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  Reflect Strands
Seven Learn Reflect Strands featuring the Professional Development Focus of the Year will be held during the 2012-2013 academic year:
- Thursday, October 11, 2012 - NCTM Regional Conference and Exposition in Dallas, Texas
- Thursday, October 25, 2012 - NCTM Regional Conference and Exposition in Hartford, Connecticut
- Thursday, November 29, 2012 - NCTM Regional Conference and Exposition in Chicago, Illinois
- Saturday, December 1, 2012 - CMC-North Conference in Pacific Grove, California
- Thursday, April 18, 2013 - NCTM Annual Meeting and Exposition in Denver, Colorado
- Thursday, May 2, 2013 - WMC Annual Conference in Green Lake, Wisconsin
- Thursday, May 2, 2013 - OAME Annual Conference in Toronto, Canada
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:
- What role does
reasoning and proof play in increasing the opportunities for communication to
help students develop mathematical understanding?
- 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?
- 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?
- 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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