Promoting Mathematical Discourse: Learning from Classroom Examples

1999 ◽  
Vol 4 (4) ◽  
pp. 216-222 ◽  
Author(s):  
Azita Manouchehri ◽  
Mary C. Enderson
Keyword(s):  
Mathematics Teachers ◽  
Mathematics Classroom ◽  
Mathematical Discourse ◽  
Professional Standards ◽  
Reform Movement ◽  
Teaching Mathematics ◽  
Directed Attention ◽  
Mathematical Inquiry ◽  
Mathematics Classrooms ◽  
New Vision

The NCTM's Professional Standards for Teaching Mathematics (1991) has directed attention to “discourse” in the mathematics classroom. This document recommends that mathematics instruction should promote students' discourse by orchestrating situations in which each individual's thinking is challenged and by asking students to clarify and justify ideas. “Discourse,” as described by the Standards document, highlights the way in which knowledge is constructed and exchanged in the classroom (Ball 1992). Teaching mathematics from the perspective of developing mathematical discourse requires building a new vision for mathematics classrooms and poses a major challenge for mathematics teachers at all levels. This challenge was recognized by D'Ambrosio (1995). She identified the need to build environments in which students construct a “personal relationship” with mathematics as one of the most important requirements for promoting and sustaining the type of discourse envisioned by the reform movement. In such environments, students engage in authentic mathematical inquiry; act like mathematicians as they explore ideas and concepts; and negotiate the meanings of, and the connections among, those ideas with others in class (D'Ambrosio 1995).

Implementing the Professional Standards For Teaching Mathematics: Teachers Building on Students' Thinking

1992 ◽  
Vol 39 (7) ◽  
pp. 32-37 ◽  
Author(s):  
Carolyn A. Maher ◽  
Amy M. Martino ◽  
Susan N. Friel
Keyword(s):  
Learning Environments ◽  
Mathematics Teachers ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Mathematical Learning ◽  
New Vision ◽  
Insight Into

Teaching mathematics from the perspective of developing in students “mathematical power” (NCTM 1989) requires the building of a new vision for learning that focuses on thinking and reasoning. This endeavor draws on many complex and interrelated domains of knowledge. The reasons some teachers are more successful than others in facilitating thoughtful mathematical learning environments are varied and intricate. Perhaps a look at classroom sessions in which students are thoughtfully engaged in doing mathematics might lend further insight into what it means to pay attention to the thinking of students as they are engaged in doing mathematics and what it means to build on students thinking. (For a discussion of what is meant by doing mathematics, see Davis and Maher [1990] and Maher, Davis, and Alston [1991a].)

Inquiry-Discourse Mathematics Instruction

2007 ◽  
Vol 101 (4) ◽  
pp. 290-300
Author(s):  
Azita Manouchehri
Keyword(s):  
Mathematics Teachers ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Mathematical Inquiry ◽  
Mathematical Structures ◽  
Approach To Teaching ◽  
Principles And Standards ◽  
Student Inquiry

Principles and Standards for School Mathematics (NCTM 2000) proposes that mathematics instruction provide opportunities for students to engage in mathematical inquiry and in meaningmaking through discourse. Mathematics teachers are encouraged to build on student discoveries in designing subsequent instruction. Natural consequences of using an inquiry-based approach to teaching include the emergence of unexpected mathematical results and the articulation of novel and different strategies by students. Anticipating the potential for such occurrences, Professional Standards for Teaching Mathematics (NCTM 1991) urges all teachers to remain flexible and responsive to student ideas in their instruction: Help students make connections among various solutions, tie student ideas to important mathematical structures, and extend student inquiry by posing questions and tasks that challenge their initial interpretations of problems or their false generalizations.

