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A study of the effects of computer assisted instruction on the teaching and learning of transformation geometry
Author
Ho, Cathleen Sze Yin
Supervisor
Cheung, John
Abstract
This study aims to investigate the effectiveness of supplementary CAI and Traditional Expository Approach (TEA) in terms of the achievement and attitude of lower ability secondary four students in Singapore. The students' response to the computer program was also investigated.
Methodology
Seventy students from the Normal Academic stream of Fairfield Methodist Secondary School in Singapore participated in the study. Two intact classes were randomly selected from the secondary four level. One was randomly assigned as the experimental CAI group and the other as the control TEA group. Both groups were taught by the same teacher for the same duration of time on transformation geometry. The same classroom instructions, practice exercises and home assignments were given. Both groups consisted of similar distribution of male and female students. Having male and female students in each group would be a more accurate simulation of the actual classroom environment as the majority of schools in Singapore is co-educational.
For the CAI group, a transformation geometry computer program was chosen to meet the objectives of the study. Worksheets were designed to supplement the software and the students worked in pairs. All the students had undergone computer awareness lessons prior to the study which would help to novelty effect of the computer usage.
For the TEA group, the computer usage time of the CAI group was replaced by lessons in the classroom with the same specific instructional objectives. Worksheets were also designed to match those designed for the CAI group with the same examples, drill questions and practice exercises.
As pretests to the treatments, the two groups of students were asked to take a Secondary Mathematics Achievement Test (SMAT) and respond to the Mathematics Attitude Inventory (MAI) which helped to examine if the two groups were comparable in terms of achievement and attitude toward mathematics.
The treatments spanned a total of 10 hour, divided onto 20 thirty-minute periods, in March and April 1994. At the end of the treatments, a 40-item objective Transformation Geometry Achievement Test (TGAT) was administered to both groups.They also responded to a transformation Geometry Attitude Inventory (TGAI) and the Mathematics Attitude Inventory for a second time (MA2). These were meant to determine the extent of the effects of the treatments to the achievements and attitude of the students. The CAI group was also asked to respond to a survey on the use of the computer program (COMP). Two weeks after these posttests were administered, a Retention Test (RET) was administered to both groups. This test consisted of all the items from the Transformation Geometry Achievement Test arranged in a different order.
The univariate t-tests were conducted for the data collected. The t-test for independent samples were used to compare the pre- and post-test group means between the experimental and control groups. The group means were from the SMAT, MA1, TGAT, TGAI, MA2 and RET and the gain scores from MA1 to MA2 and the gain scores from TGAT to RET. Specifically for the TGAT and RET, the group means in terms of the different types of geometric transformations taught (5 scales) and the cognitive levels of 'recall','understanding' and 'thinking' (3 scales) between the two groups were analyzed. For the MA1 and MA2, the data were also analyzed in terms of the six subscales of the inventory.
The t-tests for dependent samples were used to examine the effects of the treatment within each of the two groups of students. The pairs of group means compared within each group were: MA1 and MA2, TGAT and RET.
Major Findings
The CAI group appeared to have achieved better scores in TGAT compared to the TEA group. i.e. there was better mathematics achievement in transformation geometry. With closer analysis, the CAI group outperformed the TEA group in terms of translation and reflection. The visual capabilities of the computer program probably reinforced the vector movement of translation and the flipping effect of the reflection. when the achievement scores were examined according to the cognitive level of the test items, there was better geometric transformation achievement in terms of the understanding and thinking levels of cognition, but not the recall level. It is possible that the program engendered more intuitive reasoning and therefore greater understanding, where the students are able to apply the mathematical knowledge more widely.
There was no significant difference in the students' achievement scores in the retention test. This might be due to the considerable increase in the TGAT scores for the CAI group. Any further increase in scores of the retention test for the CAI group is therefore restricted.
There was a significant improvement in the attitude of the CAI group toward mathematics. It was particularly significant for the `Self-concept in mathematics' subscale of the attitude inventory used. No significant differences were found for the TEA group. Hence, we could conclude that the CAI treatment has a positive effect on the attitude of students toward mathematics especially in terms of their self-concept in mathematics.
