Building Instructional Math Muscles Balancing the Content and Process Standards

Cathy Buyrn, M.Ed.

February/March 2011 Link Lines

 math

Teachers are systematically unpacking the math standards and using student data to drive instructional design.  The Standards of Learning (SOL) drive this process in Virginia.  While the Virginia math SOL are based on the revised National Council of Teachers of Mathematics (NCTM) standards released in April of 2000, teachers may be overlooking the embedded process standards.  Most pacing guides and student data reports are focused on the familiar content standards, but teachers must also consider the harder-to-measure process standards when designing instructional activities.  According to Burns (2000), the process standards “… bring the content of the curriculum to life and make it accessible to children” (p. 41). Teachers who apply instructional strategies that balance content and process standards help students develop deeper concept comprehension and close skill gaps.

The National Council of Teachers of Mathematics Standards

 

arrow 

(NCTM, 2000).

The Virginia Math SOL Curriculum Framework documents embed the process standards within the essential knowledge and skills portion of every level of mathematics from kindergarten to calculus.  Student expectations for content standards are introduced with the phrase “The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to …” (VDOE, 2009).  The embedding of the process standards into the essential knowledge and skills portion of the content standards guides is meant to remind teachers to help provide access to the content through the process standards, as suggested by the NCTM (2000) and math expert Marilyn Burns (2000). 

The instructional questions and resource links in the table below will help teachers design instructional opportunities that address the process standards.

Process Standards
                                     (NCTM, 2000)

Instructional Questions and Resources
Problem Solving
  • build new mathematical knowledge through problem solving;
  • solve problems that arise in mathematics and in other contexts;
  • apply and adapt a variety of appropriate strategies to solve problems;
  • monitor and reflect on the process of mathematical problem solving

“What kinds of problems can I present to children that would give them the chance to grapple with important ideas and skills?” Marilyn Burns (Herrera, 2000)

Problem Solving Strategies
(Math Staff Development, 2003)  

Math Problem Solving for Upper Elementary Students with Disabilities (Montague, 2005)

Reasoning and Proof
  • recognize reasoning and proof as fundamental aspects of mathematics;
  • make and investigate mathematical conjectures;
  • develop and evaluate mathematical arguments and proofs;
  • select and use various types of reasoning and methods of proof

“What kinds of situations can I pose to children so that their reasoning is engaged and they have experience giving convincing arguments?” Marilyn Burns (Herrera, 2000)

Looking at How Students Reason
(Burns, 2005) 

Communication
  • organize and consolidate their mathematical thinking though communication;
  • communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
  • analyze and evaluate the mathematical thinking and strategies of others;
  • use the language of mathematics to express mathematical ideas precisely

“How do I involve children in talking and writing to help them communicate what they are studying and learning, and hear the ideas of others?” Marilyn Burns (Herrera, 2000)

Marilyn Burns on the Language of Math
 (Burns, 2006)

Connections
  • 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

“How do I help children see the connections among mathematical ideas rather than seeing concepts as isolated and separate from one another?” Marilyn Burns (Herrera, 2000)

vids (Math VIDS, n.d.)
Building Meaningful Student Connections

Representation
  • create and use representations to organize, record, and communicate mathematical ideas;
  • select, apply, and translate among mathematical representations to solve problems;
  • use representations to model and interpret physical, social, and mathematical phenomena

“How do I help children use the symbolism of mathematics to describe their thinking?” Marilyn Burns (Herrera, 2000)

How to Make the Most of Math Manipulatives
(Burns, 1996)

vids (Math VIDS, n.d.)
Concrete - Representational - Abstract
Sequence of Instruction

 

Assessing student mastery of the process standards is not as straightforward as measurement of the content standards.  Teachers can directly measure process standard performance with anecdotal records or rubric scores (Making Math Meaningful, n.d.).  Some teachers choose to use process standard strategies to deliver the content and only measure the impact on more discrete skills.  Whether or not you choose to directly assess process standards, it is critical that they be addressed and embedded into the design of instruction. Teachers who learn to balance the more discrete content standards with the deeper conceptual process standards will prepare students to go the distance when it comes to mathematics. 

References & Resources

Burns, M. (April, 1996). How to make the most out of manipulatives.  Instructor, (44-49), Retrieved from http://www.mathsolutions.com/documents/1996_Hands_on_Help.pdf

Burns, M. (March/April, 2000). Making sense of math standards. Creative Classroom, 14(5), Retrieved from http://www.mathsolutions.com/documents/2000_Making_Sense_Math_Stan.pdf

Burns, M. (November, 2005). Looking at how students reason. Educational Leadership, 62(26-31), Retrieved from http://www.mathsolutions.com/documents/2005_How_Students_Reason.pdf

Burns, M. (April, 2006).  Marilyn Burns on the language of math.  Instructor, (41-43), Retrieved from http://www.mathsolutions.com/documents/2006_Language_of_Math_Instructor.pdf

Herrera, T. (2000). An interview with Marilyn Burns: Meeting the standards-Don't try to do it all by yourself. ENC Focus, 8(2), 16-19. Retrieved from http://www.mathsolutions.com/documents/2002_Interview_ENC.pdf

Making Math Meaningful:  Math Process Standards Resources.  (n.d.).  Retrieved from Making Math Meaningful Wiki: http://making-math-meaningful.wikispaces.com/8+Math+Process+Standards+Resources

 Math Staff development: Process Standards. (2003, February 04). Retrieved from (Link no longer available.)

Math VIDS:  Video Instructional Development Resource. (n.d.). Retrieved from http://www.coedu.usf.edu/main/departments/sped/mathvids/index.html

Montague, M. (2005, February 28). Math problem solving for upper elementary students with disabilities.  Retrieved from http://www.k8accesscenter.org/training_resources/MathPrblSlving_upperelem.asp

National Council of Teachers of Mathematics (NCTM), (2000).  Standards for school mathematics:  Process standards.  Retrieved from http://standards.nctm.org/document/appendix/process.htm

Virginia Department of Education (VDOE), (2009). Mathematics standards of learning curriculum framework Richmond, VA: VDOE. Retrieved from http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/