Activities for Students: Inquiry into Fractals

2009 ◽  
Vol 103 (3) ◽  
pp. 206-212
Author(s):  
Raymond Siegrist
Keyword(s):  
High School ◽  
Building Block ◽  
Mathematics Students ◽  
High School Mathematics ◽  
Imaging Characteristic ◽  
High School Geometry ◽  
School Geometry ◽  
Geometry Teachers ◽  
Simple Building Block ◽  
Insight Into

The exotic images of fractals often pique the interest of high school mathematics students, and this interest presents an opportunity for geometry teachers to draw students into an investigation of transformations and patterns. By using a simple building block and fractals' self-imaging characteristic (as the figure grows, it retains the pattern established by the building block), teachers can bring construction of fractals into the high school geometry curriculum. The three activities described in this article engage students in constructing a fractal, searching a fractal for patterns, and using transformations to build different fractals. Students gain insight into patterns as their fractals grow; they flip or rotate fractal pieces by following a design and translating the pieces into place.

Let’s Use Trigonometry

1975 ◽  
Vol 68 (2) ◽  
pp. 157-160
Author(s):  
John J. Rodgers
Keyword(s):  
High School ◽  
Subject Matter ◽  
School Mathematics ◽  
High School Mathematics ◽  
Mathematics Courses ◽  
High School Geometry ◽  
School Geometry ◽  
The Subject ◽  
Order Of Presentation

All too often in the teaching of high school mathematics courses, we overlook the inherent flexibility and interdependence of the subject matter. It is easy to fall into the trap of presenting algebra, trigonometry, geometry, and so on, as separate areas of study. It is because they were taught this way traditionally. With relatively minor changes in the order of presentation, we can demonstrate to the student the vital interconnectiveness of mathematics. For example, many courses in high school geometry include a unit on trigonometry. The student learns three trigonometric ratios, namely, the sine, the cosine, and the tangent. He also learns to use the trigonometric tables to solve for an unknown side of a right triangle. Generally this material comes quite late in the year.

The Geometric Supposer: Promoting Thinking and Learning

1986 ◽  
Vol 79 (6) ◽  
pp. 418-422
Author(s):  
Michal Yerushalmy ◽  
Richard A. Houde
Keyword(s):  
High School ◽  
Equal Opportunity ◽  
Deductive Systems ◽  
High School Geometry ◽  
School Geometry ◽  
Geometry Teachers ◽  
Mathematical Systems

Traditionally, the teaching of high school geometry has emphasized the principles of deductive systems. This approach often forces students to learn how to manipulate mathematical systems while it denies them an equal opportunity to create geometry. Geometry teachers have always faced the dilemma of having to instil in their students an appreciation of deductive mathematical systems while at the same time offering them an opportunity to create mathematics. This article describes our approach in dealing with this dilemma.

Building Fractal Models with Manipulatives

1993 ◽  
Vol 86 (8) ◽  
pp. 646-651
Author(s):  
Loring Coes
Keyword(s):  
High School ◽  
Plane Geometry ◽  
Self Similarity ◽  
High School Geometry ◽  
Fractal Models ◽  
School Geometry ◽  
Insight Into

Fractals are a source of puzzlement and wonder, but they also furnish an opportunity to look at some common ideas from uncommon perspectives. Similarity, for example, is at the heart of our thinking about fractals, and it is also a key strand in high school geometry. Fractals offer a strange twist on similarity, however, and give students an opportunity to look at objects that are similar to themselves or that have self-similarity. Coming to grips with the oddities of self-similarity can give students a much deeper insight into the more conventional concepts of similarity in plane geometry.

What Should High School Geometry Be?

1968 ◽  
Vol 61 (5) ◽  
pp. 466-471
Author(s):  
Charles Buck
Keyword(s):  
High School ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
High School Mathematics ◽  
College Mathematics ◽  
High School Geometry ◽  
School Geometry ◽  
Mathematics Curricula ◽  
School Mathematics Curriculum

The question “What to do about geometry?” has for decades beset the planners of both high school and college mathematics curricula. Until the nature of the first course in high school geometry is settled, the high school mathematics curriculum cannot stabilize. If the high school geometry question could be answered, this would help the colleges to reset geometry in their curricula.

Integrating Transformation Geometry into Traditional High School Geometry

1992 ◽  
Vol 85 (9) ◽  
pp. 716-719
Author(s):  
Steve Okolica ◽  
Georgette Macrina
Keyword(s):  
High School ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
High School Mathematics ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry ◽  
Transformation Geometry ◽  
To Receive ◽  
School Mathematics Curriculum

The grades 9-12 section of NCTM's Curriculum and Evaluation Standards for School Mathematics defines transformation geometry as “the geometric counterpart of functions” (1989, 161). Further, the Standards document recognizes the importance of this topic to the high school mathematics curriculum by listing it among the “topics to receive increased attention” (p. 126). Also included on this list is the integration of geometry “across topics.”

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