The Effect of Assignments for Field-dependent/independent Students in Teaching Mathematics by Distance Education Paper Presented at AARE Annual Conference 1991 Surfers Paradise, Queensland November 26-30 Sakorn Boondao Glenn Rowley Abstract The purpose of this study was to investigate the effects of assignments for submission in teaching mathematics for field-dependent and field- independent students in distance education. Five hundred and thirty-three students from three provinces in the Central region of Thailand enrolled in a `Mathematics for Social Science' course, in the second semester of 1989, at Sukhothai Thammathirat Open University were chosen to participate in the experiment. A pre-test and the Group Embedded Figures Test (GEFT) were administered. The GEFT was also administered after the final examination. From the results of GEFT, there were respectively 86 and 82 field-dependent and field-independent students in the experimental group and 82 each in the control group. The groups were divided geographically. Both field-dependent and field-independent students in the experimental group received four sets of assignments for submission but those in the control did not. After the last assignment and before the final examination, the students in both groups completed a questionnaire. The findings revealed that assignments for submission positively affected field-dependent students' achievements. Field-dependent students who submitted assignments performed significantly better than those who did not. This was not true for field-independent students. It is argued that the characteristics of field-dependent students are most suited to the use of assignments for submission, especially those who study via distance education. INTRODUCTION The nature of distance education necessarily involves separation between students and institution. Students obtain knowledge from printed materials and some supportive assistance aids. They, mainly study individually. Thompson and Knox (1987) suggested that this mode of instruction may not be equally suited to all people. Therefore, cognitive style (field-dependence and field-independence) (Witkin et al, 1977) is introduced as a variable in this study. The characteristics of field-dependent and field-independent people are identifiable. Field-dependent people appear to employ external referents to define needs and standards, and have difficulty in maintaining their own direction. They tend to rely on others for guidance and direction. In contrast, field-independent people appear to be less influenced by authority figures and external standards, and instead are guided by their own needs and values. Field-independent people have been found to learn more than field-dependent people under conditions of intrinsic motivation. Such differences in learning may disappear when external rewards for learning are introduced (Witkin et al, 1977). In terms of the field of study, field-dependent and field-independent people are interested in different subjects. Witkin et al reported that more field-independent students like mathematics and science, while more field-dependent students are interested in social science. Mrosla (1983) studied the differences between field-dependent and field-independent cognitive styles of low and high achieving mathematics students. She found that low achieving mathematics students were more field-dependent than high achieving mathematics students. Van Blerkom (1986) revealed that field- dependence affected mathematics achievement by influencing the number of courses taken by students while in high school and college. Field-dependent persons undertook less mathematics courses than field-independent persons did. This means that the cognitive styles of field-dependence and field- independence impinge indirectly upon mathematical achievement. Overall, field-independent people tend to be more independent and autonomous, whereas field-dependent people appear to have a greater need for the provision of structure and reinforcement. Field-dependent people are associated with a preference for being with other people, whereas field-independent persons tend to have more impersonal orientation. They may need more explicit instruction in problem-solving strategies or more exact definition of performance outcomes than field-independent students, who may even perform better when allowed to develop their own strategies (Witkin et al, 1977). From these characteristics of field-dependent and field-independent people, Thompson (1984) believes that field-independent persons tend to be more suited than field-dependent persons for the methods used in a distance education program. Thompson and Knox (1987) pointed out that the people who are thought to be better suited to correspondence study have been characterised as highly motivated, self-disciplined, systematic and able to work with minimum direction. They commented that the instruction by correspondence provides only limited feedback between students and tutors. They found that although some institutions provide assignments for submission, the time between students handing in assignments and receipt of the feedback from the tutor tended to stretch from two weeks or more. They suggested that institutions of distance education should consider the cognitive styles of field-dependence and field-independence as variables to be taken into account in the design and delivery of instruction. It is found that distance education is less suitable for field-dependent students. Mathematics is seemed to a difficult subject to most of field- dependent students. To help them cover their disadvantages, assignments for submission were introduced for this study. This is because Sukhothai Thammathirat Open University (STOU for short) does not provide assignments for students, except for practical courses. And studying mathematics without or with a