Remember counting on your fingers to answer a math question in school? While most parents and teachers might think that practice is reserved for elementary students or those struggling in math, a new paper just released by youcubed, a Stanford University center dedicated to giving research based mathematics resources to teachers and parents, is supporting the use of visual mathematics. And yes, that includes using your fingers to solve a problem!
The paper, “SEEING AS UNDERSTANDING: The Importance of Visual Mathematics for our Brain and Learning,” explains that while students are encouraged to memorize math facts and calculate problems in their minds, this can actually discourage and decrease math learning, with research showing that students who approach mathematics with a memorization approach are the lowest achieving students in the world.
“Our brains use visual pathways when we are learning math – our brains actually ‘see’ a representation of fingers when we solve problems, whether or not we are actually using our fingers at the time, so training people on ways to perceive and represent their own fingers results in higher math achievement,” said co-author Dr. Jo Boaler, professor of mathematics education at Stanford Graduate School of Education and the co-founder of youcubed. “Schools do not know about this important brain research and many schools even ban students from using fingers in classrooms. While Kumon learning centers tell parents they should not allow fingers to be used and it is a ‘no, no’ for math learners, new research suggests that stopping students from counting on their fingers is akin to halting their mathematical development.”
In fact, the paper’s authors go on to note that there is not a single idea or concept that cannot be illustrated or thought about visually. “Students are made to memorize math facts, and plough through worksheets of numbers, with few visual or creative representations of mathematics or invitations to work visually. By the time most students leave elementary school they have developed the idea that visuals and manipulatives are babyish, fingers should never be used and mathematical success is about memorizing numerical methods.”
But actions like counting on your fingers, drawing shapes in the air and other visualization methods actually help the brain process math. In fact, researchers have suggested that teachers should use gestures to ground mathematical thinking, along with their verbal explanations. And educators seem to agree: When youcubed created a free set of visual mathematics lessons for grades 3-9 last summer, they were downloaded one quarter of a million times by teachers and used in every state across the US. In addition, 88 percent of teachers said they would like more of the activities, and 83 percent of students reported that the visual activities enhanced their learning of mathematics.
And visual math is not only for younger kids, but also students in middle school, high school and college. “Despite the prevalence of the idea that drawing, visualizing or working with models is low level or for young children, some of the most interesting and high level mathematics is predominantly visual,” say the researchers.
The paper lists recommendations on how teachers and parents can engage students in productive visual thinking, including:
- Using visuals, manipulatives and motion in mathematics teaching and parenting
- Providing opportunities for students to use drawing, visualizing or working with models in mathematics
- Teaching algebra visually through pattern study and generalization
- Asking students, at regular intervals, how they see mathematical ideas
- Asking students to represent mathematical ideas in a multitude of ways, such as through pictures, models, graphs, even doodles or cartoons
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