A Comparative Analysis of High School Geometry Curricula: What Do Technology-Intensive, Standards-Based, and Traditional Curricula Have to Offer in Terms Mathematical Proof and Reasoning?

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Oner, D. (2008). A Comparative Analysis of High School Geometry Curricula: What Do Technology-Intensive, Standards-Based, and Traditional Curricula Have to Offer in Terms Mathematical Proof and Reasoning?. Journal of Computers in Mathematics and Science Teaching, 27(4), 467-497. Chesapeake, VA: AACE.
Retrieved from http://www.editlib.org/p/25297.

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Journal Information

Journal of Computers in Mathematics and Science Teaching
ISSN 0731-9258
Volume 27, Issue 4, October 2008
Association for the Advancement of Computing in Education (AACE)  Chesapeake, VA

More Information on JCMST

Author

Diler Oner, Bogazici University, Turkey

Abstract

In this study, I present an analysis of high school geometry curricula regarding mathematical proof opportunities. I examined eight U.S. high school level geometry textbooks, which were categorized into three main groups: technology-intensive, standards-based, and traditional curricula. I conceptualized 'ideal' proving activity combining two fundamentally different ways of knowing: a posteriori (or experimental/empirical) and a priori (or deductive/propositional). I argued that two major forces have given rise to such conception of proving: National Council of Teachers of Mathematics-led reform that favors a 'doing' perspective of mathematics and the availability of dynamic geometry software, a genre of computer tools that allow experimentation, which enables such a vision. Using an analytical framework that maps onto this conception of proving, I investigated proof opportunities along two main dimensions: making mathematical generalizations and providing support to mathematical claims. My findings suggest that there are differences across the three types of curricula regarding the both dimensions of the proof opportunity framework. And these differences suggest important implications for students learning. My findings corroborate the expectation that standards-based curricula engage students in exploration type of activities more. However, they also show that these investigation-rich curricula do not jeopardize experiences related to deductive proof, which has been a major source of concern for many.

Keywords

• Standards
• Secondary Education
• Mathematics
• Curriculum
• Educational Technology
• Instructional Materials
• Computers
• Software

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