Math Concept Mapping

Project Description:

At the end of the year I asked my students to create a Popplet concept map showing all of the math concepts we learned over the course of the year. I was looking for a way for them to reflect on their learning and understand how math concepts are all intertwined. Through the year I knew they had seen a few connections, but not to the depth of understanding that just about every math concept is related to another. Instead, they saw each unit or concept as independent of the others. When we changed from one to another, that was a signal the work we had done previously could be forgotten or, at least, put on a back shelf, only to be accessed when absolutely necessary.

For this project, students worked as partners and created a bubble for each concept. Then students were asked to create a line connecting concepts that were related. Additionally, students were asked to explain the relationship in the comment section of the bubble, since this resource does not allow for labeling connectors.

 

Objectives:

My objectives were fairly simple. I was looking for students to think about what we had done all year and understand how math concepts connect. Typically, as we go from one concept to the next, there is a shut down of sorts, as students “finish” learning about addition and “begin” learning about multiplication. While our lessons try to make the connection, it always seemed to me that students did not fully understand the connections. Nor did they realize that all of the concepts are interrelated in some way or another. I wanted to change that.

            As students worked I listened to their conversations. At the beginning pairs of students tried to remember everything they had accomplished. One idea would remind them of another, they would overhear another group say something or a poster, chart or sign in the room would be a reminder of something else. I was pleasantly pleased at the number of concepts they were listing. Then I reminded students to make some connections. It was then that I started to hear to comments telling me this was working. I don’t remember the exact words, but I heard students talking about all of the different connections that could be made from a single bubble.

     At the end of the activity we discussed what students discovered by doing this, all of the groups reported they were especially surprised at how many of the math concepts were connected. “They all go in a big circle, “ one student commented. “Everything is connected.” Everyone else agreed. This one comment made the entire project worthwhile. It was a visual and the thinking needed to create the visual that brought it all home.

 

Future Changes and Improvements:

            In general, I am very happy with the project just as it is. I liked using Popplet as opposed to other mind mapping resources because it is simple to use and there are few extras to distract students and keep them from the task at hand.

            I do hope, however, that in the future the people running the Popplet website will add the opportunity to label the connecting lines and/or make the comments visible to people other than collaborators. The comments section allows students to really explain their thinking, but only collaborators can actually view them. Being able to turn this feature on and off would be great. Additionally, by labeling the connectors the way concept maps typically do will help students show their ideas in a very graphical way. I have made both of these suggestions to the Popplet people. They have responded that both are being seriously considered. 

            Additionally, I would like to find a way to help students remember concepts discussed at the beginning of the year without giving away too much. Mental math, for example, was a concept we spent a lot of time on, but only one group remembered it. I am afraid making a list of topics will keep students from doing the great thinking they did this year. It is something for me to ponder for the future.

            Once these maps are created, sharing them with parents, other classes we have connected with digitally and so on, along with embedding them into blogs and writing about them, gives even more meaning to the project. Since I had students do this just three days before the end of school, these opportunities were not realized, but definitely will be part of my future plans.

            A final change will be to make the project more collaborative by giving each student their own account. They would work as partners by creating the mind map synchronously on their own computers. That will also make it a bit more of an assessment for me because the additions made by each student are labeled with the creators name. We also could potentially collaborate with students in other schools, states or countries, as they build these maps together.

 

ISTE Connection to Standard:  Promote student reflection using collaborative tools to reveal and clarify students’ conceptual understanding and thinking, planning, and creative processes.

 

         This artifact reflects the standard because of the way it helped students reflect on their math learning for the year and create a visual that helped them recognize how math concepts are all intertwined.

         By making the process more collaborative as mentioned in my future plans, especially if working with teachers around the globe to build them, the collaboration has the potential to build an even deeper understanding since students in other classes will have different perspectives on the same material or add different concepts that are connected in ways my students would not envision otherwise.