


In Principles and Standards for School Mathematics, the National
Council of Teachers of Mathematics (NCTM) sets forth standards
in 10 areas that cover a broad range of math skills and understandings—five
are identified as process standards and five as content standards.
The Process Standards
Learning mathematics requires action and thinking. NCTM has identified
five processes that are especially critical to learning about mathematics:
problem solving, reasoning and proof, communicating, making connections,
and representing.
Problem Solving
For young children, this includes...
 Using simple approaches to solving mathematical problems: asking
for help, counting, trialanderror, guessingandchecking
Reasoning and Proof
For young children, this includes...
 Learning to explain how they solved a mathematical problem: describing
the steps taken verbally, in a drawing, or with concrete objects
Communicating
For young children, this includes...
 Telling others about their mathrelated work: using language, pictures
or other symbols, or concrete objects
 Beginning to use some math language: numbers, shape names, size
words, names of math materials, etc.
Making Connections
For young children, this includes...
 Using math skills in a variety of situations, not just when prompted
by an adult
 Linking their own math experiences to those of other people, in real
life or in books
 Recalling previous math experiences when engaged in current ones
Representing
For young children, this includes...
 Using simple pictures, graphs, diagrams, or dictated words to represent
their mathematical ideas
The Content Standards
Numbers and Operations
For young children, this includes...
 Recognizing and naming some written numerals
 Having a sense of quantity: knowing that the number name “three”
and the symbol “3” mean three of something
 Counting: learning the sequence of number names (1, 2, 3)
 Counting objects: learning to count an object only once, using onetoone
correspondence in counting objects and matching groups of objects
 Beginning addition: Adding two groups of concrete objects by counting
the total
 Beginning subtraction: Taking away one group of concrete objects
from another by taking some away and counting the remainder
 Comparing: understanding ideas such as more than, less than, and the
same as and having a general idea that some numbers stand for a lot
and some numbers mean a little
Geometry and Spatial Sense
For young children, this includes...
 Matching, sorting, naming, and describing shapes: circles, squares,
rectangles, and triangles
 Naming and describing shapes found in everyday environments
 Combining shapes to make new shapes
 Making shape designs that have symmetry and balance
 Understanding and using words that describe where objects are located:
over, under, through, above, below, beside, behind, near, far, inside,
outside
Patterns, Functions and Algebra
For young children, this includes...
 Identifying, copying, and making simple patterns: sequenced or repeated
organization of objects, sounds, or events
 Using patterns to predict what will come next in a sequence
 Recognizing single number patterns such as “one more”
 Noticing, describing, and explaining mathematical changes in quantity,
size, temperature, or weight
Measurement
For young children, this includes...
 Understanding and using words referring to quantities: big, little,
tall, short, long, a lot, a little, hot, cold, heavy, light
 Understanding and using comparative words: more than, less than,
bigger than, smaller than, shorter than, longer than, heavier than,
colder than
 Showing an awareness of and interest in measuring: imitating the
use of measuring tools and measuring with nonstandards units
 Comparing objects such as Which of two sticks is longer?
 Beginning to use measurement words, such as inches, feet, miles,
pounds, minutes, and hours in their language
Data Analysis, Statistics and Probability
For young children, this includes...
 Sorting objects to answer questions
 Collecting data to answer a question: keeping track of simple information gathered from a group of people or over a short length of time
 Making lists or basic graphs, with (adult) help, to organize collected data


