Focused Strategies for Middle-Grades Mathematics Vocabulary Development

2007 ◽  
Vol 13 (4) ◽  
pp. 200-207
Author(s):  
Rheta N. Rubenstein
Keyword(s):  
Mathematics Education ◽  
Middle Grades ◽  
Mathematical Thinking ◽  
Vocabulary Development ◽  
School Mathematics ◽  
One Dimension ◽  
Mathematical Language ◽  
Mathematics Vocabulary ◽  
Principles And Standards

Principles and Standards for School Mathematics reminds us that communication is central to a broad range of goals in mathematics education (NCTM 2000). These goals include students' being able to (1) organize and consolidate mathematical thinking; (2) communicate coherently with teachers, peers, and others; (3) analyze and evaluate others' strategies; and (4) use language to express mathematics precisely. One part of communication is acquiring mathematical language and using it fluently. This article addresses learning vocabulary as one dimension of mathematics communication.

Spotlight on the Principles: The Pursuit of Mathematics for All!

2005 ◽  
Vol 10 (9) ◽  
pp. 479-483
Author(s):  
Laurie Rubel ◽  
Margaret R. Meyer
Keyword(s):  
Mathematics Education ◽  
Strong Support ◽  
School Mathematics ◽  
High Expectations ◽  
Speaking Out ◽  
Reasonable Accommodations ◽  
Equity Principle ◽  
Access To Technology ◽  
Principles And Standards

“EXCELLENCE IN MATHEMATICS education requires equity—high expectations and strong support for all students.” Thus begins the Equity Principle found in Principles and Standards for School Mathematics (NCTM 2000, p. 12). It goes on to detail some of the dimensions of equity: high expectations, strong support, reasonable accommodations, worthwhile opportunities, and access to technology. People are unlikely to disagree with the stance implied by the Equity Principle. “Mathematics for all” is a rallying cry akin to “liberty and justice for all.” To disagree with the Principle would be like speaking out against motherhood or apple pie. Yet the pathway to mathematics for all is not always clear. What does equity in mathematics look like in our classrooms and schools? How would individual teachers proceed if the Equity Principle was guiding their teaching?

Felix Klein and the NCTM's Standards: A Mathematician Considers Mathematics Education

2000 ◽  
Vol 93 (8) ◽  
pp. 714-717
Author(s):  
Kim Krusen McComas
Keyword(s):  
Mathematics Education ◽  
School Mathematics ◽  
Rote Learning ◽  
German Mathematician ◽  
Evaluation Standards ◽  
10Th Anniversary ◽  
Felix Klein ◽  
Look Back ◽  
Principles And Standards ◽  
Year 2000

The year 1999 marked the 10th anniversary of the NCTM's Curriculum and Evaluation Standards for School Mathematics. It also marked the 150th anniversary of the birth of German mathematician Felix Klein, who lived from 1849 to 1925. Although the relation between these two anniversaries may not be obvious, the connection is that Klein, were he still alive today, would probably support the NCTM's Standards. As the year 2000 brings us NCTM's Principles and Standards for School Mathematics, let us look back to the year 1900 and find Felix Klein at the forefront of a movement to reform mathematics education from rote learning to more meaningful mathematical learning.

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?

Spotlight on the Principles/Standards: Problem Solving in the Middle Grades

2000 ◽  
Vol 6 (2) ◽  
pp. 105-108
Author(s):  
Carol E. Malloy ◽  
D. Bruce Guild
Keyword(s):  
Problem Solving ◽  
Mathematical Knowledge ◽  
Middle Grades ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Measurement Algebra ◽  
Principles And Standards ◽  
Mathematical Relationships

IN WHAT WAYS WOULD YOU LIKE YOUR middle-grades students to experience problem solving in the mathematics curriculum? Do you want the curriculum to capture the excitement of geometry and measurement, algebra, statistics, and number relationships? Do you want it to help students understand and build new mathematical knowledge and explore new mathematical relationships? Do you want the curriculum to be filled with opportunities for students to ponder, create, and critique arguments about mathematics? If this is your vision for your students, then you should be pleased with, and excited by, the Problem Solving Standard in Principles and Standards for School Mathematics (NCTM 2000).

