Position Statement on the Standards for Mathematical Practice Page 3

CMA Representation as legislated:

September 30, 2011

Association of Independent Kentucky Colleges and Universities

Eastern Kentucky University

Education Professional Standards Board

Kentucky Adult Education

Kentucky Association of School Administrators

Kentucky Center for Mathematics

Kentucky Community & Technical College System

Kentucky Department of Education

Kentucky Council on Postsecondary Education

Kentucky Education & Workforce Development cabinet

Kentucky Education Association

Kentucky State University

Morehead State University

Murray State University

Northern Kentucky University

University of Kentucky

University of Louisville

Western Kentucky University

September 30, 2011

Position Statement on the Standards for Mathematical Practice Page 3

The Standards for Mathematical Practice are Essential for Mathematics Proficiency: A Position Statement of Kentucky Committee for Mathematics Achievement, Kentucky Council of Teachers of Mathematics, Kentucky Education Association, and Prichard Committee for Academic Excellence

Position. To emphasize the essentialness of the Standards for Mathematical Practice[1] to mathematics proficiency and beyond, the Committee for Mathematics Achievement (CMA), the Kentucky Council of Teachers of Mathematics, the Kentucky Education Association, and the Prichard Committee for Academic Excellence advocate 1) professional development for teachers emphasizing opportunities and methods for integrating the Standards for Mathematical Practice with the Standards for Mathematical Content, 2) the use of the Standards for Mathematical Practice as a framework to evaluate mathematics curricula, and 3) assessment of student understanding of the Common Core State Standards for Mathematics (in Kentucky referred to as Kentucky Core Academic Standards (KCAS)) that incorporate the integrative nature of the Standards for Mathematical Practice and the Standards for Mathematics Content.

Rationale. The CMA supported the Common Core State Standards Initiative[2] to develop evidence-based, “fewer, clearer, and higher” mathematics standards.[3] The Common Core State Standards Initiative resulted in the issuance of the Standards for Mathematics, including both the Standards for Mathematical Content (SMC) and the Standards for Mathematical Practice (SMP). The SMC and SMP are designed as integral components of the Standards for Mathematics although they appear in separate places in the Standards for Mathematics online version. While the SMC focus on the procedures and understanding of mathematics, the designers intended for the integration of the eight SMP with the SMC to increase the depth of student understanding and to avoid student over-dependence on procedures without understanding. The SMP represent a synthesis of the NCTM Process Standards and the NRC strands of mathematical proficiency, both of which are predicated on a substantial research base in mathematics.[4],[5] The intentional integrated design of the components of the Standards for Mathematics necessitates the incorporation of the SMP in 1) professional development, 2) curriculum evaluation tools, and 3) student assessment.

Professional Development. To effectively fulfill the goals of the Kentucky Core Academic Standards (KCAS), educators must integrate the SMP and the SMC in their instruction. Pre-service and practicing educators must participate in professional development that models the integration of the SMP with the SMC as the foundation for implementing high-quality mathematics instruction. Kentucky’s process of deconstructing the KCAS content into learning targets, as well as KYAE’s standards unpacking process, must incorporate the SMP to ensure teaching and learning are not reduced to a list of steps and procedures but remain a balance of conceptual and procedural knowledge and promote higher-order thinking as recommented by NCTM4 and the NRC5. The deconstruction and unpacking processes themselves must be a professional development focus that encourages all teachers to think about and deepen their understanding of the integration of the SMP and SMC and appropriate instructional points of intersecting the two components. The focus of professional development on the integration of SMC and SMP will guide the selection and implementation of appropriate instructional strategies to enhance a specific practice during instruction. Furthermore, the SMP mirror the Kentucky Characteristics of Highly Effective Teaching and Learning (CHETL) and can be used in conjunction with the CHETL as a more “math-specific” set of guidelines for effective teaching and learning. If the SMP are held sacred and honored as a vehicle for teaching the SMC, educators will see their value and Kentucky students will benefit.

Curriculum Evaluation. Because the SMP, in concert with the SMC, are the means by which students will reach high-level thinking and become proficient in mathematics, mathematics curricula must provide opportunities to develop these eight areas of mathematical proficiency. Therefore, when administrators and mathematics teachers at all education levels, preschool through adult, consider mathematics curriculum materials for adoption[6], they must consider the following questions regarding the alignment with and support of the mathematical practices:

1) Do the materials provide opportunities for students to engage actively in a variety of mathematical practices?

2) Do the materials provide teachers ample support for integrating mathematical practices in instruction and assignments?

3) Do the formative and summative assessments in the materials reflect the mathematical practices?

4) Does the mathematical content follow the progressions and trajectories across grade levels?

Adopting curricula that support the SMP means teachers carry less of the burden to design tasks that address the SMP and instead can focus on facilitating the development of the SMP in students and choosing instructional strategies to enhance student demonstration of the practices. Also, as recommended by No Child Left Behind legislation,[7] curricula should be research-based, and since the SMP are deeply grounded in research, so too are curricula which support student development of the practices.

