Project Title CAREER Discourse Analysis A Catalyst for by twa17837

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Project Title: CAREER: Discourse Analysis: A Catalyst for Reflective Inquiry in
Mathematics Classrooms

PI: Beth Herbel-Eisenmann, Iowa State University

Project Description/Update:

Watch Your Language: The Suppression and Invitation of Dialogue in the Mathematics
Classroom

Overview:
Recent research by Beth Herbel-Eisenmann, a Michigan State University associate professor
of teacher education, illustrates how a single word – just – can help us see the use of
language in a mathematics classroom and how it can affect a student’s response to a teacher,
the instruction being provided and even the discipline of mathematics itself.

The study:
Prompted by concerns expressed by high school mathematics students, Herbel-Eisenmann
and David Wagner of the University of New Brunswick used tools borrowed from the study
of linguistics to provide a careful analysis of the use of the word just in mathematics
instruction in eight classrooms across a variety of North American school districts during the
2005-06 year. They looked at how the word was used in classroom discourse and what its use
told them about how students and teachers relate to each other in mathematics classrooms.

Wagner and Herbel-Eisenmann found that just was used much more often in mathematics
class than in general conversation; in fact, just was used nine times more often than multiply,
four times more than why and twice as often as because. The authors explain how just can
inhibit classroom dialogue and reflective thought both for teachers and students, and can even
make students feel like outsiders to the world of mathematics. A teacher’s use of just, as in
the phrase “just multiply straight across,” suggests an obvious step for the teacher that may
not be at all obvious for the student. In this way, just often had the effect of discouraging
students from asking questions and absolving teachers from identifying or explaining the
concepts behind mathematical processes. The researchers also found that just represented a
degree of frustration nearly one-quarter of the time it was used, as when a student says, “I
just don’t know what the formula is.”

Herbel-Eisenmann and Wagner acknowledge the subtle and sometimes ambiguous meanings
conveyed by just. The purpose of their analysis is not to define the nature of mathematics
classroom discourse in and of itself. “Rather,” the authors write, “we want mathematics
educators to ask, ‘What is my discourse like?’ and ‘How might I change it to reflect my
intentions?’”

What This Means for You
According to Wagner and Herbel-Eisenmann, “[i]t is important for educators in any context
to consider how the words they use open or close dialogue.” Is effective discourse strategy a
part of the professional development for teachers in your district? Do administrators look for
it in classroom observations? If we are to educate all students to high levels of achievement,


                           2008 EDC’s Center for Science Education
                               DR-K12 Projects: News & Events


we need to make sure we are including, not excluding them. In such a communication-intense
activity as education, words matter.

For More Information:
Wagner, D. and B. Herbel-Eisenmann, 2008. “Just don’t: The suppression and invitation of
dialogue in the mathematics classroom. Educational Studies in Mathematics. (2008) 67:143-
157.

Reading Between the Lines: Recognizing How Textbooks Can Affect the Mathematics
Learner

Overview:
Mathematics textbooks are typically thought of as collections of mathematical content, and
their words, diagrams and pictures as straightforward representations of mathematical ideas.
In a recent article for the publication For the Learning of Mathematics, Michigan State
University associate professor Beth Herbel-Eisenmann and her University of New Brunswick
colleague David Wagner propose that the forms these representations take can significantly
influence how students see themselves in relation to other students, their teacher, and even to
the discipline of mathematics itself. The authors propose a framework to help teachers and
other mathematics educators see how a text’s representations might influence a learner. This
awareness can help teachers plan and implement the effective use of the textbook in class.

