In the study of mathematics, students need opportunities to reflect upon their mathematical understandings. This Mathematical Concept Mapping Project involves students submitting concept maps drawn at the conclusion of instructional units to elicit further collaboration with middle school students. Concept maps are effective methods of assessing student knowledge, comprehension, synthesis, and evaluation. This project affords students a platform for illustrating and sharing their mathematical proficiency with their peers. Submitted concept maps will be compiled into the standard mathematical categories enabling teachers to quickly locate maps targeting current studies. Opportunities abound for teachers to further utilize these concept maps in their classrooms for collaboration, critical thinking comparisons, and deeper evaluation. A potential outcome of this project is to compile a resource of mathematical concept maps on the web.
In mathematics, all the standards require students to identify, interpret, reason, evaluate, and explain the connections and relationships between the various concepts they are learning. It is imperative that students be able to express those relationships in order to consolidate and strengthen their understandings as well as further evaluate these newly acquired concepts and skills. Concept maps, if completed correctly, contain concepts, linking phrases and links which clearly demonstrate student understanding. They are effective tools for reflection allowing students the opportunity to rethink how concepts have been illustrated. Their versatility, different methods of mapping and diverse applications, facilitate differentiated instruction. Peer review and class discussion deepen the learning process as students explain their maps. Students finally complete their maps and the final revision becomes a presentation worthy of display. This project gives students the stage for accomplishing that task, an authentic arena for presenting their mathematical connections.
Standard 2 – Algebraic Reasoning:
2.02 use reading, listening, viewing, speaking and writing to explain and develop mathematical ideas
Standard 3 – Geometric Reasoning:
3.02 draw and then justify conclusions
3.03 construct and follow logical arguments
3.04 use properties, models, known facts, and relationships to explain and defend their thinking
Standard 4 – Quantitative Reasoning:
4.01 make connections linking conceptual and procedural knowledge;
4.03 use connections among mathematical topics
Standard 5 - Problem Solving:
Monitor and reflect on the process of mathematical problem solving to integrate mathematical reasoning, communication and connections
Standard 6 - Reasoning and Proof:
Justify their thinking
Reinforce and extend their logical reasoning abilities
Reflect on and clarify own thinking
Standard 7 - Communication:
Organize and consolidate their mathematical thinking through communication
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
Analyze and evaluate the mathematical thinking and strategies of others
Use the language of mathematics to express mathematical ideas precisely
Standard 8 - Connections:
Recognize and use connections among mathematical ideas
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole
Recognize and apply mathematics in contexts outside of mathematics
NETS: Technology Standards:
Students develop positive attitudes toward technology uses that support lifelong learning, collaboration, personal pursuits, and productivity.
Students use technology tools to enhance learning, increase productivity, and promote creativity.
Students use productivity tools to collaborate in constructing technology-enhanced models, prepare publications, and produce other creative works.
Students use telecommunications to collaborate, publish, and interact with peers, experts, and other audiences.
This CIP is designed as a compilation of student concept maps which evidence student understandings of the mathematical concepts acquired during the middle school years. Even though concept maps can be effectively utilized throughout a unit, this project targets those concept maps that evidence solidified understanding of learned concepts and their connections. These maps are typically generated at the end of a unit as a final project. Students draw from multiple sources when compiling their maps; prior knowledge, textbooks, the Internet, classroom activities, and class discussions. Web sites on concept mapping are included as guidelines for accurate mapping skills. Individual classroom teachers will determine those concept maps appropriate for submission to the project. Concept maps must be submitted using a content mapping software. CMAP is free to download and is an excellent program for middle school students.
The Mathematical Concept Maps CIP is designed for students to work on independently or in small groups. Students will use their understanding of the unit concepts to create a concept map which communicates their conceptual understanding of and connections between mathematical concepts. They will then reflect upon their maps and revise them for presentation. Students will work on their individual laptops to create, revise, and publish their maps in the appropriate software program. Classrooms with only one computer should create concept maps on paper, reflect and revise, and then use the computer for the final creation and posting of finished maps. Once the maps are completed, the classroom teacher is responsible for submitting them to the project coordinator for posting on the CIP web site.
If you are unfamiliar with concept maps or have not used linking phrases on previous maps, I encourage you to check out the following articles on creating effective concept maps and how to facilitate mathematics instruction with concept mapping activities. For concept maps to be effective, they must clearly demonstrate student understanding. Students need to comprehend the logistics of concept maps in order to make the necessary connections between each linked concept. These two resources should encourage and challenge you as you implement concept mapping into your classroom instruction.
Further Resources/ References
Lesson Plans that implement concept maps
Afamasaga-Fuata’i, Karoline (2004, September 14). Concept maps & vee diagrams as tools for learning new mathematics topics. Retrieved June 22, 2006, from CMC 2004 Web site: http://cmc.ihmc.us/papers/cmc2004-271.pdf
Åhlberg, Mauri (2004, September 14). Varieties of concept mapping. Retrieved July 1, 2006, from CMC 2004 Web site: http://cmc.ihmc.us/papers/cmc2004-206.pdf
Baroody, Arthur J., & Bartels, Bobbye H (2001). Assessing understanding in mathematics with concept mapping. Mathematics in School. 30 no3, 24-7.
Baroody, Arthur J., & Bartels, Bobbye H. (2000). Using concept maps to link mathematical ideas. Mathematics teaching in the middle school. 5. Issue 9, 604-609.
Bartels, Bobbye H. (1995).Promoting Mathematics Connections with Concept Mapping. Mathematics Teaching in the Middle School. 1 n7, 42-49.
Freeman, Lee A. (2004, September 14). The power and benefits of concept mapping measuring the usefulness, ease of use, and satisfaction. Retrieved July 1, 2006, from CMC 2004 Web site: http://cmc.ihmc.us/papers/cmc2004-164.pdf
Karchmer, Rachel A., Marla H. Mallette, Julia Kara-Soteriou, & Donald J. Leu, Jr. (Ed.). (2005). Innovative approaches to literacy education: using the internet to support new literacies. Newark, Delaware: International Reading Association.
Novak, Joseph D. (2004, September 14). A science education research program that led to the development of the concept mapping tool and a new model for education. Retrieved June 22, 2006, from CMC 2004 Web site: http://cmc.ihmc.us/papers/cmc2004-286.pdf
Dates: September 5, 2006 – May 25, 2007
Registration Instructions: Send email to Project Coordinator
Karen C. Brown
Conrad Middle School
Wilmington, DE, USA