little help might not be enough for field-dependent people. METHOD The purpose of this study was to investigate the effects of assignments for submission in teaching mathematics for field-dependent and field- independent students in distance education. A quasi-experimental, Pretest-Postest, Non-equivalent control group design was used. This allowed the extent of group similarity to be checked and the pre-test score was able to be used for statistical control. Subjects Students who enrolled in a `Mathematics for Social Science' course for the second semester of 1989 (16th December 1989 to 30th April 1990) are those who lived in Bangkok and nearby, Samut Prakan and Nontaburi provinces, were the sample group. There were 533 students in these areas whose names were drawn from the computer. Instrumentation Pre-test The pre-test consisted of 30 multiple-choice questions on basic mathematics topics from years nine to eleven, that were required in the `Mathematics for Social Science' course. It required one hour to do the test. The reliability coefficient of the pre-test was found to be .70 (Cronbach's coefficient alpha). Group Embedded Figures Test (GEFT)This was a non-verbal speed test published by Witkin et al (1971). It is a test of students' ability to find a single form where it is hidden within a complex pattern. The GEFT contains three sections: the First Section, which contains seven very simple items intended to provide practice. The Second and Third Sections, each of which contains nine more difficult items. Time limits of two minutes for the first section and five minutes for each of the second and the third sections are set. The reliability coefficient of the GEFT for the second section was found to be .85, and for the third section was found to be .87 (Cronbach's coefficient alpha). Assignments for submissionFour assignments were set; the first assignment was based on the first three units of the course, the remaining twelve units of the course were divided equally between the second, third and fourth assignments. The first assignment covered only three units. This was to make it a little easier and encourage students to complete it. Kilroy (1986, p.68) suggested that `... if we can encourage more students to start, and subsequently attend to the first assignment with great attention, you will increase the completion rate.' The assignments contained many forms of questions including multiple-choice items, fill-in-the-blanks, questions with written answers, completion of diagrams, and true-false questions. The questions were based on the contents and the objectives of the course. For some items, hints or formulae were provided as a series of study aids to motivate students throughout their studies as suggested by Kilroy (1986). The number of items on each assignment varied with the content. Questionnaire The questionnaire was developed with the aim of surveying the characteristics of students who enrolled in the course, their reasons for enrolling at STOU, their attitudes to mathematics and to distance education, their perceptions of and their methods of study, in the mathematics for Social Science course. The questionnaire contained 73 items. The question types used included four and five point scales, fill-in-the-blanks, and multiple-choice items. The last item was open-ended to allow students to make suggestions and comments. Final examination questionsThere were 60 multiple-choice questions written by a team appointed by the university. Three hours were required to complete the examination. The reliability coefficient of the final examination was found to be .78 (Cronbach's coefficient alpha). Variables The variables in this study are: Independent variables:Groups (experimental and control) Cognitive style (field-dependence and field- independence) Dependent variable: Achievement scores on final examination. Procedures The students were divided into two groups, experimental and control. Students who lived in Bangkok, West and North, and Nontaburi province were in the experimental group (259). Those who lived in Bangkok, South and East, and Samut Prakan represented the control group (274). Even though they were not perfectly matched, the selection of geographical areas was the most suitable means of dividing the two groups, given the need to avoid direct contact between the experimental and the control groups. Non- equivalent groups might be a threat to the internal validity of the experiment. In order to ensure the equivalence of the two groups of students for field-dependent and field-independent students, a pre-test was used to provide statistical control for initial differences between them. Students were invited to take the pre-test and GEFT at a local centre that was specified in an invitation letter. A message was also broadcast on television during peak viewing hours a week before the tests. The pre-test was conducted on 16th December 1989. The first two assignments with introductory letters and detailed instructions were mailed to the experimental group on 29th December 1989, and on 3rd February 1990 the remaining two assignments were mailed. The assignments were sent two at a time to avoid the cost of posting them individually, while still ensuring that possible losses in the mail were unlikely to cause any student to miss out entirely. Students were requested to contact the researcher if the assignments did not arrive. Follow-up letters were subsequently sent to students who did not submit assignments. Students also received, with the marked assignments, a circular reminding them to submit the next assignment. The marking of assignments was carried out by the researcher. Emphasis was placed on encouraging students to complete the course. Assignments were all marked and mailed back to students within two to four days of receipt by the researcher. Allowing two days in the post each way this