Implementing the “Professional Standards for Teaching Mathematics”: Applying the Standards to the College Mathematics Classroom: Ideas and Obstacles

1993 ◽  
Vol 86 (9) ◽  
pp. 744-747
Author(s):  
Mary Kim Prichard
Keyword(s):  
Mathematics Teaching ◽  
Teacher Educators ◽  
Mathematics Classroom ◽  
School Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
College Level ◽  
College And University ◽  
University Mathematics ◽  
New Vision

This assumption that how teachers teach mathematics is fundamentally connected with how they learned it underlies the first standard of the “Standards for the Professional Development of Teachers of Mathematics.” This standard, Experiencing Good Mathematics Teaching, focuses on the role of the college and university mathematics professors in the process of reforming school mathematics teaching. It is essential that mathematics teacher educators invite and encourage college-level mathematics faculty to join them in implementing the teaching standards. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Standards for Teaching Mathematics (1991) present a new vision of school mathematics. Mathematics courses and programs of study in colleges and universities should share in this vision.

Connecting Research to Teaching: Making the Right (Discourse) Moves: Facilitating Discussions in the Mathematics Classroom

2006 ◽  
Vol 100 (2) ◽  
pp. 105-109
Author(s):  
G. T. Springer ◽  
Thomas Dick
Keyword(s):  
Education Research ◽  
Mathematics Education ◽  
Mathematics Classroom ◽  
Mathematics Education Research ◽  
Mathematical Discourse ◽  
Classroom Discussion ◽  
Special Role ◽  
Mathematics Classrooms ◽  
Principles And Standards ◽  
The Right

The mathematics classroom envisioned by the NCTM Principles and Standards (2000) is one in which teachers deliver fewer monologues and engage in more dialogues with students. The teacher is not an ordinary participant in mathematics classroom discussion but plays a special role in facilitating and steering discourse. Calls for encouraging discourse in mathematics classrooms are pervasive, and the analysis of discourse has become a prominent theme in current mathematics education research. Nevertheless, while many teachers may feel the goal is a worthy one, some may also feel at a loss as to the specific strategies or techniques that may be used to encourage and facilitate meaningful mathematical discourse among their students.

A History of Mathematical Dialogue in Textbooks and Classrooms

2001 ◽  
Vol 94 (3) ◽  
pp. 170-173
Author(s):  
Edith Prentice Mendez
Keyword(s):  
Nineteenth Century ◽  
Educational Reform ◽  
Grade Level ◽  
Mathematical Discourse ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Important Goal ◽  
Mathematical Communication ◽  
History Of ◽  
Principles And Standards

Mathematical communication is an important goal of recent educational reform. The NCTM's Principles and Standards for School Mathematics (2000), continuing an emphasis on mathematical discourse from the 1991 Professional Standards for Teaching Mathematics, has a Communication Standard at each grade level. This article examines textbooks and classrooms from antiquity through the nineteenth century in search of historical precedents for mathematical communication in the form of dialogue between teacher and student. Although we have no way of knowing how prevalent this mode of teaching has been, interest in dialogue as a tool for helping students learn mathematics has been ongoing.

Implementing the Professional Standards for Teaching Mathematics: Thinking Deeply about Knowing Mathematics

1998 ◽  
Vol 91 (7) ◽  
pp. 610-614
Author(s):  
Joanna O. Masingila
Keyword(s):  
Mathematics Teachers ◽  
Mathematical Knowledge ◽  
Secondary Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Secondary Mathematics Teachers

Most prospective secondary mathematics teachers know quite a bit of mathematics, and they know that they know quite a bit of mathematics. However, they may not be aware that some of their mathematical knowledge is not conceptually deep, connected, or broad.

Technology Tips: High-Leverage iPad Apps for the Mathematics Classroom

2014 ◽  
Vol 107 (9) ◽  
pp. 706-711 ◽  
Author(s):  
Ayanna D. Perry ◽  
Emily P. Thrasher ◽  
Hollylynne S. Lee
Keyword(s):  
Data Analysis ◽  
Mathematics Teachers ◽  
Mathematics Classroom ◽  
Mathematical Understanding ◽  
Classroom Setting ◽  
Mathematics Classrooms ◽  
School Year ◽  
Ipad Apps

The use of iPads® in the classroom is growing. In the 2013–14 school year, 57 percent of schools planned to invest in iPads (Netop 2013). This investment can benefit mathematics classrooms only if teachers know which apps they can use to help students develop deeper mathematical understanding. Although learning about and developing facility with various apps is valuable for mathematics teachers, the process can be difficult, overwhelming, and time-consuming. To get started, we recommend one app, Dropbox, that can be used to share materials within the classroom setting, and then we suggest three free, easy-to-use mathematics apps: Sketchpad Explorer, Data Analysis, and MathGraph (see the table on p. 711).

