Some Big Ideas of Algebra in the Middle Grades

Without question, mathematics in general, and algebra in particular, have served as “gatekeepers” to the study of other academic fields, such as engineering, the physical sciences, computer science, and medicine, as well as to increased vocational opportunities in technical support fields. As a result, middle school teachers have felt increased pressure both to teach algebraic concepts directly and to develop mathematical concepts in ways that will support students' formal study of algebra in the future. A recent call for manuscripts in Mathematics Teaching in the Middle School noted that “the rate of students' success with this subject has been linked to the careful, planned development of algebra as a way of thinking about and modeling various phenomena at every grade level” (NCTM 1999). Such a careful, planned development requires clearly identifying the “big ideas” of algebra that are appropriate to middle school.

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Activities for Students: Algebra on the Number Line

Mathematics Teacher ◽

10.5951/mt.104.5.0379 ◽

2010 ◽

Vol 104 (5) ◽

pp. 379-386

Author(s):

Terence McCabe ◽

M. Alejandra Sorto ◽

Alexander White

Keyword(s):

High School ◽

Middle School ◽

Number Line ◽

Instructional Tool ◽

Mathematical Concepts ◽

Absolute Value ◽

Algebraic Concepts ◽

Numerical Operations

The number line is a powerful instructional tool for teaching the meaning of many mathematical concepts taught in middle school, including numerical operations. The number line can also be used as a tool for thinking about algebraic concepts taught in high school, such as an abstract or algebraic understanding of distance, absolute value, and inequalities.

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Development and Psychometric Report of a Middle-School Mathematics Vocabulary Measure

Assessment for Effective Intervention ◽

10.1177/1534508418820116 ◽

2018 ◽

Vol 45 (3) ◽

pp. 226-234 ◽

Cited By ~ 2

Author(s):

Elizabeth M. Hughes ◽

Sarah R. Powell ◽

Joo-Young Lee

Keyword(s):

Middle School ◽

Middle School Teachers ◽

High Reliability ◽

Reliability And Validity ◽

Middle School Mathematics ◽

Mathematical Language ◽

School Teachers ◽

Mathematical Concepts ◽

Mathematics Vocabulary ◽

Language Analysis

Proficiency with mathematics requires an understanding of mathematical language. Students are required to make sense of both spoken and written mathematical terms. An essential component of mathematical language involves the understanding of the vocabulary of mathematics in which students connect vocabulary terms to mathematical concepts or procedures. In this brief psychometric report, we developed and tested a measure of mathematics vocabulary for students in the late middle-school grades (i.e., Grades 7 and 8) to determine the reliability of such a measure and to learn how students answer questions about mathematics vocabulary terms. The vocabulary terms on the measure were those terms determined as essential by middle-school teachers for success with middle-school mathematical language. Analysis indicates the measure demonstrated high reliability and validity. Student scores were widely distributed and students, on average, only answered two-thirds of vocabulary terms correctly.

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Algebra Can Be Elementary … When It's Concrete

The Arithmetic Teacher ◽

10.5951/at.36.8.0021 ◽

1989 ◽

Vol 36 (8) ◽

pp. 21-24

Author(s):

Barbara Berman ◽

Fredda Friederwitzer

Keyword(s):

Middle School ◽

School Children ◽

Middle School Children ◽

Mathematical Concepts ◽

Basic Concepts ◽

Concrete Materials ◽

Algebraic Concepts ◽

Elementary And Middle School

Effective mathematics requires more than the use of symbols or numerals. All students, and even many adults, need concrete models to understand mathematical concepts. Elementary and middle school children can understand and master basic concepts of mathematics, including algebra, when concrete materials are used to model these concepts. This article presents a rationale for these statements and describes a model for teaching early algebraic concepts using manipulative materials.

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Harry Potter and the Magic of Mathematics

Mathematics Teaching in the Middle School ◽

10.5951/mtms.10.8.0408 ◽

2005 ◽

Vol 10 (8) ◽

pp. 408-414

Author(s):

Betsy McShea ◽

Judith Vogel ◽

Maureen Yarnevich

Keyword(s):

Middle School ◽

Middle School Teachers ◽

Attitudes Toward Mathematics ◽

Harry Potter ◽

Lewis Carroll ◽

Literary Texts ◽

Mathematical Concepts ◽

Alice In Wonderland ◽

Interdisciplinary Approaches ◽

Important Time

The Middle School Years Represent an important time in the formation of an individual's lifelong attitudes toward mathematics. Middle school teachers are faced with the challenge of convincing their students that mathematics is an exciting, useful, and creative field of study. Interdisciplinary approaches to mathematics have been useful in accomplishing this goal. In particular, connecting mathematics to literature is an inventive way to capture students' interests, since examples from literature can be used to teach important mathematical concepts in an exciting and innovative manner. Many classic literary texts are rich in mathematical content, including Alice in Wonderland by Lewis Carroll and Flatland by Edwin A. Abbott. However, to stimulate students' interest, it is important to find interconnections between mathematics and current popular children's literature.

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

Mathematics Teaching in the Middle School ◽

10.5951/mtms.14.2.0078 ◽

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.

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