Graphic organizers are powerful tools that support conceptual development, language development, and skills acquisition when used appropriately. In the mathematics classroom, they can serve as powerful vehicles that facilitate discussion, provide formative assessment data, and allow students to demonstrate their thinking in creative ways.  

In order to achieve success with the use of graphic organizers, the teacher has to select the appropriate organizer, understand it, plan for how the organizer will be used to promote thinking, and develop appropriate questions and tasks.

Some organizers are teacher-led. This means the teacher facilitates the completion of the organizers. Students may be engaged in Think-Pair-Shares as a part of the process. These teacher-led organizers are fantastic for notetaking; this format creates notes that are easy to read and user-friendly. The teacher identifies critical concepts, vocabulary, and other pertinent information, and creates the template. Some topics lend themselves to the use of graphic organizers and support the use of multiple representations.

The organizer below was developed this year to show the various forms of numbers.

In some cases, the organizers are perfect exit tickets, providing the teacher with good data that can help to identify students who need intervention in the understanding of key concepts, vocabulary, and skills. Below is an example of an organizer used with 6^th grade students to determine their conceptual understanding of percents. This Concept Wheel organizer, which is useful when you want students to analyze a particular concept and provide multiple representations, properties, characteristics, and/or examples of the topic in the center.

Below is a modification of the Concept Wheel to address the conceptual understanding of the concept of percent. This organizer was used as an exit ticket. Prior to completing the exit ticket, students had been engaged in a group activity where multiple representations of percents was the focus. 

The use of interactive student notebooks is common in mathematics classrooms. When students take notes, there should be an expectation that the notes will be used as reference tools to support students’ thinking and work.  The example below shows how one student used his notes to support the creation of the graphic organizer to illustrate the hierarchy of polygons in geometry. In this case, you see a student-generated organizer. The teacher did not provide guidance on how to organize the information; however, the students in this classroom have had extensive exposure to the use of a variety of organizers, providing the prerequisite skills to create the organizer.

The organization of ideas and steps is critical to success in mathematics. For instance, when solving multi-step problems, many students do not know where—or how—to start. Sometimes this is the result of never having learned how to organize their thinking.  The Sequence Chart is a great tool to support students’ ability to organize information and approach problem solving in a more systematic manner. 

After being exposed to the use of the Sequence Chart, a group of 4^th grade students began to instinctively organize their information by outlining their steps. Below is a sample of one student’s work.

Finally, specific vocabulary may be the focus. The example below illustrates such an organizer. The inclusion of synonyms is important because in some application problems, the word area may not be used, but the concept is targeted. For example, the term “carpet” may appear in a problem, and students may be asked to determine the amount of carpet covering a floor in a room with the dimensions of 10 ft by 12 ft. The students must understand that carpet is now used synonymously with the concept of area.

A few final thoughts regarding using graphic organizers in the math classroom:

• Focus on content information that is difficult for students to understand and/or is poorly organized.
• Develop an outline of the key ideas/concepts in the target information.
• Select an appropriate graphic organizer format that will accurately represent the structure of the content information (e.g., hierarchical, compare and contrast, sequence).

Watch Bea Moore Luchin's Spring 2016 Webinar, "Communicating in Math: How to Help Students Justify their Work with Reflective Thinking."

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