On the Issue of Students’ Independent Work in Descriptive Geometry
Abstract Generated abstract
This article examines the organization and workload of students’ independent homework in a descriptive geometry course at a technical institute. Using time studies conducted in selected student groups in the 1966/67 and 1969/70 academic years, the authors compare the time required for weekly and major graphical assignments after revisions to the assignment system. The data indicate that while weekly assignment time remained nearly unchanged, simplification and redistribution of major assignments reduced total homework time from about 39 hours to about 27 hours and lessened end-of-semester overload. The article argues that time studies can help equalize assignment variants, identify excessive graphical finishing demands, and guide further reductions in extracurricular workload without weakening the course program.
Full Text
On the Issue of Students’ Independent Work in Descriptive Geometry
B. L. Stepanov, V. A. Voskresenskii
(Presented by the scientific seminar of the departments of descriptive geometry of the Tomsk higher educational institutions)
To reinforce the material in the study of descriptive geometry, all students of the institute complete homework assignments developed by the department’s staff.
These assignments cover all sections of the course and are subdivided into weekly assignments (involving the solution of one problem) and so-called “large homework assignments,” which are completed after a definite section of the course has been covered.
Previously, each student completed 14 weekly homework assignments, and beginning with the 1969/70 academic year, 10 assignments and one lettering assignment, since drafting is not studied in the first semester. These assignments are completed on any paper of size 148×210 mm.
The three large homework assignments are completed on drawing paper of formats 12 (the 1st and 2nd assignments) and 22 (the 3rd assignment). Each weekly homework assignment, as well as the 1st and 2nd large homework assignments, has 30 variants.
In completing homework assignments in descriptive geometry, a student solves problems under one and the same number in all assignments except the third large assignment. The number of the problem is communicated to the students at the beginning of the semester. For the third assignment, 50 variants have been developed. The assignment is issued by the instructor at the time specified in the calendar plan.
All work is done in pencil, with individual positions highlighted in different colors. During the semester, two one-hour tests are also conducted.
The homework assignments are periodically reviewed and updated. Thus, before the beginning of the 1969/70 academic year, new weekly assignments were developed, as well as assignments for the third large homework assignment, and the first assignment was somewhat simplified [1, 2].
The department periodically conducts time studies of the time spent on completing homework assignments in descriptive geometry. In the 1966/67 academic year, such a time study was conducted in six groups of various faculties—one group of the mechanical faculty, one of the chemical-technological faculty, and four groups of the faculty of automatic systems. In connection with the change in assignments in the 1969/70 academic year, a time study was again conducted in seven groups (one group of the mechanical faculty, one of the electric-power faculty, one of the chemical-technological faculty, and four groups of the faculty of automation and computer engineering).
At the beginning of the academic year, the students in the groups in which time-and-motion recording was conducted were given an explanation of its significance and importance, and were assigned the task, when doing homework, of recording the time they spent solving the above-mentioned problems.
Most students conscientiously approached the assigned work. Each corresponding variant of an assignment was solved by 4 to 7 people, and in all each assignment was solved by 150–200 people. This made it possible to determine the arithmetic mean time for solving each variant of an assignment, and then the arithmetic mean time for solving the problems of each topic, thereby reducing the element of chance.
The results of the time study are presented in Tables 1 and 2.
Table 1
Time required to complete homework assignments
in descriptive geometry, in minutes
| In the 1966/67 academic year | In the 1966/67 academic year | In the 1969/70 academic year | In the 1969/70 academic year |
|---|---|---|---|
| Content of the work | Time required | Content of the work | Time required |
| Projection of points in a complex drawing and in a pictorial representation | 42 | Lettering No. 5 (Russian and Latin alphabets and numerals) | 90 |
| True length of a line segment, its inclination to the planes of projection | 42 | True length of a line segment, its inclination to the planes of projection | 40 |
| Traces of a straight line | 50 | Figures in a plane | 31 |
| Figures in a plane | 41 | Line of intersection of two planes | 49 |
| Line of intersection of two planes | 48 | Perpendicularity of lines and planes | 66 |
| Perpendicularity of lines and planes | 46 | Replacement of planes of projection | 58 |
| Replacement of planes of projection | 43 | Rotation | 59 |
| Rotation | 46 | Section of a polyhedron by a plane and construction of the development | 76 |
| Superposition | 47 | Section of a curved surface by a plane and construction of the development | 105 |
| Most advantageous projection | 51 | Intersection of a straight line with a surface | 44 |
| Section of a polyhedron by a plane and construction of the development | 65 | Intersection of surfaces (special case) | 68 |
| Section of a curved surface by a plane and construction of the development | 72 | ||
| Intersection of a straight line with a surface | 43 | ||
| Construction of the third projection from two given ones and axonometry | 62 | ||
| Total for completing weekly assignments | 11 hours 38 min. | Total for completing weekly assignments | 11 hours 26 min. |
Table 2
Time Required to Complete Major Homework Assignments
in Descriptive Geometry
| In the 1966/67 academic year | In the 1966/67 academic year | In the 1969/70 academic year | In the 1969/70 academic year |
|---|---|---|---|
| Content of the work | Time required | Content of the work | Time required |
| Construction of three projections of a faceted solid, the principal lines of the base plane, and its traces | 7 hr 50 min | Construction of three projections of a faceted solid, the principal lines of the base plane | 5 hr 10 min |
| Construction of the line of intersection of planes, of a plane parallel to one of them, and of the altitude in a polygon | 5 hr 35 min | Construction of the line of intersection of planes, of a plane parallel to one of them, and of the altitude in a polygon | 5 hr 10 min |
| Construction of the line of intersection of two solids, axonometry or developments | 14 hr | Construction of the line of intersection of two solids | 5 hr |
| Total for completing the assignments | 27 hr 25 min | Total for completing the assignments | 15 hr 20 min |
It is evident from Table 1 that in solving problems on individual topics in the 1969/70 academic year, students spent more time than in the 1966/67 academic year. This was due to the fact that more difficult problems were included in the homework assignments, similar to those whose solution had caused difficulties in examinations. The construction of developments on separate sheets at a large scale also required additional time. The total time spent on solving the weekly homework assignments was approximately the same and amounted to 11 hours 38 minutes in the 1966/67 academic year and 11 hours 26 minutes in the 1969/70 academic year.
