Research Article
Mathematics’ Conceptual Knowledge of for Form Four Daily School Students in
District of PetalingUtama, Selangor
Mazlini Adnan*1,Azhar Ahmad1, Uswatun Khasanah2, MohdHairi Yusof1,
Nur Farah Atirah Baharudin1, Nur Ain Ayunni Sabri3, MohdKamarulIrwan Abdul Rahim4
1Department of Mathematics, Faculty of Science and Mathematics,
Universiti Pendidikan Sultan Idris, Malaysia
2
Department of Mathematics Education, Faculty of Education and Teacher Training, Universitas Ahmad Dahlan, Indonesia
3Faculty of Entrepreneurship and Business, Universiti Malaysia Kelantan, Kelantan, Malaysia 4Pusat PengajianPengurusanTeknologidanLogistik, Universiti Utara Malaysia
*Corresponding Author mail: mazlini@fsmt.upsi.edu.my1
Article History: Received: 10 November 2020; Revised: 12 January 2021; Accepted: 27 January 2021;
Published online: 05 April 2021
Abstract: This study aimed to examine the level of students' conceptual knowledge on mathematics. In addition, the
difference between conceptual knowledge based on gender and program was also studied. Measurement of knowledge is based on the Conceptual Knowledge Test (CKT). A total of 350 respondents were selected from five daily secondary schools in PetalingUtama, Selangor as a sample of the study. The data were analyzed using descriptive analysis to find out the level of variables measured. In order to identify the main effects and interactions between gender and program variables, inference analysis is a two-way ANOVA test performed for conceptual knowledge dimensions. The findings showed no interaction effects between gender for conceptual knowledge of mathematics (p <.05), but it showed a significant effect on the program (p> .05). In conclusion, mathematical knowledge is very important at the upper secondary level as a high level of mathematical thinking is required to ensure excellent in mathematica l achievement.This is essentially as a long time learning system and methods as well as the imitation approach and dependent on the examinations orientation has long been a measure of student achievement. The implication of this study is that basic conceptual knowledge of students' mathematics needs to be enhanced to realize Malaysia's aspiration to be in the top third place in international assessments such as TIMSS and PISA.
Keywords: Conceptual Knowledge, Secondary School Mathematics, Daily School
1. Introduction
Conceptual knowledge involves the knowledge of symbols, knowing the various mathematical facts, understanding answers after using the algorithm or procedure is correct or false(Abu Bakar, Noor Shah, Nor'ain&Bhasah, 2003).Mazlini et al. (2012) defines conceptual knowledge as a student's ability to define a concept based on several criteria in addition to recognize the relationship of a concept with another concept. Examples of conceptual knowledge are squares, broad functions, four basic operations of mathematics - addition, subtraction, multiplication and division, linear equations and integrations. According to Hiebert and Lefevre (1986), conceptual knowledge is not learned through memorization but it is through the process of reflective thinking and learning.
The definition of conceptual knowledge was also given by Kilpatrick et al. (2001) as a calculation, competency strategies, and ability to worship, formulate and solve problems, ability to suppress, ability to make reflection, describe and explain the answers and knowledge about the needs of mathematical knowledge and also have the belief in mathematics. This conceptual knowledge is formed through constructive and meaningful learning as classifying objects according to common characteristics and responding to their common characteristics (Mazlini et al., 2012). According to Baker and Czamocha (2002), when students have been able to identify, labelling and produce an example, then they have exhibited their conceptual knowledge. It is supported by Mazlini et al. (2012) which states that the conceptual knowledge of a student is related to the student's ability to give reason or justification in situations involving the definition of a concept, relationship and both in the process of solving mathematical problems. This capability can be seen in various ways either verbally or in general through the writing of homework and so on. Hence, generally, conceptual knowledge is defined as the knowledge that is the basis of the mathematical structure in which it connects mathematical ideas that can give meaning to the mathematical procedures.
Another study that supports this conceptual knowledge is the study by NikNoralhuda (2011) that examines the relationship between conceptual, procedural and metacognitive knowledge of form four students in algebraic topics. As a result of her studies, it was found that the form four students were still at a low level in conceptual
knowledge and a moderate level for procedural knowledge. The findings also found that there was no significant difference between gender for both tests but significantly different between science stream and non-science stream.
2. Methodology
This study design in the form of survey that is using test as a main instrument. This method was conducted on form four students in algebraic topics of mathematic in five secondary schools in PetalingUtama. The population of this study is all form four students in PetalingUtama. The sampling method for this study is a random cluster sampling. The distribution statistics on form four students at secondary school in PetalingUtama are 6512, consisting of 3244 male students (49.82%) and 3268 pupils (50.18%) (PPD PetalingUtama, 2015). Sample size determination for this study was based on sample determination table by Krejcie and Morgan (1970). Therefore, the researcher selected a sample of 400 people involved in this study because taking into account the return of the questionnaire from respondents who normally did not get the full return (Chua, 2012). After the questionnaire received, only 350 respondents from 5 schools were selected to complete all the instruments. From these values, the percentage of science stream students (59.4%) (208) exceeds non-science stream students (40.6%) (142). The number of respondents by gender factor showed that the number of male students (53.4%) (187) was higher than female students (46.6%) (163).
