Die voorkoms van interferensie by die leer van wiskundige leerstof
Abstract
The aim of the investigation was to show that interference occurs in learning mathematics and that it results in forgetting mathematical facts. The literature research proved that the interference theory can be
regarded as one of the most important theories of forgetting. The importance of the interference theory is emphasized by the
amount of previous research done in this field. This research proved the following:
(a) Various factors in both the teaching and learning situations can possibly cause interference. (b) Oivergent viewpoints exist as to whether interference is present or not in learning meaningful material. (c) Interference can possibly occur in mathematics as a result of the way in which units in the subject-matter show a similarity. Choice of subject-matter: The nature of the subject content of mathematics led to the deducing of five hypotheses. To test these
hypotheses various units of learning material in mathematics were selected. It is possible that mathematical subject-matter of which the concepts are different, may run logically parallel. As an example of this the geometric and arithmetic sequences were chosen. The logic of the original and interpolated subject-matter may be different while the concepts could be similar or identical. Although many examples exist, a geometric theorem and the converse of the theorem were used in this investigation. Because of the hierarchical structure of mathematics it is possible that the interpolated subject-matter may include the original subjectmatter. The subject-matter chosen for this particular case was the arithmetic sequence as original subject-matter, and the arithmetic series as interpolated subject-matter. Choice of subjects: One hundred and fifty two standard 8 pupils were divided at random into 10 groups: 5 experimental groups and
5 control groups. Teaching and testing: The tests were compiled by the researcher.
The researcher personally taught and tested the material. An attempt was made throughout to keep other factors that might influence interference, constant. Procedure: The original subject-matter was taught in a period of 40 minutes. After a rest-period of 5 minutes an evaluation test was written within 15 minutes. The interpolated material was then taught and tested in the same way. In the cases where the original and the
interpolated material were not presented, the group followed the normal class-timetable. The retention tests in the case of the retro-active paradigms were done 2 hours after the original material was taught. In the case of the pro-active paradigms the retention tests of the interpolated material were done one hour after presentation. Data: The data of the retention tests were analysed by means of the t-test for two sets of independent data. The results of the investigation show the following; (a) In the case where different units of subject-matter ran logically parallel, but consisted of different concepts, no interference could be shown. There is, however, evidence of retro-active facilitation. (b) Where the original and the interpolated subject-matter were logically different, but the concepts therein similar or identical, it was shown that pro-active interference resulted. (c) The results showed that retro-active interference occurs where the interpolated subject-matter included the original subject matter. In the case where different units of the subject-matter logically ran parallel but consisted of different concepts,no interference occurred,
but retro-active facilitation did. Thus,after the original subject matter is taught, examples in which similar logic is applied,should be given to the pupil to reinforce the original learning. Where concepts in the original and the interpolated subject-matter were similar or identical, pro-active interference resulted. From the above-mentioned it can be deduced that: (a) A clear distinction must be made between mathematical concepts and the associated logic to prevent possible interference. (b) To prevent pro-active interference, subject-matter that may lead to interference must be taught as original subject-matter or else
the interpolated subject-matter must be taught at a higher level. Retro-active interference occurred where the interpolated subject matter included the original subject-matter. Thus, pupils must be
made aware of the presence of the original subject-matter in the interpolated subject-matter while the interpolated subject-matter is being taught.
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