Mathematical Knowledge level of Primary Education Department students

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1 Mathematical Knowledge level of Primary Education Department students Charalampos Lemonidis, Helen Tsakiridou, Charalampos Kapsalis Department of Primary Education University of Western Macedonia Abstract The purpose of this study was to examine the mathematical knowledge of the student concerning their ability to deal with mathematics as part of their teaching (Tucker Alan, Cathy Kessel and Liping Ma, 2000). All the participants were undergraduate students at the Department of Primary Education, University of Western Macedonia, Greece. Throughout the study, an attempt has been made to correlate the performance of the abovementioned students with several factors, related to (1) attending mathematics courses during their university studies, (2) students background in fundamental notions in mathematics, as these have been developed during their studies in higher education. Finally, students performance in several mathematical sections was examined. The revealed that there is a statistically significant difference in students performance among different mathematical sections. Additionally, students performance is affected by their different background developed in high school, whereas previous scores in mathematical tests at university don t seem to influence their performance. 1. Sample and Materials 111 students of University of Western Macedonia, Department of Primary Education, were participated in the survey, specifically 47 second-year students and 64 first-year students. In order to explore the research questions, a questionnaire of 21 cognitive tasks was given to all participants. The survey was conducted during the period 1-30 November The content of the core-modules chosen (technical/physical, theoretical and practical) while studying at high school, as well as their scores in mathematical tests at high school and at university were recorded and considered as factors which may differentiate students performance. The score for each student was measured in a scale of 100. The techniques of t-test and ANOVA were performed for the purposes of the study (A. Gagatsis, 1991). 2. Purpose and research hypothesis The aim of the survey was to examine the level of mathematical knowledge of undergraduate students of a Department of Primary Education. In addition, the paper aims at examining the potential impact of students' mathematical knowledge on their capability to teach mathematics at school (Kai Fai Ho, John G. Hedberg, 2004). This could be proved important to identify whether future teachers have the ability to correspond to the necessity of teaching mathematics. To be more specific, the research questions were as follows: 1. Is there any difference in students performance in mathematics, before and after being taught the mathematical courses at university? 2. Do participants scores in higher education affect their scores in this survey?

2 3. Does the choice of core-modules attended in high school affect students scores in this survey? 4. Is the score of students in mathematics courses at Western University affect the participants score in current survey? 5. Do students who manage to enter the Department of Primary Education at University of Western Macedonia have any misconceptions in terms of fundamental mathematics concepts? 6. Is students performance differentiated among several mathematical sections? (e.g. geometry, fractions, algebra, analysis). 3. Results There was no statistically significant difference in students performance in mathematics, before (semester A) and after (semester E) attended the mathematical courses at university. As Table 1 shows the average success both of two groups was about 53%. Therefore, the initial hypothesis is not confirmed. Table 1: score Semester of studies Α semester Ε semester Total students Average success 52,85 52,67 52,77 Standard deviation 20,73 18,57 19,75 ANOVA revealed a statistically significant difference in students performance in the test according to their performance in high school mathematics (F 2,84 = 5,499, P<0,005). More specific, students of EXCELLENT performance in mathematics in high school record statistically significant higher performance in the test, compared with GOOD or VERY GOOD students (table 2). Table 2: score - students performance in mathematics in high school Mark at Higher education = ή <16 (GOOD) 16< x <18,5 (VERY GOOD) = ή >18,5 (EXCELLEN T) students Average success 50,39 51,04 65,64 52,77 Standard deviation 19,13 18,43 16,51 19,75 (full mark in this scale is 20) Core-modules attended in higher education were thought to be as important factor as to affect the survey. According to the data collected, all participants belong to one of the three broad 1 Of all 111 students participated in this survey, only 87 of them provided evidence about their attainment in higher education. The rest 24 students failed to give an answer to this question.

3 categories: sciences, humanity studies, technology. It is worth saying that students of the categories sciences and technology have to study more hours in mathematics each week. Table 3: score course in higher education Core-modules in higher education Sciences Humanit y studies Technology students 111 Average success 62,21 44,38 67,44 52,77 Standard deviation 14,13 19,40 12,53 19,75 There is a statistically significant difference in students performance according to the course they attended in high school (F 2,108 =18,534, P<0,005). More precisely, students attended sciences and technology courses record higher performance in the test, compared with those of humanity studies (table3). Results confirm the initial hypothesis. Table 4: score performance in Mathematic s course in university Score in < 5 7 ή 8 9 ή 10 Mathematics I (FAILUR E) 5 ή 6 (GOOD) (VERY GOOD) (EXCELLEN T) students Average success 54,43 53,10 57,44 45,59 52,77 Standard deviation 19,70 23,03 17,44 18,39 19,75 According to the initial hypothesis, students performance in mathematic course in university was expected to be one of the most important factors affecting the participants score in current survey. Students, as shown in table 4, do not confirm the initial assumption because students with EXCELLENT performance in mathematics record lower score in the test, than students with VERY GOOD or GOOD performance, even with students that failed in the course, but the difference is not statistically significant. Students performance differentiated among several mathematical sections (F 5,660 = 26,820, P<0,05). More specific, students higher performance recorded in fractions sector and their lowest performance recorded in geometry sector (table 5). Table 5: score Mathematical sectors Mathematical sector Average performance Standard deviation Geometry 42,02 25,84 Algebra 55,86 35,51 Analysis 61,26 37,35 2 Of all 111 students participated in this survey, only 102 students presented evidence about their attainment in Mathematics I. The rest nine students attended the course but either failed to sit the final exam or failed in the final exam.

