To compare is to identify similarities and differences between or among things or ideas. We each frequently engage in the process of comparing. We compare movies we have seen; we compare restaurants where we have eaten; we compare ski runs on our favorite mountains.

In the classroom, we can use this process deliberately and rigorously to deepen students' understanding of the knowledge they are learning. We can compare Heathcliff in Wuthering Heights to Mr. Rochester in Jane Eyre; we can compare the shape of the graph of y = 2x + 3 to the shape of y = 2x − 3; we can compare strategies used in the battles of Gettysburg and Antietam during the Civil War.

Before reading “Recommendations for Classroom Practice,” take some time to reflect on your current practices and beliefs about comparing by completing the Reflecting on My Current Beliefs and Practices—Comparing worksheet in Figure 1.1 (p. 10).

Figure 1.1. Reflecting on My Current Beliefs and Practices—Comparing

What is the purpose of asking students to compare?  What kinds of activities do I use to help students compare?  I can think of a time that I asked students to compare, and I was pleased with the results. Why did it go well?  I can think of a time that I asked students to compare, and I was not pleased with the results. Why did it not go well?  What questions do I have about using comparing in my classroom?

Recommendations for Classroom Practice

Comparing is a complex process that students will need to learn about and practice. In this module, we discuss several approaches to use in the classroom:

• give students a model for the process,
• use familiar content to teach students the steps for comparing,
• give students graphic organizers for comparing, and
• guide students as needed.

Give Students a Model

Students understand the process of comparing on some level because they compare things every day: “Friday's lunch in the cafeteria was better than today's”; “Fat Boy Slim's new music video is way cooler than the new 311 video”; “Ms. Bloomer's calculus class is a lot harder than Mr. Stacy's.” To push students beyond the kind of comparing that they do automatically every day, we need to teach a systematic process and hold students accountable for rigorously using it. A model for comparing might include a set of steps for students to follow like those in Figure 1.2 (p. 11).

Figure 1.2. Model for Comparing

Steps for Comparing Select the items you want to compare. Select the characteristics of the items on which you want to base your comparison. Explain how the items are similar and different with respect to the characteristics.	Steps for Comparing for Younger Students What do I want to compare? What things about them do I want to compare? How are they the same? How are they different?
(Adapted from Dimensions of Learning, Marzano et al., 1997).

Comparing activities have broad applications. The key to an effective comparison is to identify important characteristics (those that will enhance students' understanding of the similarities and differences between the items). If students are comparing Malcolm X and Martin Luther King Jr. during a history class, describing similarities and differences between the two men in terms of “where they were born” might be interesting but does not add much to students' learning. A more useful characteristic might be “religious views” or “role in the Civil Rights movement.”

We can make many comparisons at a surface level that do not contribute much to our learning. For example, we could compare the Lewis and Clark expedition to Pike's 1806 Arkansas River expedition on the basis of who went on the expeditions, how long each trip lasted, what kind of clothes the members of the expedition wore, and which expedition was written about the most. We might learn that Lewis and Clark became more famous than Pike, even though the Pike expedition was better dressed. Does this information add to our understanding of the importance of these expeditions? Probably not. Students will have a much better understanding of the Lewis and Clark expedition and Pike's 1806 expedition if they base their comparison on meaningful characteristics, such as each expedition's purpose, areas explored, and outcomes.

Use Familiar Content

Everyday comparisons can help students under stand the steps in the comparing process. For example, if students are comparing Friday's cafeteria lunch to Tuesday's lunch, they can compare them based on a set of characteristics, such as nutritional content, variety of foods, and type of cuisine. Explaining how the items are similar and different in terms of these characteristics uncovers for students the information that lies behind the claim that Friday's cafeteria lunch was “better” than Tuesday's. Understanding and following steps in a process for comparing helps students when they use the process with content knowledge.

Give Students Graphic Organizers

Students can use graphic organizers as a visual tool to help them make comparisons. A Venn diagram uses two intersecting circles to show how items are similar and different. Similarities are shown in the intersection of the circles, and differences are indicated in the parts of each circle that do not overlap. Teachers can demonstrate the use of Venn diagrams in a couple of different ways. A Venn diagram might be used to compare two things.

In the example in Figure 1.3 (p. 12), one Venn diagram is used to compare the characteristics of rain forests and deserts. The characteristics include plant life, animal life, and climate. You can also use Venn diagrams to compare one characteristic at a time.

Figure 1.3. Venn Diagram 1—Rain Forest and Desert

In the comparison shown in Figures 1.4 (p. 13) and 1.5 (p. 13), two Venn diagrams show similarities and differences between two specific places—the Amazon Rain Forest in South America and the Mojave Desert in the southwestern United States. Each Venn diagram contains similarities and differences for only one characteristic each: one for climate and one for animals.

Figure 1.4. Venn Diagram 2—Rain Forest and Desert Climate

Figure 1.5. Venn Diagram 3—Rain Forest and Desert Animals

Students can also use a comparison matrix to graphically represent similarities and differences among items (see Figure 1.6, p. 14). The comparison matrix helps students systematically organize information about the items or events they are comparing.

