The Impact of Using Technology on Students’ Achievement, Attitude, and Anxiety in Mathematics
THE IMPACT OF USING TECHNOLOGY ON STUDENTS’ ACHIEVEMENT, ATTITUDE, AND ANXIETY IN MATHEMATICS Maxima J. Acelajado, Ph.
D. De La Salle University Manila, Philippines e-mail: [email protected] edu. ph ABSTRACT This was an experimental study designed to determine the effects of using technology, specifically graphing calculators, on students’ achievement in College Algebra, attitude, and anxiety in mathematics. The respondents of the study belonged to two intact classes consisting of 66 freshman students from the College of Science, De La Salle University, Manila, who were enrolled in College Algebra during the first term, schoolyear 2002-2003.
For purposes of this study, three groups were formed, each with 22 students – the high ability group (HAG), the average ability group (AAG), and the low ability group (LAG). Only the data gathered from the 66 students comprising the three groups were considered and analyzed in this study. The respondents were given the pretests and posttests in College Algebra, Mathematics Attitude Scale (MAS) and the Mathematics Anxiety Rating Scale (MARS). The results in each case were tested for significant difference using the t-tests for dependent and independent samples.To determine if there was any significant change in the anxiety levels of the students in each group, the McNemar’s ? 2 test was applied. Significant differences were noted in the pretest and posttest mean scores in the achievement, attitude, and anxiety of the different ability groups in favor of the high ability group.
No significant difference existed between the levels of anxiety of the three groups of students, although the use of graphing calculators was found to reduce their anxiety scores. Graphing calculators were most helpful in the study of functions and their graphs and systems of equations.Positive effects of using graphing calculators include students’ improved achievement, reduced anxiety in mathematics, increased self-confidence, and active involvement of students in the learning process. INTRODUCTION Technology plays a major role in the changes taking place in our society. It has largely contributed to almost every sector: medicine, warfare, navigation and transportation, business, economy, and even in education, particularly in science and mathematics.
In this day and age of high technology, instantaneous communication, and multimedia, our learners are exposed daily to a variety of information that comes from all parts of he globe. While a good part of this information is relevant, we cannot deny the fact that there is a need to teach young people how to process the variety of available information so that they do not pick up knowledge that may be trivial, irrelevant, misleading, or incorrect. The challenge is how to keep the learner firmly anchored on a set of human values so that he may not get lost in the sea of modern-day, borderless information that threatens to wash out the core of human integrity and dignity.As mentors, it is our moral responsibility to ensure that our learners learn how to choose from the myriad of readily available data through multimedia. To be able to do this, teachers should be flexible, creative, and innovative in the classroom so that learners become critical and creative thinkers. We can do this using interactive approaches and activities to address our foremost concern of strengthening the moral fiber of our learners through opportunities inside the classroom and within classwork that would help them acquire life skills and imbibe esteemed principles and values.
It is a fact that with the growing sophistication of people’s lifestyle, students have been unconsciously demanding for materials and gadgets. The contemporary sociocultural milieu has molded the young generation into an environment of false needs so that an individual’s capacity to grasp numerous cognitive domains seems to have diminished due to his dependence on technological devices. Although it cannot be denied that the use of technological devices facilitates learning, educators should be able to teach prudent use of such devices.So when should the teacher use technology in the classroom? Or perhaps the more important question is: Why use technology? For one, technological gadgets, like a graphing calculator for instance, cut on time that in another instance will be used for paper-and-pencil drill. Thus, there is more time for explorations, analysis, and understanding of concepts. More conservative schools of thought frown upon the use of calculators.
They argue that technological gadgets, like the calculator, unconsciously force students into technology dependence.On the other hand, there are those who believe that calculators can provide mind-expanding support which students need to investigate numerical relationships. REVIEW OF RELATED LITERATURE AND STUDIES In 1978, the National Council of Teachers of Mathematics (NCTM) openly encouraged the use of calculators in the classroom as an instructional aid and computational tool. The introduction of calculators gave mathematics educators new opportunities to help their students solve mathematical problems. Several professional conferences were held to discuss and justify the effectiveness of the calculator as a teaching and learning aid.In 1980, the NCTM Board of Directors fully supported the use of calculators in all grade levels.
Over 200 researchers in the past 20 years have found the use of calculators as a powerful teaching and learning tool at all levels of mathematics instruction. Several studies on the use of instructional technology have shown that graphing calculators help improve the students’ spatial visualization skills, critical thinking ability, understanding of connections among graphical, tabular, numerical, and algebraic representations, and confidence in mathematics.These findings are evident in the studies conducted by Hembree and Dessart (1986), Rich (1990), Ruthven (1990), Alexander (1993), Pavia (1996), Porzio (1997), and Abalajon (2001). A few studies, however, specifically that of 2 Army (1991) and Tolias (1993) found that the use of this instructional tool did not make any significant difference in the mathematical performance of the experimental and control groups. So far, only the study of Giamati (1991) indicated that the control group performed better than the experimental group.Reviews of related literature as indicated in Day (1996), Green (1999), and Kissane (1999) identify the many advantages of using graphing calculators.
