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.

Do the Standards Go Far Enough? Power, Policy, and Practice in Mathematics Education

1992 ◽  
Vol 23 (5) ◽  
pp. 412-431 ◽  
Author(s):  
Michael W. Apple
Keyword(s):  
Mathematics Education ◽  
Educational Reform ◽  
Mathematical Knowledge ◽  
Mathematics Curriculum ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Policy And Practice ◽  
Conservative Movement ◽  
Evaluation Standards

Although NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Standards for Teaching Mathematics (1991) are generating considerable interest, there has been little discussion of their ideological and social grounding and effects. By placing the Standards within the growing conservative movement in education, this paper raises a number of crucial issues about the documents, including the depth of the financial crisis in education and its economic and ideological genesis and results; the nature of inequality in schools; the role of mathematical knowledge in our economy in maintaining these inequalities; the possibilities and limitations of a mathematics curriculum that is more grounded in students' experiences; and the complicated realities of teachers' lives. Without a deeper understanding of these issues, the Standards will be used in ways that largely lend support only to the conservative agenda for educational reform.

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?

Implementing the Professional Standards for Teaching Mathematics: Systemic Reform: A New Mantra for Professional Development

1996 ◽  
Vol 89 (7) ◽  
pp. 584-587
Author(s):  
Madeleine J. Long
Keyword(s):  
Professional Development ◽  
Decision Making ◽  
Educational Reform ◽  
Systemic Reform ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Educational Progress ◽  
New Ideas

Like a huge pendulum that indiscriminately sweeps aside everything in its path, educational reform sometimes adopts new ideas and approaches without fully understanding their implications for teachers, for programs, and, most important, for students. Too often, educators jump on the bandwagon, forgetting the complexities of educational progress and engaging in either-or thought and decision making.

Peer Tutoring with Mathematics Manipulatives: A Practical Guide

1996 ◽  
Vol 3 (1) ◽  
pp. 8-15
Author(s):  
Michelle M. Barone ◽  
Lyn Taylor
Keyword(s):  
Peer Tutoring ◽  
Teaching Method ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Self Awareness ◽  
Mathematical Communication ◽  
Practical Guide ◽  
Mathematics Manipulatives

Are you looking for a teaching method that enhances mathematical communication, develops self-awareness, builds mathematical confidence, and improves interrelationships among students, as recommended by the NCTM's Professional Standards for Teaching Mathematics (1991)?

One Point of View: Elementary School Mathematics Specialists: Where Are They?

1984 ◽  
Vol 32 (3) ◽  
pp. 3-50 ◽  
Author(s):  
John A. Dossey
Keyword(s):  
Elementary School ◽  
Educational Reform ◽  
Grade Level ◽  
Point Of View ◽  
School Level ◽  
Teaching Mathematics ◽  
Resource Teachers ◽  
Elementary School Mathematics ◽  
Mathematics Specialists ◽  
Source Materials

The multitude of national reports calling for the upgrading of the school cirriculum has once again brought the focus of educational reform on mathematics. The source materials for Educating Americans for the 21st Century (1983) contain the suggestion that school ystems “reassign intere ted teachers at the 4—6 grade level to become specialists at teaching mathematics … ” This call for mathematics resource teachers at the elementary school level is not new. However, it is an idea that has not received the attention it warrants.

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.

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).

From Classroom Discussions to Group Discourse

2006 ◽  
Vol 99 (8) ◽  
pp. 544-551
Author(s):  
Azita Manouchehri ◽  
Dennis St. John
Keyword(s):  
Learning Communities ◽  
Ways Of Knowing ◽  
Mathematical Discourse ◽  
Teaching Mathematics ◽  
National Council ◽  
Classroom Discussions ◽  
Mathematics Classrooms ◽  
Principles And Standards ◽  
Current Movement ◽  
Human Inquiry

The vision to transform mathematics classrooms into learning communities in which students engage in mathematical discourse is a remarkable hallmark of the current movement, led by the National Council of Teachers of Mathematics, to reform mathematics education (NCTM 1991, 2000). According to NCTM, “the discourse of a classroom—the ways of representing, thinking, talking, agreeing and disagreeing—is central to what students learn about mathematics as a domain of human inquiry with characteristic ways of knowing” (NCTM 1991, p. 34). Indeed, both the Principles and Standards for School Mathematics (2000) and Professional Standards for Teaching Mathematics (1991) recommend that teachers of mathematics provide opportunities for children of all ages to participate in mathematical discourse.

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