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.

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.

Technology Tips: When Is a Good Fit Not a Good Fit? Dynamic Regression with the TI-Nspire Graphing Calculator

2008 ◽  
Vol 102 (4) ◽  
pp. 300-305
Author(s):  
Michael Edwards ◽  
Michael Meagher ◽  
S. Asli Özgün-Koca
Keyword(s):  
Graphing Calculator ◽  
School Mathematics ◽  
Mathematical Education ◽  
National Council ◽  
Mathematics Textbooks ◽  
Multiple Points ◽  
Complex Concept ◽  
Mathematics Classrooms ◽  
Points Of View ◽  
Principles And Standards

In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics (NCTM) acknowledges the importance of exploring mathematical ideas from multiple points of view: “Different representations often illuminate different aspects of a complex concept or relationship…. The importance of using multiple representations should be emphasized throughout students' mathematical education” (2000, p. 68). In particular, NCTM notes that the introduction of technology in school mathematics classrooms provides new ways for teachers and their students to explore connections among representations: “Computers and calculators change what students can do with conventional representations and expand the set of representations with which they can work” (2000, p. 68). In this article, we discuss an interesting finding that our students made as they explored linear regression with a teacher-constructed TI-Nspire calculator document. The calculator's capability to link variables across two or more pages in the same document led students to findings that are important yet rarely discussed in school mathematics textbooks.

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.

A Little-Used Art of Teaching: The Case of Storytelling

2006 ◽  
Vol 100 (1) ◽  
pp. 64-68
Author(s):  
David E. Meel ◽  
Deborah Gyurko ◽  
Michelle Gaspar
Keyword(s):  
Mathematical Understanding ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
National Council ◽  
Working Through ◽  
New Concepts ◽  
Teaching Of Mathematics ◽  
Art Of Teaching ◽  
Principles And Standards ◽  
Math Teacher

How many students would agree with the statement “My math teacher fails in the area of creativity” when asked if their teachers try to enliven their classroom? So, where is the fun in our teaching of mathematics? In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics clearly recognizes the need for lively classrooms by stating, “Teaching mathematics well involves creating, enriching, maintaining, and adapting instruction to move toward mathematical goals, capture and sustain interest, and engage students in building mathematical understanding” (NCTM 2000, p. 18). We suggest incorporating storytelling as a means of introducing students to new concepts and working through the solution of several problems before the students even know they are investigating them.

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).

New Assessment Practices in Mathematics

1996 ◽  
Vol 178 (1) ◽  
pp. 61-71 ◽  
Author(s):  
Linda Schulman
Keyword(s):  
Learning Outcomes ◽  
Performance Standards ◽  
Assessment System ◽  
Assessment Process ◽  
Assessment Practices ◽  
National Council ◽  
Assessment Data ◽  
Mathematical Ideas ◽  
Mathematics Classrooms ◽  
Assessment Tasks

Assessment practices need to change in mathematics classrooms that adopt the curriculum standards recommended by the National Council of Teachers of Mathematics (NCTM). An assessment system that focuses on broad learning outcomes, uses tasks that are aligned with instructional practices, involves students actively in the process, and informs teachers' instructional and curricular decisions is recommended. Such an assessment process requires teachers to identify important mathematical ideas, along with performance standards that describe what students must do to demonstrate that those ideas have been learned. Open-ended questions, observations, interviews, pre- and post-assessments, self- and peer-assessments are strategies that can be used to gather evidence of students learning. Documentation strategies are needed to help teachers organize and manage assessment data. NCTM has provided six standards for assessment that teachers can use as guidelines to help them evaluate the appropriateness of assessment tasks.

scholarly journals Concreteness Fading Strategy: A Promising and Sustainable Instructional Model in Mathematics Classrooms

2020 ◽  
Vol 12 (6) ◽  
pp. 2211 ◽  
Author(s):  
Hee-jeong Kim
Keyword(s):  
Instructional Strategies ◽  
Conceptual Understanding ◽  
National Curriculum ◽  
Instructional Model ◽  
Abstract Concepts ◽  
Mathematics Classrooms ◽  
Study Support ◽  
Principles And Standards ◽  
Concreteness Fading

Conceptual understanding has been emphasized in the national curriculum and principles and standards across nations as it is the key in mathematical learning. However, mathematics instruction in classrooms often relies on rote memorization of mathematical rules and formulae without conceptual connections. This study considers the concreteness fading instruction strategy—starting with physical activities with manipulatives and gradually fading concreteness to access abstract concepts and representations—as a promising and sustainable instructional model for supporting students in accessing conceptual understanding in mathematics classrooms. The results from the case study support the validity of the concreteness fading framework in providing specific instructional strategies in each phase of concept development. This study implies the development of sustainable teacher education and professional development by providing specific instructional strategies for conceptual understanding.

Informing Learning Through the Clinical Interview

1991 ◽  
Vol 38 (6) ◽  
pp. 44-46
Author(s):  
Madeleine J. Long ◽  
Meir Ben-Hur
Keyword(s):  
Student Outcomes ◽  
Clinical Interview ◽  
School Mathematics ◽  
Assessment Tools ◽  
Teaching Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Paper And Pencil ◽  
Primary Assessment

The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Srandards for Teaching Mathematics (1989) endorse the view that assessment should be made an integral part of teaching. Although many of the student outcomes described in the Srandards cannot properly be assessed using paper-and-pencil tests, such tests remain the primary assessment tools in today's classroom.

Effective and Efficient Use of Math Writing Tasks

2018 ◽  
Vol 112 (2) ◽  
pp. 143-146 ◽  
Author(s):  
Matt M. Bixby
Keyword(s):  
School Mathematics ◽  
Clear Picture ◽  
Student Writing ◽  
National Council ◽  
Writing In Mathematics ◽  
Mathematics Class ◽  
Principles And Standards ◽  
The Many

Almost twenty years ago, the National Council of Teachers of Mathematics (NCTM) published Principles and Standards for School Mathematics (2000), which recommended that teachers should incorporate more writing into their math lessons, claiming that writing helps students “consolidate their thinking” (p. 402) by causing them to reflect on their work. In recent years, various studies point to the many benefits that can be gained by writing in mathematics class (e.g., O'Connell et al. 2005; Goldsby and Cozza 2002). Much research suggests that writing activities, if implemented effectively, can help students enjoy class more (Burns 2005) and can also help them deepen their understanding of the content (Baxter et al. 2002). In addition to benefiting students, student writing benefits teachers as well by providing a clear picture of what their students understand and even deepening understanding of the content for teachers themselves (Burns 2005; Pugalee 1997).

Let's Talk: Promoting Mathematical Discourse in the Classroom

2007 ◽  
Vol 101 (4) ◽  
pp. 285-289 ◽  
Author(s):  
Catherine A. Stein
Keyword(s):  
Mathematical Discourse ◽  
School Mathematics ◽  
Mathematical Concepts ◽  
Student Discourse ◽  
Principles And Standards

As part of reform-based mathematics, much discussion and research has focused on the idea that mathematics should be taught in a way that mirrors the nature of the discipline (Lampert 1990)—that is, have students use mathematical discourse to make conjectures, talk, question, and agree or disagree about problems in order to discover important mathematical concepts. In fact, communication, of which student discourse is a part, is so important that it is one of the Standards set forth in Principles and Standards for School Mathematics (NCTM 2000).

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