by NCTM President J. Michael Shaughnessy
NCTM Summing Up, January 2011
Last April, at the start of my presidency, I alerted NCTM members that the Council would be concentrating on three significant ongoing issues during my term—and perhaps continuing beyond my term:
(1) Continuing our efforts to link research and practice throughout all NCTM publications and initiatives
(2) Providing support for teachers and teacher leaders in the interpretation and implementation of the Common Core State Standards (CCSS)
(3) Sustaining our focus on mathematical reasoning and sense making in all mathematics classrooms.
In past messages, I’ve informed you about the Council’s work to link research and practice, particularly through the recommendations of the Research Agenda Project (May Summing Up President’s Message), and I’ve also reported on NCTM’s new resources and joint efforts with other organizations regarding the CCSS (November Summing Up President’s Message).
As we begin the New Year, I want to provide further information on NCTM’s progress on our most important work—NCTM’s Reasoning and Sense Making Initiative. Some special resources and events that are underway to support this initiative in the coming year include the following:
- Additional books and print resources
- Enhanced Web-based resources
- Video and multimedia cluster resources
- A Reasoning and Sense Making Institute for secondary teachers and teacher leaders in the summer of 2011
NCTM Print Resources for Reasoning and Sense Making
In the fall of 2009, NCTM released Focus in High School Mathematics: Reasoning and Sense Making. This publication provides the Council’s official position on the teaching and learning of secondary mathematics. Focus in High School Mathematics represents NCTM’s continued effort to emphasize the critical role of the Process Standards outlined in Principals and Standards for School Mathematics in the teaching and learning of mathematics. We focused first at the secondary level because of what we observed:
“Currently, many [secondary] students have difficulty because they find mathematics meaningless….With purposeful attention and planning, teachers can hold all students in every… mathematics classroom accountable for personally engaging in reasoning and sense making, and thus lead students to experience reasoning for themselves rather than merely observe it.” —NCTM 2009, pp. 5–6
Lending support to Focus in High School Mathematics: Reasoning and Sense Making are five companion books that elaborate on content strands and some NCTM Principles fromPrinciples and Standards for School Mathematics. Three books, on Algebra, Geometry, and Statistics and Probability, were published in 2009 and 2010.
A fourth book, Focus in High School Mathematics: Fostering Reasoning and Sense Making for All Students, focuses on equity in the reasoning initiative and will be available soon. A fifth book focuses on incorporating technology in students’ mathematical reasoning and sense making, and that book should be available later in 2011.
New NCTM Web Resources Focused on Reasoning and Sense Making
A PowerPoint presentation that includes an overview of NCTM’s Reasoning and Sense Making Initiative is available to members on the NCTM website. This downloadable resource also contains an initial set of five examples that are drawn from the Reasoning and Sense Making books. These reasoning tasks are presented in a supporting framework that includes suggestions for teachers on launching them, ideas for reflecting on student work, and possible follow-up activities to assess student reasoning. A Task Development group has been appointed by the NCTM Board to continue developing and posting additional tasks on the NCTM website throughout 2011.
Video Clips of Secondary Students Engaged in Reasoning and Sense Making
The use of video clips showing students engaged in reasoning about mathematical tasks has been growing in our profession by leaps and bounds. Video clips are currently used in classroom research, for professional development, and as teaching tools offering opportunities for students to explain how other students reason about their mathematics. However, most of the current video clips that show students engaged in reasoning and sense making in mathematics feature elementary or middle school students. Video clips of secondary students are few and far between, unfortunately. A major piece of our NCTM initiative this past year has been carried out by a new Video Task Force that is looking into the creation of prototype video clips of secondary students engaged in mathematical reasoning. The task force hopes to accompany the video clips with related tools such as live audio-pen recordings of students working, resources for teacher reflection and discussion, and support materials for professional development. Several prototype videos will be presented at the February meeting of the NCTM Board of Directors as this work continues to evolve.
New Event: Secondary Institute on Reasoning and Sense Making in Mathematics
NCTM will hold a new event during the summer of 2011: Infusing the Classroom with Reasoning and Sense Making: An NCTM Interactive Institute on High School Mathematics. This three-day secondary institute, designed for teachers, teacher leaders, and mathematics supervisors, will take place in Orlando, July 28–30. Special keynote presentations and ongoing work sessions are planned to help educators—
- improve their understanding of how reasoning and sense making are integral to teaching with the Common Core State Standards for Mathematics, as well as state standards and provincial guidelines.
- gain strategies for creating and maintaining a high school classroom infused with reasoning and sense making.
- learn to select, develop, and use mathematical tasks to reveal students’ thinking and to engage students in reasoning and sense making.
NCTM will also offer a special institute for elementary and middle school teachers in Baltimore, August 9–11. That institute, Algebra Readiness for Every Student will focus on algebraic reasoning and sense making in grades 3–8 and provide support for teachers in the interpretation and implementation of the algebra standards within the Common Core State Standards.
Final Thoughts
The resources and professional development opportunities found in NCTM’s Reasoning and Sense Making Initiative can help you carry out the vision of Principals and Standards for School Mathematics: To promote problem solving, critical reasoning, mathematical connections, increased communication and flexible representations of mathematical ideas among our students. The NCTM Reasoning and Sense Making Initiative resonates with the Standards for Mathematical Practice that are part of the Common Core State Standards. The vision of how mathematics should be taught was first put forth in Principles and Standards—to nurture reasoning and sense making in all our students’ mathematical experiences. We are far from realizing this vision today, particularly within the secondary classrooms. However, the Council is committed to providing creative support for teachers to incorporate reasoning and sense making into students’ mathematical activities every day.