What has pedagogical research into the correlation between math and music unveiled? This question is easy to answer as long as we do not get into the absolutes of what is known as abstract reasoning. The research thus far has produced some very interesting findings, but no conclusions yet. We know musicians who happen to be very good at math, but we also know mathematicians who cannot advance past the basics of reading musical notation.
Let's get to the easy answer first: a virtuoso piano player may feel as she is terrible at math, but the abstract reasoning she mastered to become a great musician suggests that she could be great at math, but she would have to be interested in that particular subject. Cognitive neuroscientists at Boston Children's Hospital have observed clear changes in the brains of students who play musical instruments; the observations are related to the development of motor and auditory skills that synchronize with musical patterns and intervals, which in turn can be expressed in mathematical terms.
A piano player must count when performing. It does not matter whether the performance is of a classical piece composed by Beethoven or a free-form jam with a blues band; piano players will count notes, rhythms, and arpeggios even if they do so unconsciously. Since all counting is numerical, it stands to reason that musicians are good with numbers, but there is a certain mystery attached to this valid assumption. What we still do not know is if some children are born with musical talent and decide to "feed their brain" by learning music; it could also be the other way around, which would imply that music changes the brain and improves cognitive function. We are more inclined to think of the latter, and this is somewhat explained by the classical music and math homework phenomenon.
Australian researchers at the University of Canberra have noticed that math students who listen to Beethoven, Mozart, and Strauss masterpieces tend to do better with their math assignments; however, exactly why this happens has not been determined either.
What we do know is that many musicians become very curious about math, geometry, and physics. This was the case with jazz legend John Coltrane and his version of the tonal circle, which he believed combined music theory with Euclidean geometry principles. As Coltrane's musical ability grew exponentially, he became interested not just in math but also philosophy and spirituality, and he is hardly the only musician along these lines; we also have:
- Virtuoso pianist Eugenia Cheng, who researches math paradoxes at the University of Sheffield.
- Composer Phillip Glass, whose "Einstein on the Beach" opera is based on advanced math subjects.
- Guitarist Brian May of Queen has a Ph.D. in astrophysics.
- Laurie Anderson has incorporated algebra on some of her avant-garde rock compositions.
Not knowing with certainty what connects music and mathematical skill on a cognitive level should not stop you from integrating these two subjects within your homeschooling curriculum. Here are some ideas to help you in this regard:
Music and sounds can be used to illustrate and compare mathematical concepts and ideas. Let's think about early learners and how they can grasp the idea of making comparisons before they go on to learn about measurements. Let's look at some home classroom exercises:
- Using the volume knob or meter of an audio device, play a sound, and adjust the output so that it sounds softer and louder.
- Using your voice, make a sound that your student can not only mimic but also reproduce at higher or lower volume depending on the exercise.
- Using a percussion instrument, which could be a pencil on a table, play a number of beats as you count them. Increase and decrease the count so that your student can compare.
- Repeat the exercises above with clapping. Encourage your student to produce comparison sounds through clapping.
Introduce Music Notation Symbols
Although it may seem complicated to present breve, minim, and crotchet symbols to young children, you would be surprised how fast they can grasp these concepts from an early age. Start by drawing the semibreve whole note and playing a single beat. Cut down the beat by a half and draw the minim symbol. Drop the beat to a quarter and draw the crochet. Have your student mimic the length of the beat on the toy instrument you used, preferably a toy keyboard; as he or she plays the beat, point to the symbols to encourage recognition. Before you know it, your student will start thinking about fractions.
Similar to alphabet songs, musical pieces that focus on numbers and counting are mnemonic devices that stimulate learning by tautology. You probably still remember counting songs from your own childhood; the fact that you can still sing them or play them in your mind proves just how effective they were. Perhaps your educators kept things simple with songs such as "One Potato, Two Potato," but you should know that the counting song catalog is very extensive. You can find quite a few of these songs, some of them dealing with number categories and even multiplication, by searching on YouTube Kids. When your homeschooling student is ready to learn arithmetic operations, think back to these songs and the music notation strategy above; you will want to teach addition and subtraction following a rhythm in order to create a fun tautology.
Recognizing Visual and Musical Patterns
We are living through a glorious age of video game development, but it is up to parents of homeschooling students to take advantage of the right titles. Rhythm games such as Guitar Hero, Rock Band, and Dance Dance Revolution can go a long way in stimulating the crucial cognitive process known as pattern recognition. Remember John Coltrane and his circle of tones theory? He explained that the complex structures of music he had learned to create through saxophone performance were patterns he extrapolated when he listened to the rhythm section; in other words, he envisioned melodic patterns that he felt he needed to complete. In rhythm video games, players are challenged to replicate musical patterns that they first hear and then see on the screen. With this kind of game, there is also the added bonus of developing reflexes, but the development of pattern recognition skills is the primary benefit.
In the end, the integration of music and math in your homeschooling curriculum can not only be a great combination in terms of opening minds but also making lessons more fun and interactive. You really have nothing to lose and a lot to gain from this clever combination of learning topics. Even if your students do not grow up to be musicians or mathematicians, the cognitive workout they get from both music and math will certainly help them as they grow up and take on greater academic challenges. The connection between math and music is probably more complex than what we will ever know; there is a chance that we will never fully comprehend it, but this does not really matter. What is important is that children can discover the joys of this connection from an early age.