Thursday, July 18, 2024

More math teaching could be like music instruction. (Photo: Vladvictoria via Pixabay)

The debate over how to teach math equitably and effectively has been raging in the United States for more than 50 years. Here in Cambridge, there’s been a lot of recent discussion over whether math classes are meeting the needs of all students, especially those at both ends of the achievement spectrum. Parents of struggling students are upset because their kids are not progressing to grade-level performance, while parents of students who find grade-level math easy are upset because their kids are not challenged.

The fact that in some Cambridge schools a single math classroom can have students that are five to seven grades apart in their learning presents a particular and unique challenge. Knowledge of school mathematics is very much like a building: If a foundation or a piece of a lower floor is missing, the building cannot stand. For example, long division requires multiplication and subtraction skills. If a child struggles with multiplication or subtraction, long division will be very difficult. The same is true for algebra – it is impossible to perform algebraic operations without knowing arithmetic.

Because the profile of each student is different, it is important to meet students where they are. If someone already mastered the topic being taught, they need to be able to do something of value to maintain their interest in the subject and continue learning. Otherwise, students become bored and by extension find the entire subject uninteresting and irrelevant. Similarly, if a student has gaps in their knowledge, it makes no sense to keep explaining topics that are beyond their comprehension; they will become confused and start to feel “they just can’t do math.” In both examples, a potential math student has been lost.

What makes sense is to fill in the gaps for those who struggle and expand topics for those who are ready, keeping both types of students engaged and interested in math. Not only does this make sense, it is an equitable solution in which all students – regardless of ability to pay for outside tutors or enrichment classes – will be able to access material at their learning level.

The great news is that Cambridge already has a model for teaching this way. This is exactly how the Cambridge Public Schools district teaches instrumental music.

Students come into orchestra or band with differing levels of preparation: Some have never held an instrument, while others have been playing regularly for years. Rather than having every child try to play the same notes in the same way, music teachers adapt to the students in front of them. They assign music that is appropriately challenging to each level of student, building up students’ skills and stamina. If someone cannot play a whole scale yet, they start by playing just a few notes. If someone can play a solo, they’re provided more complex pieces. When the entire band or orchestra comes together for a performance, all children have a role, play together and feel like they are part of the community. The result is that children find joy in music and feel accomplished as they learn to play at a pace that works for them.

This is all well and good, but music education does not have an MCAS test. How could this approach in math achieve the required benchmarks?

A music model can be the exact thing to raise standardized scores in math. One key reason students are not performing at grade level in MCAS is because something is missing. The “something” is a combination of fundamental skills and curiosity and interest in the material to stay engaged. By connecting with students in small groups via pull-out lessons, we can help them gain missing skills and/or dive deeper into a topic to maintain the students’ interest.

The instrumental music program is one of the gems of the Cambridge Public School system. Let us teach math the way we teach music – so every child can achieve their potential. In practice, this will mean providing small-group pull-outs just like in music. It would mean hiring more teachers to make this possible. If any one district can do it, it is Cambridge Public Schools.


Nataliya Yufa is co-founding director of The Cambridge Math Circle. Dennis Carlone is a Cambridge city councillor.