I had the pleasure of observing one of the richest math classes I’ve seen in a while. It was rich, not necessarily because of the complexity of the math problems that the students solved, but because of the way that the teacher engaged with words to help her students understand the reason for the mathematical algorithms they practiced. She weaved the origins of the vocabulary into a lovely tapestry of mathematical understanding.

The lesson was about determining multiples of given numbers using their previous knowledge of factors and products. The teacher first taught the students the origin of the word factor, which comes from the Latin word “facere”, or “to make”. She explained that when we multiply, the “makers” of the solution are the numbers that show how many copies of another number we need. Next, she explained the word product as the derivative of the word “producere”, which means “to bring forth”. “You see class,” she said, “the factors, or makers of the problem, help to bring forth the product!” She could have stopped there, but she continued talking about words.

Next, this teacher brought out a large piece of paper and began to fold it into equal sections of four. She wrote a number 2 on one of the folds, and explained that the word “multiply” comes from the Latin words for “many folds”. She turned back to the first 2, and explained how we can make one copy, or fold, of the number 2 to demonstrate that the first multiple, or fold, of 2 is 2. She carefully walked the class through each fold, and asked the students to calculate the second, third, and the fourth multiples based on the folds. Finally, she gave the students a sheet of paper and asked them to work through a strategy for showing the 7th multiple of 3.

Besides being a carefully thought out lesson with vocabulary instruction, guided practice, manipulatives, and lots of practice, this lesson highlighted for me the power of words. A well-rounded vocabulary doesn’t just increase students’ comprehension of the material – it empowers them to explore new depths of understanding, and to develop a strong connection with those first mathematicians who developed the words factor, product, and multiple. Teaching students to play with words helps them to enter into the great conversations that shape our classical curricula, and our understanding of how we represent patterns in nature using language. English-rich classrooms enliven our students’ minds, and I witnessed how this precise attention to word origins formed the framework of an excellent lesson.