Joint Position Statement of the National Association for the Education of Young Children and the National Council of Teachers of Mathematics



The NCTM and NAEYC affirm that high quality, challenging, and accessible mathematics education for 3 – 6 year old children is a vital foundation for future mathematics learning. In every early childhood setting, children should experience effective, research based curriculum and teaching practices. Such high quality classroom practice requires policies, organizational supports, and adequate resources that enable teachers to do this challenging and important work.
In a high quality preschool classroom mathematics education should include:
      • building on children’s experience and knowledge, basing the mathematics curriculum and teaching practices on knowledge of children’s cognitive, linguistic, physical, and social emotional development,
      • providing for children to interact with mathematical ideas,
      • integrating mathematics with other activities,
      • providing ample time to explore and manipulate materials,
      • actively introducing mathematical concepts, methods and language through a range of experiences and teaching strategies
      • supporting children’s learning by continually assessing children’s knowledge, skills, and strategies






The Preschool Mathematics Standards

New Jersey’s Preschool Standards for Teaching and Learning in Mathematics mirror the Common Core’s goals for mathematics (sometimes referred to as ‘big ideas’) and the learning trajectories, or pathways that children will follow from preschool through grade 12 to reach these goals. The preschool standards are ordered according to the domains used in the Common Core State Standards for mathematics:

Preschool Standard
Preschool Standard Content
Common Core Domain Alignment
Standard 1
Standard 1 is about number sense:
-children’s understanding of numbers and quantities.
Counting and Cardinality
Standard 2
Standard 2 is about number sense:
-children’s understanding of number relationships and operations.
Counting and Cardinality
Standard 3
Standard 3 is about children’s ability to:
-compare,
-order; and
-begin to measure.
Measurement and Data
Standard 4
Standard 4 is about:
-children’s ability to identify and use shapes; and
-children’s understanding of position in space.
Geometry

In a high-quality preschool classroom, preschoolers are intentionally introduced to and engage in the ‘big ideas’ of mathematics. Teachers note children’s interests and strengths in addition to assessing each child’s prior experience and informal knowledge, effectively integrating differentiated math experiences into all aspects of children’s daily routines and transitions.
With a comprehensive preschool curriculum as the vehicle, continuous (performance based) assessment of what each child in the class knows and is able to do translates into purposefully planned, standards based teaching practices. The teaching practices section of the preschool mathematics standards provides samples of activities and explorations for each of the learning outcomes.

There are four preschool mathematics standards:

Standard4.1: Children begin to demonstrate an understanding of number and counting.


Standard 4.2: Children demonstrate an initial understanding of numerical operations.

Standard 4.3: Children begin to conceptualize measurable attributes of objects.

Standard 4.4: Children develop spatial and geometric sense.



Mathematics in a Preschool Classroom
Preschool children use mathematics to make sense of their world. They ask for more, they hold up three fingers to tell us how old they are, they count, stack blocks, and see patterns in their environment.
As an early childhood educator, you play an important role in bridging the informal understanding of math with more formal mathematics. You bridge the gap by the way you design the classroom. You should design the learning environment so that there are math materials in all interest areas. In the preschool classroom there is both child exploration of materials as well as teacher directed and intentional activities for mathematics.
The Creative Curriculum organizes their content information based on the National Council of Teachers of Mathematics content standards in five areas.

They are:
1. Numbers and Operations
2. Geometry and Space
3. Measurement
4. Patterns
5. Data Analysis

The purpose of this wiki is to give teachers a clearer understanding of the components in math in order to help them observe children and make sound judgments in planning for their success in mathematics.


Numbers and Operations


At the preschool level, number and operations concepts involve nine different areas. (TCC p. 7)

1. Counting: Children must learn three things: the number sequence, one to one correspondence, and that the last number named when counting a set tell how many are in the set.
2. Quantity (Sense of Number): understanding how many are in a set.
3. Comparisons (More and Fewer): children can often tell which has more or less.
4. Order (ordinal numbers): most young children have no problem with first. Second and so
forth comes with practice.
5. Numerals: Children need time to investigate numbers. Writing numbers is not an important
skill in preschool. It is more important that the children see numbers displayed and begin to understand what the numbers represent.
6. Combining Operations (Adding): Children often can put sets of objects together to find out how many in all.
7. Separating Operations (Subtracting): The operation of taking away is a common separating operation and one that young children understand.
8. Sharing Operations (Dividing): Children begin to understand this concept by sharing objects such as toys and snacks. When working with young children the concept of fair share will have to be taught.
9. Set-Making Operations (Multiplying): When children pass out birthday treats, materials making equal sets of cookies for all, giving everyone four crayons, etc. they are beginning to develop the concept of multiplying.


Geometry and Spatial Sense



There is so much more to investigate than circles, squares, triangles, and rectangles! The following are four important geometry concepts children need to explore:

Shape: Start with 3D shapes. Children need to recognize, build with, illustrate, describe attributes, compare, and sort shapes. Ecourage children to predict what will happen when they build and creates with shapes.

Space: Use words such as: near, under, top, bottom, by, righ, left. Children should be able to find shapes and objects when given simple verbal instructions.

Transformations: Moving shapes by positioning them into a new position, flipping them over, turning and combining them are all geometric skills children should be exposed to.

Visualization: Children should be able to picture geometric shapes mentally. Give children opportunities to see pictures or drawings from different angles, or perspectives (from the top, bottom, and sides).



Measurement

I’m bigger than you! I am four years old. This is too heavy.
These are things we hear preschoolers say a lot. Children naturally use measurement and comparing language. There are three measurement topics that should be explored by preschool children. They include:
Measurement Attributes: Children must describe the attributes of length (how long or tall something is), capacity (how much something holds), weight (how heavy something is), and area (how much space is covered).
Comparing and Ordering: Begin by comparing two objects by specific attributes (taller, shorter, holds more or less, heavier or lighter and covers more or less space than the other). Then, they describe one object against another. Lastly, children compare three or more objects or events and place them in order.
Measurement Behaviors and Processes: Actual measurement involves assigning a number to an attribute of an object. This skill takes years to learn. Young children begin to understand measurement by experimenting with non standard measurement tools; yarn, straws, plastic links, etc.


Patterns (Algebra)

It is key to understand basic algebraic concepts of mathematics. Children begin to identify simple patterns by: consistent daily schedule, the phrases in poems and songs, the repeated color patterns throughout the classroom, patterns on s shirt, etc. Patterns should be easily recognized and described by young children. This is followed by extending patterns. Lastly children can translate one pattern to another by reading the pattern in their own words and and then reading it another way. For example the pattern above can be read as apple, bananas, apples, bananas… or clap, snap, clap, snap.

Data Analysis

There are three important ideas that involve concepts of data analysis.

Sorting and Classifying: Children sort objects by separating a group of objects from a larger collection. Children usually start by sorting by color, then by size, and then shape. After items have been sorted and classified, the data needs to be organized so it can be represented and communicated to others.

Representing Data: Many teachers do this by using pictures, objects, and graphs. When data is displayed and labeled correctly comparisons can be made and children can describe what they see. Often times, children become the data. They can stand in a line if they like cheese, red apples, ice cream, etc. After, they can draw pictures to represent their preferences and organize their data.