Supporting the development of algebraic thinking in middle school: a closer look at students’ informal strategies

2004 ◽  
Vol 23 (4) ◽  
pp. 371-388 ◽  
Author(s):  
Debra I. Johanning
Keyword(s):  
Middle School ◽  
Algebraic Thinking ◽  
Informal Strategies

Developing Algebraic Thinking through Pattern Exploration

2006 ◽  
Vol 11 (9) ◽  
pp. 428-433 ◽  
Author(s):  
Lesley Lee ◽  
Viktor Freiman
Keyword(s):  
Middle School ◽  
Middle Grades ◽  
Algebraic Thinking ◽  
School Mathematics ◽  
Scientific Disciplines ◽  
Algebraic Language ◽  
Principles And Standards ◽  
Relationship Of ◽  
The Relationship ◽  
Repeating Patterns

Pattern exploration is A pivotal activity in all mathematics, indeed in all the scientific disciplines. Children who are attempting to express perceived patterns mathematically are in an excellent position to learn algebraic language and engage in algebraic activity. Principles and Standards for School Mathematics (NCTM 2000) acknowledges the relationship of pattern exploration and algebraic thinking by placing pattern work within the Algebra strand. Yet one can undertake considerable pattern exploration without engaging students in any algebraic thinking whatsoever and teachers may, themselves, be unclear about how patterns can be used to further algebraic thinking. Work with repeating patterns in the early grades, or teaching patterns as a “topic” in the middle grades, may not foster the development of algebraic thinking in students. In this article, we will address this question: How can teachers exploit pattern work to further algebraic thinking and introduce the formal study of algebra in middle school?

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.

Call for Manuscripts for Focus Issue: Algebraic Thinking

1995 ◽  
Vol 1 (7) ◽  
pp. 538
Keyword(s):  
Middle School ◽  
Mathematics Teaching ◽  
Teaching And Learning ◽  
Middle Grades ◽  
Algebraic Thinking ◽  
Wide Range ◽  
Nature Of Teaching

The January-February 1997 issue of Mathematics Teaching in the Middle School is planning a focus issue on algebraic thinking to feature a wide range of articles that address the changing nature of teaching and learning algebra in the middle grades.

Building Conceptual Bridges from Arithmetic to Algebra

2002 ◽  
Vol 7 (6) ◽  
pp. 326-331
Author(s):  
Joseph G. R. Martinez
Keyword(s):  
Middle School ◽  
Elementary School ◽  
Algebraic Thinking ◽  
School Mathematics ◽  
Elementary School Mathematics ◽  
Early Grades

How can we help students make the transition from elementary school mathematics to middle school algebra? Although algebraic thinking and some important concepts are now routinely taught in the early grades, some students still approach algebra as an alien domain with an incomprehensible language.

Building Bridges to Algebraic Thinking

1997 ◽  
Vol 2 (4) ◽  
pp. 208-212
Author(s):  
Roger Day ◽  
Graham A. Jones
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Middle School Teachers ◽  
Algebraic Thinking ◽  
Physical Models ◽  
School Students ◽  
Instructional Goals ◽  
Use Of Technology ◽  
Mathematical Relationships ◽  
Elementary And Middle School

In spite of the fact that middle school teachers have been urged to develop algebraic thinking in their students (Lawson 1990; NCTM 1989; Phillips et al. 1991), the question of how to initiate that process may still be problematic for many teachers. Although it is important to suggest that explorations into algebraic thinking should emphasize “physical models, data, graphs and other mathematical relationships” (NCTM 1989, 102) and to recognize that “numerical and graphical problem-solving techniques become accessible strategies … through the use of technology” (Demana and Waits 1990, 53), teachers need help in building a bridge between their current instructional goals and new goals that emphasize an earlier introduction to algebraic thinking. In this article, we describe and illustrate an approach to algebraic thinking that is based on an extension of the problem-solving tasks typically investigated by elementary and middle school students.

Do You Understand Your Algorithms?

2006 ◽  
Vol 12 (1) ◽  
pp. 42-47
Author(s):  
Jamar Pickreign ◽  
Robert Rogers
Keyword(s):  
High School ◽  
Middle School ◽  
Middle School Students ◽  
School Districts ◽  
Middle School Teachers ◽  
Algebraic Thinking ◽  
Computational Algorithms ◽  
Successful Completion ◽  
School Teachers ◽  
School Students

Because an increasing number OF school districts requires the successful completion of an algebra course to graduate from high school, many middle school teachers are beginning to focus more attention on introducing algebraic thinking to their students (NCTM 2003). Consequently, it becomes important to consider ways to ensure that these experiences are meaningful and connected to arithmetical experiences from the earlier grades. We believe that presenting middle school students with activities that involve exploring computational algorithms—how and why they work—can contribute to the development and promotion of algebraic thinking.

Embedding Algebraic Thinking throughout the Mathematics Curriculum

2005 ◽  
Vol 11 (2) ◽  
pp. 86-93
Author(s):  
G. Patrick Vennebush ◽  
Elizabeth Marquez ◽  
Joseph Larsen
Keyword(s):  
Middle School ◽  
Data Analysis ◽  
Mathematics Curriculum ◽  
School Curriculum ◽  
Algebraic Thinking ◽  
Middle School Curriculum ◽  
Geometry Problem

Like love, algebra is where you find it. You can locate it almost anywhere in the middle school curriculum if you know where to look and what to look for. But with so many demands on our time, we often forget to look. We take problems at face value, and we assume that a geometry problem is just a geometry problem or that a data analysis activity is only about data analysis. If we scratch below the surface, however, we can find rich opportunities for algebraic thinking lurking in number explorations, measurement tasks, and geometry investigations.

Exploring Patterns in Nonroutine Problems

1997 ◽  
Vol 2 (4) ◽  
pp. 262-269
Author(s):  
Frances R. Curcio ◽  
Barbara Nimerofsky ◽  
Rossana Perez ◽  
Shirel Yaloz
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Algebraic Thinking ◽  
School Students ◽  
The Past ◽  
Instructional Activities ◽  
Essential Components ◽  
Heterogeneously Grouped ◽  
Nonroutine Problems

For the past several years, we have been examining ways to introduce notions of algebra to our heterogeneously grouped middle school students. Through our experiences of designing instructional activities that integrate nonroutine, nontraditional problems. we found a meaningful way to involve students in exploring and formalizing patterns, conjecturing about the patterns they identify, verbalizing relationships between and among elements in patterns, and eventually generalizing and symbolizing the relationships—all essential components of algebraic thinking (Silver, in press).

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