scholarly journals Establishing a Community of Discourse Through Social Norms

2018 ◽  
Vol 9 (1) ◽  
pp. 5-17
Author(s):  
Sara Brooke Mullins
Keyword(s):  
Social Norms ◽  
Educational Research ◽  
Classroom Environment ◽  
Teacher Educators ◽  
Mathematics Classroom ◽  
Mathematical Discourse ◽  
Mathematical Discussion ◽  
Policy Makers ◽  
Mathematics Classrooms ◽  
National Organizations

Abstract While researchers, educators, state and national organizations, and policy makers are taking strides to help transform traditional mathematics classrooms into inquiry-based classrooms, they fail to address how to bridge the gap between creating discussions to developing mathematical discourse. One key component for producing inquiry-based classrooms is to have effective discussions (Smith & Stein, 2011). However, to have effective discussions, social norms must be in place that promote active participation from students (Sherin, 2002). Therefore, the purpose of this paper is to synthesize educational research on social norms in the mathematics classroom to identify key components teacher educators can focus on to help teachers establish and implement social norms that promote sustainable inquiry-based classrooms. Results suggest social norms must be developed through collaboration of the teacher and students, the classroom environment must be supportive of mathematical discussion, and finally, norms should be (re)negotiated to help change students’ ways of thinking.

Rousing Mathematics Classroom Discourse out of the Ice Age

2014 ◽  
Vol 45 (3) ◽  
pp. 397-400
Author(s):  
Victoria Hand ◽  
Tamsin Meaney
Keyword(s):  
Mathematics Education ◽  
Classroom Discourse ◽  
Mathematics Classroom ◽  
Mathematical Discourse ◽  
Ice Age ◽  
Cultural Hybridity ◽  
Global Culture ◽  
Mathematics Classrooms ◽  
Hierarchical Nature

Our connected world is exploding with images and sounds of cultural hybridity and fluidity. Mathematics classrooms, however, remain frozen in time. One consequence of this inertia is that mathematics education, rather than being a way to provide opportunities that lead to better lives for students, continues to limit those opportunities by reproducing existing societal inequities (Ernest, 2009). The inertia continues despite Herculean efforts by a range of stakeholders in mathematics education to broaden and diversify the voices participating in classroom mathematical conversations. What does the contrast between the increasingly dynamic and “flattened” (Friedman, 2005) nature of our global culture and the static and hierarchical nature of the mathematics classroom have to do with a book about classroom mathematical discourse and issues of equity?

Implementing the “Professional Standards For Teaching Mathematics”: Questioning in the Mathematics Classroom

1993 ◽  
Vol 41 (2) ◽  
pp. 88-91 ◽  
Author(s):  
Nancy Nesbitt Vacc
Keyword(s):  
Secondary School ◽  
Mathematics Classroom ◽  
Current Level ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Active Engagement ◽  
Methods Courses ◽  
Beliefs About Mathematics ◽  
Great Sense ◽  
Level Of Understanding

For many of us, implementing the Professional Standards for Teaching Mathematics (NCTM 1991) in our classrooms makes great sense. It is clearly reasonable that if students are to develop an understanding of and an ability to use mathematical applications in a variety of contexts (NCTM 1989). they should have meaningful and relevant experiences that will actively engage them in constructing their own knowledge. Also, that active engagement needs to be accompanied by opportunities for students to talk about what they already know and don't know and what they are doing as they strive to extend or change their current level of understanding. For many teachers, however. offering this type of instruction means changing their beliefs about mathematics instruction. After all, most of us are products of elementary and secondary school classrooms in which the teachers told us what we needed to know or do and we listened to and did what they told us to do. What we were thinking about during this interaction often did not matter, and we were unaware that it should. This same type of discourse existed in many of our methods courses. The instructor spent most of the class telling us what we needed to know so that we could tell our future students what they needed to know. Fortunately, we have come to the realization that this style of teaching is not as effective as once thought, and consequently we need to change what we are doing. However, how we go about making needed changes in our teaching is unclear.

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