Instruments for measuring this conceptual level have been taken and modified from NikNoralhuda (2011) study. Respondent's conceptual knowledge (CK) consisted of 13 items showing the value of Kuder Richardson 21 (KR21) obtained was 0.670 which is equivalent to the alpha of Cronbach 0.670. Table 2 shows the distribution of the items contained in the conceptual knowledge test used in this study. There are two parts in the instrument used, namely part A: personal information of respondents; part B: Conceptual Knowledge Test. Part A contains questions to get respondents' demographic information in terms of program, gender and mathematical grade results at the end of form three. While part B is a question of conceptual knowledge test (13 items) which involved optional questions and open questions. This test was analyzed using the SPSS version 21 program.
3. Result and Discussion
Conceptual Knowledge
Overall, the mean score of the conceptual knowledge form four students is 67 out of 100 total marks. Based on the score of this conceptual knowledge test, the score is categorized as being at a moderate level (mean = 2.01, s.d = 1.02). Specifically, 130 (37%) students are at an excellent level, 140 (40%) students are at moderate level, 28 (8%) students are at low level and 52 (15%) students are at very low level. The results of this study indicate that the level of the form four student knowledge level is at a moderate level.
Conceptual Knowledge of form four students based on gender and program
Analysis of the difference score for knowledge and the effects of main factors on the independent variables was done using two-way ANOVA analysis.
Table 1. Level of Conceptual Knowledge based on Gender
Variable Gender Mean s.d
Conceptual Knowledge Male Female 58.98 60.66 24.482 21.915
The interpretation of the mean value in Table 1 shows the level of conceptual knowledge is moderate for both gender, with mean = 58.98 and standard deviation = 24.48 for male students. While for female, mean is 60.66 and standard deviation = 21.915. Of these mean values, it is observed that female get higher scores than boys.
Table 2. Level of Conceptual Knowledge based on Program
Interpretation of the mean value as in Table 2 shows that the level of conceptual knowledge is moderate for non-science flow with mean = 55.57 and standard deviation = 24.34 for science stream with min =
Variable Program Mean s.d
Conceptual Knowledge Science Non-Science 62.63 55.57 22.18 24.34
62.63 and standard deviation = 22.18. In conclusion, students of science stream higher the level of conceptual knowledge of their mathematics compared to non-science stream students.
Difference of Conceptual Knowledge based on Gender and Program
Before the two-way ANOVA Test can be performed on the conceptual knowledge score based on gender and program, testing of the score should be done using the Levine test.Table 3 shows the mean of each group. Mean for male science stream is 63.06, slightly different from non-science stream male with mean 53.99. Mean for female science stream is 62.21 also slightly different from non-science stream female is 57.86.
Table 3. Mean Score of Conceptual Knowledge based on Gender and Program
Gender Program Mean s.d N
Male Science 63.06 22.991 103 Non-Science 53.99 25.450 84 Total 58.98 24.482 187 Female Science 62.21 21.452 105 Non-Science 57.86 22.649 58 Total 60.66 21.915 163 Total Science 62.63 22.178 208 Non-Science 55.57 24.337 142 Total 59.77 23.304 350
Table 4. Levine Test Score of Conceptual Knowledge Form Four Student
F dfl df2 Sig.
1.348 3 346 0.259
The Levine test in Table 4 shows the variance of each group for independent variables (Score CKT) significantly different, F (3,346) = 1.348, p> .05. This means the variance value in each group of respondents of the study is no different. The survey data comply with ANOVA test requirements.Two-way ANOVA test results showed no major effect of the independent variable Gender [F (l, 346) = .354, p> .05]. However, there is a significant effect on the independent variables of Program [F (l, 346) = 6.97, p <.05] to the dependent variable Conceptual Knowledge Level. The effect of the interaction between the two independent variables of Gender and Program to the dependent variable did not exist significantly [F (l, 346) = .863, p> .05] (Table 5).
Table 5. ANOVA Test of Conceptual Knowledge based on Gender and Program
Source of Variation Sums of Square df Mean Square F Sig.
Model correction 4757.863a 3 1585.954 0.032 2.970
Reflection 1162183.583 1 1162183.583 0.000 2176.198 Gender 189.176 1 189.176 0.552 0.354 Program 3721.314 1 3721.314 0.009 6.968 Gender * Program 461.028 1 461.028 0.353 0.863 Error 184778.926 346 534.043 Total 1439716.000 350 Total Correction 189536.789 349
The main impact and effect of interactions between the two independent variables contribute 2.5% to the changes in dependent variables. This means that only a small change of 2.5% of the Conceptual Knowledge Level score in this study is due to gender, program and combination between gender and program.