Similarly, related studies such as those of Hansen (1986), Estes (1990), Mclendon (1991), Chandler (1992), Devantier (1992), Edwards (1996), Almeqdadi (1997), Craigheads and Heck (1997), Embse (1997), Hinerman (1997), Stick (1997), Rodil (2000), and Acelajado (2001) share the same findings that students who used graphing calculators in their mathematics classes had better achievement and more favorable attitude toward the subject than those who did not use calculators.Previous researches revealed that graphing calculators enhance the students’ mathematics achievement by minimizing the routine calculations which often interfere with the learning of important concepts and processes. Graphing calculators enable students to compute faster and more accurately, leaving more time for concept development. As far as the effects of intervention on students’ achievement in mathematics are concerned, almost all studies ever conducted found significant differences between the experimental and control groups in favor of the group that was exposed to the intervention.To mention a few, some of these are as follows: the use of visual aids in high school mathematics by Facundo (1993); the use of mathematical games in high school Algebra by Buzon (1996); the use of cooperative learning approach in Calculus by Legaspi (1997); the use of activity-oriented instruction technique in Plane Trigonometry by Ragual (1999); and use of graphing calculators in Integral Calculus by Rodil (2000) and ANMATH1 by Acelajado (2001).
Mathematics and science and technology have no doubt brought about marked changes in our society as evidenced by their diverse effects on practically all aspects of human life.Remarkable advances in science and technology could not have been possible without the application of certain mathematical procedures. However, the science that made possible the Industrial Revolution seems to have dehumanized man. Valle (1986) argued that the pervasive effects of science and technology on the family, the occupational life, and the economy gave the impetus for a change in teaching methodologies. The present direction in education should primarily be concerned with values development, emphasizing on the dignity and worth of man and his capacity for self-realization through reason.Education should not only focus on concepts of grammar structure, or on science ideas, or on mathematical operations.
Education should be able to teach how these concepts can further uphold human values and promote human welfare. Values are important as they give the people common orientations and a basis for individual and unified collective action, and a sense of purpose and direction. Man’s adjustment to the wonderful, but sometimes horrible, products of science and technology is presently a critical issue which merits ethical, moral, and political considerations.Through education, the students are expected to become self- 3 actualizing persons aware of their environment, open to change and continuous learning, and endowed with desirable human values. This simply means that the end-in-view is to develop well-rounded, independent, and responsible citizens. In the article on Value Formation and Education for National Reconstruction written by Salazar (1986), she pointed to that fact that the ultimate development of an individual is not so much on facts and concepts, skills and techniques, but on values.
This is further affirmed by Quisumbing (1988) who asserted that relevant quality education should equip people not only with basic literacy and employable skills but also with social values and moral foundation. She also mentioned that the true test of quality education is the degree to which one can share what he has learned with others to improve the quality of life. Similar global observations were evident in the argument posed by Merck et al (1988) who commented that educators in European, American and Oriental countries should take action to uplift the moral development of their students.The educative process must, therefore, include some sort of value classification, value orientation, and value judgment.
Education should provide for the students’ growth in human experiences and personality development through proper stimulation, direction, and guidance. As such, it is not enough that values education is included in the curriculum. Classroom teachers should work together to inculcate values in whatever subject matters they are handling. Several research works using different interventions were already conducted to determine their effects on students’ attitude toward mathematics.Limjap (1996) found that using the constructivist teaching strategy helped develop in students the attitudes such as belief in what they do, commitment and responsibility for their learning, risktaking in classroom learning, and accountability for their mistakes. Legaspi (1997) observed a significant difference in the posttest attitude scores of college students who were taught Calculus in favor of those who were exposed to the cooperative learning approach.
On the other hand, no significant difference was found between the mean posttest attitude scores of the experimental and control groups in the study of Acelajado (1994) where the experimental and control groups were taught College Algebra using Filipino and English, respectively, as media of instruction and that of Buzon (1996) where the experimental group used mathematical games in class. Another noncognitive domain that affects students’ achievement in mathematics is anxiety. In fact, many experienced teachers recognize that anxiety is sometimes equated with poor performance and avoidance of certain subjects in school.Betz (1978) and Tobias (1980) asserted that most students feel anxious and tense when manipulating numbers and solving mathematical problems. Mathematics anxiety is a psychological state engendered when a student experiences or expects to lose self-esteem in confronting a mathematical situation. Such anxiety prevents a student from learning even the simplest mathematical task.
It has been found that negative feelings and attitudes toward mathematics intruded on the development of formal reasoning powers.Ward (1989) and Trichett (1997) emphasized that there are times when anxiety causes excitement, energy, more creativity, more productive thinking, more expansive original solutions, and higher performance in particular intellectual tasks. However, too much anxiety limits, 4 constricts, and paralyzes one’s mind, interfering with new learning and performance in school. Sundararajan (1995) asserted that extremely high, uncontrolled anxiety levels affect students’ ability to perform in school, resulting in poor academic progress and high dropout rates.Since it is difficult to do what one does not feel like doing, the learner should be made to see that a subject is interesting and worth learning.