gave a normal turn-around time of six to eight days. It was recommended that the turn- around time should not be more than a week (Rekkedal, 1973), or that a total turn-around time of less than 14 days should be the norm (Northcott and Thompson, 1987). The questionnaire was sent to students in both groups on 3rd April with a request for it to be returned by 18th April. Three follow-up letters were sent sequentially. An extra questionnaire was attached with the second letter in case the first one was lost. During the tutorial sessions, the tutors also asked students to submit assignments and return the questionnaires. The final examination was conducted on 28th April. The GEFT was also administered immediately after the final examination session to those who did not do it at the beginning of the semester. The participation rates of the two groups for the assignments, pre-test, GEFT, questionnaire and final exam are shown in Table 1. Table 1 Participation rates for the assignments, pre-test, GEFT, questionnaires and final exam. 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� Groups Pre- GEFT Assignments Question- Final test 컴컴컴컴컴컴컴컴� naires exam 1 2 3 4 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� Expt (259)17% 68% 43% 36% 23% 15% 76% 65% Ctrl (274)20% 64% 84% 62% 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� From Table 1, the assignment return rate was quite low since the assignments set could not form part of the students' course assessment grade. It was anticipated that there might well be some reluctance to participate on a purely voluntary basis. It was the first time that students had been given assignments to do. The idea was unfamiliar to them. Ten students submitted assignments but did not give their names or identity numbers, making it impossible to return the assignments or to include them in the experiment. Some students completed assignments but did not submit them because they were past the due date. No statistical data is available from these students. Also seven assignments did not reach the students because of changes of address or being lost in the mail. Five students had re-enrolled in the course in anticipation of failing the exam from the previous semester. On receiving their results those who passed withdrew their enrolments. These situations were reported to the researcher by students in conversation and by mail. This progressive decline in assignment submission was subsequently reflected in an attendance rate of approximately two thirds of the enrolled students at the course examination. There were a number of reasons for the poor attendance at the examination. Firstly, in the second semester many students of this program enrolled in both the Mathematics for Social Science course and the Accounting course. The examination schedules for these two courses overlapped. Many students regarded the Accounting course as the easier of the two and put off the Mathematics exam. Secondly, the system allows students who miss an exam to sit a make up paper four months later. Finally, many of the students also work full time making it quite difficult to find the time for the three courses that they would normally enrol in. This was another major reason for putting off their study in the Mathematics for Social Science course. from many studies reported that adult students give time-related reasons for discontinuing their studies. They dropped subjects because of their work commitments and/or timetabling problems. From the GEFT results, students were grouped into field-dependent and field-independent, according to their scores in relation to the median. Witkin et al (1977) found that males and females did not perform equally on the speed test. Males usually received higher scores than females. In this study, males and females were classified according to their respective GEFT medians. Students who scored above the median for their gender were classed as field-independent and those below the median as field-dependent. The median for males and females were 12 and 10 respectively. Therefore, field- independent students are - males who received scores higher than or equal to 13 and females who received scores higher than or equal to 11. Field- dependent students are - males whose scores are equal to or lower than 11, and females whose scores are equal to or lower than 9. Students (male or female) whose GEFT score was exactly on the median for the gender were excluded from the analyses. There were 89 and 82 field-dependent and field- independent students, respectively in the experimental group, and 82 each in the control group. HYPOTHESES The null hypotheses related to the main variables can be expressed as follows. 1 There are no differences between the mean achievements of field- dependent and field-independent students in the two groups. 2 Within the experimental group, there are no differences between the mean achievements of field-dependent and field-independent students who submitted assignments and those who did not. RESULTS The Statistical Package for Social Science (SPSS-X) was used to compute the data. Analyses of variance, means and standard deviations, and the chi- squared test were used to analyses tha data. Demographic characteristics of field-dependent and field-independent students within the experimental and the control groups were compared. The chi-squared test was used to test the difference. In general, field- dependent and field-independent students within the groups had similar backgrounds. One out of the 15 variables showed a significant difference. Within the experimental group, a significant difference was found between the wages of field-dependent and field-independent students. The latter tended to receive higher incomes than the former. This did not apply to the control group. Within the control group, field-independent students had significantly stronger