Linguistic Challenges in Mathematics

Citation: Mary J Schleppegrell (2007): The Linguistic Challenges of Mathematics Teaching and Learning: A Research Review, Reading & Writing Quarterly, 23:2, 139-159

The study of linguistics and mathematics education is based on the premise that we use language in order to participate in ways of knowing. Language and learning cannot be separated. In the case of mathematics, the goal of the teacher is to move students from more informal (everyday) ways of using language and understanding to more formal ways of understanding. In the case of mathematics education, this means the goal is for students to use more technical language of the discipline in effective ways; this formal language is called the ‘mathematical register’.

A mathematical register, “is a set of meanings that is appropriate to a particular function of language, together with the words and structures which express these meanings. We can refer to a ‘mathematics register’, in the sense of the meanings that belong to the language of mathematics (the mathematical use of natural language, that is: not mathematics itself), and that a language must express if it is being used for mathematical purposes. (p. 195)

The mathematical register includes semiotic systems such as symbols, oral language, written language graphs and diagrams. It also includes grammatical patterns. One central aspect of Schleppegrell’s research review is that language issues is math are not solely about terminology or specialized terminology. Rather mathematical reasoning uses grammatical patterns that are dense and quite different from informal language use. Mathematical thinking is not just about using precise terms but the way that one uses terms must also be precise. For example, in explanations, teachers or students might use number operations (such as squaring) as nouns rather than verbs. Teachers may also fail to recognize that students use terminology in ways that are different from the ways that teachers intend it to be used. Students tended to use mathematical terminology as description, sequence or choice while teachers use mathematical terminology for classification, principles and evaluation. In one example a teacher and student pair are working with tangrams. The teacher uses the term parallelogram as a classification but the student uses it as a description.

Some strategies for developing the mathematical register include:

-interactive activities that allow students to construct meaningful discourse about mathematics

-verbal explanation of word problems

-develop connections between everyday meanings of words and their mathematical meanings

-recognize and use technical language rather than informal language wen defining and explaining concepts

-explicitly evaluate the use of technical language

-use writing but be explicit about not writing in a narrative form. Rather use other forms of writing such as procedures, descriptions/classifications, explanations/findings and arguments about math theorems

There are two tensions that teachers encounter as they teach the math. One is the dilemma of mediation: this is when a teacher has to decide when it is best to validate the perspective of the learner by listening and when to introduce more formal ways of explaining concepts. The second is the dilemma of transparency: this is when a teacher has to decide when to talk and when not to talk. Scleppenberg also described how focus on linguistics is important for low SES and culturally diverse learners.

STOP:

One idea that I took away from this article is about the effective use of writing in mathematics teaching. A few weeks ago, in my post about ethno-mathematics, I questioned if the discussions and writing I am using in math class is working for ELL learners. Last week, the Marion and Walter article talked about creating a culture of mathematicians by having students create math academic journals that are posted up in the room and critiqued by peers. Schleppegrell’s article states that in order to use writing to further mathematical understanding it should not just be narrative but rather teacher should explicitly teach students how to use writing for procedural and explanatory purposes. To me, this reminded me of our conversation about genre last week and how important it is to teach different genres.

It also made me think about primary learners and how sometimes their math journal writing seems to show pseudo-mathematical understanding. This article makes me wonder if this is because young students are writing in a narrative way? Developing a sense of story is a huge component of Kindergarten curriculum.  Furthermore, students only recently learned that the orientation of a symbol changes its meaning: ‘p’ is different from ‘q’ is different from ‘b’ is different than ‘d’. Now, we expect them to understand that numbers don’t magically change but that we perform operations on them and then they change.  That a 6 and 7 are nouns, but that a + and – are verbs. Looking at this developmentally, I can see how this would be extremely confusing to a young person.

Question:

There is a common held assumption that math as the least language-dependent subject. What do you think? Agree or disagree? How did this assumption come to be?