Some teaching approaches and anxiety reduction programs that have been tried to reduce mathematics anxiety are group counseling and behavior modification procedures by Crouch (1971); integration strategy by Hendel and Davis (1978); use of calculators by Martin (1980); rational emotive therapy by Puerto (1988); and cooperative learning approach by Macatangay (1999).The motivation to learn and perform better in mathematics is affected by the learning procedure, the instructional materials and technology used, along with a number of noncognitive factors such as attitude and anxiety. Astin (1993) emphasized that well designed lessons with interesting activities become meaningful only when they affect the student in the process. Moreover, Stuart (2000) asserted that innovations in the methods of teaching and the use of teaching aids may improve students’ feeling of success and may help them develop confidence in mathematics.Most experimental studies that used graphing calculators in teaching/learning mathematics revealed significant differences in favor of the experimental group. Thus, the present study simply classified the respondents into three ability groups that were allowed to use the graphing calculators.
The effects of using graphing calculators on each group’s achievement, attitude and anxiety in mathematics were then investigated. OBJECTIVES With achievement, attitude, and anxiety in mathematics as variables and the use of graphing calculator as intervention, this study sought to: 1. etermine if any significant difference exists in the achievement of the different ability groups in College Algebra before and after the experiment; 2. identify topics in College Algebra that can be learned best by using graphing calculators; 3. determine if there is any significant change in the respondents’ attitude and anxiety in mathematics before and after the experiment; and 4.
gather students’ insights about the graphing calculator as an instructional technology.It was hypothesized that the use of graphing calculators as a teaching/learning tool would improve students’ achievement and attitude and reduce their anxiety in mathematics. 5 METHODOLOGY This study utilized the experimental method of research. The respondents of the study were 66 first year college students from the College of Science, De La Salle University, enrolled in Math111 (College Algebra) during the first term, school year 2002-2003. The respondents belonged to two intact classes. The students were grouped according to their scores in the diagnostic test that was administered to them on the first week of classes.
Based on the results of the diagnostic test, the members of the groups were identified and labeled as follows: the high ability group (HAG, the top 22 students), the average ability group (AAG, the middle 22 students), and the low ability group (LAG, the bottom 22 students). Before the start of the experiment, the students were given an orientation as to how the lessons will be taught with the use of graphing calculator. The experiment lasted for 10 weeks, from June to August 2003, with the researcher handling the two intact classes which were scheduled on the same day, three times a week, one hour per meeting.The following instruments were used: (1) teacher-made test to measure students’ achievement in Math111; (2) the Mathematics Attitude Scale (MAS), a 50-item questionnaire used in the study of Dela Rosa (1990) and Limjap (1996); (3) the Mathematics Anxiety Rating Scale (MARS), a 10-item questionnaire by Freedman (1997) which measures a wide variety of specific situations associated with mathematics classes, courses, problems and tests; and (4) an open-ended questionnaire which solicited from the students their insights about using graphing calculators in mathematics.The test paper of each respondent in all instruments of this study was scored.
Each score was converted to percent. Moreover, the pre- and post-experiment perceptions of all respondents about each item in the MAS, categorized into affective, behavioral, and cognitive dimensions, and MARS were taken and compared. Pretest and posttest results of the respondents in the instruments of this study were analyzed to determine the respondents’ achievement in Math111, attitude and anxiety in mathematics.The results in each case were tested for significant difference using the ttests for dependent and independent samples. For purposes of describing the attitude and anxiety of the respondents, a detailed presentation of the respondents’ pretest and posttest means and standard deviations in the affective, behavioral and cognitive dimensions of MAS and in the MARS is included in this paper.
Moreover, an informal interview with a random sample of respondents on matters related to mathematics attitude and anxiety was conducted to validate their responses in the questionnaires used in this study.At the end of the experiment, a questionnaire was used to gather the students’ insights on the use of graphing calculators in mathematics. RESULTS AND DISCUSSION To determine the respondents’ achievement in MATH111 and their attitude and anxiety in mathematics, their mean pretest and posttest scores were computed and tested for significance of difference. The result is shown in Table 1. 6 Table 1.
Summary of Descriptives for the Variables of the Study in All Ability Levels Achievement in MATH111 ABILITY LEVEL/ STATISTIC Lowest Pretest Score Highest Pretest Score Pretest Mean Score Standard Deviation Pretest) Lowest Posttest Score Highest Posttest Score Posttest Mean Score Standard Deviation (Posttest) Mean Gain Standard Deviation (Mean Gain) Computed t-value t (tabular, ? = . 01, df = 20) = 2. 53 Attitude toward Mathematics HAG n=22 67 88 79. 23 9. 84 78 95 86.
94 10. 34 7. 71 11. 02 2. 53 (HS) AAG n=22 69 90 75.
82 11. 01 75 92 84. 16 10. 82 8. 34 10.
80 3. 38 (HS) LAG n=22 58 87 72. 40 10. 80 79 94 86. 50 10. 05 14.
10 12. 51 4. 48 (HS) Anxiety in Mathematics HAG n=22 39 89 74. 15 13. 48 21 85 43.
98 13. 83 30. 17 11. 15 7. 33 (HS) AAG n=22 51 91 79. 41 13.
23 39 83 52. 30 14. 1 27. 11 12. 50 6.
40 (HS) LAG n=22 42 93 83. 23 15. 14 37 87 48. 60 15. 16 34.
63 13. 24 7. 58 (HS) HAG n=22 12 38 28. 26 5. 39 46 98 80.
