ERIC Number: EJ1034788
Record Type: Journal
Publication Date: 2013-Sep
Reference Count: 3
The Geoboard Triangle Quest
Allen, Kasi C.
Mathematics Teacher, v107 n2 p113-118 Sep 2013
In line with the Common Core and Standards for Mathematical Practice that portray a classroom where students are engaged in problem-solving experiences, and where various tools and arguments are employed to grow their strategic thinking, this article is the story of such a student-initiated problem. A seemingly simple question was posed by students in a geometry class years ago: How many triangles can you make on a geoboard? Geoboard Triangles problems are based upon a Checkerboard Squares problem: How many squares are in a checkerboard? Over the years, patterns in the strategies that students use when encountering the Geoboard Triangles problem have been documented. Time has changed the tools that students have at their disposal--from physical geoboards and dot paper sketches to a range of computer-based applications--making it possible for students to represent their ideas more readily, organize their work, and arrive at a solution that they can verify. Regardless of the strategies they choose, students working to solve the Geoboard Triangles problem benefit from a classroom culture in which all feel comfortable generating conjectures and questions. The practice serves to remind students of the diversity of ideas being discussed in the room and to broaden their own thinking, especially when they find themselves losing momentum or getting stuck. This personal investment motivates students to learn and persist in mathematics. The article concludes with a reminder for teachers to make time for students to explore and make sense of what they discover, and to give them choices about how they will proceed along their path of exploration.
Descriptors: Geometry, Geometric Concepts, Problem Solving, Mathematics Instruction, Academic Standards, State Standards, Mathematics Activities, Secondary School Mathematics
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: firstname.lastname@example.org; Web site: http://www.nctm.org/publications/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Secondary Education
Authoring Institution: N/A