mathematical backgrounds than field-dependent students, but this was not true of the experimental group. Achievement comparison The final examination was analysed by The Office of Registration, Records, and Evaluation, STOU, who reported that there were 986 students throughout the country who attended the final examination. The range of scores were from 0 to 52 from a possible 59 points. The population mean was 21.07 and standard deviation was 7.12. Analysis of variance was employed to assess the significance of differences in the mean achievements of field-dependent and field-independent students between the experimental and the control groups. Note that the experimental group consisted not only of students who submitted, but also students who failed to submit assignments. These analyses are summarised in Table 2. Table 2 Comparison between the experimental and control groups on students' achievements for field-dependent and field- independent students. 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Variables Experimental group Control group 컴컴컴컴컴컴� 컴컴컴컴컴� Mean SD N Mean SD N F p 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� Pre-test Field-dependent 11.524.67425 10.143.31928 1.555 .218 Field-independent 14.055.41119 13.003.45021 .549.463 Final Examination Field-dependent 21.327.20878 19.496.10972 2.804.096 Field-independent 23.077.73168 21.747.57062 .981.324 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Table 2 shows no significant differences between the experimental and the control groups on the pre-test or the final examination for field-dependent or field-independent students. Although no significant differences are in existence, field-dependent students in the experimental group performed slightly better than those in the control group. As mentioned above, the experimental group included not only students who submitted, but also those who failed to submit assignments, this might affect the indifferent outcome between the experimental and control groups. And the number of students who attended the pre-test was very small, about a third less than those who attended the final examination. Within the experimental group, the results of students of both cognitive styles who submitted assignments (one or more), and those who did not, were compared. Analysis of variance was used to test differences for statistical significance. The data are summarised in Table 3. Table 3 Comparison of students' achievements within the experimental group of those who submitted and those did not submit assignments for field-dependent and field-independent students. 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Variables Submitted Assignments 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� Yes No 컴컴컴컴컴� 컴컴컴컴컴� Mean SD N Mean SD N F p 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Pre-test Field-dependent12.174.52818 9.864.981 7 1.243 .276 Field-independent13.144.81814 16.606.731 5 1.550 .230 Final examination Field-dependent22.476.46955 18.578.24023 5.014 .028 Field-independent24.407.39035 21.677.94833 2.160 .146 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 The data in Table 3 indicated that no significant differences were found in the mean achievements on the pre-test for field-dependent or field- independent students within the experimental group between students who submitted assignments (one or more) and those who did not. Note that the number of students who did the pre-test was very small. In general, the mean scores on the final examination for field-dependent or field- independent students who submitted assignments were higher than the scores of those who did not, but the difference was statistically significant for field-dependent students only. This tendency indicates that the submission of assignments positively affects the outcome. Achievement of students in the experimental group who submitted one or more assignments and those in the control group were compared for both field- dependent and field-independent students. Analysis of variance was used to test the differences for statistical significance. The results are shown in Table 4. Table 4 Comparison of students' achievements between those within the experimental group who submitted assignments and those in the control group for field-dependent and field-independent students. 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Variables df F Probability 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Pre-test field-dependent 1,44 3.057 .087 field-independent 1,33 .010 .919 Final examination field-dependent 1,125 7.081 .009 field-independent 1,95 2.805 .097 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Table 4 shows no significant differences on the pre-test for field- dependent or field-independent students between the results of the two groups. A significant difference exists for field-dependent students (p=.009), but not for field-independent students (p=.097) between those in the experimental group who submitted assignments and those in the control group on the final examination. However, the results indicate an effect in the same direction. Achievements of field-dependent or field-independent students who submitted at least one assignment tend to be higher than those in the control group who were not provided with any assignments, (also see Tables 2 and 3). Achievements for field-dependent and field-independent students in the experimental group who did not submit assignments and those in the control group were compared. Analysis of variance was conducted to test the differences for statistical significance. The results are presented in Table 5. Table 5 Comparison of students' achievements between students in the experimental group who did not submit assignments and students in the control group for both field-dependent and field- independent students. 