Bala, Ritu. (2012). A Study of Errors and Misconceptions in Mathematics at Elementary School Stage in Punjab. Unpublished. Ph.D., Education. Himachal Pradesh University, Shimla.

1. To construct and standardize Three-Tier Concept Achievement Test in Mathematics for elementary school students. 2. To find out the level of performance of elementary school students on three-tier concept achievement test in Mathematics. 3. To find out the percentage of elementary school students who committed errors and misconception on Three-Tier concept achievement test in Mathematics. 4. To study the dimensions of errors and misconceptions of rural and urban elementary school students on Three-Tier concept achievement test in Mathematics. 5. To study the dimensions of errors and misconceptions of male and female elementary school students on Three-Tier concept achievement test in Mathematics. 6. To study the patterns of errors and misconceptions on Three-Tier Concept Achievement Test in Mathematics among elementary school students. 7. To identify the sources of errors and misconceptions of elementary school students in Mathematics. 8. To suggest remedies for clearing misconceptions of the elementary school students and rectifying errors in Mathematics.1. There is no significant difference between rural and urban elementary school students in Mathematics on Three-Tier Concept Achievement Test in Mathematics in terms of: (i) Achievement (ii) Concept Achievement (iii) False Positives (iv) Lack of Knowledge (Concept Achievement Wise) (v) Errors (vi) Misconception (vii) False Negatives (viii) Lack of Knowledge (Misconception Wise) (ix) Confidence 2. There is no significant difference between male and female elementary school students in Mathematics on Three-Tier Concept Achievement Test in Mathematics in terms of: (i) Achievement (ii) Concept Achievement (iii) False Positives (iv) Lack of Knowledge (Concept Achievement Wise) (v) Errors (vi) Misconception (vii) False Negatives (viii) Lack of Knowledge (Misconception Wise) (ix) Confidence

Students studying at the elementary school stage in Punjab comprised the universe of the study. All the 6th class students who are studying in government elementary, high and senior secondary schools of Punjab were the target population in the present study. The state comprises of 20 districts and a network of 15325 elementary schools, 1739 Government high schools and 1382 Government senior secondary schools, which have 6th class (elementary school stage). Since it is not possible to cover the whole population in descriptive studies, the researcher has to resort to sampling. Multi-stage sampling was employed for the selection of sample for the study. Following random procedure, 8 districts out of 20 were selected at the first stage. These were Bathinda, Fatehgarh Sahib, Kapurthala, Ludhiana, Mansa, Moga, Patiala and Sangrur. Hence the target area covered 40% of the total region. At second stage, a list of high schools and senior secondary schools situated in each of these eight districts was made. A sample of 4 or more schools from each district, out of which 2 or more schools from rural area and 2 or more schools from urban area was randomly drawn. Then 62 or more rural students and 62 or more urban students were selected randomly from sampled schools in each district. Out of 62 students, 31 or more male students and 31 or more female students were selected for the sample. Thus, 1000 students from 44 schools comprised the sample for present study, which includes equal number of male & female students and rural & urban students.Three-Tier Concept Achievement Test in Mathematics Name of the developer: Ritu Bala Dimensions/ Components: (i) Achievement; (ii) Concept Achievement; (iii) False Positives; (iv) Lack of Knowledge (Concept Achievement Wise) (v) Errors; (vi) Misconception; (vii) False Negatives; (viii) Lack of Knowledge (Misconception Wise) and (ix) Confidence. The target group was 6th Class Students. The reliability of the test was calculated by calculating coefficient alpha and came out to be 0.69. Validity Co-efficient: First, Correlation between students scores on the first two tiers and confidence level on the third-tier was found and criterion validity was established. Second, Content validity was established by giving the test to Mathematics experts and Language ExpertThe study was completed in two phases. In phase-A, Three-Tier Concept Achievement Test in Mathematics was constructed and standardized and in phase-B, field work was doneIn order to achieve the objectives of the study, percentage analysis, descriptive statistics, namely frequency distributions, central tendencies and variability were used to explain the achievement score, concept achievement score, false positives, lack of knowledge (Concept Achievement Wise), error score, misconception score, false negatives, lack of knowledge (Misconception Wise) and confidence level, on Three-Tier Concept Achievement Test in Mathematics. The use of t-test was made to test the significance of mean differences in performance of the elementary school students across location and gender in terms of different dimensional scores, namely, achievement scores, concept achievement scores, false positives, lack of knowledge (concept achievement wise), error scores, misconception scores, false negatives, lack of knowledge (misconception wise).

1 The results indicate that there is no significance difference in the performance of rural and urban elementary school students. 2 The results indicate that there is no significance difference in the performance of male and female elementary school students

The results of the study show that students commit errors due to mistakes, lack of knowledge or due to misconceptions. These misconceptions are resistant to change and abrupt the learning process. The teachers are required to take students misconceptions into account. The more the teachers know about their students misconceptions the more guidance they will be able to provide them to learn. This would also contribute to the professional development of Mathematics teachers. Smith and Anderson (1993) and Lawrenz (1986) advocated that during (pre-service and in-service) teacher education programmes the teachers should be given opportunities to identify misconceptions held by the pupils in their classrooms. Teachers can use the Three-Tier Concept Achievement Test in Mathematics for formative evaluation to assess the misconceptions of the 6th class students about the geometrical concepts. The findings of this study would facilitate teachers in planning and implementation of relevant measures to reduce the incidence of students misunderstandings about the concept of geometry. A teacher should focus on students cognitive level to eliminate misconceptions, because all the students in elementary schools and most of the students in secondary schools learn concepts at concrete levels. Therefore the major focus of instructions for those students should be on creating links between concrete experiences and abstract concepts and on excepted difficulties in establishing such links. When students create this linkage in their mind, they are going to correct their misconceptions and develop meaningful understanding of new concept. Therefore, the highest priority for Mathematics teacher should be to pay attention to cognitive development with the help of activities because experience makes concepts more believable and understandable (Marek, 1986). Mathematics laboratory can be of great help to make students learn concepts at concrete level with complete understanding. Identification of students misconceptions in Mathematics for the unit of geometry by Three-Tier Concept Achievement Test in Mathematics can give some feed back to the text book editors. They can include activities for experimentation in Mathematics laboratory.

Keyword(s): Study of Errors, Misconceptions in Mathematics, Elementary School , Mathematics Education, Elementary Education

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