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.

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?

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/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).

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.

Families Ask: Understanding Mathematics and Basic Skills

2001 ◽  
Vol 7 (1) ◽  
pp. 8-9
Author(s):  
Daniel J. Brahier
Keyword(s):  
School Districts ◽  
Teaching Practices ◽  
Real Life ◽  
School Mathematics ◽  
Curriculum Materials ◽  
Community Members ◽  
Evaluation Standards ◽  
Life Problems ◽  
Hands On ◽  
Principles And Standards

Since the publication of Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and Principles and Standards for School Mathematics (NCTM 2000), many school districts and teachers have implemented new curriculum materials to achieve the vision of the Standards. In addition, many educators have adopted a constructivist viewpoint in their teaching practices, resulting in hands-on lessons for children and the use of real-life problems, visual and hands-on approaches, and invented strategies for solving problems. In the context of reform, however, parents and community members are prone to question whether their children will actually “learn the basics” when engaged in hands-on, real-life investigations.

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.

MIM: Math in Motion for K–2

2008 ◽  
Vol 15 (4) ◽  
pp. 196-200
Author(s):  
Cheryl Chevalier ◽  
Mary H. Pippen ◽  
Dorothy Stevens
Keyword(s):  
Professional Development ◽  
Developmentally Appropriate ◽  
School Mathematics ◽  
Grade Levels ◽  
Hands On ◽  
Principles And Standards

In spring 2002, the authors attended an algebra workshop sponsored by the NCTM Academy for Professional Development. The workshop presented algebraic standards and activities exploring each aspect of the Learning Principle from Principles and Standards for School Mathematics (NCTM 2000). The hands-on activities were developmentally appropriate for students at grade levels K–2 and could easily be transferred into our classrooms to enhance the curriculum.

Short Takes: Another Good Idea: Pasta Symmetry

2007 ◽  
Vol 12 (9) ◽  
pp. 516-517
Author(s):  
Tara Windle
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Middle Grades ◽  
Assessment Tool ◽  
Rotational Symmetry ◽  
Authentic Assessment ◽  
School Mathematics ◽  
School Students ◽  
Mathematical Ideas ◽  
Principles And Standards

Students enjoy the chance to be creative, especially those in the middle grades. Teachers can channel that creative energy into an authentic assessment tool that students will love. Principles and Standards for School Mathematics states that students in middle school are expected to “apply transformations and use symmetry to analyze mathematical situations” (p. 232). Our students have also been challenged to “recognize and apply mathematics in contexts outside of mathematics” (p. 274) and to “create and use representations to organize, record, and communicate mathematical ideas” (p. 280). Using card-stock paper, glue, gold spray paint (optional), and as many varieties of pasta as I could find, I gave my sixthgrade middle school students the opportunity to convince me that they understood the concepts of reflectional and/or rotational symmetry while creating a unique piece of art.

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