4 . Fractions 71,17 19,57 score 52,77 19,75 It can also be said that that the lowest performance refers to geometrical solidly. Comparing this performance with students performance in questions referring to the rest of mathematical sectors, the conclusion is that there is statistically significant difference. The mathematical sector in which students achieved the highest score is fractions. The existing difference between students performance in fractions and students performance in the rest of mathematical sectors included in questionnaire is statistically significant, as test ANOVA revealed. 4. Discussion This survey was conducted in order to explore students knowledge in mathematics before and after attending the Mathematics courses. The above aim constitutes the main research question. As it has been explained so far (see table 1), the do not confirm the hypothesis that students who had attended the obligatory mathematical courses would score higher, because their performances were relatively unchanged. Probably, some other factors have contributed to this result. To be more specific, students of E semester who attended Mathematics I, II, II may have improved their knowledge in mathematics, but it is also possible that students of A semester had better performances in mathematics during their studies in higher education (see table 2). In these terms, students of A semester seem to remember well what they had been taught in high school. This good memory seems to be the compensative factor, comparing the performances of the two groups of students in this questionnaire. The knowledge of students belonging to E semester derives from their experiences at Florina s Pedagogical Faculty, while the respective knowledge of students belonging to A semester derives from their experience as students in higher education. Based on the survey, it can be concluded that participants encountered more difficulties when they had to deal with problems of geometry. This may highlight students weaknesses in this sector. Of course, geometrical tasks were theoretically more difficult, because students had to find the mathematic formula first (in order to calculate volume or surface), and then to do the calculations needed. Additionally, these tasks were the last in questionnaire and students were probably tired or were less willing to give answers, because they knew that their participation in this survey would not improve their university grade. Analyzing the of each question, it was obvious that students encountered more difficulties with some specific tasks (task 3, task 9 and task 20). In task 3 which refers to even numbers, note that the percentage of students failed was 99%. 96,4% of participants failed to deal with task 9 in which students were asked to define what a rhombus is. Finally, most students also failed to give a right answer to task 20 in which they had to calculate the surface and the volume of a given cylinder. The percentage of failure in this case was 91%. According to Mathematics curriculum, students in grade E and F of primary school must be taught how to calculate the surface and volume of a given solid figure. All students participated in this survey will be soon asked to teach in primary schools either as part of their practice or as well-prepared and trained teachers. However, the survey suggest that these students have many misconceptions or have not developed fundamental concepts in mathematics.

5 As it has been mentioned, the mathematics courses that students had been taught in higher education are another important factor which influences their knowledge, and consequently their achievements in present survey. In this case, what students had been taught in mathematics varies according to what core-modules they had decided to attend. The of this survey confirm this hypothesis because there are significant differences among students who had attended different core-modules (see table 3). The last sector mentioned in initial hypothesis which was expected to affect the survey was students performance in Mathematics courses taught at Florina s Pedagogical Faculty. However, neither this hypothesis was confirmed as the final are in contrast with initial hypothesis. Students who had lower scores in Mathematics tests organized by Florina s Pedagogical Faculty scored higher in this survey compared with those students who had higher marks in the same tests in Mathematics (mark 9 or 10). The latter group of students had the lowest average performance. All in all, based on the presented in this study, it can be concluded that students mathematics knowledge is not directly affected by mathematics courses organized at Florina s Pedagogical Faculty. It seems to be correlated with their background in mathematics as this has been formed during their studies in higher education (core-modules and performance in high school). Additionally, students seem to encounter more difficulties in dealing with specific sectors of mathematics. This fact may prevent them from carrying out successfully their teaching tasks in mathematics. 5. References! Gagatsis, A, Teaching Mathematics, Afoi Kiriakidi, Thessaloniki 1991 (in Greek).! Cai, J. Why do U.S. and Chinese students think differently in mathematical problem solving? Impact of early algebra learning and teachers beliefs. Journal of Mathematical Behavior, 23, 2004.! Kai Fai Ho, John G. Hedberg, Teachers pedagogies and their impact on students mathematical problem solving, Journal of Mathematical Behavior, 24.! Tucker Alan, New Thinking about the Mathematical Education of Teachers, NCTM, October 2000.! Cathy Kessel and Liping Ma, What We Think That Elementary Teachers Need, NCTM, October 2000.