A significant difference in the attitude toward Transformation Geometry, in favour of the CAI group, was found. The use of the CAI mode of instruction appeared to have promoted a more positive attitude toward Transformation Geometry among the students.
There was no significant difference between the transformation geometric achievement within the CAI group when their TGAT and RET scores were compared. Again, it confirmed that the higher achievement scores achieved for the CAI group for the TGAT caused the results of this comparison to be restricted. For the TEA group, no significant differences were found except for the items that were classified `combination of transformations'.
There was no significant difference for gain scores from TGAT to RET between the two groups, in terms of all types of transformation and level of cognition.
Within the CAI group, significant difference in the attitude toward mathematics before and after the treatment (from MA1 to MA2) was found. Specifically, the difference for the subscale `Perceptions in Mathematics' was significant. There was no significant difference in attitude toward mathematics before or after treatment within the TEA group.
Gain scores from MA1 to MA2 showed significant difference in the attitude toward mathematics in favour of the CAI group. Further analysis showed that the difference was significant for the CAI group in the subscales: `attribution of success and failure', `motivation in mathematics' and `self-concept in mathematics'. That is, the CAI group showed a greater improvement in their attitude toward mathematics than the TEA group.
The mean score of the survey on the use of the Computer Program (COMP) indicated that the students generally enjoyed the use of this program to explore transformation geometry. The students found the instructions for using the problem easy to follow and were motivated to use the program.
For the qualitative data collection, all the students from both the experimental and control groups were ranked separately into lists according to their score for TGAT, RET, MA1, MA2 and TGAI. They were also ranked according to the increase or decrease in score from TGAT to RET, and from MA1 and MA2. Three students who scored the highest, and three students who scored the lowest for each list were selected for interview by the researcher.
The qualitative data collection revealed that the computer was useful in helping the students visualize the transformations better, especially reflection, and the rotation component of the program needs improvement. Most of the students seemed to find these worksheets easy to follow and was able to work on them. Some students also pointed out that the program would be better if it had multimedia capabilities and was more interactive in nature.
Methodology
Seventy students from the Normal Academic stream of Fairfield Methodist Secondary School in Singapore participated in the study. Two intact classes were randomly selected from the secondary four level. One was randomly assigned as the experimental CAI group and the other as the control TEA group. Both groups were taught by the same teacher for the same duration of time on transformation geometry. The same classroom instructions, practice exercises and home assignments were given. Both groups consisted of similar distribution of male and female students. Having male and female students in each group would be a more accurate simulation of the actual classroom environment as the majority of schools in Singapore is co-educational.
For the CAI group, a transformation geometry computer program was chosen to meet the objectives of the study. Worksheets were designed to supplement the software and the students worked in pairs. All the students had undergone computer awareness lessons prior to the study which would help to novelty effect of the computer usage.
For the TEA group, the computer usage time of the CAI group was replaced by lessons in the classroom with the same specific instructional objectives. Worksheets were also designed to match those designed for the CAI group with the same examples, drill questions and practice exercises.
As pretests to the treatments, the two groups of students were asked to take a Secondary Mathematics Achievement Test (SMAT) and respond to the Mathematics Attitude Inventory (MAI) which helped to examine if the two groups were comparable in terms of achievement and attitude toward mathematics.
The treatments spanned a total of 10 hour, divided onto 20 thirty-minute periods, in March and April 1994. At the end of the treatments, a 40-item objective Transformation Geometry Achievement Test (TGAT) was administered to both groups.They also responded to a transformation Geometry Attitude Inventory (TGAI) and the Mathematics Attitude Inventory for a second time (MA2). These were meant to determine the extent of the effects of the treatments to the achievements and attitude of the students. The CAI group was also asked to respond to a survey on the use of the computer program (COMP). Two weeks after these posttests were administered, a Retention Test (RET) was administered to both groups. This test consisted of all the items from the Transformation Geometry Achievement Test arranged in a different order.
