Learning basic reasoning skills can help young students get a better grasp on math in the early grades — and sets them up for success all the way into their future careers, according to education researchers at the University of Alberta.
Lynn McGarvey, math education professor in the Faculty of Education, says something as simple as drawing a building with perspective offers a powerful lesson in mathematical concepts.
Perspective drawing involves spatial reasoning, the ability to visualize and mentally manipulate objects. Spatial reasoning is considered more valuable to long-term success in math and science than memorizing computational skills and basic algorithms, says McGarvey.
“Most of what we do in problem-solving, in any field, has a visual component to it. So if we can help children understand that visual side of things, they’ll improve in all fields, including math, engineering, chemistry, computer science, physics.”
McGarvey notes that spatial reasoning isn’t an innate gift. It can be learned and it improves through different experiences like drawing and playing games.
In her research, children in grades 2 to 5 use an area of mathematics called projective geometry as they learn to shift their understanding between 3D objects and 2D images of those objects, such as making a perspective drawing of a simple building.
The perspective drawings create a visual conflict they learn to resolve: They can see that the vertical lines representing the simple building’s corners are different lengths on paper, but in real life those corners are all the same height.
Such skills aren’t typically part of elementary school math curriculum, yet “the research is showing that children in early education need a lot of experiences like these to help them understand mathematics all the way through school,” says McGarvey. Otherwise, she says, they’ll start simply memorizing the right answers and, as math problems get more complex, they’ll become frustrated and give up on math and other STEM subjects.
More than fun and games
Janelle McFeetors, associate professor in elementary mathematics education, says board games can be a terrific tool for improving not only visualization skills, but also deductive reasoning.
She has created a website with online resources for teachers and families, featuring board games that promote these skills. It offers instructions for playing the various games, explains how specific games help strengthen particular skills, and provides questions and prompts to help students reflect on the math skills they’ve learned.
When students predict moves in advance or decide on the best spot to place their game piece, they’re practising visualizing, McFeetors points out. When they convince themselves or other players of the best move to make, they’re using deductive reasoning. It all builds their confidence in problem-solving and in seeing themselves as mathematical thinkers.
“I believe we have begun to challenge the idea of what ‘back to the basics’ means. Rather than emphasizing arithmetic as a basic skill in mathematics, it really is reasoning that is basic to mathematical thinking and learning.”
Relating math to real-world problems
For high school students, Kwesi Yaro, assistant professor of mathematics education, seeks to strengthen their data literacy — the ability to put data into context by finding it, interpreting it and communicating it — by connecting it to sustainable development goals.
In one of his research projects, Yaro is empowering teachers to use credible and accessible big data such as global air quality indices or food prices. The teachers could then use these data to create activities that allow their students to apply math to real-world problems, analyzing the data for trends and making predictions.
When students think critically about climate change or hunger through mathematics, math becomes relatable to their lives and more engaging to them, says Yaro. It also lays the foundation for skills in computational thinking and mathematics modelling that are critical for careers in data science and artificial intelligence.
In other research, Yaro is interviewing new immigrant families in Edmonton to discover how they support their children in learning math. He explains that the students’ diverse backgrounds are an asset, not a barrier.
“It’s like having another language,” he says. “Having the ability to reframe that math concept in another language really helps (students) understand the concept better … and it’s the duty of the school to encourage such practices and different ways of knowing.”
This story was originally published by the Faculty of Education. It has been edited for length and content.