10 Playful Spatial Reasoning Provocations

View our new spatial reasoning blog post: 10 Playful Spatial Reasoning Provocations Part 2 here.

As our kindergarten team continues to learn more about children and their development in spatial thinking and reasoning, we are continually searching for and creating meaningful provocations and experiences where children can construct their own learning in this area. We are also becoming increasingly aware of the significant interactions we can have with children to help deepen their understanding of spatial reasoning by using gestures, spatial vocabulary, questions and challenges.

Above is a simple composition provocation based on the book, “Dreaming Up” by Christy Hale engaging children in block play. This would be an early stage of composition. Whereas using more of a variety of shapes of blocks and larger scale would add complexity to their skills. Through these experiences children may move from trial and error to manipulating shapes by turning and flipping mentally before putting pieces down.

Spatial reasoning is an indicator of future success in mathematics, can improve, and starts at a young age. There is often such a strong focus on number sense in early learning that exploring and consolidating understanding of spatial reasoning can take a back seat. Spatial thinking activities are an amazing way to afford multiple entry points for different learners as well as support STEM or STEAM learning. They also can be tied to other concepts across all strands in math. For these reasons our early years team is taking a keen interest on how we can help nurture spatial thinking. Since our program has a strong focus on inquiry and constructing knowledge through play, we’ve created some early math experiences to deepen children’s understanding of spatial reasoning which can be view below.

Spatial reasoning is an indicator of future success in mathematics.

• “spatial thinking skills and geometric reasoning play a critical role in the development of problem-solving skills, mathematical learning, and reading comprehension” (Clements & Sarama, 2011; Wheatley, Brown, & Solano, 1994; Casey et al., 2008).

Spatial reasoning can improve.

• Research also shows that spatial thinking can be improved through an assortment of activities and across all age groups (Uttal et al., 2013)

Spatial Thinking Skills Start Young.

• Doug Clement’s Learning Trajectories for Primary Mathematics shows the developmental stages for Spatial Thinking.
• For further information, view a video from Doug Clements as he describes different developmental levels within the Composing Geometric Shapes learning trajectory.

Low-tech coding and map-making encourages students to visualize, practice giving directions, code, use spatial language, and verify through navigation. This provocation inspired by the story, “Henry’s Map” by David Elliot, brought a new dimension to story-retells for us. 

What the Ontario Kindergarten Curriculum has to say about spatial reasoning

• In the “Mathematics in an inquiry stance” section of the document, it mentions that children are encouraged to reveal their thinking about shapes and spatial relationships? p.26
• 17.2 communicate an understanding of basic spatial relationships (e.g., use terms such as “above/below”, “in/out”, “forward/backward”; use visualization, perspective, and movements [ flips/reflections, slides/translations, and turns/ rotations]) in their conversations and play, in their predictions and visualizations, and during transitions and routines. p. 232
• 20.3  compose pictures, designs, shapes, and patterns, using two-dimensional shapes; predict and explore re ective symmetry in two-dimensional shapes (e.g., visualize and predict what will happen when a square, a circle, or a rectangle is folded in half ); and decompose two-dimensional shapes into smaller shapes and rearrange the pieces into other shapes, using various tools and materials (e.g., stickers, geoboards, pattern blocks, geometric puzzles, tangrams, a computer program)
• 20.4  build three-dimensional structures using a variety of materials and identify the three- dimensional gures their structure contains. p. 246
• In Belonging and Contributing the expectations discuss who’s involved in a community and what ways people contribute. A challenge example encourages children to explore multiple perspectives of an arrangement of cubes. p. 139

Below are some experiences that we’ve provided for our early math learners to help encourage spatial thinking.

Spatial Thinking and Problem-Solving

Experiences where children put the shapes within the lines expands their understanding of being able to see the individual parts in relation to the whole.

A clear plastic table cloth with Sharpie paint pen shapes drawn on it invites children to use different materials to compose different shapes. Children will use spatial thinking to flip, rotate, and/or reflect shapes to ensure the pieces fit inside the shapes.

Butcher paper is another flexible mat where lines can be created as guidelines for spaces in which the blocks must fit. This provocation is about totem poles since one of our students expressed an interest in them.

Exploring Spatial Thinking in Composing and Comparing

This is a wooden tetris board called, “wooden intelligence” that we purchased from http://www.wish.com. Some children work on symmetry, play games that take turns creating symmetry with these boards. If you don’t have a board we created our own tetris pieces below.

If you don’t have the wooden tetris game above, you can create your own with craft cubes. These are simply craft cubes from the dollar store glued together in regular tetris shapes. Since visualization and perspective play an important role in spatial reasoning we added and 3-sided mirror.

Exploring Spatial Thinking in Symmetry

We cut pieces of cork board from Home Depot to provide a mat for this invitation to learn. The tape line encourages symmetrical thinking.Clear Mac-Tac from the Dollar Store taped on top of an easel sticky-side out with a line drawn down the middle sets the stage for children to construct symmetrically on a vertical surface.

Exploring Spatial Thinking in Number Sense

Spatial thinking is relevant in all areas of mathematics. When children are trying to figure out how many more they need to make 3 from 2, they can use their spatial understanding of the quantity of 2 to determine how many more are needed to make 3. Spatial thinking can be a powerful tool in solving composition and decomposition problems. The above photo is merely craft cubes from the dollar store glued together with numbers written on. These remind me of those amazing Sumblox.

Above are some inexpensive pieces of wood from Home Depot. We used a wood burner to make the lines, but a Sharpie would do the trick. We added the numeral on one end and subitizing dots on the other. When we have math table exploration time some children will build numbers, order numbers, add, and think of one more or one less. At other times children will build towers and enclosures with them. Adding these blocks into small world play can encourage children to bump into math.

Tips and Tricks to Encourage Spatial Thinking

• Invite children to predict how they can manipulate shapes as this will help increase their ability to mentally flip, rotate, slide and improve their spatial language.
• Invite children to compare formations of 2D and 3D objects. How are they the same? How are they different? Can you manipulate any parts to make them the same? This will also encourage children to mentally rotate.

We’d love to hear from you. Please share with us how your early years teams are fostering spatial thinking with your early learners. 

Further Reading

Learning Trajectories for Primary Grades Mathematics 

Ontario Kindergarten Curriculum

Paying Attention to Spatial Reasoning

Why Spatial Reasoning is Crucial for Early Math Education