This school year I am going to share a monthly focus as a way for educators in our district (and beyond, of course!) to think together, collaborate and share ideas around K-12 mathematics education. On the list are number sense, estimation, reasoning, spatial awareness…it is a list in progress so suggestions are welcome.
My intentions are to begin each month with a blog post highlighting a focus area in our BC mathematics curriculum and connecting it to the broader field of mathematics education. I plan to share links to websites and resources, share books that I have found helpful and provide examples of mathematical tasks from Richmond classrooms. During each month, I will also tweet out related links, ideas, blog posts and photographs from classrooms.
For December let’s consider what is spatial reasoning?
Spatial reasoning is based in dynamic processes with a focus on mental understanding and physical transformation. It is comprised of many elements and the current research in this area is looking at the interaction of these elements. Some “math verbs” associated with the elements of spatial reasoning include:
de/re/composing re/arranging relating mapping symmetrizing visualizing perspective-taking locating
intersecting transforming scaling folding sliding rotating reflecting balancing imagining comparing
One of our five mathematical big ideas in our BC mathematics curriculum focuses on spatial relationships. The K-9 “meta” big idea is: We can describe, measure, and compare spatial relationships. At each grade level, there is a specific big idea around geometry and measurement concepts that connects to the curricular content for that grade level such as thinking about composing and decomposing two and three-dimensional shapes. Connected to this are the curricular competencies of visualize to explore mathematical concepts and represent mathematical ideas in concrete, pictorial and symbolic forms.
Spatial reasoning in young children is an indicator of future overall school success, as well as more specifically, literacy and numeracy (multiple research studies across disciplines including Duncan et al, 2007 – cited in Davis, 2015). It is not a pre-determined trait but is something that is malleable and can be learned. Spatial reasoning and geometry are foundational to disciplines such as astronomy, architecture, art, geography, biology and geology and are an essential part of STEM/STEAM education and future careers.
Many elementary teachers in our district have been inspired by the Canadian book Taking Shape: Activities to Develop Geometric and Spatial Thinking. In Taking Shape, the Canadian authors offer five key areas as their focus for spatial reasoning:
- composing and decomposing 2D images and 3D objects
- locating, orienting, mapping and coding
Math mentor teacher Michelle Hikida from Diefenbaker Elementary has used rich tasks from this book with her grades 2&3 students and shared this work at our elementary math focus afternoon. Students are engaged in creative and critical thinking as well as communicating and collaborating while thinking through these tasks.
As there is a heightened focus on computational thinking and coding, we can see strong connections between spatial awareness and reasoning as students think about creating programs and commands to move objects through pathways and around obstacles such as when programming a Spher0 or using a coding program like Scratch.
Spatial thinking and reasoning also are an important aspect in linking models to abstract phenomenon such as in calculus. Graphing calculators such as desmos support connection-making between visual-spatial models and abstract expressions.
How could you nurture the development of spatial reasoning with your students?
What math to math connections are you making?
What connections to your students’ interests and other curricular disciplines are you making?
Taking Shape: Activities to Support Geometric and Spatial Thinking K-2 by Joan Moss et al
Five Compelling Reasons for Teaching Spatial Reasoning to Young Children:
Paying Attention to Spatial Reasoning: K-12 Support Document for Paying Attention to Mathematics Education, Ontario Ministry of Education, 2014 (available as a pdf online)
Spatial Reasoning in the Early Years: Principles, Assertions, and Speculations by Brent Davis and the Spatial Reasoning Study Group, 2015
Understanding Geometry by Kathy Richardson
Learning and Teaching Early Math: The Learning Trajectories Approach by Douglas Clements & Julie Sarama
Open Questions for the Three-Part Lesson: Geometry and Spatial Sense K-3, 4-8 by Marian Small & Ryan Tackaberry