Table 6. Mean of Conceptual Knowledge based on Gender
Gender Mean s.d 95% Confidence Interval
Lower Bound Upper Bound Male Female 58.523 60.036 1.699 1.890 55.182 56.318 61.864 63.754
The data in Table 6, estimated mean marginal for gender independent variables shows the mean female (mean = 60.04) over the mean of male (mean = 58.52). This significantly indicates that female is more likely to have a high level of conceptual knowledge than male.
Table 7. Mean of Conceptual Knowledge based on Program
Program Mean s.d 95% Confidence Interval
Lower Bound Upper Bound Science Non-Science 62.634 55.925 1.602 1.973 59.482 52.045 65.786 59.805
The data in Table 7, estimated marginal means for program-independent variables shows the mean value of the science stream (mean = 62.63) over the mean of non-science stream (min = 55.93). This significantly shows that students from science stream are more likely to have a high level of mathematical conceptual knowledge than students in non-science streams. The standard deviation value shows the difference obtained when the study was repeated. The small value of the standard deviation in the table shows that if the review is re-performed, the mean value obtained similar. This shows the data of this study is reliable.
Table 8. Mean Score of Conceptual Knowledge Form Four Student
Gender Program Mean s.d 95%Confidence
Lower Bound Interval Upper Bound Male Science 63.058 2.277 58.580 67.537 Non-Science 53.988 2.521 49.029 58.947 Female Science 62.210 2.255 57.774 66.645 Non-Science 57.862 3.034 51.894 63.830
In Table 8, estimated marginal mean for the combination of both variables show mean values for male students in the science stream (mean = 63.06), overriding the mean value of male students in non -science stream (mean = 53.99), while female students in the science stream, (mean = 62.21) outgrew the mean for female in non-science stream (mean = 57.86). This suggests that significantly, for male students, the level of conceptual knowledge is higher for the program of science and the same situation also applies to female. This proves that gender variables do not have a significant impact on the level of mathematical knowledgebut program variables have a significant effect on the dependent variable.
Figure 1 shows that there is a significant effect for variable program and gender. However, both are not inter-related (graph do not cross) against dependent variables in this study. In this case there is no parallel effect interaction between male and female students. Available for both science and non-science, students from science stream have higher level of procedural knowledge than students from non-science stream. However, female in non-science streams are better in conceptual knowledge than male.
The two-way ANOVA test results for gender-free and program samples on the dependent variable of the conceptual knowledge stage showed that the main effects of the flow-free variables [F (l, 346) = 4.14, p <.05]. However, for gender-independent variables [F (l, 346) = .342, p> .05], it was found to have no effect on the conceptual knowledge level of form four students surveyed. The effect of the interaction between the two independent variables against dependent variables [F (l, 346) = 20.785, p> .05], does not exist significantly. The same analysis results are also obtained for the main effects of independent variables on the stage of conceptual knowledge. The main impact of gender variables [F (l, 346) = .354, p> .05] did not affect the conceptual level of knowledge. However, for the independent variable of the program [F (l, 346) = 6.97, p <.05] there is a significant effect on the dependent variable.
The results of the data analysis also showed that the main effects and interaction effects between the two independent variables accounted for a small fraction of 2.5% on the level of conceptual knowledge of mathematical form four students. This means that less than 3.0% of the conceptual level of knowledge score is due to gender and flow factor while more than 97.0% is due to other factors not studied in this study.
The findings show that the conceptual knowledge of female is better than male students. However, the findings of this study differ from that of the National Assessment and Educational Progress (NAEP) which in some of its studies to evaluate the development of education in Denver shows that male students have better achievements than female in high school mathematics (Erickson & Erickson, 2004). Similarly, in terms of applying knowledge and mathematical skills, a study on Grade 12 students in British Columbia schools shows that male is significantly better than female. This study found that the conceptual knowledge of female is better than male students. From psychological aspects, female is more likely to understand a cognitive knowledge because of their ability to research and analyze critically. But male is more focused on mastering hands-on or process knowledge. Based on the findings, it also shows that the program also affects students' mathematical achievement, especially at upper secondary level. In addition, the findings are also in line with the study by Nur Aida (2017) in terms of program. Nur Aida found students in the science stream is better conceptual knowledge than students in non-science streams.
4. Conclusion
In conclusion, mathematical knowledge is very important in the upper secondary level since a high level of mathematical thinking is needed to ensure success in mathematical achievement. Knowledge of the understanding of a mathematical concept belonging to a student is an important asset for all educators. This knowledge not only can assist educators in understanding the actions and thoughts of students while solving a mathematical problem, but it can also help educators to prepare in the appropriate teaching and learning process. Often educators are too focused on the teaching process that only emphasizes skills of solving problems and letting students find out the relationship or link between the concepts they are learning. Students are only expected to achieve a formal level of thinking in view of the topics contained in the syllabus.
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