#12. The use of precise language in math: A means of apprenticing students in the discipline

(Accountable Talk®: Accurate Use of Knowledge and Reasoning)

Posted on August 19th, 2014

From the Institute for Learning, this is Victoria Bill.

The use of precise language develops from the time children are young when developing language at home. A child describes his surroundings and at his side his mother revoices his words, adding new vocabulary that is more descriptive or precise. In mathematics, precision is also valued. It does not just mean "correct calculation of answers." It also means precise use of mathematical language and communication of mathematical reasoning, as reflected in the Common Core State Standards for Mathematical Practice, which explicitly call for students to attend to precision in both calculation and language.

Consider this statement by a student, "3/4 of a cake is 3 out of 4 pieces of cake." The teacher revoices. "You're saying that 3/4 of a cake is 3 pieces that are each a 4th in size?"

Is there a meaningful distinction between these two statements? Maybe it will help you if you think about 6/4 of a cake. Students who are brought up talking about the amount the first way will say, "6 out of 4 pieces of cake." They are likely to pause when they then try to imagine 6 out of the 4 pieces and end up puzzling, "How can there be 6 pieces when there are only 4 pieces?" Now think about the students who heard "3 pieces that are each a 4th" with the emphasis being on the size of the piece, rather than the number of pieces. They are less likely to struggle when hearing 6/4 because they understand that it is possible to have 6 pieces that are each a 4th in size. Without the use of precise language, students will find it difficult, if not impossible, to make sense of and communicate the underlying mathematical meaning inherent in a problem.

So let’s stick with the concept of fractions. Consider another example. Sometimes we hear students say that 6/8 can be reduced to 3/4. The use of the word “reduce” implies that the quantity of 6/8 is now of lesser value than 3/4. After all, "reduce" does mean to "bring down to a smaller size" as in "reduce one's weight by 10 pounds." A more precise way of referring to the relationship between 6/8 and 3/4 is to say that, "6/8 is simplified to an equivalent form 3/4." Imprecise language such as "reduce" versus precise language such as "simplify to an equivalent fraction" might be one reason why students struggle to understand that 6/8 = 3/4.

Use of precise language in a classroom can help develop students' understanding. Lack of precise language can impede students' understanding of a concept and may even lead to the development of misconceptions in mathematics.

So watch out for imprecise use of language, your own and students'. Use precise language to model and apprentice students in the field of mathematics. Revoice students' imprecise statements with precise language to gently correct without embarrassing students.

Victoria Bill

Victoria Bill is the Chair of the Institute for Learning's mathematics Disciplinary Literacy Team.

More information on Victoria Bill.