Mathematics is an integrated field of study with dynamic connections. Mathematics is not a collection of separate strands or standards, even though it is often partitioned and presented in this manner. When students connect mathematical ideas, their understanding is deeper and more lasting, and they come to view mathematics as a coherent whole. They see mathematical connections in the rich interplay among mathematical topics, in contexts that relate mathematics to other subjects, and in their own interests and experiences. Through high quality instruction that emphasizes the interrelatedness of mathematical ideas, students learn not only mathematics but also about the utility of mathematics.
Students should come both to expect and to capitalize on connections, using insights gained in one mathematical context to verify conjectures in another. For example, elementary school students link their knowledge of the subtraction of whole numbers to the subtraction of decimals or fractions. Middle school students might collect and graph data for the circumference (C) and diameter (d) of a set of different sized circles. They could extend their previous knowledge in algebra and data analysis to recognize that the values nearly form a straight line, so C/d is between 3.1 and 3.2 (a rough estimation of π).
Students should connect mathematical concepts to their daily lives, as well as to applications from the sciences, social sciences, literature, business or the arts. Moreover, rich mathematical problems enable students to recognize the value of mathematics in examining personal, cultural, and societal issues. For example, high school students might work with a drug store chain to determine where it should locate a new pharmacy in their neighborhood on the basis of analyses of demographic and economic data.
Instructional programs from pre-kindergarten through grade 12 should enable all students to—
- 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.
The focus of the year gives all teachers, school leaders, and teacher educators the resources to recognize and utilize mathematical connections to expand students’ learning opportunities.
Learn Reflect Strands
Five Learn Reflect Strands featuring the Professional Development Focus of the Year will be held during the 2009-2010 academic year:
- Thursday, October 22, 2009 - NCTM Regional Conference and Exposition in Boston , Massachusetts
- Friday, October 23, 2009- Northwest Mathematics Conference in Whistler, British Columbia, Canada
- Thursday, November 5, 2009 - NCTM Regional Conference and Exposition in Minneapolis , Minnesota
- Thursday, November 19, 2009 NCTM Regional Conference and Exposition in Nashville , Tennessee
- Thursday, April 24, 2010 - NCTM Annual Meeting and Exposition in San Diego, California
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. How has your understanding of mathematics connections been changed, challenged, or confirmed?
2. What role do connections play in developing students’ insights about and understanding of mathematics?
3. What do you do and/or what will you do in your instruction to emphasize the interrelatedness of mathematical ideas?
4. How will you create classroom experiences that value and build upon the connections between mathematics and students’ prior knowledge, lived experiences, and personal interests?
Recent Focus of the Year Topics