Stanford University researchers aim to dispel the belief that students should not use their fingers to learn mathematics
Taking a more visual approach to math instruction at the K-12 and higher-ed levels could dramatically change brain development as it relates to future math success, according to a new paper from Stanford researchers.
“SEEING AS UNDERSTANDING: The Importance of Visual Mathematics for our Brain and Learning,” supports the use of visual mathematics and developing “finger discrimination” in students because it could result in higher math achievement.
According to co-authors Stanford University mathematics researcher Dr. Jo Boaler and brain researcher Dr. Lang Chen, the human brain can visualize a representation of the fingers during math problems. This provides an opportunity for further research and pedagogical development.
“Neuroimaging has shown that even when people work on a number calculation, such as 12 x 25, with symbolic digits (12 and 25) our mathematical thinking is grounded in visual processing,” according to the paper.
In fact, a 2015 study cited in the paper found that found that when 8-13-year-olds were given complicated subtraction problems, the region of the brain that deals with perception and representation of the fingers, called the somatosensory finger area, lit up, even though the students did not use their fingers.
Next page: Strategies to help students take a more visual approach to math learning
“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, a Stanford University center that provides research-based resources for teaching and learning mathematics, in a press release. “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.”
Math instruction today offers a number of factors that work against what this new research has revealed about brain development, including a focus on memorization, nearly exclusive focus on numerical and abstract thinking, and the practice of discouraging students from using their fingers for counting.
Now that research shows visual pathways have great potential for further math achievement, parents and teachers can help students develop visual areas of their brains in many ways, 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
“Visual mathematics helps students at any level formulate ideas and develop understanding,” said Dr. Boaler. “In fact, the quality of six-year-olds’ perception and representation of fingers has been found to be a better predictor of future mathematics success than performance on tests of cognition.”