Exploring Algebraic Patterns through Literature

1997 ◽  
Vol 2 (4) ◽  
pp. 274-281
Author(s):  
Richard A. Austin ◽  
Denisse R. Thompson
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Position Statement ◽  
Algebraic Thinking ◽  
School Mathematics ◽  
School Students ◽  
Evaluation Standards

Activities that engage middle school students in investigating and extending patterns are essential in developing students' algebraic thinking. The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) for grades 5-8 and the position statement on “Algebra for Everyone” (NCTM 1994) describe the importance of using patterns and relationships to develop algebraic thinking.

Mathematics Projects Promote Students' Algebraic Thinking

1997 ◽  
Vol 2 (4) ◽  
pp. 282-288
Author(s):  
Carol E. Malloy
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Mathematics Teachers ◽  
Middle School Mathematics ◽  
Algebraic Thinking ◽  
School Mathematics ◽  
School Students ◽  
Evaluation Standards ◽  
Verbal Rules

Teachers in all curricular areas, especially science, have encouraged students to develop projects to extend their knowledge of specific phenomena. As middle school mathematics teachers grapple with methods to help students enhance algebraic thinking, they should consider the power of the mathematics project. My experiences with students have demonstrated that mathematics projects must be structured as investigations in which students work cooperatively and where the mathematics in the proj-ects is substantial. Projects can provide middle school students with the opportunity to investigate, conjecture, and reach mathematical conclusions that require algebraic thinking, as recommended in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). This article describes how various projects helped middle school students harness their experiences and construct mathematical conclusions through algebraic thinking Students employed algebraic thinking as they used number patterns and verbal rules to “explore the interrelationships of these representations” (NCTM 1989, 102) and reach conclusions in their projects.

Birthdays and the Binary System: A Magical Mixture

1997 ◽  
Vol 3 (1) ◽  
pp. 6-12
Author(s):  
Karen S. Karp ◽  
Robert N. Ronau
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Binary System ◽  
School Mathematics ◽  
School Level ◽  
Birth Date ◽  
School Students ◽  
Evaluation Standards ◽  
System A ◽  
Middle School Level

Middle school students rank their birthday as being the most important day of the year for them and one that they eagerly anticipate, according to an informal poll. Teachers can capitalize on this interest by engaging them in the mathematical birth-date activities described in this article. Applications and tasks that are relevant to students' lives have been shown to motivate students at the middle school level, according to the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).

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.

Connecting Measurement and Architecture: Building an Inflatable

2007 ◽  
Vol 13 (3) ◽  
pp. 144-149
Author(s):  
Elizabeth D. Gray ◽  
Denise Tullier-Holly
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Real World ◽  
School Mathematics ◽  
Classroom Experiences ◽  
School Students ◽  
The Real ◽  
Mathematical Connections ◽  
Principles And Standards

Middle school students need to see connections between mathematics and the real world. However, they often learn mathematics as a set of distinct topics or separate strands, because a majority of the available textbooks tends to present it that way, and teachers tend to follow the textbooks. According to Principles and Standards for School Mathematics (NCTM 2000), our students should be made aware of mathematical connections explicitly so that the manner in which topics are connected is obvious. McClain (1996) suggests that if teachers offer classroom experiences in which students can see connections, then “the vibrant discipline of mathematics actively engages students in their own learning” (p. 682).

Polygon Capture: A Geometry Game

1998 ◽  
Vol 4 (2) ◽  
pp. 90-94
Author(s):  
William M. Carroll
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Conceptual Understanding ◽  
Sixth Grade ◽  
Fifth Grade ◽  
School Students ◽  
Problem Solving Skills ◽  
Evaluation Standards ◽  
Different Levels ◽  
School Curricula

The curriculum and evaluation standards for School Mathematics (NCTM 1989) calls for an increased role for geometry in the primary and middle school curricula. An important mathematical strand in its own right, geometry also provides opportunities to promote and assess mathematical communication, reasoning, and problem-solving skills. Unfortunately, many students lack the vocabulary and the conceptual understanding needed to desctibe geometric relationships. This atiicle describes a game, Capture the Polygons, that I have designed to help middle school students think about geometric properties and the relationships among them. A version of the game has been tested in firth- and sixth-grade classes as part of the field test of Fifth Grade Everyday Mathematics (Bell et al. 1995). Observations of classes playing the game, as well as feedback from their teachers, indicate that students find the game challenging but fun. Depending on the background of the students, it can be played at different levels of difficulty.

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.

Take Time For Action: The Number of Trials Does Matter

2002 ◽  
Vol 8 (2) ◽  
pp. 106-108
Author(s):  
Leslie Aspinwall ◽  
James Tarr
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
School Mathematics ◽  
School Students ◽  
Principles And Standards

PRINCIPLES AND STANDARDS FOR SCHOOL Mathematics (NCTM 2000) calls for middle school students to develop and evaluate inferences that are based on data. Combining or “pooling” data from simulations reduces the likelihood of drawing incorrect inferences. But are your students aware that more accurate inferences can be drawn from larger sets of data and that smaller samples are more likely to produce unusual results?

scholarly journals The Voces Project: Investigating How Latino/a Immigrant Children Make Sense of Engaging in School and School Mathematics

2013 ◽  
Vol 15 (2) ◽  
Author(s):  
John C. Knudson-Martin
Keyword(s):  
United States ◽  
Middle School ◽  
Middle School Students ◽  
Social Environment ◽  
The United States ◽  
Immigrant Children ◽  
School Mathematics ◽  
Institutional Factors ◽  
Mexican Immigrant ◽  
School Students

This study investigates how a group of Mexican immigrant children in the United States made sense of engaging in school and school mathematics.  The research focused on a population of Latino/a middle school students who were a distinct minority, building a model that shows how a complex set of cognitive, sociocultural, and institutional factors mediated these students’ engagement and success in school.  The results of this research will help educators understand the complex social environment that faces immigrant children and impacts their performance and engagement in school and school mathematics.

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