Watch Your (Mathematics) Language!

If you step into a Long-View mathematics class, you’re apt to hear students reading mathematics expressions using language that seems a little different.

In reading an addition expression such as 41 + 17, for example, you’d hear a Long-View student say “forty-one and seventeen” rather than “forty-one plus seventeen.” While this may seem like a subtle substitution, there is a great deal of deliberate thought underneath this use of language that supports our young mathematicians as they develop strong conceptual understandings that will transfer across all of arithmetic to Algebra. Language is actually one of the most under-utilized models in school mathematics. Not at Long-View. Thoughtful use of language that supports conceptual development and thinking is a part of the fabric of every Long-View math lesson.

At Long-View, we read an addition expression using the language “and” instead of “plus.” The reason for this is that the word “plus” infers that something is getting bigger, but that does not always hold true in every addition expression. In the below expression, for example, the result is a smaller number (i.e. -8) and not a larger one, as the word “plus” might incorrectly denote to a child.

-3 + -5 = -8

This inconsistency matters. When we help a young child construct understanding of a concept, we want to be sure that the idea will hold true for all mathematics, not just the problem in front of the child today. We do not want the concept to be limited in any way – we don’t want the ideas they learn to “expire” after a few years of mathematics work. We want the ideas to be deep and to hold true from arithmetic to Algebra.

The idea that “when we add two numbers the result is something bigger,” supported by the use of the word “plus” for the addition sign, is very limited. At Long-View, our students construct an understanding that addition is the concept of combining like terms. And that idea of “combining” is made clear with the use of the word “and” for the addition sign.

Additionally, when approaching a subtraction expression, you will hear Long-View kids use the word “lose” instead of “minus.” Again, we are interested in supporting lasting conceptual development, and the language we use can be a model for strong and clear thinking.

For a young child, losing something makes much more sense than “minusing.” The word “lose” describes action and is meaningful. After all, “10 losing 4” or “10 and a loss of 4” actually brings to mind a clear idea; “10 minus 4” really does not. Additionally, the language of “loss” will seamlessly support students as they make the transition to working with integers.

10 + -4

Long-View kids work with integers very early. They read this above expression as “ten and a loss of 4” and readily understand, through the supportive model of language, that this is the same as 10 - 4, or “ten losing four.”

10 + -4  = 10 - 4

Not only should we watch our language in mathematics classrooms, but we should be purposeful about the choices we make around symbolic notation. We want our oral language and the symbolic notation to work together to support conceptual understandings.

In many classrooms, teachers traditionally write multiplication facts like this: 4 x 7. Interestingly, the “x” was introduced as a symbol for multiplication in 1631 and was chosen for religious reasons, as it looked similar to the Christian cross. The haphazard symbol has persisted into the 21st century and while it feels like a familiar touchstone to many of us, it actually is yet another example of something we teach young children that quickly expires and does not persist to upper level mathematics.

At Long-View, we use parentheses to notate multiplication: rather than writing 4 x 7 we instead write 4(7). This notation helps ensure a more seamless connection across arithmetic and to Algebra. Additionally, this notation of parentheses supports language that models the concept more clearly. 4(7) is read as “four sevens” or “four of seven,” which conjures up a very specific idea that transfers across mathematics to expressions such as ½(¾), which is read as “ one half of three fourths.” “One half of three fourths,” rather than “one half times three fourths” supports a much clearer understanding of the underlying concept of multiplication.

Mark Twain once said, “The difference between the right word and the almost-right word is like the difference between lightning and lightning bug.” This is just as true within mathematics. At Long-View we are purposeful about every part of our mathematics instruction, and language is no exception.