Representations have always been a very important part of teaching mathematics. The visuals and hands on experiences help to aide the teachers by assisting them in relaying important topics and concepts to the students. By having a representation, the students are more likely to remember what they have learned, and recall the lesson when it comes time to take a test or do their homework.
Within mathematics, many different manipulatives are used to enhance learning. Among the most commonly used are tangrams. The seven pieces that make up a set of tangrams have value well beyond their small size. One of their most important values, other than providing educational entertainment to students, is the introduction of geometric properties and theorems.
When introducing the idea of using tangrams, it is good to tell the old Chinese folktale about how they came to be. The story goes as follows, “A young boy named Tan wished to give the emperor a beautiful tile. As he carries the tile to the palace, he accidentally drops it and it breaks it into seven pieces. Tan tries and tries to restore the tile to its original shape. In the process, he finds out that he can create all sorts of fascinating pictures with the seven pieces of his tile. The seven tile pieces are what are now called tangrams.” (Tackling Tangrams, 2000)
This story illustrates that tangrams can be used a method of discovery, as well as for enjoyment since many pictures can be formed. It also helps students to see why they are able to form a square, which is the main basis for the manipulative. It is beneficial to give the students some time to play and explore with the tangrams after the story is told so they can find different pictures.
By having the students use investigation, a teacher is able to establish a trusting classroom atmosphere as well as have the students see that abstract concepts are very meaningful. (Conundrum, 2001)
By definition, “a tangram is an ancient Chinese puzzle that provides another avenue for exploring rational number concepts.” (Teaching and Learning, 83) They are very useful to explore number concepts as well as in guided discovery. Tangrams are used for many things, including, understanding fractions, relating areas, discovering the Pyth...
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...om. Guided discovery through concrete materials will take over all math classes soon. As long as tangrams are among them, the students will learn a lot and retain the information for a lot longer.
“Areas of Tangram Pieces.” http://mathforum.org/trscavo/tangrams/area.html.
“Developing Geometric Understandings and Spatial Skills through Tangram Puzzles.” http://illuminations.nctm.org/index_d.aspx?id=168
Hatfield, Mary. “Use of Manipulative Devices: Elementary School Cooperating Teachers Report.” School Science and Mathematics. Volume 94, Issue 6. October 1994.
“More Tangram Activities.” http://mathforum.org/trscavo/tangrams/activities.html
Naylor, Michael. “Tangram Tricks.” Teaching Pre K-8. 32 no 8, 26-7. May 2002.
“The Pythagorean Theorem with Tangrams” http://www.math.wichita.edu/history/activities/geometry-act.html#pyth-tan.
Rigdon, Deanna. “Tackling Tangrams.” Teaching Children Mathematics. 6 no 5, 304-5.
Rubenstein. Teaching and Learning Middle Grades Mathematics. Key College Publishing. California. 2004
Thatcher, Debra. “The Tangram Conundrum.” Mathematics Teaching in the Middle School. 6 no 7, 397-9. March 2001.
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