Figure 1.6. Comparison Matrix—Basic Measures

	Items to be compared
Characteristics	1-cm square	2-cm square	Rectangle: width 4 cm length 6 cm	Rectangle: width 3 cm length 7 cm	Rectangle: width 3 cm length 8 cm
Perimeter	4 cm	8 cm	20 cm	20 cm	22 cm
Area	1 sq. cm	4 sq. cm	24 sq. cm	21 sq. cm	24 sq. cm
Conclusions	Two rectangles can have the same perimeter, but different areas. That also means that a square and a rectangle could have the same perimeter, but different areas. Also, two rectangles can have the same area, but different perimeters. If you double the size of a square, the perimeter doubles, but the area increases 4 times.
Blackline master available, p. 352

You may need to provide more detailed instructions when students use a comparison matrix. Including a space for students to write their conclusions helps them bring together the pieces of the comparison and reflect on what they have learned.

Guide Students As Needed

When students are first learning to use the process of comparing, you can give them more of the information they need to complete the task. For example, you might identify the items to compare and the characteristics to use in the comparison. In this case, students describe how the items are similar and different based on the characteristics you have identified. You also might ask students to summarize what they have learned. Although these structured comparisons are somewhat limiting because students are working with a defined set of items and characteristics, this structure can be very useful when teaching students the process of comparison.

After students have had some practice completing more structured comparison activities, you can give less structure and less guidance. For this type of activity, you might identify the items for students to compare and ask them to choose the characteristics upon which to base the comparison. Students have more freedom and they also must think and work more independently. As they become more comfortable with the process of comparing, students must grapple with the issue of choosing meaningful characteristics to use to compare items you have identified.

Tools to Facilitate Comparing in the Classroom

To guide your students effectively you need to be confident of your own understanding of how to use comparing. Figure 1.7, Checking My Understanding—Comparing (p. 16), gives you an opportunity to apply what you have learned in the previous discussion. If you find it difficult to complete the comparison matrix, we suggest you reread “Recommendations for Classroom Practice.” The other assessment and planning tools that follow will help you guide your students when using comparing processes in the classroom.

Figure 1.7. Checking My Understanding—Comparing

Complete this matrix by adding one more living thing and one more characteristic. Focus on similarities and differences.
	Items to be compared
Characteristics	Pine Tree	Tulip	Elephant	Shark
External body features
Habitat
Sources of energy
What knowledge did you need to complete this task?  What insights did you gain about the process of identifying similarities and differences while using the comparison matrix?
Blackline master available, p. 352

Assessing the Impact on Students

Rubrics are one tool you can use to gauge students' progress. Sample rubrics are provided in Figure 1.8 (p. 17) for evaluating students' progress in using the comparing process. These rubrics can be revised, when appropriate, for students to use as part of the self-assessment process to help them reflect on their work.

Figure 1.8. Rubrics for Comparing

Comparing Rubric	Comparing Rubric for Younger Students
4  The student uses important, as well as some less obvious, characteristics to compare the items. The student accurately identifies the similarities and differences and explains his conclusions in a way that shows a complete and detailed understanding of the items.	4  The student uses important features to compare the items. The student also uses some features that are not easily seen. The student identifies similarities and differences without making mistakes. The student tells what she learned in a way that shows a complete understanding of the items.
3  The student uses important characteristics to compare the items. The student accurately identifies the similarities and differences and explains his conclusions.	3  The student uses important features to compare the items. The student identifies similarities and differences without making mistakes. The student tells what she learned.
2  The student uses characteristics to compare the items, but not the most important characteristics. The student's comparison and conclusions show some misconceptions about the items.	2  The student uses features to compare the items, but the student does not use the most important features. The student makes some mistakes in the comparison.
1  The student uses insignificant characteristics to compare the items. The student's comparison and conclusions show many misconceptions that indicate the student does not understand the items.	1  The student uses features that are not important to compare the items. The student makes some big mistakes in the comparison.
0  Not enough information to make a judgment.	0  The student does not try to do the task.

Planning Classroom Activities and Assessing Myself

Answering a series of questions will help you discover how you might use the strategies for using comparing presented in this module. You can use the Planning for Comparing Worksheet, Figure 1.9 (p. 19), to guide your thinking when planning comparing activities for students.

Figure 1.9. Planning for Comparing Worksheet

What knowledge will students be learning?  Do I need to set aside time to teach students comparing? How will I teach them the process?  Will I ask students to use a graphic organizer?  How much guidance will I provide students?  How will students explain their work and communicate their conclusions?  How will I monitor how well students are doing with comparing?  What will I do to help students who are not comparing effectively?

Rubrics help assess student learning. You can also use a tool to assess yourself—how effectively you are using comparing strategies. Use Figure 1.10 (p. 20) to evaluate your effectiveness in teaching comparing strategies.

Figure 1.10. Assessing Myself—Comparing

Module Reflection

Review your responses to the questions in Figure 1.1, Reflecting on My Current Beliefs and Practices—Comparing (p. 10). How has this module affected your thinking about teaching and learning? What have you learned about yourself as a teacher and learner? Use the space provided to record your thoughts.

• Reading this information affirms some of what I already knew about comparing
• Now, I better understand some things about comparing
• I think I will change how I use comparing in my classroom