Transformations and Technology: What Path to Follow?

2004 ◽  
Vol 9 (7) ◽  
pp. 392-397
Author(s):  
Brad Glass
Keyword(s):  
High School ◽  
Middle School ◽  
Elementary School ◽  
Middle School Mathematics ◽  
Geometer's Sketchpad ◽  
Geometric Transformations ◽  
High School Geometry ◽  
School Geometry ◽  
Mathematics Curricula ◽  
The Relationship

Many of the new elementary sCHOOL and middle school mathematics curricula provide students with opportunities to encounter geometric transformations. Some of the curricula (e.g., MATHThematics, Math Trailblazers, and Investigations in Number, Data, and Space) introduce transformations (such as translations, reflections, and rotations) as motions (slides, flips, and turns) undergone by familiar shapes. How can we make the most of these experiences to ensure that our students are prepared for high school geometry courses? One way is to find out what students understand about transformations and to address any misconceptions they have regarding transformations. In working with eight eighth-grade prealgebra students, I identified one possible misconception as they completed a set of activities using The Geometer's Sketchpad (Jackiw 2001). The students focused on the path followed by a shape, rather than on the relationship between the preimage and image shapes, thereby leading them to incorrect conclusions regarding the equivalency of transformations. The technology-based activities helped some of the students begin to rectify this misconception.

On My Mind: Proof and the Middle School Mathematics Student

1995 ◽  
Vol 1 (7) ◽  
pp. 516-518
Author(s):  
James M. Sconyers
Keyword(s):  
High School ◽  
Middle School ◽  
Middle School Students ◽  
Middle School Mathematics ◽  
Basic Logic ◽  
School Students ◽  
High School Geometry ◽  
School Geometry ◽  
Mathematics Student ◽  
Geometry Class

Is proof perceived as being rigid and formal? Something that students should first encounter in high school? Does a concern involve students' having difficulty when they finally confront the idea of proof, perhaps in their high school geometry class? One likely reason for this unease with proof is that it is so often left out of any work in mathematics until students reach high school. They are then overwhelmed, since it is so unfamiliar. This outcome is not inevitable. Middle school students are capable of grasping the basic logic of proof and should be given the opportunity to encounter it.

Doing Algebra in Grades K-4

1997 ◽  
Vol 3 (6) ◽  
pp. 346-356
Author(s):  
Zolman Usiskin
Keyword(s):  
High School ◽  
Elementary School ◽  
Elementary School Teachers ◽  
Elementary Grades ◽  
School Teachers ◽  
High School Geometry ◽  
School Geometry

About thirty-five years ago the movement to incorporate geometry into the elementary grades began. To many elementary school teachers, the mention of the word geometry brought back memories of a high school geometry course that dealt with abstraction and proof. The thought of teaching children this geometry was naturally viewed with incredulity.

The Incorporation of Geometer’s Sketchpad in a High School Geometry Curriculum

2013 ◽  
pp. 639-646
Author(s):  
Lisa Ames ◽  
Heejung An ◽  
Sandra Alon
Keyword(s):  
High School ◽  
High School Students ◽  
Conceptual Knowledge ◽  
Inductive Reasoning ◽  
Thinking Skills ◽  
Geometer's Sketchpad ◽  
School Students ◽  
Mathematics Standards ◽  
High School Geometry ◽  
School Geometry

The Common Core State Mathematics Standards (CCSSM) recommend that technology should be integrated into teaching and learning Mathematics. This chapter addresses how the Geometer’s Sketchpad computer program can support students’ thinking skills and learning outcomes in a high school geometry class, in particular for more effectively addressing the High School Geometry Standards (CCSSM: G.CO.10, G.CO. 11, and G.CO. 12). The findings from the study presented in this chapter indicate that this tool can help high school students increase their learning of geometry in terms of inductive reasoning and conceptual knowledge, but may not help improve students’ motivation to learn geometry.

Using The Geometer's Sketchpad to Visualize Maximum-Volume Problems

2000 ◽  
Vol 93 (3) ◽  
pp. 224-228 ◽  
Author(s):  
David C. Purdy
Keyword(s):  
High School ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Geometer's Sketchpad ◽  
Maximum Volume ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry ◽  
Traditional Courses

An underlying tenet of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and other movements toward reform in school mathematics is breaking down content barriers between traditional mathematical topics, with the goal of teaching mathematics as a logically interconnected body of thought. As teachers move toward integrating the various areas of mathematics into traditional courses, problems that were once reserved for higher courses, for example, precalculus and calculus, now surface earlier as interesting explorations that can be tackled with such tools as the graphing calculator. One such problem is the well-known maximum-volume-box problem. Although this problem and related optimization questions have been common in advanced algebra, precalculus, and calculus textbooks, they have only recently found their way into high school geometry textbooks, including Discovering Geometry: An Inductive Approach (Serra 1997).

The Incorporation of Geometer’s Sketchpad in a High School Geometry Curriculum

2013 ◽  
pp. 102-109
Author(s):  
Lisa Ames ◽  
Heejung An ◽  
Sandra Alon
Keyword(s):  
High School ◽  
High School Students ◽  
Conceptual Knowledge ◽  
Inductive Reasoning ◽  
Thinking Skills ◽  
Geometer's Sketchpad ◽  
School Students ◽  
Mathematics Standards ◽  
High School Geometry ◽  
School Geometry

The Common Core State Mathematics Standards (CCSSM) recommend that technology should be integrated into teaching and learning Mathematics. This chapter addresses how the Geometer’s Sketchpad computer program can support students’ thinking skills and learning outcomes in a high school geometry class, in particular for more effectively addressing the High School Geometry Standards (CCSSM: G.CO.10, G.CO. 11, and G.CO. 12). The findings from the study presented in this chapter indicate that this tool can help high school students increase their learning of geometry in terms of inductive reasoning and conceptual knowledge, but may not help improve students’ motivation to learn geometry.

Families Ask: Geometry: More than Just Shapes

2006 ◽  
Vol 12 (2) ◽  
pp. 100-101
Author(s):  
David Allen
Keyword(s):  
High School ◽  
Elementary School ◽  
High School Students ◽  
School Experiences ◽  
Complex Relationship ◽  
Abstract Reasoning ◽  
Thought Processes ◽  
School Students ◽  
High School Geometry ◽  
School Geometry

Think back to the geometry you experienced as an elementary school student. Now recall a problem from high school geometry. Often, geometry tasks at the younger grades are limited to identifying shapes or labeling properties; in high school, students are expected to use abstract reasoning to prove a complex relationship. Instruction in geometry has traditionally been overlooked during middle school, which causes a gap between elementary school experiences and the thought processes required in high school.

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.

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