If you place a new piece of music in front of an accomplished professional musician, he or she likely will be able to play at least the main melody and harmony lines without a struggle. An experienced “sight reader” can quickly predict the combination of notes and chords from a glance at the key signature, which indicates which notes will be sharp, flat, or natural in the piece. This sight-reading ability stems from not only years of playing different pieces of music but also regular practice of key signatures and scales. She has mastered the fundamentals of music.
Sight reading also works in math education. Researchers (see Journal of Neuroscience and the Psychonomic Bulletin & Review) have found that mental math — the ability to do calculations in your head without the aid of a calculator or a pencil — is crucial to learning advanced mathematical concepts. Students can achieve this ability just as the accomplished musician does: practicing the fundamentals.
Cognitive scientist Daniel T. Willingham explains mental math in his book “Why Don’t Students Like School.” Working memory, or the short-term memory used in thinking and applying concepts, is limited, representing the “fundamental bottleneck of human cognition,” he writes. Think of working memory as a room with only a fixed amount of square footage in which to store knowledge.
To process more information, students must condense the basic concepts, such as key signatures in music or times tables in mathematics, to allow more room to focus on advanced ones. Mastering mental math allows students to do quick calculations in their heads, freeing them to concentrate on more challenging problems.
Students who succeed in mental math are…
- Focused. Because students aren’t distracted by large numbers, they concentrate on the logic of the problem.
- Efficient. Easier problems are solved more quickly, which leaves more time for difficult problems.
- Fearless. As students are able to do more math in their head, they are more and more confident in their abilities.
Mental math requires continual practice of addition, subtraction, division, and multiplication. But Willingham cautions that over drilling these concepts can zap a student’s motivation to learn. Simply put, it’s no fun. This may be why mental math is not incorporated into some classrooms. At Reasoning Mind, rather than using a drill-and-kill approach to memorization, we incorporate mental math skills into an animated, colorful world of instruction to keep the students practicing and having fun doing it. (If you’d like a tour, sign yourself up for a guest account at RM City.)