ACADEMIC DISCOURSE IN THE SECONDARY MATHEMATICS CLASSROOM

By a Guest Blogger Rebecca DesRoches

This blog post was originally submitted as a paper for EDUC731 course at Bethel University, Graduate School of Education, College of Adult and Professional Studies. It has been edited to fit the blog genre.

I have chosen to focus my reading and research of the academic discourse specific to my discipline: the secondary mathematics classroom.   In studying the readings and videos assigned for this class, I have grown to appreciate the importance of academic discourse in classrooms and found myself drawn to understand the language of the mathematics classroom in particular.   While there are parallels across the many disciplines, the idiosyncrasies of the challenges one faces in mathematics continue to intrigue me.

It is my intent in this paper to explore some of these specific challenges and to list some of the productive approaches toward a healthy pedagogy, which I have encountered in my research.   Essentially, I will focus on two guiding questions:

What are the specific challenges embedded in academic discourse for the secondary mathematics classroom?  

What guidelines can help to begin to address these challenges?

There is a large body of work available discussing the topic of mathematics discourse in secondary classrooms as educators explore the transition from the conventional view of teaching with the teacher as the giver of knowledge to the reform-inspired vision of the mathematics classroom, where

“the role of the teacher is diversified to include posing worthwhile and engaging mathematical tasks; managing the classroom intellectual activity including the discourse; and helping students understand mathematical ideas and monitor their own understanding” (Herbel-Eisenmann, 2009).

Mathematics is sometimes said to be a universal language.   The danger of this definition rests in the implication that once the language is ‘spoken’ one can communicate clearly across all linguistic barriers.  ”Formal mathematical vocabulary is not a set of self-evident factually objective terms that transcend debate or even controversy” (Barwell R. , 2005). While the universality of the language of mathematics is true on some levels, it is also far too simplistic an understanding of the complexities students face in the study of this discipline.

Even if mathematical language can be considered universal, then the language of ‘doing mathematics within the classroom’ is far from being universal.

The language of the exploratory talk, the discourse-specific mathematical talk, the mathematical talk and writing taking place in the language of instruction, was often understood and used in a non-equivocal way…It appears clear to us that during the process of constructing, developing or expanding a particular concept or procedure the mathematical language associated with it is not necessarily shared, or understood in an agreed way.   (Planas, 2001)

Whether an English language learner or a native speaker, each one faces a challenge in learning to converse within the mathematics register.   Moschkovich writes, “The communicative competence necessary and sufficient for competent participation in mathematical discourse practices… [involves] specialized vocabulary, syntax, organization, register and discourse practices” (Moschkovich, 2012).  Moschkovich suggests that the presence of ELL learners in the classroom can help build an awareness of the linguistic challenges we face as classroom teachers:

I want us to stop thinking about English learners as the problem.  I instead think of English learners as a gift, because when we hear imperfect language with an accent, or it’s not quite right in its tense, it’s as if we have a window into language, and it reminds us that even if you’re in a monolingual English class, with kids who are all kids who are native English Speakers, there are language issues going on there as well, and we tend to forget that, unless we walk into a classroom where you have some English learners (Moschkovich, 2012).

Adler describes the language of learning mathematics as involving dilemmas: the dilemma of code-switching or developing spoken mathematical English versus ensuring meaning, the dilemma of modeling mathematical English versus talking too much, the dilemma of mediation or validating pupil meaning versus developing communicating competence, and the dilemma of transparency or the visibility versus invisibility of language as a resource for learning (Adler, 1998).

Barwell describes the challenge between the mathematics register and everyday language as a “particular and problematic source of ambiguity for students” (Barwell, 2005).   He goes on to add that he feels an inflexible attitude between these two types of language is counterproductive.

A rigid distinction between formal and informal language in the mathematics classroom is not necessarily productive.

Informal language can be used to explore and develop sophisticated mathematical ideas and to participate in mathematical practices… I do not wish to suggest that students should not learn to use formal aspects of mathematical discourse.   This learning, however, is not identical with learning mathematical vocabulary.   Rather students’ development of the use of mathematical discourse is intertwined with their development of mathematical thinking.   Ambiguity acts as an important resource for students and teachers, serving as a means of articulating between thing and discourse (Barwell, 2005).

In an exciting study funded by the National Council of Teachers of Mathematics, titled, “Promoting Purposeful Discourse: Teacher Research in Mathematics promoting classroom discourseClassroom”, a team of university researchers and classroom teachers worked together to delve into this area of academic discourse.   They identified some key features of the particular challenges for mathematical discourse:

  1. The use of language for content learning versus social organization purposes.
  2. The delicate balance of language in the classroom as an expression of power, authority, and control and the theory of politeness.

“One person, the teacher, is responsible for controlling all the talk that occurs while class is officially in session – controlling not just negatively, as a traffic officer does to avoid collisions, but also positively, to enhance the purposes of education” (Herbel-Eisenmann, 2009).