65 9. 84 52. 39 6. 96 21. 90 (HS) AAG n=22 8 29 21.
32 6. 15 41 85 75. 12 9. 60 53. 80 7. 34 22.
13 (HS) LAG n=22 6 17 14. 11 5. 89 39 78 64. 08 10. 53 52.
97 7. 51 19. 43 (HS) HS – Highly Significant Table 1 shows a highly significant difference in the respective pretest and posttest mean scores of each ability group. This confirms the findings of previous studies that similarly used graphing calculators as the only intervention in the experiment.Moreover, assuming normality of population, about two-thirds of the total number of respondents have posttest achievement mean scores ranging from 70. 81 to 90.
49 for the HAG, from 65. 52 to 84. 72 for the AAG, and from 53. 55 to 74. 61 for the LAG; their posttest attitude mean scores ranged from 74.
60 to 97. 28 for the HAG, from 73. 34 to 94. 98 for the AAG, and from 76. 45 to 96.
55 for the LAG; and their posttest anxiety mean scores ranged from 30. 15 to 57. 81 for the HAG, from 33. 44 to 63. 76 for the AAG, and from 37.
49 to 67. 11 for the LAG.All tests of significance of difference applied on the pretest and posttest mean scores in each variable turned out to be significant in favor of technology integration. The HAG registered the highest mean achievement, followed by the AAG and then the LAG, with the AAG showing the highest mean gain. This supports Sueltz’ (1979) contention that performance in higher mathematics largely depends on the learner’s mathematical ability and understanding of basic mathematical concepts. This also points to the fact that technology integration facilitated knowledge acquisition of the respondents.
As regards attitude toward mathematics and mathematics anxiety, it can be gleaned from the table that the greatest improvement occurred among the respondents from the LAG. This may be due to the confidence in mathematics earned by these respondents brought about by technology integration. To identify the topics in the syllabus for Math111 that were learned best with the help of graphing calculators, the respondents’ overall pretest and posttest mean scores and standard deviations were computed so with the t-test for significance of difference and the results are shown in the following table. Table 2. Means, Standard Deviations and t-test Results of the Respondents on the Different Topics in College Algebra (n = 66) Quiz 1 2 3 Topic Real Numbers Algebraic Expressions Rational Expressions Exponents and Radicals Linear and Quadratic Equations in One Variable Linear and Quadratic Inequalities in One Variable Systems of Linear Equations in Two Variables Systems of Linear Equations in Three Variables Functions and Their Graphs Pretest Mean sd 37.
24 15. 23 28. 51 14. 76 30. 24 16.
35 21. 34 15. 92 31. 27 14. 82 19. 43 32.
14 29. 57 20. 93 12. 2 15. 12 14.
85 11. 28 Posttest Mean sd 71. 21 14. 82 83. 45 15. 03 62.
30 15. 01 79. 43 14. 56 72. 35 13.
91 76. 41 78. 62 73. 31 84. 05 14.
25 14. 73 15. 62 13. 84 t-value 12. 99 (HS) 21. 19 (HS) 11.
73 (HS) 21. 87 (HS) 16. 42 (HS) 24. 57 (HS) 17. 89 (HS) 16. 49 (HS) 28.
72 (HS) 4 t (tabular, ? = . 01, df = 64) = 2. 39 HS – Highly Significant The respondents registered the highest mean gain on Functions and Their Graphs, followed by the mean scores on Exponents and Radicals, Linear and Quadratic Inequalities in One Variable, and Algebraic Expressions.The least mean gain with technology integration is seen in the topic on Rational Expressions. Apparently, the topic on functions and their graphs was learned best with the use of graphing calculators and this may be accounted for by the fact that toward the end of the term, the respondents may have already mastered and gained facility in using graphing calculators and that their knowledge of previous lessons helped them understand new lessons.
Apparently, the respondents enjoyed looking at the table of values and the graph of each function simultaneously and they were able to describe the behavior of the function better.As in the case of Exponents and Radicals, the respondents’ background knowledge in high school mathematics may have helped them understand the lessons better. On the other hand, the other topics required more exploration, visualization and analysis. It is worth mentioning that the respondents had better scores in the last few topics in the syllabus and this indicates that the impact of technology integration is felt just at this point. The t-test applied to these data revealed significant differences among the respondents’ scores in all the topics covered in Math111.Table 3 shows the distribution of the respondents according to the results of their preexperiment and post-experiment attitude mean scores and the results of the ? 2 test of significance of change applied on the data of the study.
8 Table 3. Results of ? 2 test on Attitude toward Mathematics Applied to the Different Ability Groups Pre-Experiment and Post-Experiment Levels GROUP High Ability Average Ability Low Ability OVERALL Negative to Positive 6 8 12 26 Negative to Negative 2 3 2 7 Positive to Positive 14 11 8 33 S – Significant Positive to Negative 0 0 0 0 ?2 value 3. 85 3. 47 1. 26 2. 61 Remarks S NS NS NS ?2 (tabular) (1 df, ? 0.
