Fraction Representation: The Not-So-Common Denominator among Textbooks

2008 ◽  
Vol 14 (2) ◽  
pp. 78-84
Author(s):  
Thomas E. Hodges ◽  
JoAnn Cady ◽  
R. Lee Collins
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Mathematics Curriculum ◽  
Visual Representations ◽  
Middle School Mathematics ◽  
Common Denominator ◽  
School Students ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Support Students

Using visual representations, such as symbols, drawings, and graphs, helps middle school students reason about and understand mathematics. These representations support students' learning and help them communicate their mathematical ideas. Representations also help them organize their thinking, make connections among mathematical concepts, and model the mathematics that they see in the real world (NCTM 2000). The middle school mathematics curriculum seeks to move students in a logical progression from concrete models to drawings and pictures and finally to abstract symbols. Representations can assist students in making this transition.

Cognitive Effects of a Logo-Enriched Mathematics Program for Middle School Students

1988 ◽  
Vol 4 (4) ◽  
pp. 443-452 ◽  
Author(s):  
Sandra V. Turner ◽  
Michael L. Land
Keyword(s):  
Middle School ◽  
Cognitive Development ◽  
Middle School Students ◽  
Mathematics Curriculum ◽  
Common Factor ◽  
Control Group ◽  
Minimal Amount ◽  
School Students ◽  
Mathematical Concepts ◽  
Logo Programming

This study investigated the effect of learning Logo on middle-school students' understanding of specific mathematical concepts and on their level of cognitive development. Students in the Logo Group ( n = 91) learned Logo for one hour a week for sixteen weeks as part of their regular mathematics curriculum. The Control Group ( n = 90) did not participate in the Logo program but received the full allotted time for their regular mathematics curriculum. No significant differences were found between the two groups in their understanding of mathematics concepts or in their growth in cognitive development. However, among the students in the Logo Group, those who learned the most Logo gained significantly more than those who learned a minimal amount of Logo both in their understanding of the mathematics concepts and in their level of cognitive development. When the High Logo group was compared to the Control Group, and also to a matched subset of the Control Group, there were large differences in favor of the High Logo group, but the results were not significant. The findings of this study suggest that cognitive development, achievement in mathematics, and achievement in Logo programming all share a common factor and that students who do well in one area are also likely to do well in the other two areas.

On My Mind: Proof and the Middle School Mathematics Student

1995 ◽  
Vol 1 (7) ◽  
pp. 516-518
Author(s):  
James M. Sconyers
Keyword(s):  
High School ◽  
Middle School ◽  
Middle School Students ◽  
Middle School Mathematics ◽  
Basic Logic ◽  
School Students ◽  
High School Geometry ◽  
School Geometry ◽  
Mathematics Student ◽  
Geometry Class

Is proof perceived as being rigid and formal? Something that students should first encounter in high school? Does a concern involve students' having difficulty when they finally confront the idea of proof, perhaps in their high school geometry class? One likely reason for this unease with proof is that it is so often left out of any work in mathematics until students reach high school. They are then overwhelmed, since it is so unfamiliar. This outcome is not inevitable. Middle school students are capable of grasping the basic logic of proof and should be given the opportunity to encounter it.

Listening to Middle School Students' Algebraic Thinking

2000 ◽  
Vol 6 (3) ◽  
pp. 156-161
Author(s):  
John P. Smith ◽  
Elizabeth A. Phillips
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Mathematics Curriculum ◽  
Algebraic Thinking ◽  
School Students ◽  
The Core ◽  
K 12

NO PART OF THE K–12 MATHEMATICS curriculum is more fluid and controversial than introductory algebra. Content and assessment issues lie at the core of this debate: What algebra skills and understandings are important? What kind of evidence suggests that students possess these skills? Neither question can be answered in simple terms; in fact, no single “right” answer may exist for either one.

