A comparison of two techniques of teaching selected geometry concepts through construction

The problem posed'in this study was to investigate two methods used to teach selected elementary geometric concepts through construction. One way, called the traditional method, used the straightedge and compass in making the constructions. The other method, called the paperfolding method, used the technique of folding creases in paper to make the construction. The basic underlying problem considered in the paper was whether or not an alternative to the traditional construction method could be used as an effective teaching vehicle in introducing some basic elementary geometry concepts to high school students with no previous experience with a high school geometry course. This alternative technique was called paperfolding.

The experimental study involved two classes of tenth grade Algebra I, part II students, each consisting of twenty students having relatively the Same DIQ scores on the OTIS LESSON MENTAL ABILITY TEST, a nationally standardized mental aptitude test. All the students in this course had the exact same previous mathematical courses, therefore their mathematics background was relatively the same.

A series of six lesson plans was prepared for the experimental group which emphasized making the constructions by folding paper. A separate series of lesson plans was prepared for the control group which emphasized making the constructions by using straightedge and compass. Both sets of lesson plans were similarly designed and written in order that the same material be covered in six consecutive school days, each lesson taking a fifty-minute time period. The researcher taught the lesson plans to the experimental group and another teacher in the same mathematics department as the researcher taught the control lesson plans to the control group.

Before and after the actual teaching of the lesson plans, both groups were given a test to obtain pretest and posttest scores which would be used in analyzing the data. The test was used for the pretest and the posttest. It was designed and validated by Ben H. Cheatham, Jr. under the direction of K. P. Kidd, D. E. Small, B. K. Plunkett, and E. J. Davis, a panel of mathematics educators and professors at the University of Florida.

When the teaching of the lessons and the testing was finished, the researcher had a pretest score, an Iq score, and a posttest score to use in analyzing the data. An analysis of covariance was used on the data in an attempt to determine if the paperfolding teaching technique of constructions resulted in more effective gains for students than the technique emphasizing the use of straightedge and compass.

When the analysis of covariance was completed, no significant difference was found to exist between the experimental and the control groups using pretest and Iq scores as a covariate. However, the mean score on the posttest was slightly higher for the experimental group than the control group even though the control group had a higher mean IQ score and a higher mean pretest score. A possible solution to this higher score could have been the result of the teaching techniques, the differences in attitudes of students, and/or the differences in the teacher's experience of teaching geometry.