The univariate t-tests were conducted for the data collected. The t-test for independent samples were used to compare the pre- and post-test group means between the experimental and control groups. The group means were from the SMAT, MA1, TGAT, TGAI, MA2 and RET and the gain scores from MA1 to MA2 and the gain scores from TGAT to RET. Specifically for the TGAT and RET, the group means in terms of the different types of geometric transformations taught (5 scales) and the cognitive levels of 'recall','understanding' and 'thinking' (3 scales) between the two groups were analyzed. For the MA1 and MA2, the data were also analyzed in terms of the six subscales of the inventory.
The t-tests for dependent samples were used to examine the effects of the treatment within each of the two groups of students. The pairs of group means compared within each group were: MA1 and MA2, TGAT and RET.
Major Findings
The CAI group appeared to have achieved better scores in TGAT compared to the TEA group. i.e. there was better mathematics achievement in transformation geometry. With closer analysis, the CAI group outperformed the TEA group in terms of translation and reflection. The visual capabilities of the computer program probably reinforced the vector movement of translation and the flipping effect of the reflection. when the achievement scores were examined according to the cognitive level of the test items, there was better geometric transformation achievement in terms of the understanding and thinking levels of cognition, but not the recall level. It is possible that the program engendered more intuitive reasoning and therefore greater understanding, where the students are able to apply the mathematical knowledge more widely.
There was no significant difference in the students' achievement scores in the retention test. This might be due to the considerable increase in the TGAT scores for the CAI group. Any further increase in scores of the retention test for the CAI group is therefore restricted.
There was a significant improvement in the attitude of the CAI group toward mathematics. It was particularly significant for the `Self-concept in mathematics' subscale of the attitude inventory used. No significant differences were found for the TEA group. Hence, we could conclude that the CAI treatment has a positive effect on the attitude of students toward mathematics especially in terms of their self-concept in mathematics.
A significant difference in the attitude toward Transformation Geometry, in favour of the CAI group, was found. The use of the CAI mode of instruction appeared to have promoted a more positive attitude toward Transformation Geometry among the students.
There was no significant difference between the transformation geometric achievement within the CAI group when their TGAT and RET scores were compared. Again, it confirmed that the higher achievement scores achieved for the CAI group for the TGAT caused the results of this comparison to be restricted. For the TEA group, no significant differences were found except for the items that were classified `combination of transformations'.
There was no significant difference for gain scores from TGAT to RET between the two groups, in terms of all types of transformation and level of cognition.
Within the CAI group, significant difference in the attitude toward mathematics before and after the treatment (from MA1 to MA2) was found. Specifically, the difference for the subscale `Perceptions in Mathematics' was significant. There was no significant difference in attitude toward mathematics before or after treatment within the TEA group.
Gain scores from MA1 to MA2 showed significant difference in the attitude toward mathematics in favour of the CAI group. Further analysis showed that the difference was significant for the CAI group in the subscales: `attribution of success and failure', `motivation in mathematics' and `self-concept in mathematics'. That is, the CAI group showed a greater improvement in their attitude toward mathematics than the TEA group.
The mean score of the survey on the use of the Computer Program (COMP) indicated that the students generally enjoyed the use of this program to explore transformation geometry. The students found the instructions for using the problem easy to follow and were motivated to use the program.
For the qualitative data collection, all the students from both the experimental and control groups were ranked separately into lists according to their score for TGAT, RET, MA1, MA2 and TGAI. They were also ranked according to the increase or decrease in score from TGAT to RET, and from MA1 and MA2. Three students who scored the highest, and three students who scored the lowest for each list were selected for interview by the researcher.
The qualitative data collection revealed that the computer was useful in helping the students visualize the transformations better, especially reflection, and the rotation component of the program needs improvement. Most of the students seemed to find these worksheets easy to follow and was able to work on them. Some students also pointed out that the program would be better if it had multimedia capabilities and was more interactive in nature.
Date Issued
1997
Call Number
QA601 Ho
Date Submitted
1997