Socrates and the Three Little Pigs: Connecting Patterns, Counting Trees, and Probability

1999 ◽  
Vol 5 (3) ◽  
pp. 156-161
Author(s):  
Denisse R. Thompson ◽  
Richard A. Austin
Keyword(s):  
Middle School ◽  
South Carolina ◽  
New Jersey ◽  
Middle School Students ◽  
Mathematics Curriculum ◽  
School Curriculum ◽  
School Students ◽  
Middle School Curriculum ◽  
Curriculum Frameworks ◽  
Counting Trees

Explorations of concepts of chance should be a part of the middle school curriculum, as indicated in the mathematics curriculum frameworks developed by several states (Florida 1996; South Carolina 1993; New Jersey 1996). The challenge for teachers is to find contexts that interest middle school students and motivate them to explore these ideas.

Take Time for Action: Perimeter or Area? Which Measure Is It?

1999 ◽  
Vol 5 (1) ◽  
pp. 20-23
Author(s):  
Michaele F. Chappell ◽  
Denisse R. Thompson
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Conceptual Understanding ◽  
Physical Environment ◽  
Mathematics Curriculum ◽  
School Students ◽  
The Past ◽  
Fundamental Understanding ◽  
K 12

During the past twenty years, documents have recommended that the mathematics curriculum include measurement for all grades, K–12 (NCTM 1980, 1989). Indeed, students interact daily with measurement in their physical environment, for example, by finding the distance from home to school, their height and weight, and wall space for posters. Adolescents bring to the classroom varied conceptions of measurement, which may be in the form of basic applications or general formulas. All too often, a fundamental understanding of these ideas is sacrificed while students learn general formulas. This situation is particularly true for attributes of perimeter and area. To what extent do middle school students possess a conceptual understanding of these measurement concepts?

The Representational Value of Hats

2008 ◽  
Vol 14 (1) ◽  
pp. 4-10
Author(s):  
Jane M. Watson ◽  
Noleine E. Fitzallen ◽  
Karen G. Wilson ◽  
Julie F. Creed
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
History Of Mathematics ◽  
Graphical Representations ◽  
Data Sets ◽  
School Students ◽  
Mathematical Ideas ◽  
History Of ◽  
The Way

The literature that is available on the topic of representations in mathematics is vast. One commonly discussed item is graphical representations. From the history of mathematics to modern uses of technology, a variety of graphical forms are available for middle school students to use to represent mathematical ideas. The ideas range from algebraic relationships to summaries of data sets. Traditionally, textbooks delineate the rules to be followed in creating conventional graphical forms, and software offers alternatives for attractive presentations. Is there anything new to introduce in the way of graphical representations for middle school students?

A Case and Techniques for Computers: Using Computers in Middle School Mathematics

1979 ◽  
Vol 26 (6) ◽  
pp. 53-55
Author(s):  
Larry L. Hatfield
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Middle School Mathematics ◽  
Growing Up ◽  
Instructional Programs ◽  
School Students ◽  
Home Management ◽  
Home Computers ◽  
Family Leisure ◽  
Computer Based

Computers are rapidly becoming accessible to everyone. The costs of purchase have continued to decrease, with the recent mini processors and microprocessors representing pricing breakthroughs, and inexpensive microcomputers being promoted as persona l, home computers. Though much of their suggested usages to date relate to family leisure or home management, some vendors offer packages for computer-based games and drills involving mathematical ideas. Instructional programs will become increasingly available as the marketplace develops. Today's middle school students are growing up in a computerized society. Students probably feel more comfortable (often excited and curious) with the prospects of “everyman” routinely using computers than do many adults, who still view computers as complex and futuristic.

3-D Graphing, Contour Graphs, Topographical Maps, and Matrices Using Spreadsheets

1999 ◽  
Vol 92 (2) ◽  
pp. 166-174
Author(s):  
Louis Feicht
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Three Dimensional ◽  
First Year ◽  
School Students ◽  
Mathematical Concepts ◽  
Younger Age ◽  
Hands On ◽  
College Calculus ◽  
Topographical Maps

Modern spreadsheets can make powerful mathematical concepts accessible to students at a younger age than ever before. Contours and three–dimensional graphing are topics that were previously reserved until well into the first year of college calculus. Three–dimensional graphing now can be successfully taught to middle school students with the assistance of a computer spreadsheet. This combination of the computer with hands-on activity exposes students to numerical and graphical representations of data on the same spreadsheet “page” and forces them to make connections between the two forms of data.

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