New vocabulary words, generalized formulae, and prior knowledge-the ideas stack up by the end of a new unit. I often ask, “Have my students really learned all of this?” Best teaching practices allow time for students to synthesize their thinking before a summative assessment.  One way this can be done effectively is a concept map, a diagram representing all the ways a student connects different ideas in their head. I find that as more justified connections are made, the more deeply the knowledge is demonstrated. It is visual and collaborative but the problem is that in practice, not every student is sure how to parse out what they know to even begin. They delay for too long because they are overwhelmed and then rush at the end of the period to get it done, often relying on following another team’s setup. I suggest there is a better way to allow for more student ownership in the process of mapping.

The first time I introduced the concept this school year was to students in my high school geometry class during unit 2: Angle Relationships and Measurement. One example of student work is shown below:

To create this map, my students followed these procedures:

• Students work in teams to create a list of vocabulary words important to Unit 2: Angle Relationships and Measurement in order to build relevancy. First I challenged students to create a list of relevant vocabulary words. “It’s a competition,” I said and asked the students to take out their binders of notes and toolkits, but to keep them closed until the last minute of brainstorming.
• Students share out words to generate a comprehensive class list. I used a whiparound for each team to share their total. I pulled the list of the team with the greatest total and read it aloud to the class. Teams checked off words that they had in common. Then I asked for volunteers to share which words were missing from the list in order to have a comprehensive list of words. The range of words for teams in my classes was from 6 to 35. Additionally, a number of student added formulae.    
• Teacher models connecting words in order to set expectations. To model making connections among words, I  pointed out how messy the arrows became which created the need for the pre-cut vocabulary word cards. I instructed the class that the next task was going to help organize their connections better. I set expectations by posting the following three important things to remember: (1) Talk only to your team about math. (2) Different teams are going to think different ways. (3) The goal is to make sure you have a clear picture of how you think at the end.

• Students sort the vocabulary cards. I suggested sorting words in “we know’ and “we don’t know yet” piles. I expected students to use one another, their notes, the textbook’s glossary, and/or the teacher to identify the definitions. Then I instructed students to group the words into 3 to 5 categories. Once students identified their categories, I asked them to make connections within each category (like sub-categories). Finally I asked them to look for connections that would demonstrate meaning between one category and another.  I assessed student knowledge of math concepts and monitored students by circulating the room to listen as students moved through each step. I intervened and asked students to do a quick Google search to find examples of varied concept maps from different industries to inspire more complex connections. 

• Students participate in a gallery walk in order to practice giving and receiving effective feedback. Student teams circulated the room to examine the reasoning of others. Specifically, I asked them to look for one connection that was unique from what they identified. The intent was for students to now reflect on their own connections to think about any adjustments they can make. This was informal feedback so students added verbal comments about the connections and offered organizational suggestions to their own work.
• Teacher posts exemplars of student work to serve as anchors for the next round of concept maps in a future unit. My plan is for students to add effective feedback to another team’s concept map. I added feedback to the exemplars using “you” language to point out specific details and will instruct students to use the same format in order to continue the feedback loop. As part of ownership of learning, students getting feedback from the teacher and others will allow them to ultimately consider how to improve their own work.

Asking students to take ownership of all that they have learned can be a daunting task, but I have found that using concept maps brings groups of students together and allows them to form a consensus so that they know what they know.  Don’t worry if every team doesn’t get out of the isolated categories stage, especially if this is the first time they’ve attempted a concept map. Mastery takes time.

A few final pointers that I have experienced with concept maps:

• Assign different colored markers to each team member to ensure equity of student voice.
• Only give glue and large paper when students have established categories. When building fluency, students should speak first about their ideas before beginning to write them down.
• Employ team roles to help manage this task. For example, the Resource Manager can make sure the markers are recapped and the Facilitator can make sure all team member ideas are heard.
• Students can add their own words. A few student teams wanted to add the word measure, for instance.
• Post-its can be used when students are providing feedback to one another on future concept maps.

Concept maps have had a significant impact on student learning in my classroom. I plan to use them every other unit, approximately three or four times a school year.