Grandfather Tang Goes to High School

2006 ◽  
Vol 99 (7) ◽  
pp. 522-526
Author(s):  
Iris DeLoach Johnson
Keyword(s):  
High School ◽  
Middle School ◽  
Middle School Students ◽  
Middle Grades ◽  
School Mathematics ◽  
High School Mathematics ◽  
Convex Polygons ◽  
School Students ◽  
Powers Of 2 ◽  
Elementary And Middle School

Grandfather Tang's Story (Tompert 1990) has been read in many elementary and middle school classrooms in which students engage in mathematical discoveries of simple geometric terms and relationships. In the middle grades it is possible to engage in more sophisticated investigations, which include reasoning about fractions, percents, and powers of 2. Middle school students may also engage in informal proof to show “that there are in fact just thirteen possible convex polygons that can be made from the seven Tangram pieces” (Bradford 2002, p. 4). Because “the tangram is a versatile manipulative” that can support more mathematics than originally meets the eye (Thatcher 2001, p. 394), it is time to seek a place for this story in high school mathematics classes.

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.

Developing Conceptual Understanding of Relations and Functions with Attribute Blocks

1997 ◽  
Vol 3 (3) ◽  
pp. 186-190
Author(s):  
Robert J. Quinn
Keyword(s):  
High School ◽  
Middle School ◽  
Middle School Students ◽  
Elementary Students ◽  
Conceptual Understanding ◽  
Middle Grades ◽  
School Curriculum ◽  
National Council ◽  
School Students ◽  
Formal Curriculum

Much attention has recently been focused on students in the middle grades. The unique difficulties and characteristics of this group have prompted the National Council of Teachers of Mathematics to refer to them as “children in transition” (NCTM 1989, 68). Middle school students continue to rely on concrete experiences to construct knowledge but are starting to develop the ability to think abtractly (NCTM 1989, 68). Thus, the middle school curriculum should build “a bridge between the concrete elementary school curriculum and the more formal curriculum of the high school” (NCTM 1989, 102). The series of lessons described in this article extends the concrete experiences that many elementary students have had with attribute blocks to provide middle school students with informal opportunities to explore the concepts and properties of relations and functions.

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