Spatial Reasoning

Heather Melville- Grade 4 Math and Science

In July 2013, I had the privilege to work with students, teachers, Galileo Network experts and researchers at the University of Calgary. (Brent Davis – Professor and chair of mathematics education, Krista Francis Poscente – IOSTEM Director). We met in May to discuss the research portion of the spatial reasoning project. In that one day in May I discovered the importance of spatial reasoning as I went through my own testing and problem solving activities. I learned very quickly that this is a skill that needs to be taught and explored throughout our education. We cannot assume that everyone will be in an environment that allows for this particular skill to be enhanced. I am a believer in providing students with every opportunity to reach for goals that may potentially transpire into future careers. In discussion with the researchers and their knowledge, it was apparent that the careers people choose are based in part by what their spatial reasoning capabilities are.

(Wai, Lubiniski & Benbow as cited in Twyman, 2012)

Spatial reasoning is the ability to see the relationship between objects in both two and three dimensions. It is one of the eight intelligences encompassed in the multiple intelligence theory. We as learners use a variety of these intelligences to dictate how we learn, problem solve and move forward past any challenges we are faced. (Spatial. Linguistic, Logical-mathematical, Kinesthetic, Musical, Interpersonal, Intrapersonal, Naturalist)

Dr. Gerald Grow describes the examples of spatial reasoning this way:

The spatial intelligence manifests in a variety of ways. Transforming mental images is a spatial skill that engineers and designers depend on. When a hiker pauses with map and compass, it is the spatial intelligence that conceptualizes the path. Through the spatial sense, a painter "feels" the tension, balance and composition of a painting. Spatial ability is also "the more abstract intelligence of a chess master, a battle commander, or a theoretical physicist" (194), as well as the familiar ability to recognize objects, faces, and details. www.longleaf.net/ggrow/7In/Spatial.html

The students involved with the Robotics camp were first interviewed and tested in the same way the teachers were before the camp began. It was important to achieve a base line of what they knew before the camp to assess their growth. The one week/ half day camp involved building a Lego Mindstorms Robot and programming it to perform a certain task. It was a challenging goal for 8-9 year olds. The majority of the camp was student driven with very little instruction. Given the robot

kits and computers, working in small groups and having experts facilitating the camp, all the students were able to achieve their goals. They then were tested at the end of the camp to further the research process. (Results are being analyzed and the research is ongoing). Every afternoon of the camp, the teachers and researchers collaborated to brainstorm a curriculum re-design and discuss the outcomes of what was witnessed in the morning. As a teacher, it was very enlightening to be able to focus my attention on one intelligence and finding the importance of spatial reasoning in what I do in the classroom. I was enthusiastic to discover ways to present this to my own students in a manner that allowed for cross-curricular integration.

I knew I could bring a robotics unit into my grade 4 science with “Building Things that Move” and “Wheels and Levers”. I also wanted to find ways to use more spatial reasoning within the math curriculum. Over the summer I happened across a store in the U.S. that carried wooden puzzles that forced you to look at various angles and sort out how all the pieces work together. I bought them and brought them into my classroom. The students love when I give them time to work with other students to “play” with these puzzles. When they do manage to solve them there is an enormous amount of satisfaction and a sense of accomplishment.

Marla Paxton and I, (My Math/Science partner) introduced Origami into our math "Problem of the Week". The students were asked to take a 2D picture of origami instruction and build the 3D piece they had selected. Once that was accomplished they made an iMovie showing the step-by-step process of their origami. The terminology expressed in these movies showed that these 9 year olds are quite capable of deeper mathematical thinking. They related this project to real applications, talked through geometry concepts, were capable of expressing fractions, can organize their thoughts and express themselves in a variety of ways. Given the freedom to explore various apps on their iPads, every iMovie was unique and every student accomplished the expectations set out for the problem presented.

As we move forward in the school year we are finding more ways to present spatial reasoning in the classroom without it being a separate entity. Hands on learning will be apparent in our classrooms with the use of manipulatives, problem solving puzzles, transferring knowledge from 2D to 3D, the tearing apart of numbers and then rebuilding them to allow for a deeper understanding of mathematics and the exploration of the world around us.

What began as a one week camp has transpired into a passion for transferring spatial reasoning skills to my students. I continue to give them choice to their preferred style of learning but it is important to enhance such a skill as spatial reasoning. It is a skill that will diminish if not taught and used within our lives. I encourage educators to look at all learning styles and find ways to incorporate them into the lessons being explored in the classroom.

(Wai, Lubiniski & Benbow as cited in Twyman, 2012)

Twyman, A. (2012, November). Space and math: Why spatial understanding is
vital for gender equality, SES equality,
and preparing our children for the future. Presented at the Early Years
Spatial Reasoning: Learning and Teaching (12w2189), BIRS, Banff.