Improving Data Analysis through Discourse

2000 ◽  
Vol 5 (8) ◽  
pp. 548-553
Author(s):  
Kay McClain ◽  
Maggie McGatha ◽  
Lynn L. Hodge
Keyword(s):  
Data Analysis ◽  
Mathematics Classroom ◽  
Effective Communication ◽  
National Council ◽  
Classroom Norms ◽  
Mathematical Ideas ◽  
Mathematical Arguments ◽  
Teacher’S Role ◽  
Mathematical Discussions ◽  
Asking Questions

The National Council of Teachers of Mathematics has been advocating the importance of effective communication in classrooms since the release of its Standards documents (NCTM 1989, 1991). This emphasis is echoed in Richards's (1991) description of an inquiry classroom (see also, e.g., Ball [1993]; Cobb, Wood, and Yackel [1991]; Lampert [1990]). In this setting, the teacher's role is to guide the negotiation of classroom norms to enable the teacher and students together to engage in meaningful mathematical discussions, which include asking questions, solving problems, posing conjectures, and formulating and critiquing mathematical arguments. An increased emphasis on communication in the mathematics classroom allows students the opportunity to discuss and validate mathematical ideas and to make and evaluate conjectures and arguments.

New Challenges to the Research Community: Reflections of the Research Advisory Committee

1998 ◽  
Vol 29 (5) ◽  
pp. 499-502
Keyword(s):  
Teaching Practice ◽  
Mathematics Classroom ◽  
Mathematics Learning ◽  
Research Community ◽  
National Council ◽  
Mathematical Ideas ◽  
Education Community ◽  
Research Findings ◽  
New Challenges ◽  
Children’S Thinking

Drawing on several decades of research findings, the National Council of Teachers of Mathematics (NCTM) produced, between 1989 and 1995, three volumes of Standards in which members of the mathematics education community formulated new visions of mathematics learning, teaching, and assessment. These new visions comprise an ambitious agenda for the mathematics classroom—one that includes, but surpasses, mastery of facts and procedures, the mainstay of extant practice—designed to engage students in the exploration of mathematical ideas and their interrelationships. Students would now be invited to articulate their ideas, and teachers to identify and mobilize those elements in children's thinking upon which stronger conceptions can be built. Paralleling this ambitious departure in teaching practice, new means of assessment were proposed to capture progress toward these far-reaching goals.

It's a Home Run! Using Mathematical Discourse to Support the Learning of Statistics

2007 ◽  
Vol 101 (4) ◽  
pp. 250-256 ◽  
Author(s):  
Kathleen S. Himmelberger ◽  
Daniel L. Schwartz
Keyword(s):  
Mathematics Classroom ◽  
Mathematical Thinking ◽  
National Council ◽  
Instructional Programs ◽  
Group Discussions ◽  
Good Communication ◽  
Mathematical Ideas ◽  
Positive Effects ◽  
Procedural Fluency ◽  
Learning Mathematics

The Standards developed by the National Council of Teachers of Mathematics (2000) state that instructional programs should enable all students to communicate mathematical ideas. The Standards indicate that good communication includes the ability to express organized and precise ideas as well as the ability to analyze and evaluate the mathematical thinking of others. Learning mathematics goes beyond procedural fluency; it also includes learning to discuss mathematical ideas. For this purpose, small groups have become a frequent configuration in the mathematics classroom. When combined with a suitable exercise, small-group discussions can have positive effects on mathematical understanding.

Links to Literature: A Remainder of One: Exploring Partitive Division

2000 ◽  
Vol 6 (8) ◽  
pp. 517-521
Author(s):  
Patricia Seray Moyer
Keyword(s):  
Children's Literature ◽  
Mathematical Knowledge ◽  
Mathematics Classroom ◽  
Children’S Literature ◽  
National Council ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Mathematics Problems ◽  
Mathematical Symbols ◽  
Everyday Experiences

Children's literature can be a springboard for conversations about mathematical concepts. Austin (1998) suggests that good children's literature with a mathematical theme provides a context for both exploring and extending mathematics problems embedded in stories. In the context of discussing a story, children connect their everyday experiences with mathematics and have opportunities to make conjectures about quantities, equalities, or other mathematical ideas; negotiate their understanding of mathematical concepts; and verbalize their thinking. Children's books that prompt mathematical conversations also lead to rich, dynamic communication in the mathematics classroom and develop the use of mathematical symbols in the context of communicating. The National Council of Teachers of Mathematics (1989) emphasizes the importance of communication in helping children both construct mathematical knowledge and link their informal notions with the abstract symbols used to express mathematical ideas.

Technology in the Mathematics Classroom

2011 ◽  
pp. 114-133 ◽  
Author(s):  
Robin J. Ittigson ◽  
John G. Zewe
Keyword(s):  
Decision Making ◽  
Teaching And Learning ◽  
Mathematics Classroom ◽  
Information Support ◽  
Visual Images ◽  
National Council ◽  
Problem Solving Skills ◽  
Mathematical Ideas ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics

According to the National Council of Teachers of Mathematics, technology is essential in teaching and learning mathematics. It influences how mathematics should be taught and enhances what students learn. Calculators and computers present visual images of mathematical ideas for students. They help students organize information, support investigations, and develop decision-making, reflection, reasoning, and problem-solving skills.

