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DeJarnette, Anna F.; Rosado Lausell, Sahid L.; González, Gloriana – Mathematics Teacher, 2015
How can geometry teachers design great tasks that allow students to make connections among interrelated concepts and expand their geometric reasoning skills? Many curricular materials provide problems for students to apply a single geometric concept. However, these problems do not always promote reasoning opportunities for students, because…
Descriptors: Geometry, Geometric Concepts, Task Analysis, Mathematics Activities
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Viro, Julia – Mathematics Teacher, 2014
Constructing viable arguments and reasoning abstractly is an essential part of the Common Core State Standards for Mathematics (CCSSI 2010). This article discusses the scenarios in which a mathematical task is impossible to accomplish, as well as how to approach impossible scenarios in the classroom. The concept of proof is introduced as the…
Descriptors: Mathematics Instruction, Mathematical Concepts, Validity, Mathematical Logic
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Gonzalez, Gloriana; DeJarnette, Anna F. – Mathematics Teacher, 2013
What does problem-based instruction do for students and teachers? The open-ended geometry problem presented in this article, along with examples of students' work on the problem, illustrates how problem-based instruction can help students develop their mathematical proficiency. Recent studies have shown that students who experience problem-based…
Descriptors: Mathematical Logic, Mathematics Instruction, Geometry, Geometric Concepts
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Bannon, Thomas J. – Mathematics Teacher, 2009
In this article, the classic problem of finding three ways to determine the probability that the pieces of a stick randomly broken in two places will form a triangle is analyzed anew. To be useful in the classroom, an application must be incorporated into an often-crowded curriculum. What is nice about this triangle problem is that it fits in…
Descriptors: Geometric Concepts, Probability, Geometry, Mathematics Instruction