Introduction to Geometry - Art of Problem Solving

(3 credits)Prerequisites: or permission of instructor. Logic and problem solving will be used to discover geometric concepts. Examples from theorems of great mathematicians of the past will be studied. Students will be expected to understand and construct logical arguments. Use of technology to explore geometric relationships will be an integral part of the course.

Geometry - Art of Problem Solving

Klee, V.
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Problem Solving in Geometry | Johns Hopkins Center for Talented Youth

Our novel methodology uses (i) deductive reasoning to generate a partial program from logical constraints, (ii) numerical methods to evaluate the partial program, thus creating geometric models which are solutions to the original problem, and (iii) inductive synthesis to read off new constraints that are then applied to one more round of deductive reasoning leading to the desired deterministic program. By the combination of methods we were able to solve problems that each of the methods was not able to solve by itself.

Algebra: Word Problems: Solving Geometry Problem (1) - YouTube

We describe a framework that combines deductive, numeric, and inductive reasoning to solve geometric problems. Applications include the generation of geometric models and animations, as well as problem solving in the context of intelligent tutoring systems.

Developing Key Understanding of Geometry through Problem Solving and Concep...
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10.2 Probability with Geometry Part 1 - Art of Problem Solving

Students regularly struggle with mathematical tasks, particularly those concerning non-routine problems in geometry. Although educators would like for their learners to transfer their knowledge to non-routine and real-life situations, students run into a number of difficulties. The goal of this exploratory study was to analyze three participants’ problem solving processes in a dynamic geometry software (DGS), and therefore, gain insights about how DGS was used to support solving non-routine geometry problems. Here I viewed the DGS as a cognitive tool that can enhance and reorganize the problem solving process. The three participants were in different phases of their educational career in mathematics and/or mathematics education (bachelor, master, and doctoral student). Only one problem—the Land Boundary Problem—from the TIMSS video study will be discussed here. In this problem, the participants had to straighten a bent fence between two farmers’ land so that each farmer would keep the same amount of land. All three participants solved the problem, but used the same computer-based problem-solving tool differently. While a DGS allowed and supported some participants to discover new methods of thinking, and unanticipated ways of using it, it also inhibited the problem solving processes through development of tool-dependency by some. Its different use was dependent on the presence of managerial decisions, ability to manage different resources, and problem solving experience. Based on these findings, I make recommendations for technology-embedded problem solving with an emphasis on the importance of appropriate tool use in educational settings and offer some teaching methods that may be worthwhile for research.

MATH 1420 - Logic, Problem Solving and Geometry - Acalog ACMS™

Logic, Problem Solving and Geometry is an exploration of various topics in geometry and logic. Problem solving skills are emphasized. This course may fulfill general education mathematics requirements for elementary education majors (but not for other majors.)

Prerequisites & Notes
Prerequisites: MATH 0895 (MLS 5)

MATH 1420♢ - Problem Solving, Geometry and Statistics

In Problem Solving in Geometry, students apply geometric concepts to solve sets of word problems at varying levels of difficulty. This course provides an excellent foundation for students who will be advancing into Honors Geometry or Honors Algebra II. Students will have their understanding checked with graded assessments, which include quizzes, homework, tests, and cumulative midterm and final exams.