The Importance of Spatial Reasoning
What is Spatial Reasoning?
Spatial abilities include being able to think about:
- how objects look when rotated (e.g., if you turn a V to the side, where will the opening be)
- how objects look from different angles, (e.g., what a pyramid looks like from the side or if you were looking at it from above)
- how objects look on the inside (e.g., if you slice a cylinder down the middle of the circle on top and open it up you will see a rectangle!)
- how parts of an object fit together, such as being able to imagine that if two triangles are put together a certain way, they would make a rectangle
- how positions of objects relate to each other, such as understanding that a car is inside a garage or a tree is behind a fence.
Information taken from https://dreme.stanford.edu/news/spatial-reasoning-why-math-talk-about-more-numbers; Development & Research in Early Math Education; Spatial Reasoning: Why Math Talk is About More Than Numbers.
Click each picture for a suggestion.
What skills does spatial reasoning develop?
Many math concepts develop from a student's experiences with spatial reasoning including:
· Location, distance, direction
· 2D and 3D shapes and their attributes
· Patterns, that lead to algebraic relationships
· Symmetry and geometric transformation
· Geometric measurement
Spatial reasoning skills support the arts and artistic careers, along with many career fields in STEM that now use 3D technology such as medicine, architecture, computer sciences, chemistry, geology, geography and more.
Spatial reasoning is important because we live in a 3D world!
The paper in the pic was folded in half horizontally, then vertically, then horizontally again. The left bottom corner was cut out. What will the paper look like when its unfolded?
Activities you can do at home.
- Composing/Decomposing shape patterns using blocks. I have a free template on my website you can print and cut apart if you don't have any shape blocks at home.
- Spatial visualization - looking at a 3D figure from different perspectives, or imagining the hidden cubes.
- Nets and folding activities - What does the net look like? How many ways can the net be made?
- Congruence through Orientation Problems and Transformation - How many unique 3D figures can you build using a set number of cubes? Modeling transformations of a figure (translation, rotation, reflection on or off a plane)
- Working visual memory - Draw a shape or figure. Hold it up for 5 seconds. Then have students try to recreate it from memory. Other skills in this area include subitizing* , number line relationships, and measuring with a ruler, especially from a point other than zero. (See info on subitizing below)
- Patterning - build several figures in a pattern. Students can identify the pattern, extend it, or develop a table that leads to a rule.
- Use graphs and maps - interpret patterns in functions or on plots, investigate maps, explore patterns in other types of graphs.
- Model Pythagorean relationships, similarity vs congruence, explore the views of a figure, and investigate right triangle relationships including trigonometry.
Some information taken from "Paying Attention to Spatial Reasoning K-12: Support Document for Paying Attention to Mathematics Education" Ontario Ministry for Education
Nets & Attributes of 3D Figures activity
The activity instructions in printable/shareable pdf is linked here.
The data table link is found here. Be sure to save a copy to your own google drive and make sure your students do the same so they can't change the original doc.
What is Subitizing?
Use dominos, dice, playing cards without numbers, tally marks, ten frames, or even fingers to have students develop this skill.
As students get older, use money, 100 grid models, and images of number lines (zero to one marked) along with a point marked on the interval. Have students try to identify the value of a quantity as quickly, accurately, and confidently as possible and keep developing this valuable skill!
Math is Integral
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Kelli D. Mallory, Ed.D.