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Variables df F Probability 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Pre-test field-dependent 1,33 .034 .855 field-independent 1,24 2.996 .096 Final examination field-dependent 1,93 .332 .566 filed-independent 1,93 .002 .964 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Table 5 shows no significant differences in students' achievements between the experimental and the control groups. Note that the number of students who did not submit assignments in the experimental group is very low, when compared to those in the control group. It indicates that field-dependent and field-independent students in the experimental group who received assignments but did not submit them, gained similar results to those in the control group who did not receive any assignments. DISCUSSION The findings in this study showed that assignments influenced field- dependent students' achievements. Field-dependent students who submitted assignments (one or more) performed significantly better than those who did not. This does not apply to field-independent students, but the results are in the same direction. There were no significant differences in mean scores of field-dependent and field-independent students between those in the experimental group who did not submit assignments, and those in the control group. This corresponds to Witkin et al (1977) who stated that field- dependent students preferred the method which enabled them to associate with people and rely on the others' guidance and direction. They learn better when external rewards for learning are introduced. They achieve higher marks when they have extra guidance (Witkin et al, 1977). Therefore, it can be concluded that assignments for submission affect field-dependent students. Assignment for submissions are suited to field-dependent students, because of their characteristics. That is, firstly, the questions from assignments can direct them to follow the course's objectives. Students are enabled to control their progress (Baath, 1980, 1976; Holmberg, 1989; and Khan, 1987). Secondly, the close communication with their tutor can reduce their feeling of isolation, because the tutor contributes personal encouragement and gives them warmth and confidence. The motivation gained from the tutor is a major benefit from the interaction (Anand, 1979; Ganor, 1988; Siaciwena, 1989). Thirdly, the comments from the tutor can give the guidance enabling them to review the lessons. If their answers were wrong, the comments from a tutor will indicate what they misunderstood. If their answers were right, the comments will boost their confidence (Kilroy, 1986). These benefits are matched to field-dependent students who studying at a distance. It is suggested that the University should take account the cognitive style of learning and teaching in the preparation of course materials. This will enable disadvantaged students the opportunity to optimise their knowledge and learning capacity. REFERENCES Anand, Satayapal (1979). University without walls: Correspondence Education in India. New Delhi: Vikas Publishing House PVT. Baath, J. A. (1980). Postal Two-Way Communication in Correspondence Education an Empirical Investigation. (Report No. ISBN 91-23-92305- 9). (ERIC document Reproduction Service No. ED 224 466). Baath, J. A. (1976). Postal Contacts and Some Other Means of Two-way Communication: Practice and Opinions at a Number of European Correspondence Schools. (Pedagogical Report, No.5), University of Lund, Department of Education. Ganor, Margalit. (1988). Assignment construction and evaluation in distance education in Sewart, David & Daniel, John S. (eds.), Developing Distance Education Paper Submitted to the 14th World Conference in Oslo 9-16 August, 207-210. Holmberg, Borje. (1989). Theory and Practice of Distance Education. London: Routledge. Khan, Ahmed Noor. (1987). Student Assignment: A Vital Component Of Continuous Assessment In Distance Education Pakistan Journal of Distance Education, 4(2), v-vi. Kilroy, Charles. (1986). The Significance of the First Assignment. Epistolodidaktika, 1, 66-77. Mrosla, Helen Pauline. (1983). Differences Between Field-Dependent/Field- Independent Cognitive Styles of Low and High Achieving Mathematics Students, (Doctoral dissertation, University of North Texas, 1983). Dissertation Abstracts International, 44, 2397. Northcott, P. H. & Thompson, D. J. (1987). Assignment Turn-around time: What Should Be expected? How Can Be Achieved? (Project File No. 87/51): Victoria: Deakin University, Distance Education Unit. Rekkedal, Torstein. (1973). The written Assignments in Correspondence Education Effect of Reducing Turn-Around Times. Distance Education, 4(2), 252-231. Siaciwena, Richard M. C. (1989). An Evaluation of Tutor Marked Assignments at The University of Zambia. Research in Distance Education, 1(3), 4- 8. Thompson, Gordon. (1984). The cognitive style of field-dependence as an explanatory construct in distance education Drop-out. Distance Education, 5(2), 286-293. Thompsons, Gordon & Knox, Alan B. (1987). Designing for Diversity: Are Field-Dependent Learners Less Suited to Distance Education Programs of Instruction? Contemporary Educational Psychology, 12, 17-29. Van Blerkom, Malcolm L. (1986). Mathematical Ability in College Students: A Causal Analysis. (Paper presented at the Annual Convention of the American Psychological Association). (ERIC document Reproduction Service No. 268 473) Witkin, H. A., Moore, C. A., Goodenough, D. R. & Cox, P. W. (1977). Field- Dependent and Field-Independent Cognitive Styles and their Educational Implications. Review of Educational Research, 47(1), 1- 64. Witten, Colonel Vaughan. (1989). Field Dependence - Field Independence: The relationship of Cognitive Style and Academic Achievement (Witkin) (Doctoral dissertation, North Carolina State University, 1989). Dissertation Abstracts International, 50, 3194.