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.

Assessing For Learning: Using Calculators in Assessing Mathematics Achievement

1987 ◽  
Vol 35 (2) ◽  
pp. 21-23
Author(s):  
David E. Williams ◽  
Ann McAloon ◽  
G. Edith Robinson
Keyword(s):  
Mathematics Education ◽  
Mathematics Achievement ◽  
Integrated Curriculum ◽  
Elementary Mathematics ◽  
Mathematics Classroom ◽  
Position Statement ◽  
National Council ◽  
Community Group ◽  
Support Materials ◽  
Extensive Training

In it “Position Statement on Calculators in the Mathematics Classroom” the National Council of Teachers of Mathematics recommends that calculators be integrated into all aspect of school mathematics, including class work, homework, and evaluation (NCTM 1986). This author cited the need for a comprehensive calculator proj ect encompassing all facet as of elementary mathematics education, a project that should include the development of a calculator-integrated curriculum. an extensive training program for teachers, the development of curriculum-support materials, change in textbook, workshops for parents and community group, and a change in evaluation of mathematics achievement (Williams 1987).

On Blocks, Stairs, and Beyond: Learning about the Significance of Representations

2007 ◽  
Vol 101 (5) ◽  
pp. 340-344
Author(s):  
Laurie H. Rubel ◽  
Betina A. Zolkower
Keyword(s):  
National Council ◽  
Classroom Activity ◽  
Instructional Programs ◽  
Mathematical Representations ◽  
Mathematical Ideas ◽  
Grade Levels

The National Council of Teachers of Mathematics (2000) recommends that students at all grade levels be provided with instructional programs that enable them to “create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among mathematical representations to solve problems; and use representations to model and interpret physical, social, and mathematical phenomena” (p. 67). This article describes a particular classroom activity used to highlight the significance of mathematical representations.

How Does Your Mathematical Garden Grow?

2007 ◽  
Vol 13 (2) ◽  
pp. 68-76
Author(s):  
Shari A. Beck ◽  
Vanessa E. Huse ◽  
Brenda R. Reed
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Real Life ◽  
Middle School Mathematics ◽  
Content Standards ◽  
Mathematical Communication ◽  
Mathematical Ideas ◽  
Application Problem ◽  
Multiple Process ◽  
Problem Solving Process

Imagine a middle school mathematics classroom where students are actively engaged in a real-life application problem incorporating multiple Process and Content Standards as outlined by NCTM (2000). Sounds of mathematical communication arise as students use multiple representations to help connect mathematical ideas throughout the problem-solving process. Students apply various types of reasoning and explore alternate methods of proof while working attentively on applications that incorporate Number and Operations, Algebra, Geometry, and Measurement.

Professional Development: Preparing Teachers to Present Techniques of Exploratory Data Analysis

1994 ◽  
Vol 1 (2) ◽  
pp. 166-172
Author(s):  
Christine A. Browning ◽  
Dwayne E. Channell ◽  
Ruth A. Meyer
Keyword(s):  
Professional Development ◽  
Elementary School ◽  
Data Analysis ◽  
Exploratory Data Analysis ◽  
Real Data ◽  
National Council ◽  
Evaluation Standards ◽  
School Classroom ◽  
Exploratory Data ◽  
Mathematics Curricula

Why Study Statistics? We are bombarded every day with an overwhelming amount of information presented in various forms. If we are to interpret and understand the information, we must be familiar with the methods and tools of statistics. Developing an understanding and an appreciation of statistics should begin in the elementary school classroom. The National Council of Teachers of Mathematics's document Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) states that the mathematics curricula for grades K-4 and 5-8 should include experiences with data analysis that involve students in collecting, organizing, describing, and interpreting data. Burrill (1990) suggests that such experiences should use real data whenever possible, progress from the concrete to the pictorial to the abstract, and use calculators and computers whenever appropriate.

Activites for Students: Dynamic Diagrams

2001 ◽  
Vol 94 (7) ◽  
pp. 566-574
Author(s):  
Elizabeth George Bremigan
Keyword(s):  
Mathematics Classroom ◽  
Mathematical Problem ◽  
Visual Representations ◽  
Mathematical Concept ◽  
Mathematics Textbooks ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Mathematical Problems

Reasoning with visual representations is an important component in solving many mathematical problems and in understanding many mathematical concepts and procedures. Students at all levels of mathematics frequently encounter visual representations—for example, diagrams, figures, and graphs—in discussions of mathematical ideas, in mathematics textbooks, and on tests. Teachers often use visual representations in the classroom when they present a mathematical problem, explain a problem's solution, or illustrate a mathematical concept. Although they frequently encounter and use visual representations in the mathematics classroom, neither teachers nor students may explicitly recognize the power of reasoning with visual representations or the potential for misconceptions that can arise from their use.

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