The framework:
Herbel-Eisenmann and Wagner organize their framework into five questions: how might a
textbook position students in relation to mathematics? In relation to their peers? To their
teacher? To other people? To their own experiences? The authors illustrate their framework
with examples from two particular textbooks but note that it can be applied usefully to any
mathematics textbook. Herbel-Eisenmann and Wagner employ the linguistic tools of critical
discourse analysis to examine the language choices textbook authors make and how those
choices reflect or exclude particular types of relationships. They cite the use of pronouns –
we versus you – and the modality of the text – the degree of certainty conveyed by will versus
could – as words that can position the learner as within the community of people doing
mathematics or outside it, precluding or inviting conjecture on the part of the learner.
“Mathematics seems to address the student literally, with sentences structured in the
imperative mood,” observe Herbel-Eisenmann and Wagner, who go on to note that many of
the verbs (such as write, calculate or copy) are “scribbler” imperatives that students can do
independently of other people, while “thinker” imperatives (describe, explain, prove) imply a
sense of community with others. The authors acknowledge the tension between the personal
and impersonal in mathematics, and wonder “how students’ experiences of mathematics
would differ if their textbooks did more to recognize persons, their contexts and
mathematisation.”


What This Means for You
If rigor, relevance and relationships are the new “three Rs” of education, this article suggests
that textbooks can play an important role not just in rigor but also in how students experience
relevance and relationships in schools. Having teachers look at and discuss how the texts
they use represent the subject matter and its relevance and relationship to their students can



                           2008 EDC’s Center for Science Education
                               DR-K12 Projects: News & Events


help them design and use effective instructional strategies and help students reach the new,
more rigorous goals required to succeed in our knowledge economy.

For More Information:
Hebel-Eisenmann, B. and D. Wagner, 2007. A Framework for Uncovering the Way a
Textbook May Position the Mathematics Learner. For the Learning of Mathematics, 27, 2,
8-14.


Publications/Resources:
Herbel-Eisenmann, B. (2007). From intended curriculum to written curriculum:
     Examining the "voice" of a mathematics textbook. Journal for Research in
     Mathematics Education, 38(4), 344-369.

Herbel-Eisenmann, B. & D. Wagner. (2007). How a textbook might position a
     mathematics learner. For the Learning of Mathematics, 27(2), 8-14.

Wagner, D. & B. Herbel-Eisenmann. (2008). "Just don't": The suppression and invitation
    of dialogue in mathematics classrooms. Educational Studies in Mathematics, 67(2),
    143-157.

Herbel-Eisenmann, B. & E. D. Phillips. (2008). Analyzing student work: A context for
     connecting and extending algebraic knowledge for teaching. C. Greenes & R.
     Rubenstein (Eds.) Algebra and algebraic thinking in school mathematics:
     Seventieth yearbook (pp. 295-311). Reston, VA: NCTM.

Herbel-Eisenmann, B., D. Wagner, V. Cortes. (2008, July). Encoding authority:
     Pervasive lexical bundles in mathematics classrooms. Proceedings of the XX
     Conference of the International Group for the Psychology of Mathematics
     Education (PME).

Herbel-Eisenmann, B., M. Cirillo, & K. Skowronski. (in press). Why classroom discourse
     deserves our attention! A. Flores (Ed.) Mathematics for all: Responding to
     diversity, Grades 9-12. Reston, VA: NCTM.

Herbel-Eisenmann, B. & M. Schleppegrell. (in press).'What question would I be asking
     myself in my head?' Helping all students reason mathematically. M. Ellis (Ed.)
     Mathematics for all: Responding to diversity, Grades 6-8. Reston, VA: NCTM.

Herbel-Eisenmann, B. (in press). Negotiation of the "presence of the text": How might
     teachers' language choices influence the positioning of the textbook? Chapter to
     appear in Remillard, Herbel-Eisenmann, Lloyd (Eds) Research perspectives on
     teachers' use of mathematics curriculum materials.




                           2008 EDC’s Center for Science Education
                             DR-K12 Projects: News & Events


Presentations:
RESEARCH CONFERENCE PRESENTATIONS

Cirillo, M. & B. Herbel-Eisenmann. (April, 2007). The validation of a questionnaire to
      describe teacher communication behavior in the mathematics classroom.
      Presentation at the Annual Meeting of the AERA, Chicago.

