the teacher. A score of 3.0 indicates that the student has learned the target knowledge as articulated by the teacher. A score of 2.0 indicates that the student understands or can perform the simpler information and skills relative to the learning goal but not the more complex information or processes. A score of 1.0 indicates that on his or her own the student does not demonstrate understanding of or skill regarding the learning goal, but with help the student does. Finally a score of 0.0 indicates that even with help the student does not demonstrate understanding or skill relative to the learning goal.

To design a formative assessment for a particular learning goal, a teacher must ensure that the assessment contains items or tasks that apply to levels 2.0, 3.0, and 4.0. For example, reconsider the scale for number sense reported in Figure 1.11. To design an assessment regarding this topic, the teacher would make sure she has items that represent score values of 4.0, 3.0, and 2.0. She would include some items or tasks on the test that require students to order and compare whole numbers to the millions, decimals to thousandths, and fractions with like denominators. She would include items or tasks that require students to convert between equivalent forms of fractions, decimals, and whole numbers. Likewise she would include some items or tasks that require students to represent factors and multiples of whole numbers through 100. Success on these tasks would indicate a score value of 3.0. To determine whether students should receive a score value of 2.0, the teacher would include items that address simpler aspects of the learning goal. She might assess knowledge of basic terminology such as millions, thousandths, like denominator, factor, and multiple. Finally, to determine whether students deserve a score value of 4.0, she would include items or tasks that go beyond what she had addressed in class. For example, she might include items or tasks that require students to convert composite numbers that had not been addressed in class.

Scoring assessments designed around the simplified or complete scale is a matter of examining the pattern of responses for each student. (For a detailed discussion, see Classroom Assessment and Grading That Work [Marzano, 2006].) In the beginning of the unit, students would most likely receive low scores on these assessments. However, by the end of the unit students should show growth in their scores. This is at the heart of formative assessment—examining the gradual increase in knowledge for specific learning goals throughout a unit.

Action Step 5. Have Students Chart Their Progress on Each Learning Goal

Because formative assessments are designed to provide a view of students' learning over time, one useful activity is to have students chart their own progress on each learning goal. To do so, the teacher provides a blank chart for each learning goal that resembles the one shown in Figure 1.12.

Figure 1.12. Student Progress Chart

Source:

The chart in Figure 1.12 has already been filled out. The first column represents an assessment given by the teacher on October 5. This student received a score of 1.5 on that assessment. The second column represents the assessment on October 12. This student received a score of 2.0 on that assessment; and so on. Having each student keep track of his or her scores on learning goals in this fashion provides them with visual views of their progress. It also allows for powerful discussions between teacher and students. The teacher can discuss progress with each student regarding each learning goal. Also, in a tracking system such as this one the student and teacher are better able to communicate with parents regarding the student's progress in specific areas of information and skill. Finally, note that the chart has places for students to identify the progress they wish to make and the things they are willing to do to make that progress.

Action Step 6. Recognize and Celebrate Growth

One of the most powerful aspects of formative assessment is that it allows students to see their progress over time, as depicted in Figure 1.12. In a system like this one, virtually every student will succeed in the sense that each student will increase his or her knowledge relative to specific learning goals. One student might have started with a score of 2.0 on a specific learning goal and then increased to a score of 3.5; another student might have started with a 1.0 and increased to a 2.5—both have learned. Knowledge gain, then, is the currency of student success in a formative assessment system. Focusing on knowledge gain also provides a legitimate way to recognize and celebrate—as opposed to reward—success. Recall the discussion in the research section regarding rewards and intrinsic motivation. Whereas tangible reward has weak support for its use, verbal reward has moderate support. That research notwithstanding, even verbal recognition when used as a way to control student behavior externally is questionable. This action step recommends that knowledge gain for each student be recognized and celebrated. Such behavior seems more directly aligned with Deci, Ryan, and Koestner's (2001) call to acknowledge students in a way that promotes self-regulation.

To illustrate, a chart like the one in Figure 1.13 can be constructed for each student. This figure indicates that the student has gained 2 points on learning goal 1, 0.5 points on learning goal 2, and 2.5 points on learning goal 3. When knowledge gain has been recognized, it can be legitimately celebrated. For example, teachers might hold informal and verbal celebrations by asking all students who gained 0.5 points for a specific learning goal to stand and be acknowledged by a round of applause from their classmates, then all students who gained 1.0 points, and so on. Such celebrations could occur for each learning goal and at the end of each unit or grading period. In this context of recognition and celebration, teachers could also acknowledge those students who obtained high scores (i.e., scores of 3.0 and higher) on learning goals.

Figure 1.13. Individual Student's Knowledge Gain Chart

Summary

When considering the first instructional design question—What will I do to establish and communicate learning goals, track student progress, and celebrate success?—teachers should think about three basic elements. First, establishing and communicating learning goals involves distinguishing between learning goals and learning activities and then writing learning goals in a suitable format. Second, tracking student progress involves using formative assessments and a scale designed specifically for formative assessments. It also involves charting student progress on individual learning goals. Third, celebrating success involves recognizing and acknowledging students' knowledge gains.




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