Using Concept Diagrams to Promote Understanding in Geometry

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and the van Hiele model for geometric thought (Crowley 1987) advocate increasing students' understanding of geometric properties and relationships as they enter the intermediate anil middle grades.

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Promoting Number Sense in the Middle Grades

Mathematics Teaching in the Middle School ◽

10.5951/mtms.1.2.0114 ◽

1994 ◽

Vol 1 (2) ◽

pp. 114-120

Author(s):

Barbara J. Reys

Keyword(s):

Common Sense ◽

Mathematics Teaching ◽

Teaching And Learning ◽

Middle Grades ◽

Number Sense ◽

School Mathematics ◽

Evaluation Standards ◽

Mathematics Teaching And Learning ◽

Way Of Thinking

Phrases such as “number sense,” “Operation sense,” and “intuitive understanding of number” are used throughout the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) to describe an intangible quality possessed by successful mathematics learners. Number sense refers to an intuitive feeling for numbers and their various uses and interpretations, an appreciation for various levels of accuracy when computing, the ability to detect arithmetical errors, and a common-sense approach to using numbers (Howden 1989; McIntosh, Reys, and Reys 1991). Number sense is not a finite entity that a student either has or does not have but rather a process that develops and matures with experience and knowledge. It does not develop by chance, nor does being skilled at manipulating numbers necessarily reflect this acquaintance and familiarity with numbers. Above all, number sense is characterized by a desire to make sense of numerical situations, including relating numbers to context and analyzing the effect of manipulations on numbers. It is a way of thinking that should permeate all aspects of mathematics teaching and learning.

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Van Hiele Levels of Geometric Thought Revisited

Mathematics Teacher ◽

10.5951/mt.84.3.0210 ◽

1991 ◽

Vol 84 (3) ◽

pp. 210-221

Author(s):

Anne Teppo

Keyword(s):

Classroom Practice ◽

School Mathematics ◽

Evaluation Standards ◽

Van Hiele ◽

Van Hiele Levels ◽

Van Hiele Theory ◽

Geometric Thinking ◽

Geometry Curriculum

The purpose of this article is to reexamine the van Hiele theory of levels of geometric thinking and to compare this theory with the geometry curriculum recommended by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). Examples of activities for students are included to illustrate the ways in which van Hiele's theory can be translated into classroom practice.

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Racing to Understand Probability

Mathematics Teaching in the Middle School ◽

10.5951/mtms.3.2.0162 ◽

1997 ◽

Vol 3 (2) ◽

pp. 162-170

Author(s):

Laura R. Van Zoest ◽

Rebecca K. Walker

Keyword(s):

Middle Grades ◽

Curriculum Change ◽

School Mathematics ◽

Evaluation Standards

One curriculum change proposed by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989, 109) is an increased focus on probability in the middle grades.

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Spotlight on the Principles/Standards: Data in the Middle Grades: A Probability WebQuest

Mathematics Teaching in the Middle School ◽

10.5951/mtms.7.2.0090 ◽

2001 ◽

Vol 7 (2) ◽

pp. 90-95

Author(s):

Fran Arbaugh ◽

Carolyn Scholten ◽

N. Kathryn Essex

Keyword(s):

Middle Grades ◽

School Mathematics ◽

Evaluation Standards ◽

Principles And Standards

“Spotlight on the Standards” focuses on the grades 6–8 content and process standards found in NCTM's Principles and Standards for School Mathematics (2000). The articles compare NCTM's Curriculum and Evaluation Standards for School Mathematics, published in 1989, with the Principles and Standards relating to the middle grades and suggest ways that teachers might incorporate Standards-based practices into their instruction.

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Implementing the Standards: Teaching Discrete Mathematics in Grades 7–12

Mathematics Teacher ◽

10.5951/mt.83.5.0362 ◽

1990 ◽

Vol 83 (5) ◽

pp. 362-367

Author(s):

Eric W. Hart ◽

James Maltas ◽

Beverly Rich

Keyword(s):

Middle Grades ◽

School Mathematics ◽

Discrete Mathematics ◽

Evaluation Standards ◽

Mathematics Standards

The NCTM's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989) explicitly recommends discrete mathematics for inclusion in the 9-12 curriculum, and many of the recommendations for the middle grades can be addressed by teaching discrete mathematics in grades 7 and 8. In this article we examine how discrete mathematics can be taught in grades 7-12. We shall first briefly discuss what is meant by discrete mathematics.

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The effect of the instruction based on Van Hiele model on the geometrical thinking levels of preservice elementary school teachers

Procedia - Social and Behavioral Sciences ◽

10.1016/j.sbspro.2009.01.029 ◽

2009 ◽

Vol 1 (1) ◽

pp. 154-159 ◽

Cited By ~ 4

Author(s):

Tolga Erdoğan ◽

Soner Durmuş

Keyword(s):

Elementary School ◽

Elementary School Teachers ◽

School Teachers ◽

Van Hiele ◽

Van Hiele Model

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An instrument for measuring performance in geometry based on the van Hiele model

Educational Research and Reviews ◽

10.5897/err2016.2801 ◽

2016 ◽

Vol 11 (13) ◽

pp. 1194-1201 ◽

Cited By ~ 1

Author(s):

B S aacute nchez Garc iacute a Ana ◽

Bel eacute n Cabello Ana

Keyword(s):

Van Hiele ◽

Van Hiele Model

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One Point of View: Reclaiming School Mathematics

The Arithmetic Teacher ◽

10.5951/at.37.8.0004 ◽

1990 ◽

Vol 37 (8) ◽

pp. 4-5

Author(s):

Portia Elliott

Keyword(s):

Mathematics Education ◽

Mathematics Curriculum ◽

Point Of View ◽

School Mathematics ◽

Evaluation Standards ◽

Design Change

The framers of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) call for a radical “design change” in all aspects of mathematics education. They believe that “evaluation is a tool for implementing the Standards and effecting change systematically” (p. 189). They warn, however, that “without changes in how mathematics is assessed, the vision of the mathematics curriculum described in the standards will not be implemented in classrooms, regardless of how texts or local curricula change” (p. 252).

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Transition Boards: A Good Idea Made Better

The Arithmetic Teacher ◽

10.5951/at.38.5.0004 ◽

1991 ◽

Vol 38 (5) ◽

pp. 4-8

Author(s):

John T. Sutton ◽

Tonya D. Urbatsch

Keyword(s):

Conceptual Understanding ◽

Mathematics Curriculum ◽

School Mathematics ◽

Evaluation Standards ◽

Addition And Subtraction ◽

School Mathematics Curriculum

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) recognizes that addition and subtraction computations remain an important part of the school mathematics curriculum and recommends that the emphasis be shifted to the understanding of concepts. Transition boards are simple devices to aid students' conceptual understanding.

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Implementing the Standards: the Measurement Standards

The Arithmetic Teacher ◽

10.5951/at.37.2.0022 ◽

1989 ◽

Vol 37 (2) ◽

pp. 22-26

Author(s):

Mary Montgomery Lindquist

Keyword(s):

School Mathematics ◽

Evaluation Standards ◽

Measurement Standards

Clear expectations for the measurement curricula of grades K–8 are expressed in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). The statements in figure 1 are discussed in the Standards. Central to both the K–4 and 5–8 standards is the process of measuring, which can help students build understanding about measuring and make connections among various measurement concepts and skills.

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