Abstract
The purpose of this study was to investigate two of Piaget's projective spatial groupings and to study their relationship to concepts involving phases of the moon for college astronomy students. Other topics investigated were gender-related differences in task performance and the relationship between task performance and rank or grade in the astronomy course.
One hundred subjects enrolled in a one-semester introductory astronomy core course were individually interviewed and given six tasks. The tasks were: (1) Mountains (IGP(,4)), coordination of perspectives; (2) Mountains and Stars, coordination of outside-in and inside-out points of view; (3) Tilt of Cone and Rings (IGP(,8)), coordination of views of an object undergoing plane rotations; (4) Person-Centered Phases of the Moon, dealing with lunar phases from the observer's own viewpoint; (5) Earth-Centered Model Phases of the Moon, using a model to deal with phases from the viewpoint of an Earth-observer; and (6) Top-On Drawing Phases of the Moon, using a two-dimensional top-view drawing of the Earth-Sun-Moon system.
A modified scalogram analysis (Chilton, 1966) indicated that five of the tasks scaled in increasing difficulty. The sixth task could not be included in the scalogram as too few subjects passed it. Since it had the lowest proportion of passing scores, it was combined with the other data to give the following order from least to most difficult; Mountains (IGP(,4)), Tilt of Cone and Rings (IGP(,8)), Mountains and Stars, Person-Centered Phases of the Moon, Earth-Centered Model Phases of the Moon, and Top-On Drawing Phases of the Moon. It was concluded that the mental structures for IGP(,4) and IGP(,8) were necessary but not sufficient for dealing with problems about phases of the moon.
Chi square tests for two independent samples were used to test for gender-related differences in performance on task subscores for each task. No significant differences was found for any task.
Kruskal-Wallis tests were done to investigate the relationship between task subscores and grade in the astronomy course. No relationship was found for the five most difficult tasks. There was a relationship for the Mountains task, contributed by the ""A"" students who all scored at the highest level on the task. Chi square tests showed no significant difference in task performance for any task between science oriented students (who had completed 20 semester hours or more of math and science courses) and non-science oriented students enrolled in the astronomy course.
Several educational implications were drawn from this research. First, the majority of students enrolled in the general-education astronomy course could not use the mental structures for projective space. Seventy-three percent performed at the highest level on the Mountains task, while only 35 percent could successfully complete the Tilt of Cone and Rings task. Only 12 percent could use a top-on drawing similar to that presented in most textbooks to predict and explain lunar phases for several different lunar positions. This material had previously been presented in the astronomy course. Many concepts presented in astronomy courses require the use of projective spatial relationships, and the assumption that college students have and can use the appropriate mental structures is not justified. As a result, many of the teaching materials and classroom presentations may be inappropriate for these students. The results of this study can be used as a basis to design activities for high school and college astronomy classrooms to provide more appropriate opportunities for enhancing the development of spatial mental structures.
