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Professional Development Focus of the Year 2012-2013


Reasoning and Proof:  Is it true?  Convince me!

Elementary School Resources 
Middle School Resources  
High School Resources      


Why Reasoning and Proof?

The intent of this yearlong focus on reasoning and proof is to help teachers, school leaders, and teacher educators expand their view of how reasoning and proof should be an active part of all students’ learning of mathematics. This focus helps to support effective mathematics teaching, enhance mathematics learning, and influence what mathematics is taught.  The beauty of mathematics is accessible to students through the means of reasoning and proof. Students are able to work at higher levels of generalization, model and solve complex problems, and be more logical in their decision-making. 

The Principles and Standards for School Mathematics states that all students should be able to, “recognize reasoning and proof as fundamental aspects of mathematics; make and investigate mathematical conjectures; develop and evaluate mathematical arguments and proofs; and select and use various types of reasoning and methods of proof” (p. 56). Mathematical power comes when students have the ability to make reasoning and proof a habit of mind for all topics in mathematics. Although the term “proof” has been narrowly perceived as a geometry topic, it is really an essential link that connects all content areas. Reasoning and proof are as important for the first grader seeing than 2+3 is always five as it is for the algebra student making sense of rate of change. This ability helps students increase their opportunity for learning, for recognizing real-life social contexts and for creating a positive disposition for the future.  

By making “reasoning and proof” a Focus of the Year, we hope to launch this topic forward as an essential vehicle for learning mathematics in the 21st century. It can help students recognize patterns and find new relationships between mathematical topics. They will be able to make more sense of the mathematics they are learning by providing more efficient ways to represent, analyze, and communicate their mathematical ideas. When reasoning and proof is used strategically, it can lead to a deeper understanding of the five mathematics content standards for all students. Furthermore, reasoning and proof should not be thought of as an “extra” or “add-on” but as an integral part of every lesson taught in the mathematics classroom.  Constant use of reasoning and proof allows students to believe that logical mathematics reasoning is the authority within the classroom rather than the status of the person sharing their thoughts. This helps develop a student who is ready to be a productive part of our future society.

learn  Learn learn-reflect arrow Reflect Strands 

Seven Learn learn-reflect arrow Reflect Strands featuring the Professional Development Focus of the Year will be held during the 2012-2013 academic year:

The strands begin with a Kickoff session for all participants, continue with sessions for all grade bands, and culminate with Reflection sessions that allow participants to discuss the following questions:

  1. What role does reasoning and proof play in increasing the opportunities for communication to help students develop mathematical understanding?
  2. How does stressing reasoning and proof influence your instructional decisions? In addition, how do your instructional decisions influence how reasoning and proof should be stressed?
  3. How does reasoning and proof drive the lifelong learning of significant mathematics to all students? How is equity and diversity also promoted by stressing reasoning and proof?
  4. How are you thinking differently about your use of reasoning and proof because of participating in the Learn-Reflect strand? What are some of the steps you plan to take to promote reasoning and proof in your classroom/school?

Recent Focus of the Year Topics 



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