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.

Soundoff: Make Room for Dancing

1995 ◽  
Vol 88 (1) ◽  
pp. 6-7
Author(s):  
Larry E. Askins
Keyword(s):  
Mathematics Education ◽  
Mathematics Teachers ◽  
School Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Evaluation Standards ◽  
Clear Vision

As mathematics teachers, we are eager for an optimistic view of what our classrooms can become during this decade and beyond. I believe that NCTM's Professional Standards for Teaching Mathematics (1991) and Curriculum and Evaluation Standards for School Mathematics (1989) present a clear vision for making mathematics education successful in the 1990s. However, the documents mean nothing if individual teachers fail to take deliberate steps toward realizing that vision.

Math through the Mind's Eye

2005 ◽  
Vol 99 (4) ◽  
pp. 246-250 ◽  
Author(s):  
Sara P. Fisher ◽  
Christopher Hartmann
Keyword(s):  
Mathematics Teachers ◽  
Visually Impaired ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
Principles And Standards ◽  
New Perspective ◽  
Mind's Eye

This paper considers recommendations from the Principles and Standards for School Mathematics (PSSM) in relation to pedagogy for the visually impaired. The authors present three examples of ways that mathematics instruction for blind learners can employ representations in ways that are consistent with PSSM. In reflecting on these examples, the authors identify lessons for all mathematics teachers. The nature of these accommodations provide a new perspective on the recommendations in the PSSM.

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].)

Animating Geometry with Flexigons

1994 ◽  
Vol 87 (8) ◽  
pp. 602-606
Author(s):  
Ruth McClintock
Keyword(s):  
Language Skills ◽  
School Mathematics ◽  
Professional Standards ◽  
Physical Models ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Evaluation Standards ◽  
Grade Levels ◽  
Conversation Piece

Viewing mathematics as communication is the second standard listed for all grade levels in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). This emphasis underscores the need for nurturing language skills that enable children to translate nonverbal awareness into words. One way to initiate discussion about mathematical concepts is to use physical models and manipulatives. Standard 4 of the Professional Standards for Teaching Mathematics (NCTM 1991) addresses the need for tools to enhance discourse. The flexigon is a simple and inexpensive conversation piece that helps students make geometric discoveries and find language to share their ideas.

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.

Professional Development: Teachers' Communication and Collaboration Keys to Student Achievement

1995 ◽  
Vol 1 (6) ◽  
pp. 454-458
Author(s):  
Helene J. Sherman ◽  
Thomas Jaeger
Keyword(s):  
Professional Development ◽  
Student Achievement ◽  
Educational Reform ◽  
Mathematics Teaching ◽  
School Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Professional Satisfaction ◽  
Evaluation Standards ◽  
Instructional Changes

The curriculum and evaluation standards for School Mathematics (NCTM 1989) and the Professional Standards for Teaching Mathematics (NCTM 1991) have served as both stimuli for, and responses to, numerous formal and informal programs, conferences, and conversations calling for educational reform and improvement in mathematics teaching. After all the plans are drawn and all the objectives are written, however, reform is most likely to occur and make a lasting difference when teachers are aware of the need for improvement, have a voice in planning it, and derive a real sense of professional satisfaction from implementing the instructional changes.

Standards-Based Teaching: Alive and Well in Portugal

2001 ◽  
Vol 6 (9) ◽  
pp. 538-542
Author(s):  
Iris DeLoach Johnson
Keyword(s):  
Mathematics Teaching ◽  
Teaching Practices ◽  
Teaching And Learning ◽  
Large Scale ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Mathematics Reform ◽  
Reform Movements ◽  
Mathematics Teaching And Learning ◽  
Principles And Standards

NCTM'S Professional Standards for Teaching Mathematics (1991) emphasizes that teachers are “the key” to changing mathematics teaching and learning. Given that mathematics reform movements have never brought about “large-scale changes in teachers' behavior and teaching practices” (Hitch 1990, p. 2), Willis (1992) lamented that “whether the standards will actually produce sweeping changes in the way mathematics is taught and learned in U.S. classrooms remains to be seen” (p. 1). With Principles and Standards for School Mathematics (NCTM 2000), we continue to ask the vital question, How can we induce teachers to implement the Standards?

Lollipop Statistics

2003 ◽  
Vol 9 (1) ◽  
pp. 12-15
Author(s):  
Dianne S. Goldsby
Keyword(s):  
High School ◽  
Middle School ◽  
High School Students ◽  
School Mathematics ◽  
Constructivist Approach ◽  
School Students ◽  
Area Of Interest ◽  
Approach To Teaching ◽  
The 1950S ◽  
Principles And Standards

AS NCTM'S Principles and Standards for School Mathematics (2000) points out, students should work directly with data to understand the fundamentals of statistical ideas. Teachers should also introduce statistics in a way that will capture the attention of students of varying abilities and interests. The constructivist approach to teaching emphasizes the idea that students work better when presented with tasks that are meaningful and relevant; in other words, they expend energy on topics that interest them (Brahier 2000). One way to harness that energy in the classroom is to teach with music, an area of interest for most middle school and high school students. This article describes the use of the 1950s hit “Lollipop” (Ross and Dixon 1986), heard in the movie Stand by Me, as a launching point to introduce ideas of counting, working with frequency tables, and graphing data.

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