05) = 3. 841 NS – Not Significant It is evident from the table that with technology integration a significant change in attitude toward mathematics occurred only among the respondents of the high ability group. The table also reveals that there were more respondents who had a change of attitude from negative to positive and nobody had a change of attitude from positive to negative. Although the change in attitude levels was not significant for the average and low ability groups, the raw scores in the instrument showed that about 70% of the total number of respondents had an increase in their attitude scores.These scores, however, did not merit change of attitude levels among respondents as per the scale used in this study. Compared to the other ability groups, the low ability group had the most number of respondents with a change in attitude levels.
This indicates that technology integration has inspired more respondents from the low ability group to like mathematics. Table 4 shows the distribution of the respondents according to the results of their pre-experiment and post-experiment anxiety mean scores and the results of ? 2 test applied on the data of the study. Table 4 Results of the ? Test of Change of Anxiety in Mathematics Applied to the Different Ability Groups Pre-Experiment and Post-Experiment Levels GROUP Anxious to Not Anxious 11 10 15 36 Anxious to Anxious 6 7 6 19 Not Anxious to Not Anxious 5 5 1 11 Not Anxious to Anxious 0 0 0 0 ? 2 value 2. 43 3. 02 0.
39 1. 78 Remarks High Ability Average Ability Low Ability OVERALL NS NS NS NS ?2 (tabular) (1 df, ? = 0. 05) = 3. 841 NS – Not Significant It can be noted from the table that there are more respondents from the low ability group who had a change of anxiety levels from anxious to not anxious. Comparing the 9 omputed and the tabular values of ? 2 , it can be noted that the changes in the anxiety levels of the respondents in all ability groups were not significant at the 0. 05 level.
Based on the respondents’ raw scores in the instrument, it was found that about 74% of the total number of respondents had reduced anxiety scores. However, in some of them the change was not enough to merit a change of anxiety level, from anxious to not anxious. The remaining 26% of the respondents maintained their original anxiety level and this may be so because they were not yet fully convinced of the merits of the use of graphing calculators.This implies that the use of graphing calculators is not enough to spell a difference in the anxiety levels among the respondents of the different groups. However, the use of graphing calculators has improved the anxiety levels of the low ability respondents than the high ability respondents.
Tables 5, 6, 7, and 8 show the item per item presentation of the overall perceptions of the respondents’ pretest and posttest mean scores, standard deviations, and t-values in the different components of the MAS and MARS. Table 5. Means, Standard Deviations and t-values of the Items in the Affective Dimension of the Mathematics Attitude Scale Item No. 2 3 5 7 14 15 17 19 23 25 29 34 Statement Mathematics is my favorite subject. I hate Mathematics.
I am always anxious in a Mathematics class. I am afraid to take a Mathematics course. I am uncomfortable with the thought of taking a mathematics subject. I feel confident in solving problems in mathematics. It makes me nervous to even think about having to take so many units of Mathematics in my coursework. I enjoy mathematics class more than any class.
How I wish Mathematics would be completely deleted from my course curriculum. I do not enjoy in my mathematics class.I am always tense in a mathematics class I find mathematics a very interesting and exciting subject. I dread mathematics as if it were a contagious disease. PRETEST Mean 3. 19 (Undecided) 2.
45 (Disagree) 3. 06 (Undecided) 2. 69 (Undecided) 2. 67 (Undecided) 3. 02 (Undecided) 2. 95 (Undecided) 2.
86 (Undecided) 2. 48 (Disagree) 2. 83 (Undecided) 2. 84 (Undecided) 3. 38 (Undecided) 2.
34 (Disagree) sd 1. 29 1. 22 0. 99 1. 27 1.
17 1. 04 1. 19 1. 19 1. 25 1.
13 1. 08 1. 12 1. 16 POSTTEST Mean 3. 87 (Agree) 1. 98 (Disagree) 2.
75 (Undecided) 2. 05 (Disagree) 2. 01 (Disagree) 4. 5 (Agree) 3. 23 (Undecided) 3. 52 (Agree) 2.
26 (Disagree) 2. 51 (Undecided) 2. 43 (Disagree) 4. 01 (Agree) 1. 48 (Strongly Disagree) sd 1.
35 1. 02 1. 39 1. 30 1. 37 1.
51 2. 03 2. 17 1. 92 1. 73 1. 34 1.
52 1. 96 t-value 2. 303 S -1. 869 NS -1. 149 NS 2.
227 S 2. 317 S 3. 553 S 0. 752 NS 1. 687 NS -0.
607 NS -0. 979 NS -1. 507 NS 2. 110 S -2. 388 S 10 36 40 46 I find mathematics boring and dull. I feel helpless whenever I solve a mathematics problem.
I am interested in solving mathematical problems. Strongly Disagree Disagree 2. 44 (Disagree) 2. 70 (Undecided) 3. 56 (Agree) 1.
09 1. 0 1. 04 1. 39 (Strongly Disagree) 2. 38 (Disagree) 3. 91 (Agree) 2.
01 1. 42 1. 60 -2. 904 S -1. 127 NS 1.
160 NS 1. 00 – 1. 49 1. 50 – 2. 49 2. 50 – 3.
49 Undecided 3. 50 – 4. 49 Agree 4. 50 – 5. 00 Strongly Agree S – Significant NS – Not Significant It can be gleaned from Table 5 that no significant difference exists in the respondents’ overall affective attitude toward mathematics although majority of the posttest scores are higher than the corresponding pretest scores.