Call for Manuscripts: Big Ideas of Algebra

2009 ◽  
Vol 15 (7) ◽  
pp. 429
Keyword(s):  
High School ◽  
Middle Grades ◽  
School Mathematics ◽  
Big Ideas ◽  
Solid Foundation ◽  
Principles And Standards

“By viewing algebra as a strand in the curriculum from prekindergarten on, teachers can help students build a solid foundation of understanding and experience as a preparation for moresophisticated work in algebra in the middle grades and high school” (NCTM Principles and Standards for School Mathematics, p. 37).

scholarly journals Developing purposeful mathematical thinking: a curious tale of apple trees

2012 ◽  
Vol 6 (3) ◽  
pp. 85-103
Author(s):  
Janet Ainley
Keyword(s):  
Mathematics Education ◽  
Real World ◽  
Mathematical Thinking ◽  
Task Design ◽  
Mathematical Understanding ◽  
School Mathematics ◽  
Apple Trees ◽  
The Real

In this paper I explore aspects of the ways in which school mathematics relates to the “real” world, and argue that this relationship is an uneasy one. Through exploring the causes of this unease, I aim to expose some problems in the ways in which context is used within mathematics education, and argue that the use of context does not ensure that the purposes of mathematics are made transparent. I present and discuss a framework for task design that adopts a different perspective on mathematical understanding, and on purposeful mathematical thinking. Desarrollo de un pensamiento matemático intencionado: un relato curioso de manzanos En este artículo exploro aspectos de las maneras en que las matemáticas escolares se relacionan con el mundo “real” y argumento que esta relación es preocupante. Al explorar las causas de esta preocupación, me propongo exponer algunos problemas que surgen de las formas en que se usa el contexto en Educación Matemática y argumento que el uso del contexto no asegura la transparencia de los propósitos de las matemáticas. Presento y discuto un esquema para el diseño de tareas que adopta una perspectiva diferente sobre la comprensión de las matemáticas y el pensamiento matemático intencionado.Handle: http://hdl.handle.net/10481/19524

Connecting Geometry and Algebra in the Middle Grades

2011 ◽  
Vol 16 (6) ◽  
pp. 316
Keyword(s):  
Middle Grades ◽  
School Mathematics ◽  
Geometric Representation ◽  
Algebraic Representation ◽  
Principles And Standards ◽  
And Algebra

Welcome to the 2011 Focus Issue, which highlights connections between geometry and algebra that teachers can leverage in the middle grades. NCTM's Principles and Standards for School Mathematics (2000) recommends that students in the middle grades experience both the geometric representation of algebraic ideas and the algebraic representation of geometric ideas. By making these connections, students see that mathematical topics are related. They are not just a collection of isolated facts in seemingly disjoint fields but facts that often have many extensive connections.

The Pythagorean Theorem with Jelly Beans

2008 ◽  
Vol 14 (4) ◽  
pp. 202-207
Author(s):  
Jeong Oak Yun ◽  
Alfinio Flores
Keyword(s):  
Middle Grades ◽  
Empirical Approach ◽  
School Mathematics ◽  
Pythagorean Theorem ◽  
Geometric Shapes ◽  
Hands On ◽  
Principles And Standards

principles and standards for school mathematics advocates an experimentation approach to middle-grades geometry study (nctm 2000). Students are asked to explore and examine a variety of geometric shapes and discover their characteristics and properties using hands-on materials. They also create inductive arguments about the pythagorean relationship. This empirical approach to the pythagorean theorem, for example, will lay the foundation for analytical proofs.

Writing Samples to Understand Mathematical Thinking

2002 ◽  
Vol 7 (9) ◽  
pp. 517-520
Author(s):  
Dianne S. Goldsby ◽  
Barbara Cozza
Keyword(s):  
Mathematical Thinking ◽  
School Mathematics ◽  
Mathematics Students ◽  
Principles And Standards

NCTM's Principles and Standards for School Mathematics emphasizes the need for all students to organize and consolidate their mathematical thinking through communication and to communicate their mathematical thinking coherently to others (NCTM 2000). Writing helps students focus on their own understandings of mathematics: “Students gain insights into their thinking when they present their methods for solving problems, when they justify their reasoning to a classmate or teacher, or when they formulate a question about something that is puzzling them” (NCTM 2000, pp. 60–61).

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

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.

Sign in / Sign up

Export Citation Format

Share Document