Using Concept Maps to Link Mathematical Ideas

2000 ◽  
Vol 5 (9) ◽  
pp. 604-609
Author(s):  
Arthur J. Baroody ◽  
Bobbye H. Bartels
Keyword(s):  
Concept Maps ◽  
School Mathematics ◽  
National Council ◽  
Important Research ◽  
Mathematical Ideas ◽  
Standards Documents

The National Council of Teachers of Mathematics's standards documents (1989, 1991, 1995) emphasize making and assessing connections. Why are connections so important? Research suggests that understanding can be viewed as a connection between two pieces of information (Ginsburg 1977), and an understanding of elementary concepts is essential for mathematical power, for example, applying school mathematics to everyday tasks, inventing mathematical procedures, understanding and solving genuine problems, and comprehending more advanced mathematical ideas. The degree of a student's understanding is determined by the number, accuracy, and strength of connections (Hiebert and Carpenter 1992; Resnick and Ford 1981). A concept is well understood if it has many links to other aspects of knowledge that are accurate and strong.

Delving Deeper: New Life for an Old Topic: Completing the Square Using Technology

2010 ◽  
Vol 104 (3) ◽  
pp. 230-236
Author(s):  
Steve Phelps ◽  
Michael Todd Edwards
Keyword(s):  
Mathematics Teaching ◽  
Mathematical Structure ◽  
School Mathematics ◽  
National Council ◽  
Mathematical Ideas ◽  
Use Of Technology ◽  
Teachers And Students ◽  
Principles And Standards

Mathematics teaching has always been a curious blend of the old and the new. As the use of technology becomes more commonplace in school classrooms, this blend becomes even more pronounced. When teachers and students revisit traditional topics using technology, they are afforded opportunities to connect mathematical ideas in powerful, previously unimagined ways. The National Council of Teachers of Mathematics (NCTM) captures the importance of connections clearly in its Principles and Standards for School Mathematics (2000): “The notion that mathematical ideas are connected should permeate the school Technologymathematics experience at all levels. As students progress through their school mathematics experience, their ability to see the same mathematical structure in seemingly different settings should increase” (p. 64).

Evaluation of Empowerment in a High School Geometry Class

1997 ◽  
Vol 90 (9) ◽  
pp. 738-741
Author(s):  
Carolyn Ridgway ◽  
Christopher Healy
Keyword(s):  
High School ◽  
School Mathematics ◽  
National Council ◽  
Mathematical Ideas ◽  
High School Geometry ◽  
School Geometry ◽  
Geometry Class

Since the publication of the Curriculum and Eualuation Standards for School Mathematics in 1989, the National Council of Teachers of Mathematics has been encouraging teachers to give more responsibility and choice to students. Students become mathematically empowered as they solve problems together in a community oflearners, communicate with one another concerning mathematical ideas, and use reason and logic to defend their work. To teach in accordance with these standards has required teachers to sruft the ways in which they view and manage their classrooms (Frye 1991).

Combinatorics Connections: Playoff Series and Pascal's Triangle

1992 ◽  
Vol 85 (7) ◽  
pp. 532-535
Author(s):  
Bonnie H. Litwiller ◽  
David R. Duncan
Keyword(s):  
Real World ◽  
School Mathematics ◽  
Discrete Mathematics ◽  
National Council ◽  
Major Theme ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Pascal’S Triangle ◽  
Pascal's Triangle ◽  
The Relationship

One major theme of the National Council of Teachers of Mathematic's Curriculum and Evaluation Standards far School Mathematics (1989) is the connection between mathematical ideas and their applications to real-world situations. We shall use concepts from discrete mathematics in describing the relationship between sports series and Pascal's triangle.

Implementing the “Assessment Standards for School Mathematics”: Some Practical Possibilities for Alternative Assessment

1997 ◽  
Vol 90 (1) ◽  
pp. 46-49
Author(s):  
Cathy G. Schloemer
Keyword(s):  
Real World ◽  
Alternative Assessment ◽  
Mathematics Classroom ◽  
Secondary Mathematics ◽  
School Mathematics ◽  
National Council ◽  
The Real ◽  
Assessment Standards ◽  
Standards Documents

Imagine that you are a teacher in a secondary mathematics classroom, working hard to implement the precepts of the Standards documents {National Council of Teachers of Mathematics 1989, 1991, 1995). In particular, you are focusing on getting your students to (1) make connections between mathematics and the real world, (2) reason and communicate mathematically, and (3) value mathematics. A colleague with whom you often share classroom concerns and successes stops by during a rare quiet moment and, in the course of conversation about your most recent classroom endeavors, asks, “How is it going?” How might you reply?

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.

National Council of Teachers of Mathematics: The Council's drive to improve school mathematics

1963 ◽  
Vol 10 (6) ◽  
pp. 368-375
Author(s):  
Frank B. Allen
Keyword(s):  
School Mathematics ◽  
National Council ◽  
Local Organizations ◽  
Teaching Of Mathematics ◽  
High Degree

According to our Articles of Incorporation, the object of the National Council of Teachers of Mathematics is “To assist in promoting the interest of mathematics in America, especially in the elementary and secondary fields, by holding meetings for the presentation and discussion of papers, by conducting investigations for the purpose of improving the teaching of mathematics, by the publication of papers, journals, books, and reports: thus, to vitalize and coordinate the work of many local organizations of teachers of mathematics and to bring the interest of mathematics to the attention and consideration of the educational world.” I believe that any impartial review of our accomplishments will support the conclusion that we have achieved a high degree of success in the attainment of this objective.

In the classroom: Including the newer mathematics with the regular program of the primary grades

1963 ◽  
Vol 10 (4) ◽  
pp. 212-216
Author(s):  
Edwina Deans ◽  
Rose Koury
Keyword(s):  
Elementary School ◽  
Elementary Education ◽  
Primary Grades ◽  
School Mathematics ◽  
Elementary School Mathematics ◽  
Mathematical Ideas

The following mathematical ideas have been adapted from the article, 'Including the Newer Mathematics with the Regular Program of the Primary Grades' by Rose Koury, Assistant Specialist for Elementary Education, U. S. Office of Education, and Edwina Deans, Specialist, Elementary School Mathematics, U. S. Office of Education. The article was published in the February, 1962, issue of The Arithmetic Teacher.

Developing Spatial Thinking In The Middle Grades: Designing A Space Station

1990 ◽  
Vol 37 (6) ◽  
pp. 59-63
Author(s):  
Barbara Moses
Keyword(s):  
Elementary School ◽  
Mathematics Curriculum ◽  
Space Station ◽  
Physical World ◽  
School Mathematics ◽  
Spatial Thinking ◽  
National Council ◽  
Elementary School Mathematics ◽  
Geometric Figures ◽  
Spatial Sense

The recently published Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics, Commission on Standards for School Mathematics 1989, 21) clearly states that educators should devote less attention to “ complex paper-andpencil computations” and “rote memorization of rules.” The time currently spent in the elementary school mathematics curriculum on these topics should instead be devoted to other areas, such as geometry and problem solving. Students should “visualize and represent geometric figures with special attention to developing spatial sense” and learn to appreciate “geometry as a means of describing the physical world” (p. 112). But elementary school mathematics textbooks typically contain few activities that deal with the development of spatial sense.

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.

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