Assessment. As an integral component of the Kentucky Core Academic Standards, the SMP must also be an integral component of a balanced assessment system that includes both formative and summative assessment of students’ mathematical knowledge and proficiency. Balanced assessment systems use a variety of assessment methods, such as extended written response, performance tasks, oral communication opportunities,[8] as well as carefully constructed multiple choice questions. In concert, the assessment methods can allow for student demonstration of both mathematical content knowledge and mathematical practice while allowing teachers the opportunity to gain insight into the different facets of students’ mathematical proficiency, that is, students’ demonstration of the SMP. Successful balanced assessment implementation is dependent upon teachers who are knowledgeable in the methods of assessment that will promote appropriate mathematical practices. Educators who have a comprehensive understanding of assessment can better design and implement systems that provide an in-depth view of a student’s mathematical understanding. A balanced assessment system will align with instruction and curricula that integrate the SMP and SMC.

Conclusion. The design of the Standards for Mathematics intentionally calls for the integration of the Standards for Mathematical Practice with the Standards for Mathematical Content. Both components, therefore, must be integrated throughout instruction, curricula, and a balanced assessment system. With the Standards for Mathematical Practice clearly evident in instruction, curricula, and a balanced assessment system, mathematics students will recognize the practices as necessary habits-of-mind that demonstrate their ability to think deeply and flexibly as a proficient mathematics student. And, students who choose to further their study of mathematics-related fields will have a solid foundation in mathematical practices needed for success in those fields.

References

CMA Response to Legislation. (Feb 2009). Unpublished document.

Common Core State Standards Initiative. (2010). Common Core State Standards Common Core State Standards for Mathematics: http://www.corestandards.org.

Gonzales, P., Williams, T., Jocelyn, L., Roey, S., Kastberg, D., Brenwald, S. (2008). Highlights from TIMSS 2007: Mathematics and Science Achievement of U.S. Fourth- and Eighth-Grade Students in an International Context. NCES 2009-001: National Center for Education Statistics.

Hiebert, J. (2003). What research says about the NCTM standards. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A Research Companion to Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.

Kentucky Department of Education. (2011, July 2). Characteristics of highly effective teaching and learning. Retrieved http://www.education.ky.gov/KDE/Instructional+Resources/Highly+Effective+Teaching+and+Learning/HETL+Common+Characteristics.tm

Individuals with Disabilities Education Improvement Act of 2004, Pub. Law No. 108-446, 108th Congress (2004).

B McCallum. (2011, July 9). Curriculum analysis tool. [Web log comment]. Retrieved from http://commoncoretools.wordpress.com/2011/07/09/curriculum-analysis-tool/

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

National Research Council. (2001). Developing proficiency in teaching mathematics. In J. Kilpatrick, J. Swafford & B. Findell (Eds.), Adding it Up: helping children learn mathematics. Washington, DC: National Academy Press.

No Child Left Behind Act of 2001, Public Law 107-110, 107th Congress (2001).

Stiggins, R. Arter, J. A., Chappuis, J., & Chappuis, S. (2004). Classroom assessment for student learning: Doing it Right—Using it well. Oregon: The Educational Testing Service.

Supporting Materials

Standards for Mathematical Practice

(A description of the Standards for Mathematical Practice can be found at

http://www.corestandards.org/the-standards/mathematics/introduction/standards-for-mathematical-practice/

September 30, 2011

Position Statement on the Standards for Mathematical Practice Page 3

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning. return

September 30, 2011

Position Statement on the Standards for Mathematical Practice Page 3

Kentucky Committee for Mathematics Achievement (CMA)

The Kentucky Legislature formed the CMA in 2005 (KRS 158.842). The charge to the CMA includes:

· “develop a multifaceted strategic plan to improve student achievement in mathematics at all levels,”

· “have the ongoing responsibility for providing advice and guidance to policymakers in the development of statewide policies and in the allocation of resources to improve mathematics achievement,” and

· “collaborate with the Center for Mathematics” return

National Council of Teachers of Mathematics (NCTM) Process Standards

(Highlights of each process standard can be found at http://www.nctm.org/standards/content.aspx?id=322)

September 30, 2011

Position Statement on the Standards for Mathematical Practice Page 3

· Problem Solving

· Connections

· Reasoning and Proof

· Representations return

· Communication

September 30, 2011

Position Statement on the Standards for Mathematical Practice Page 3

National Research Council (NRC) Strands of Mathematical Proficiency

· Conceptual understanding—comprehension of mathematical concepts, operations, and relations

· Procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately

· Strategic competence—ability to formulate, represent, and solve mathematical problems

· Adaptive reasoning—capacity for logical thought, reflection, explanation, and justification

· Productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. return

September 30, 2011

[1] For podcasts with resources and classroom examples of the Standards for Mathematical Practice, developed by the Kentucky Department of Education Office of NxGL and the Leadership Networks, click here.

[2] Common Core State Standards Initiative. (2010). Common Core State Standards Common Core State Standards for Mathematics: http://www.corestandards.org.

[3] CMA Response to Legislation. (Feb 2009). Unpublished document.

[4] National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

[5] National Research Council. (2001). Developing proficiency in teaching mathematics. In J. Kilpatrick, J. Swafford & B. Findell (Eds.), Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.

[6] A curriculum analysis tool is available at http://commoncoretools.wordpress.com/2011/07/09/curriculum-analysis-tool/

[7] No Child Left Behind Act of 2001, Public Law 107-110, 107th Congress (2001).

[8] Stiggins, R. Arter, J. A., Chappuis, J., & Chappuis, S. (2004). Classroom assessment for student learning: Doing it Right—Using it well. Oregon: The Educational Testing Service.