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# Geometry and Spatial Sense

Geometry is one of the primary areas of emphasis in the pre-k years.

Geometry is foundational to an understanding of mathematics and especially important to young children.  The study of geometry involves shape, size, position, direction, and movement and is descriptive of the physical world we live in.  Children’s spatial sense is their awareness of themselves in relation to the people and objects around them.

Copley, J.V. 2010. The young child and mathematics. 2nd edition. Washington, DC: NAEYC; Reston, VA:National Council of Teachers of Mathematics. (p. 99)

What should you be teaching in pre-k programs? The National Council of Teachers of Mathematics (NCTM) developed Curriculum Focal Points in 2006 for all grade levels, including pre-kindergarten.  Curriculum focal points highlight the most important mathematical topics for each grade level.  They are the topics that should be considered as the basis for decisions about curriculum development. (www.nctm.org).  Geometry is one of these topics.

## Pre-Kindergarten Curriculum Focal Points (NCTM)

Geometry: Identifying measureable attributes and comparing objects by using these attributes.

Children identify objects as “the same” or “different,” and then “more” or “less,” on the basis of attributes that they can measure.  They identify measurable attributes such as length and weight and solve problems by making direct comparisons of objects on the basis of those attributes.

## Tennessee’s Early Learning Developmental Standards

Tennessee’s Early Learning Developmental Standards (TN-ELDS) identified Learning Expectations and Performance Indicators aligned to the math area of Geometry and Spatial Sense as represented below.

4 to 5 years (49 through 60 months)
 Component Learning Expectations (examples) Performance Indicators (examples) By the end of the age span Correlations Geometry and Spatial Sense Becomes aware of personal space during active explorations of physical environment Builds an increasing understanding of directionality, order, and positions o objects, and words such as up, down, over, under, top, bottom, inside, outside, in front, and behind. K.3.2 Explores and recognizes the size, shape, and spatial arrangement of real objects. Identified and labels several shapes (e.g., circle, square, triangle, rectangle) K.3.1

Excerpted from TN Early Childhood Curriculum Standards http://tn.gov/education/ci/earlychildhood/sec3math.pdf

An additional resource for thinking about what and how you should teach about geometry and spatial sense to 4-5 year old children is the Learning Paths chart below that aligns knowledge with sample teaching strategies.

 Content Area Examples of Typical Knowledge and Skills From Age 3 Age 6 Sample Teaching Strategies Geometry and Spatial Sense Begins to match and name 2-D and 3-D shapes, first only with same size and orientation, then shapes that differ in size and orientation (e.g., a large triangle sitting on its point versus a small one sitting on its side). Recognizes and names a variety of 2-D and 3-D shapes (e.g., quadrilaterals, trapezoids, rhombi, hexagons, spheres, cubes) in any orientation. Describes basic features of shapes (e.g., number of sides or angles). Introduces and labels a wide variety of shapes (e.g., skinny triangles, fat rectangles, prisms) that are in a variety of positions (e.g., a square or a triangle standing on a corner, a cylinder “standing up” or horizontal). Involves children in constructing shapes and talking about their features. Uses shapes, separately, to create a picture. Describes object locations with spatial words such as under and behind and builds simple but meaningful “maps” with toys such as houses, cars, and trees. Makes a picture by combining shapes. Builds, draws, or follows simple maps of familiar places, such as the classroom or playground. Encourages children to make pictures or models of familiar objects using shape blocks, paper shapes, or other materials. Encourages children to make and talk about models with blocks and toys. Challenges children to mark a path from a table to the wastebasket with masking tape, then draw a map of the path, adding pictures of objects appearing along the path, such as a table or

Excerpted from Learning Paths and Teaching Strategies Chart in Promoting Good Beginnings:  Early Childhood Mathematics. NAEYC/NCTM Joint Position Statement, 2002, updated 2010.