Moyer, J., G. Lloyd, J. Cai, & B. Herbel-Eisenmann. (March, 2007). Teachers' use of
    reform materials and traditional textbooks. Symposium at the Annual Meeting of
    the NCTM Research Presession, Atlanta.

Herbel-Eisenmann, B., G. Lloyd, & J. Remillard (Organizers & Presenters) D. Pimm, B.
     Jaworski, E. Phillips, M. Larson, T. Cooney, & L. Davenport (Panel Members).
     (March, 2007). Perspectives from research and practice: Interactions between
     teachers and curriculum materials. Symposium at the Annual Meeting of the NCTM
     Research Presession, Atlanta.

Cirillo, M. & B. Herbel-Eisenmann. (April, 2008). "Mathematicians are lazyŠWe're lazy
      bums": An investigation of teachers' framings of mathematicians in their
      classrooms. Presentation at the Annual Meeting of the AERA, New York.

Herbel-Eisenmann, B., M. Staples, J. Choppin, & D. Wagner. (October, 2007).
     Discussion group on mathematics classroom discourse. In Teruni (Ed.) Proceedings
     of the 29th annual meeting of the North American Chapter of the International
     Group for the Psychology of Mathematics Education (PME-NA), Tahoe, Nevada,
     USA.

Wagner, D. & B. Herbel-Eisenmann. (October, 2007). Discursive tools for suppressing
    and inviting dialogue in the mathematics classroom. In Teruni (Ed.) Proceedings
    of the 29th annual meeting of the North American Chapter of the International
    Group for the Psychology of Mathematics Education (PME-NA), Tahoe, Nevada,
    USA.

Cirillo, M. & B. Herbel-Eisenmann. (October, 2007). Mathematicians are lazy bums: An
      investigation of teachers' framings of mathematicians. In Teruni (Ed.) Proceedings
      of the 29th annual meeting of the North American Chapter of the International
      Group for the Psychology of Mathematics Education (PME-NA), Tahoe, Nevada,
      USA.

Cirillo, M. & B. Herbel-Eisenmann. (October, 2007). Activity structures in middle grades
      mathematics classrooms. In Teruni (Ed.) Proceedings of the 29th annual meeting of
      the North American Chapter of the International Group for the Psychology of
      Mathematics Education (PME-NA), Tahoe, Nevada, USA.

Herbel-Eisenmann, B. & M. Cirillo. (October, 2007). Collaborating with middle grades
     mathematics teachers to improve classroom discourse. In Teruni (Ed.) Proceedings



                         2008 EDC’s Center for Science Education
                            DR-K12 Projects: News & Events


     of the 29th annual meeting of the North American Chapter of the International
     Group for the Psychology of Mathematics Education (PME-NA), Tahoe, Nevada,
     USA.

PRACTITIONER conference presentations (w/ project participants)
Herbel-Eisenmann, B., J. Krusi, J. Obrycki, L. Lyddon Hatten, J. Marks, D. Dowling, P.
     Groenwald, T. Cass, A. Shindelar, M. Cirillo, & K. Skowronski. (March, 2007).
     What I learned over my summer vacation about classroom discourse. Symposium at
     the Annual Meeting of the NCTM, Atlanta.

Herbel-Eisenmann, B., M. Cirillo, K. Skowronski, J. Krusi, T. Cass, A. Shindelar, J.
     Obrycki, L. Lyddon Hatten, D. Dowling, J. Marks, P. Groenwald. (October, 2007).
     Lessons learned and actions taken: How discourse readings impacted our
     classrooms. Symposium offered at the Regional Meeting of NCTM, Kansas City.

Krusi, J., Herbel-Eisenmann, B., M. Cirillo, K. Skowronski, T. Cass, A. Shindelar, J.
     Obrycki, L. Lyddon Hatten, D. Dowling, J. Marks, P. Groenwald. (October, 2007).
     Partners in CRI2ME tackle classroom discourse. Symposium offered at the
     Regional Meeting of NCTM, Kansas City.




                        2008 EDC’s Center for Science Education

								
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