  1. The use of language in the calculational (focusing on what students did or how they did it) versus the conceptual approach (focusing on why the students did what they did and how it relates to the bigger picture).
  2. The best use of questioning to deepen students’ understanding.
  3. The use of wait time (both before and after a student responds), pauses and pacing in the language of the classroom.
  4. Helping students learn specific terms associated with mathematical learning.
  5. The use of revoicing (teacher to student; student to student) or repeating another person’s words through repetition, expansion, rephrasing and reporting.
  6. The intentional development of acceptable mathematical arguments (Herbel-Eisenmann, 2009).

Teaching mathematics most certainly involves a complex process of balancing many features of discourse at the same time:

Mathematics teachers must know, for example, when to simply present information and when to withhold it; when to provide explanations and when to elicit them from students; when to supply notation and language for shared use in the class and when to encourage students to invent symbols; and when to encourage students to speak freely and when to monitor their ideas and challenge them to justify their thinking (Herbel-Eisenmann, 2009).

Moschkovich offers many helpful suggestions for tackling some of these issues in the classroom which help to synthesize the suggestions one encounters in most research  (Moschkovich, 2012):

  • Focus on students reasoning, not accuracy in using language

“If the goal is to support student participation in a mathematical discussion and in mathematical practices, determining the origin of an error is not as important as listening to the students and uncovering the mathematical content in what they are saying” (Moschkovich, 2012).

In particular, it is important to include the English learner in the learning process, recognizing they are fully able to contribute even as their command of the language is maturing.

  • Shift to a focus on mathematical discourse practices (explaining, abstracting, generalizing, conjecturing, justifying, etc) and move away from simplified views of language.

“Instruction should move away from interpreting precision to mean using the precise word, and instead focus on how precision works in mathematical practices” (Moschkovich, 2012).

Aim to teach for understanding, deepening a student’s ability to think critically and interact with the ideas they are learning.   The Common Core Standards provide a strong philosophical foundation on which to build your work.   Seek to provide diverse opportunities for speaking, listening, reading and writing.   Encourage students to take risks.

  • Recognize and support students to engage with the complexity of language in math classrooms

Classroom mathematics works in multiple modes, representations, forms of text, types of talk, audiences.   Remember each aspect is a learning moment for your students.   Language is a resource not a deficit.

  • Treat everyday language and experiences as resources, not as obstacles

“Instruction needs to consider everyday and scientific discourses as interdependent, dialectical and related rather than assume they are mutually exclusive” (Moschkovich, 2012).

Rather than discouraging everyday language, find ways to connect academic math to the language students’ use in everyday life.

  • Uncover the mathematics in what students say and do

Learn to uncover the mathematics in the language of your students.   Help them move into more conventional manners of communication but do not be discouraged when they use their own lingo or vocabulary.   Probe their ideas embedded in their own words.

Use talk to effectively build on students’ everyday language as well as developing their academic mathematical language; providing interaction, scaffolding and other supports for learning academic mathematical language; making judgment about defining terms and allowing students to use informal language in mathematics classrooms, and deciding when imprecise or ambiguous language might be pedagogically preferable and when not (Moschkovich, 2012).

The plethora of contemporary studies outlining the distinct challenges faced in the mathematics classroom sets the stage for the exploration of productive approaches to the challenges in the days ahead.

The healthiest approach to facing all challenges in life begins with the admission that there is a problem.

The traditional approach with the teacher as the source of all knowledge inadvertently placed the onus on the student: those who were mathematically inclined understood, those who were not, did not, and those who were lazy, obviously just didn’t care.   The contemporary understanding of the role of the teacher places a much greater level of responsibility on the teacher to adapt his/her techniques and approach to better suit the learning of our students so that every child can be successful.   These are most certainly exciting times in the classroom as we explore educationally healthy solutions to these everyday realities.


References:

Adler, J. (1998). A Language of Teaching dilemmas: Unlocking the Complex Multilingual Secondary Mathematics Classroom. For the Learning of Mathematics , 18 (No. 1), 24-33.

Barwell, R. (2005). Ambiguity in the Mathematics Classroom. Language and Education , 19 (No 2), 118-126.

Barwell, R. L. (2005). Applied linguistics and mathematics education: more than words and numbers. Language and Education , 19 (2), 141-146.

Cavanagh, S. (2005, July 12). Math: the Not-So-Universal Language. Retrieved May 16, 2016, from Education Week:

Herbel-Eisenmann, B. (2009). Promoting Purposeful Discourse: Teacher Research in Mathematics Classrooms. National Council of Teachers of Mathematics. Reston: The National Council of Teachers of Mathematics.

Moschkovich, J. (2012, June). Math, the Common Core and Language. Retrieved from Understanding Language: Language Literacy + Learning in the Content Areas

Planas, N. G. (2001). Teaching Mathematics in Multilingual Classrooms. Educational Studies in Mathematics , 47 (No. 1), 7-33.


rebecca desroches

Rebecca and her husband, Andy, have been living outside of Canada for the last sixteen years.   After time in Portugal, Mozambique, Kenya, and Saudi Arabia they are excited to have the opportunity to work in Dubai, United Arab Emirates, for the American School of Dubai.     Parents of two amazing kids in Canadian universities and happy owners of two quirky golden retrievers, they love their work with students in the Middle East.   Rebecca teaches high school mathematics (Algebra II, Pre-Calculus) to juniors and seniors and relishes the opportunity to bring this subject to life for her students. 

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