They have better conviction regarding their attitude on aspects like having mathematics as a favorite subject.They are, however, still uncertain about their feelings toward mathematics, that is, they are not sure if they are simply tense, helpless, nervous, happy, confident or uncomfortable with it. The respondents agree that they are interested in solving mathematical problems and disagree that mathematics is boring and dull. In general, scores were improved and this indicates an improvement of students’ affective attitude toward mathematics. The small values of the standard variations show evidences that the perceptions of the respondents about their feelings toward mathematics are in agreement.Table 6.
Mean Ratings, Standard and t-values of the Items in the Behavioral Dimension of the Mathematics Attitude Scale Item No. 6 9 10 11 18 20 24 27 31 32 33 Statement I become patient and persevering in mathematics courses. Mathematics makes me think logically. Mathematics trains me to be systematic. Mathematics trains me to be disciplined I find time to help my classmates solve problems in Mathematics.
When doing mathematics, I don’t care whether my solutions are right or wrong. Mathematics stimulates me. I hesitate to enroll in a course with many Mathematics requirements.I try to understand the solutions of my peers in Mathematics. I am hesitant to attend my mathematics classes.
I am willing to share my insights about solving mathematical problems. PRETEST Mean sd 3. 53 0. 94 (Agree) 4. 10 0.
72 (Agree) 4. 01 0. 83 (Agree) 3. 81 (Agree) 3. 55 (Agree) 1.
99 (Disagree) 3. 40 (Undecided) 2. 82 (Undecided) 4. 08 (Agree) 2. 41 (Disagree) 3. 72 (Agree) POSTTEST Mean sd 4.
01 1. 03 (Agree) 4. 34 0. 92 (Agree) 4. 51 1. 02 (Strongly Agree) 3.
95 0. 99 (Agree) 3. 97 1. 15 (Agree) 1. 63 1.
07 (Strongly Disagree) 3. 98 1. 21 (Agree) 3. 20 1. 23 (Undecided) 3. 99 (Agree) 2.
9 (Disagree) 4. 02 (Agree) 0. 89 1. 27 1. 03 t-value 2.
177 S 1. 290 NS 2. 405 S 0. 672 NS 1. 758 NS -1.
569 NS 2. 433 S 1. 456 NS -0. 503 NS -1. 252 NS 1. 401 NS 0.
87 0. 98 0. 98 0. 90 1. 10 0. 70 1.
00 0. 88 11 37 42 43 44 45 48 49 50 I usually feel sleepy in my Mathematics class. I am very attentive in a mathematics class. I misbehave in my mathematics class because I cannot understand a thing. I solve other exercises in mathematics in addition to the assigned ones.
My mind travels far when I am in my mathematics class. I seek help whenever I find difficulties in mathematics.I am ashamed to participate in any discussion that involves Mathematics. I maintain a pleasant attitude in my Mathematics classes. Strongly Disagree Disagree 2.
64 (Undecided) 3. 49 (Undecided) 2. 14 (Disagree) 3. 16 (Undecided) 2. 54 (Undecided) 3. 98 (Agree) 2.
46 (Disagree) 3. 82 (Agree) 1. 11 0. 90 0. 92 1. 09 0.
97 0. 90 1. 05 0. 75 2. 41 (Disagree) 4. 17 (Agree) 2.
39 (Disagree) 3. 95 (Agree) 1. 96 (Disagree) 4. 02 (Agree) 1. 90 (Disagree) 3.
95 (Agree) 1. 07 1. 03 1. 04 1. 29 1. 21 1.
07 1. 23 1. 02 -0. 944 NS 3. 144 S 1.
139 NS 2. 958 S -2. 365 S 0. 181 NS -2. 190 S 0. 49 NS 1.
00 – 1. 49 1. 50 – 2. 49 2. 50 – 3. 49 Undecided 3.
50 – 4. 49 Agree 4. 50 – 5. 00 Strongly Agree S – Significant NS – Not Significant Even with the use of graphing calculators, it can be seen from the table that no significant difference exists in the overall behavior of the respondents toward mathematics. Obviously, they had stronger conviction that mathematics trains them to be systematic and logical and to care for their solution to problems, promotes discipline, patience, perseverance, and willingness to share his insights about solving mathematical problems..
They disagree, however, that they do not care whether their solutions are right or wrong, or that they misbehave in class because they cannot understand the lesson, or are ashamed to participate in any discussion that involves mathematics and hesitate to attend mathematics class. As a whole, they are undecided as to whether mathematics stimulates them or they want to enroll in courses which require many mathematics subjects, whether they feel sleepy or attentive in a mathematics class or their minds travel far when attending a mathematics class or solving additional exercises.Very little variations in the responses can be noted from the values of the standard deviations reflected in the preceding table. This indicates homogeneity among respondents in their perceptions of their behaviors in mathematics-related situations. As a whole, the respondents behave positively in so far as mathematics is concerned. This implies that they can afford to maintain composure amidst “odds and ends” in pursuing mathematics-related activities.
