Promoting Algebraic Reasoning Using Students' Thinking

2001 ◽  
Vol 6 (9) ◽  
pp. 508-514
Author(s):  
Joyce W. Bishop ◽  
Albert D. Otto ◽  
Cheryl A. Lubinski
Keyword(s):  
Mathematics Education ◽  
Education Reform ◽  
Research Council ◽  
National Research Council ◽  
Mathematical Understanding ◽  
Algebraic Reasoning ◽  
Mathematical Notation ◽  
Mathematical Concepts ◽  
Evaluation Standards ◽  
Geometric Patterns

The changing applications of mathematics have contributed to a shift from the perception that mathematics is a fixed body of arbitrary rules to the realization that the discipline is “a vigorous active science of patterns” (National Research Council 1989, p. 13). NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) recommends using patterns to promote mathematical understanding and, in particular, algebraic reasoning. A number of other mathematics education reform documents make similar recommendations (e.g., AAAS [1989]; National Research Council [1990]; Steen [1990]; NCTM [2000]). Researchers have begun to identify different approaches that students use to reason about patterns (Bishop 1997; MacGregor and Stacey 1993; Orton and Orton 1996; Stacey 1989). Research also shows that using students' thinking about patterns can help them develop a better understanding of mathematical concepts and the representations that reflect those concepts (Carey 1992; Fennema, Carpenter, and Peterson 1989). This article illustrates how students' thinking about geometric patterns can be used to help them develop algebraic reasoning and to make sense of mathematical notation and symbols.

Promoting Mathematics Connections with Concept Mapping

1995 ◽  
Vol 1 (7) ◽  
pp. 542-549
Author(s):  
Bobbye Hoffman Bartels
Keyword(s):  
Mathematics Education ◽  
Concept Mapping ◽  
Real World ◽  
Research Council ◽  
Real Life ◽  
National Research Council ◽  
Mathematical Concepts ◽  
The Real ◽  
Mathematical Connections ◽  
Reform In Mathematics Education

Recent documents calling for reform in mathematics education stress promoting mathematical connections during instruction (NCTM 1989; National Research Council 1989, 1990). Mathematical connections are important because they link mathematical concepts to each other and to the real world. When teachers emphasize these connections during instruction, mathematics becomes less compartmentalized and more cohesive and has relevance to real life. In addition, stressing mathematical connections during instruction helps students develop better and deeper understandings of mathematics.

Achievement Tests in Primary Mathematics: Perpetuating Lower-Order Thinking

1991 ◽  
Vol 38 (9) ◽  
pp. 4-9 ◽  
Author(s):  
Constance Kamii ◽  
Barbara Ann Lewis
Keyword(s):  
Mathematics Education ◽  
Research Council ◽  
National Research Council ◽  
Current Method ◽  
Achievement Tests ◽  
Achievement Testing ◽  
Evaluation Standards ◽  
Standardized Achievement Tests ◽  
Method Of Evaluation ◽  
Harmful Effects

The Curriculum and Evaluation Standards (NCTM 1989) states that if we want to improve the nation's mathematics education, it is necessary to change the current method of evaluation that depends on standardized achievement tests. The National Research Council (1989) is even more explicit about the harmful effects of achievement testing.

Using Performance Assessment to Determine Mathematical Dispositions

1992 ◽  
Vol 39 (6) ◽  
pp. 40-47
Author(s):  
Judith Collison
Keyword(s):  
Information Technology ◽  
Performance Assessment ◽  
Educational Change ◽  
Mathematics Instruction ◽  
Research Council ◽  
National Research Council ◽  
Mathematical Understanding ◽  
Evaluation Standards ◽  
Intellectual Courage ◽  
Personal Attitudes

The proliferation of information and information technology demands educational change, especially in mathematics. The emphasis must shift from mere acquisition to the use of information to deepen mathematical understanding and appreciation. The NCTM 's Curriculum and Evaluation Standards (1989) envisions a new curriculum. Among its goals are the development of “mathematical power,” or “numeracy” (National Research Council 1989) and an appreciation of the beauty and power of mathematic (NCTM 1989). Mathematics instruction must not merely expand students' knowledge of mathematics but must also foster intellectual courage and a set of positive personal attitudes, or dispositions, that enable and empower students.

Linking Teacher Interests or Backgrounds to Real-World Experiences for Students

1994 ◽  
Vol 41 (6) ◽  
pp. 300-303 ◽  
Author(s):  
Jim Dorward ◽  
Steve Archibald
Keyword(s):  
Mathematics Education ◽  
Real World ◽  
Research Council ◽  
American Association ◽  
National Research Council ◽  
National Council ◽  
Major Theme ◽  
Everyday Experience ◽  
The World ◽  
Reform In Mathematics Education

A major theme in calls for reform in mathematics education is the recognition of the need to connect the study of mathematics to the rest of the world (American Association for the Advancement of Science 1989; National Research Council 1991; National Council of Teachers of Mathematics 1989). For some, this connection is obvious. For many, however, mathematics is perceived as a set of rules and procedures that have little to do with everyday experience.

