Spatial Reasoning and NCTM Standards
It is important for educators to understand the geometry content included in NCTM’ s Principles, Standards, and Expectations for pre-K to second-grade students, so they can integrate spatial reasoning and geometric knowledge into their early childhood curriculum. The standards and expectations that are addressed while working with pattern block puzzles include the following.
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
In pre-K through grade 2, each and every student should
› Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes › Describe attributes and parts of two- and three-dimensional shapes › Investigate and predict the results of putting together and taking apart two- and three-dimensional shapes
Apply transformations and use symmetry to analyze mathematical situations
In pre-K through grade 2, each and every student should
› Recognize and apply slides, flips, and turns › Recognize and create shapes that have symmetry
Use visualization, spatial reasoning, and geometric modeling to solve problems
In pre-K through grade 2, each and every student should
› Create mental images of geometric shapes using spatial memory and spatial visualization › Recognize and represent shapes from different perspectives
Source: National Council of Teachers of Mathematics. Principles, Standards, and Expectations. nctm. org / Standards-and-Positions / Principles-and-Standards / Principles,-Standards,-and-Expectations.
They can create their own designs, which can involve both symmetrical and asymmetrical patterns. They also can learn about the interchangeable relationships among the shapes; for example, two trapezoids, three rhombuses, or six triangles can form a hexagon. However, this information alone does not promote the spatial reasoning about angles and area that research shows is necessary for geometry learning and development( NAEYC & NCTM [ 2002 ] 2010).
As a beginning preschool teacher, I( Christina) found pattern blocks intriguing. Thinking they had possibilities for fostering children’ s geometric knowledge, I made them a permanent material in my classrooms. Yet whenever I placed pattern blocks on a table and engaged with them during activity time, I discovered the children were not nearly as intrigued as I. They would join me, but they seldom stayed longer than a few minutes, even when I added commercially produced pattern block design cards and strips.
Children’ s lack of interest led me to search for more intriguing activities. Eventually, I created pattern block puzzles. Using the individual pattern blocks, I created my own designs, taped the blocks together, and traced around the outside of the blocks on paper. A parent volunteer then cut those designs out of 1 / 8-inch-thick plywood to create the puzzles( see“ How to Create Pattern Block Puzzles” on page 79). These pattern block puzzles were open-ended and had multiple solutions, which gave children the opportunity to engage in spatial reasoning. The empty space in the center of the plywood was a problem children solved by filling the space with differently shaped pattern blocks. The goal was to fill the empty spaces without any gaps.
After I placed pattern blocks and the new pattern block puzzles on a table, I observed that children flocked to the activity. Not only did they come, they stayed for long periods of time all year long. Because the puzzles were always available during self-directed play, children often stayed for the entire activity time.
78 Young Children
Summer 2025