The simplification of the first major homework assignment, and especially of the third, in which the construction of axonometry was transferred to the next semester in drawing, significantly reduced the time required for their completion (27 hours 25 minutes in the 1966/67 academic year and 15 hours 20 minutes in the 1969/70 academic year).
As the timing study showed, in all, each student spent on average 39 hours 03 minutes completing homework assignments in the 1966/67 academic year and 26 hours 46 minutes in the 1969/70 academic year. The change in the assignment made it possible to reduce the time required for its completion by approximately 30%. And since the completion of the third major homework assignment falls in the last weeks of the semester, the reduction of its labor intensity by almost a factor of three (5 hours instead of 14) reduced the overall overload of students at the end of the semester.
The distribution of time for completing the assignments by week is presented in Fig. 1. (In the 1966/67 academic year students studied for 16 weeks, and in the 1969/70 academic year for 14.) In constructing this graph, we proceed from the fact that the student completes the weekly assignment while preparing for the next practical class, and the major homework assignments in the last week before the due date, although the plan allocates three weeks for each assignment. An exception is made for the third major homework assignment in the 1966/67 academic year. One week before the due date, students bring this assignment completed in thin lines, and the following time it is fully ready, taking into account the comments made by the instructor. The time for completing it is assigned to the 15th and 16th weeks.
Fig. 1.
Despite the fact that solving problems in descriptive geometry is graphical in character, it can nevertheless be divided into two stages: in the first, the solution plan is laid out and the problem is executed with thin lines; in the second, the graphical finishing of the problem is carried out using colored pencils, the border and title block are drawn, the statement of the problem is written, etc. Although such a division is purely conditional, it is still of interest how much time is spent on carrying out each of these stages. Therefore, when solving the weekly problems, each student, in addition to the total time spent solving the problem, also indicated the time spent on its graphical finishing.
Conclusions
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The analysis carried out showed that, depending on the students’ ability to write in standard lettering, the time required for the graphical finishing of the work also changes; it ranges from 30 to 60% of the total time for solving the problems.
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Time study not only makes it possible to determine how much time a student spends on independent work in descriptive geometry, but also to compare the time required to complete different variants of the same assignment, i.e., indirectly to determine whether the different problems of one assignment are of equal difficulty and whether the students solving one or another variant are in equal conditions; and, if there is a large difference in the time, to introduce changes into the assignments, equalizing them.
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We have established that there are still possibilities for reducing the amount of time students spend on independent work in descriptive geometry. Such reserves may include:
a) reducing the amount of execution and drawing of auxiliary finishing inscriptions in title blocks by replacing the latter with rubber stamps;
b) simplification of assignments, but not to the detriment of the program being studied.
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The issues raised in the present article concerning research into the workload of students with graphic assignments in descriptive geometry are topical issues of modern methodology, at a time when the abundance of incoming scientific information in all disciplines studied compels us to seek ways of saving and reducing extracurricular time for the study of all disciplines prescribed by the curriculum.
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The beginning of such work, in our view, may serve for the further study of students’ independent work not only in descriptive geometry, but also in other subjects taught at a higher technical school.
REFERENCES
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A. Ya. Bezrukov, Z. A. Beloglazova, A. I. Glazyrina, L. S. Plotnikov, E. M. Popov, S. F. Sibirtsev, L. S. Skripov, N. I. Tikhonova, N. N. Chakhlova. Problem Book in Descriptive Geometry. Tomsk, Tomsk State University Publishing House, 1965.
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N. A. Boyarko, V. A. Voskresenskii, T. F. Gorbunova, E. V. Petrova, E. M. Popov, I. F. Selyaeva, S. G. Skobennikov, L. S. Skripov, B. L. Stepanov, N. N. Tikhonova, L. K. Trikashnaya, N. N. Chakhlova. Problem Book in Descriptive Geometry. Tomsk, Tomsk Polytechnic Institute Publishing House, 1969.