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.

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.

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.

Low Tech, 198, And The Geometry Of The Calculator Keys

1990 ◽  
Vol 37 (5) ◽  
pp. 30-33
Author(s):  
Alan Zollman
Keyword(s):  
Problem Solving ◽  
High Technology ◽  
Upper Elementary ◽  
Problem Posing ◽  
National Council ◽  
Interesting Aspect ◽  
Grade Levels ◽  
School Classroom ◽  
The Impact

The National Council of Teachers of Mathematics recommends that … mathematics programs take full advantage of the power of calculators and computers at all grade levels” (NCTM 1980, 8). Somehow, without meaning to, the calculator has taken a subsidiary role to the computer in the implementation of NCTM's An Anemia for Action recommendation. High technology is getting the majority of education's emphasis, while low technology, namely the calculator, is not having the impact that it could in the elementary school. This situation prevails despite the fact that 98 percent of this country's population uses calculators in everyday mathematics applications (Saunders 1980). It is time to reaffirm the viable role of the calculator in mathematics education (NCTM 1987). This article presents an interesting aspect of the geometrical array of the keys on a calculator that can be turned into a problem-solving, problem-posing situation for the upper elementary or middle school classroom. Read this article with a calculator in hand.

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.

Why Elementary Algebra Can, Should, and Must Be an Eighth-Grade Course for Average Students

1987 ◽  
Vol 80 (6) ◽  
pp. 428-438 ◽  
Author(s):  
Zalman Usiskin
Keyword(s):  
Mathematics Education ◽  
Secondary Mathematics ◽  
Ninth Grade ◽  
Eighth Grade ◽  
First Year ◽  
National Council ◽  
Seventh Grade ◽  
Elementary Algebra ◽  
Grade Levels ◽  
One Year

Elementary or first-year algebra is the keystone subject in all of secondary mathematics. It is formally studied by students from grade levels as early as seventh grade and as late as college, but begun and completed more often in ninth grade than at any other time. The main purpose of this article is to question that timing. The conclusion to be argued here is that most students should begin the study of algebra one year earlier than they now do. This conclusion is contrary to a recommendation currently subscribed to by the National Council of Teachers of Mathematics and to the views of a number of leaders in mathematics education. I attempt to show here that these leaders have been misguided.

Early Childhood Corner: Storyboards for meaningful patterns

2010 ◽  
Vol 16 (6) ◽  
pp. 325-329
Author(s):  
Lucille P. Dubon ◽  
Kathryn G. Shafer
Keyword(s):  
Early Childhood ◽  
Mathematical Reasoning ◽  
Second Graders ◽  
National Council ◽  
Instructional Programs

Patterns are an important element of developing children's mathematical reasoning. In elaborating ways in which “instructional programs from prekindergarten through grade 12 should enable all students to understand patterns, relations, and functions” (NCTM 2000, p. 90), the National Council of Teachers of Mathematics specifies that representing and interpreting patterns are skills that kindergartners through second graders should build toward developing a robust understanding of algebra.

Focal Points—Grades 3 and 4

2008 ◽  
Vol 14 (8) ◽  
pp. 466-471
Author(s):  
Randall I. Charles ◽  
Paula B. Duckett
Keyword(s):  
National Council ◽  
Focal Points ◽  
Series Introduction ◽  
Grade Levels ◽  
Grade 8

This is the fourth in a series of articles exploring the use of the 2006 National Council of Teachers of Mathematics (NCTM) publication Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence. The series introduction by NCTM President Skip Fennell, explaining what Curriculum Focal Points are and why NCTM developed them, appeared in the December 2007/January 2008 issue of Teaching Children Mathematics (page 315). In subsequent TCM articles, the authors of the various grade bands discuss Focal Points for one or two grade levels. Because one principle of Curriculum Focal Points is that of cohesive curriculum, in which ideas develop across the grades, we encourage teachers of all grade levels to read the full series.

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.

scholarly journals Analysis of Mathematical Representation Ability Based on Level of Reading Interest in Geometry Course

2021 ◽  
Vol 5 (2) ◽  
pp. 271
Author(s):  
Destia Wahyu Hidayati ◽  
Arie Wahyuni
Keyword(s):  
Data Analysis ◽  
Reading Level ◽  
Mathematical Representation ◽  
Research Subjects ◽  
Reading Levels ◽  
Ability Test ◽  
Mathematical Representations ◽  
Mathematical Ideas ◽  
Literacy Activities ◽  
Reading Interest

Reading literacy activities are currently being held by all levels of education. Literacy activities have a positive effect on students in understanding information. The ability to understand information can be realized through mathematical representation, which is one of the main elements in mathematical understanding. This research can help educators in mapping the mathematical representation ability based on the reading interest of students. The purpose of this research is to identify which indicators can be mastered by students who have reading interests at high, medium, and low levels. This research is qualitative. The research subjects were students of the Mathematics Education Department of Ivet University. The data collection procedures used were scale, test, and interview. The instruments of this study were the reading interest scale, mathematical representation ability test, and interview sheets. The data analysis technique of this study adopted data analysis techniques from Miles and Huberman. The conclusions of this study are (1) students with high and medium reading levels have the ability to represent mathematical representations to model and interpret physical, social, and mathematical phenomena; have the ability of mathematical representations to create and use representations to communicate mathematical ideas or concepts; have the ability of mathematical representations in selecting, applying, and translating mathematical representations to solve problems, (2) students with a low reading level have lacked on the ability of mathematical representations to use representations to model and interpret physical, social, and mathematical phenomena, thus it caused them couldn’t mastering the ability of mathematical representations to create and use representations to communicate mathematical ideas or concepts and the ability of mathematical representations to select, apply, and translate mathematical representations to solve problems. Keywords: mathematical representation ability, reading interest, geometry.

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.

Sign in / Sign up

Export Citation Format

Share Document