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Mathematical Practices

The Common Core Standards for Mathematics includes “Standards for Mathematical Practice.”

“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).”  From Common Core State Standards for Mathematics

The Math Teacher Toolkit for Kindergarten through 3rd Grade offers specific explanation and examples of the eight (8) practices described in the Common Core Standards.
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 sure of structure.
8. Look for and express regularity in repeated reasoning.

More on these practices can be found by linking to Mathematical Practices.
For the Pre-K classroom, the Mathematical Processes identified by NCTM (National Teachers of Mathematics) may be helpful in supporting practices with 4-5 year old mathematics students.

“Young children learn by doing.  That familiar adage is true, but it represents only part of the picture; in reality, children learn by doing, talking, reflecting, discussing, observing, investigating, listening, and reasoning. To learn mathematics, children must be actively involved with mathematics content (e.g. number and operations, geometry, measurement) and, importantly, with the processes of mathematics, defined by NCTM as: problem solving, reasoning, communication, connections, and representation.”

Copley, J.V. 2010. The young child and mathematics. 2nd edition. Washington, DC: NAEYC; Reston, VA:National Council of Teachers of Mathematics,  p.29.

NCTM Process Standards in Mathematics

 Process Standard Description Problem-Solving Problem solving involves drawing upon previous knowledge to solve a unique problem.  It is a primary means by which children develop mathematical understanding. Reasoning and Proof Reasoning and proof encompasses developing and evaluating mathematical arguments. Communication The communication standard encourages children to formulate and express their mathematical thinking. Connections The connections standard includes interconnections among various areas of mathematics, as well as the relationship between mathematics and other curricular areas. Representation Representation encompasses the variety of methods that children use to model and communicate mathematical concepts.

Source: Moomaw, Sally and Hieronymus, Brenda, (2011) More Than Counting: Standards-Based Math Activities for Young Thinkers in Preschool and Kindergarten. St. Paul, MN: Redleaf Press, p.5