Table 7. Mean Ratings, Standard Deviations and t-values of the Items in the Cognitive Dimension of the Mathematics Attitude Scale Item No. Statement I would like to work in a Mathematics-related field. PRETEST Mean sd 2. 82 1. 20 (Undecided) POSTTEST Mean sd 3. 51 1. 49 (Agree) t-value 2. 281 S 12 8 12 13 16 21 22 26 28 30 35 38 39 41 47 Mathematics is just like playing a game for me. Mathematics is so difficult that only those who are gifted can understand it. I believe that Mathematical theories are very important since scientific and technological advancements depend a great deal on them. I think Mathematics is irrelevant. I think Mathematics is challenging. Mathematics develops one’s understanding and logical thinking. I should always come prepared for my mathematics lass. I think people who do well in Mathematics are weird. I feel responsible for finding and checking errors in my solutions in mathematics. A person who is good in Mathematics has a great chance to succeed in many fields of endeavor. A good Mathematics training is a big advantage in entering any line of work. I believe life can go on without Mathematics. I feel that Mathematics is needed in everyday life situations. Studying mathematics deprives me of the chance to attend to more fruitful and enjoyable activities. 2. 59 (Undecided) 2. 23 (Disagree) 3. 73 (Agree) 1. 16 1. 12 0. 93 3. 27 (Undecided) 1. 96 (Disagree) 3. 2 (Agree) 1. 34 0. 97 1. 13 2. 427 S -1. 153 NS 0. 389 NS 2. 00 (Disagree) 4. 35 (Agree) 4. 29 (Agree) 3. 88 (Agree) 1. 81 (Disagree) 3. 82 (Agree) 3. 96 (Agree) 3. 98 (Agree) 2. 32 (Disagree) 3. 83 (Agree) 2. 60 (Undecided) 1. 03 0. 74 0. 84 0. 91 0. 93 0. 78 0. 91 1. 87 (Disagree) 4.. 42 (Agree) 4. 71 (Strongly Agree) 4. 29 (Agree) 1. 62 (Disagree) 4. 02 (Agree) 4. 41 (Agree) 3. 87 (Agree) 1. 96 (Disagree) 4. 28 (Agree) 2. 78 (Undecided) 1. 01 . 93 1. 02 1. 27 1. 09 . 96 1. 32 -0. 570 NS 0. 373 NS 0. 718 NS 1. 660 NS 0. 839 NS 1. 023 NS 1. 775 NS -0. 456 NS -1. 275 NS 1. 894 NS 0. 692 NS 0. 93 1. 17 0. 99 1. 2 1. 21 1. 35 1. 13 1. 29 1. 00 – 1. 49 Strongly Disagree 1. 50 – 2. 49 Disagree 2. 50 – 3. 49 Undecided 3. 50 – 4. 49 Agree 4. 50 – 5. 00 Strongly Agree S – Significant NS- Not Significant Very clearly, the overall difference in the posttest and pretest scores of the respondents in the cognitive dimension of attitude, though not significant, show improvement of their thinking about mathematics. As reflected in Table 7, the respondents agree that mathematical theories are important to science and technology and that mathematics is challenging, and that it develops one’s understanding and logical thinking.Also, they agree that a good training in mathematics is a big advantage in entering any line of work; it gives an individual a great chance to succeed in many fields of endeavor; and it is needed in everyday life. Moreover, they agree that they have to come to mathematics class prepared. 13 On the other hand, they disagree that mathematics is so difficult and irrelevant, that the people who do well in it are weird, and that life can go on without mathematics. However, they are undecided about wanting to work in a mathematics-related field. As a whole, the respondents generally think positively of mathematics-related situations.They seemed to concur with each other since all the items yielded small standard deviations. Their undecisiveness in their perceptions of some items may be due to the fact that they came from different institutions of learning with varied standards, as well as the fact that they had different psychosocial background which influence and affect their academic outlook, specifically in mathematics. Table 8 shows the mean scores of the respondents in each item of the Mathematics Anxiety Rating Scale. Table 8. Means and Standard Deviations of the Items in the Mathematics Anxiety Rating Scale Item No. 2 3 4 5 Statement I cringe when I have to go to a mathematics class. I am uneasy about going to the board in a mathematics class. I am afraid to ask questions in a mathematics class. I am always worried about being called in a mathematics class. I understand mathematics now, but I worry that it’s going to get really difficult soon. I tend to zone out in a mathematics class. I fear mathematics more than any other subject. I don’t know how to study for a mathematics test. It’s clear to me in a mathematics class, but when I go home it’s like I was never there. I’m afraid I won’t be able to keep up with the rest of the class in mathematics.PRETEST Mean 2. 13 (Sometimes Anxious) 1. 66 (Sometimes Anxious) 2. 30 (Sometimes Anxious) 2. 34 (Sometimes Anxious) 2. 36 (Sometimes Anxious) 2. 05 (Sometimes Anxious) 2. 53 (Frequently Anxious) 2. 51 (Frequently Anxious) 2. 07 (Sometimes Anxious) 1. 67 (Sometimes Anxious) sd POSTTEST Mean sd 2. 01 1. 05 (Sometimes Anxious) 1. 80 1. 09 (Sometimes Anxious) 2. 08 1. 39 (Sometimes Anxious) 1. 96 . 92 (Sometimes Anxious) 2. 05 1. 96 (Sometimes Anxious) 2. 37 (Sometimes Anxious) 2. 21 (Sometimes Anxious) 2. 33 (Sometimes Anxious) 2. 36 (Sometimes Anxious) 1. 48 (Rarely Anxious) 1. 58 1. 87 1. 32 1. 49 t-value -0. 46 NS 0. 551 NS -0. 715 NS -1. 360 NS -0. 693 NS 0. 968 NS 0. 862 NS 0. 585 NS 0. 924 NS -0. 717 NS 1. 34 1. 18 1. 36 1. 53 2. 04 6 7 8 9 1. 37 1. 42 1. 43 1. 31 10 1. 20 1. 17 14 1. 00 – 1. 49 1. 50 – 2. 49 Rarely Anxious Sometimes Anxious 2. 50 – 3. 49 Frequently 3. 50 – 4. 49 Generally Anxious 4. 50 – 5. 