Research Advisory Committee Report: NCTM Standards Research Catalyst Conference

1991 ◽  
Vol 22 (4) ◽  
pp. 293-296
Keyword(s):  
Mathematics Education ◽  
Education Reform ◽  
Teaching And Learning ◽  
School Mathematics ◽  
Assessment Practices ◽  
Committee Report ◽  
Evaluation Standards ◽  
Education Community ◽  
New Research ◽  
New Phase

The Curriculum and Evaluation Standards for School Mathematics initiated a new phase in mathematics education reform. The Standards document presents both a vision and a plan for change in mathematics instruction and assessment. The principles on which the Standards document is based establish a new research agenda (Commission on Standards for School Mathematics, 1989) that offers the potential not only to contribute to the growing base of scientific knowledge about mathematics teaching and learning, bur also to complement and inform the efforts of mathematics educators to reform current curricular, pedagogical, and assessment practices. It is both the hope and the expectation of the mathematics education community that major changes will occur in the teaching and learning of mathematics. At this juncture, we need some form of documentation of the anticipated change.

Implementing The K–4 Mathematics Standards in Kentucky

1993 ◽  
Vol 41 (3) ◽  
pp. 166-169
Author(s):  
William S. Bush
Keyword(s):  
Mathematics Education ◽  
Education Reform ◽  
School Administrators ◽  
Department Of Education ◽  
University Faculty ◽  
Classroom Teachers ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
The Past ◽  
Education Of Students

The state motto of Kentucky is “United We Stand—Divided We Fall.” Never has this creed been so evident than through the recent statewide mathematics education reform efforts in grades K–4. Over the past two years, university faculty, classroom teachers, school administrators, public policymakers, the Kentucky Department of Education, and corporations have developed partnerships to initiate systemic changes in the mathematics education of students in grades K–4. These groups banded together to enact for Kentucky the vision set forth by the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).

Research Into Practice: Constructivist Learning and Teaching

1990 ◽  
Vol 38 (1) ◽  
pp. 34-35 ◽  
Author(s):  
Michael T. Battista
Keyword(s):  
Educational Research ◽  
Effective Teachers ◽  
Research Council ◽  
National Research Council ◽  
Mathematical Understanding ◽  
Constructivist Learning ◽  
Compelling Evidence ◽  
Learning And Teaching

In reality, no one can teach mathematics. Effective teachers are those who can stimulate students to learn mathematics. Educational research offers compelling evidence that students learn mathematics well only when they construct their own mathematical understanding (MSEB and National Research Council 1989, 58).

Research Advisory Committee Report: Mathematics Education Reform and Mathematics Education Research: Opportunities, Obstacles, and Obligations

1990 ◽  
Vol 21 (4) ◽  
pp. 287-292
Keyword(s):  
Mathematics Education ◽  
Education Reform ◽  
National Research Council ◽  
National Commission ◽  
Committee Report ◽  
National Council ◽  
Nation At Risk ◽  
Education Community ◽  
And Mathematics ◽  
Excellence In Education

The mathematics education community is engaged in a level of refonn activity of remarkable breadth and intensity. This most recent context of educational refom1 was established in the early 1980s, in part through reports such as A Nation at Risk (National Commission on Excellence in Education. 1983). The content-based counterparts of these documents include the Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics, 1989a), Everybody Coums (National Research Council, 1989), Project 2061: Science for All Americans (American Association for the Advancement of Science, 1989), and the forthcoming Professional Standards for Teaching Mathematics (National Council of Teachers of Mathematics, 1989b).

Hypermedia: a Vehicle for Connections

1993 ◽  
Vol 40 (8) ◽  
pp. 430-432
Author(s):  
Beatrice C. Babbitt ◽  
Virginia Usnick
Keyword(s):  
Mathematics Education ◽  
Research Council ◽  
National Research Council ◽  
American Education ◽  
Mathematical Ideas ◽  
Use Of Technology ◽  
And Mathematics

In recent years, numerous reports have called for reform in American education in general and mathematics education in particular (e.g., Leitzel[1991]; NCTM [1991]; National Research Council [1989, 1990, 1991]). One suggested reform is revamping the curriculum to include mathematics more relevant to society and student current needs. In addition to changing the curriculum. these report have recommended changes in the method used to teach the curriculum. Among the suggested changes in methodology are an increased use of technology and opponunities for students to connect mathematical ideas.

Soundoff: Are Teachers Prepared to Implement The Standards?

1990 ◽  
Vol 83 (4) ◽  
pp. 248-251
Author(s):  
Michael B. Fiske
Keyword(s):  
Mathematics Education ◽  
National Research Council ◽  
School Mathematics ◽  
National Commission ◽  
National Council ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Nation At Risk ◽  
Excellence In Education ◽  
Societal Expectations

The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989) presents a view of precollege mathematics t hat stresses the development of mathematical power. Framed within the context of students' needs, societal expectations, and engaging teaching, the Standards proposes to define the mathematical content of school mathematics. It responds to the crisis in mathematics education described in Everybody Counts: A Report to the Nation on the Future of Mathematics Education (National Research Council 1989), A Nation at Risk (National Commission on Excellence in Education 1983), and Educating Americans for the 21st Century (National Science Board Commission on Precollege Education in Mathematics, Science, and Technology 1983). Although representing a consensus of mathematics educators, the Standards does not present a research basis for its recommendations (NCTM 1988) and thus at times stands at odds with the descriptive accounts of current mathematics teaching practices found in The Underachieving Curriculum (McKnight et al. 1987) and The Mathematics Report Card (Dossey, Mullis, Lindquist, and Chambers 1988). This article examines implications for teaching of explicit and implicit assumptions in the Standards and compares them with other views in the literature.

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