00 Almost Always Anxious S – Significant NS – Not Significant Table 8 shows that before and after technology integration, the respondents were sometimes anxious about going to a mathematics class, solving a problem on the board, asking a question in class, and remembering things discussed in class.Sometimes, they were worried about being called in class and about the topics becoming difficult. They were frequently anxious about the best way of studying for a mathematics test. Based on their mean responses to the items in the questionnaire after the experiment, it was noted that they have learned how to study for a mathematics test and they have overcome their fear of the subject and the problem of keeping up with their classmates. The use of graphing calculators must have provided them with additional confidence in mathematics.As regards the students’ perceptions regarding the use of graphing calculators in mathematics, it is worth mentioning here that the pre-interview with a random sample of respondents revealed the following anxieties: (1) visualizing functions is difficult and drawing their graphs is time-consuming; (2) the time allotment for discussion of concepts and examples is too limited; (3) presentation of lessons in mathematics is boring; (4) manual computation discourages them a lot; and (5) they are not sure of themselves when it comes to mathematics.The post interview with the same set of students revealed that they became more interested in computing, tabulating, and graphing functions and that they gained enough confidence in their ability in mathematics. Their active involvement in learning College Algebra and their ability to visualize what they were studying must have reduced their fears of mathematics. The respondents’ insights regarding the use of the graphing calculators confirmed most of the arguments found in the related literature and studies.The respondents agreed that graphing calculators facilitate graphing of functions and made algebraic, graphical, and numerical connections among mathematical topics more significant to the students. IMPLICATIONS The results of this study give credence to the fact that one’s propensity in higher mathematics courses is founded on his understanding of basic mathematics concepts and his natural intelligence in the subject. However, the use of graphing calculators supplements and facilitates students’ understanding of mathematics.This study revealed that the use of graphing calculators improved achievement and attitude toward mathematics to a certain extent, and reduced anxiety in mathematics. However, a number of respondents had difficulties using graphing calculators so that there is a need for an extensive training of students on the use of the different function keys of the calculator. 15 Integrating technology into teaching College Algebra proved to be challenging and enlightening to the students. Apparently, connections among the different ways of visualizing mathematical relationships were easily established and reinforced with the use of graphing calculators.As students went through the process, their attitude toward mathematics improved and they became more confident, thus reducing their anxiety in doing related tasks. Educators, especially those trained in the traditional pedagogical methods, need not be cynical about the present social events affecting the teaching-learning situation. The functionalist theory of social change underscores that when a certain structure of a particular system does not function the way it should be is enough evidence that a certain method or process should be changed and disregarded.This social phenomenon explains why a society constantly undergoes transformation. Mathematics anxiety is a global problem which calls for a better curriculum, competent teachers, improved teaching strategies, appropriate learning aids, and prudent use of technology in the classroom. Thus, it is best to realign the contents of the course syllabus that will include laboratory hours for the full integration of graphing calculators in teaching-learning mathematics.The mathematics department should make the calculator available to all students in the same manner that books and other references in the library are made available to the students. Inasmuch as using the calculator properly needs to be taught, a funded seminar-workshop on integrating this technology in classroom activities should be held for both teachers and students. In so far as pedagogy and training are concerned, the challenge to the mathematics teacher is how to devise ways that will feed the mind, the heart and the soul of the learner.With mathematics widely perceived as intimidating and difficult, the teacher should know how to make the learner appreciate mathematics and how he can learn to become more human while learning the fundamentals and intricacies of mathematics. This paper encourages the mentor to break out of the traditional static teaching shell and to explore opportunities that will allow for more creativity so that students remain interested, focused, and enthusiastic throughout the mathematics course.Innovative teaching techniques shall turn the largely perceived mathematics subject as palatable and even enjoyable. As regards material development, it has been proven that well-designed lessons with interesting activities become meaningful only when they affect the student in the process. Relevant teaching approaches, such as the use of technology have significantly improved the students’ feeling of success and helped develop their confidence in mathematics. The result is better performance and desirable achievement in a subject largely perceived as difficult.The use of the technology made the students realize and appreciate the fact that mathematics is not a “burden” subject but rather a relevant learning area that is present in almost all aspects of their everyday living. 16 There is a need to re-orient the youth so that they will realize that science and technology, or any knowledge for that matter, can only be beneficial if it is used discriminately and with prudence. 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