CC BY-NC-ND
0Available online at www.sciencedirect.com
V ScienceDirect Procedia
Social and Behavioral Sciences
Procedia Social and Behavioral Sciences 8 (2010) 213-218
International Conference on Mathematics Education Research 2010 (ICMER 2010)
Comparison of Basic Mathematic Skills between Students with
Different Studying Approaches
Ghasem Rekabdara*, Bahare Soleymanib
a'bIslamic Azad University -Abadan Branch, Iran
Abstract
The purpose of this research was to compare basic mathematic skills based on the students studying approaches. In order to carry out this study, a sample of 139 students in the second (spring) semester of 2009 academic year studying in Ahwaz university were chosen through a cluster method at random. Approaches Study Skills Inventory for Students (ASSIST) is used to measure the student studying approaches. Based on Bayesian information criterion (BIC) regarding ASSIST scale, the students are classified into three groups. By two-step cluster method analysis the students are classified as strategic, surface and deep studying approaches. The findings of one-way (ANOVA) show that students' mathematic basic skills were significantly different among students who adopted different studying approaches viz-a-viz strategis, surface and deep approach. LSD post hoc test indicated that the students with the deep studying approach have higher basic mathematical skills in comparison with that of students with surface and strategic studying approaches.
© 2010 Elsevier Ltd. All rights reserved.
Keywords: Studying approaches, Mathematics skills, ASSIST scale, Cluster analysis
1. Introduction
Today's students live and work in the twenty-first century, in an era dominated by computers, world-wide communication, and by a global economy. Jobs that contribute to this economy require workers who are prepared to absorb new ideas, to perceive patterns, and to solve unconventional problems. Mathematics is the key to opportunity for these jobs (Steen, 1989). Despite these applications of mathematics in life and professions, mathematics is still troublesome and a leading anxiety for most people and students.
Research in mathematics education indicates that there are many factors influencing mathematics performance and achievement. A review of literature on mathematics, self-concept, mathematics self-efficacy, learning styles, mathematics anxiety, and attitude toward mathematics has shown that these variables are related to mathematics performance and achievement (McCoy, 1992; Bassant, 1995; Ma, 1999).
ELSEVIER
* Corresponding author. Tel.: +98-631-4456344; fax: +98-631-4456344. E-mail address: ghasem_rekabdar@yahoo.com.
1877-0428 © 2010 Published by Elsevier Ltd. doi:10.1016/j.sbspro.2010.12.029
One of the variables probably related to mathematics performance is the studying approach. The studying approach refers to how a learner is engaged in the subject matters. Biggs (2003) has identified three different approaches to studying: i) deep approaches are characterized by a preference to work conceptually and are driven by intrinsic curiosity. ii) strategic approaches are characterized by a focus on obtaining high marks and organized studying; and iii) surface approaches are characterized by an intention to achieve a pass, avoid too high a workload, misunderstanding requirements, and or thinking that factual recall is all that is required. Finding indicated that surface approach is associated with a less successful academic performance and deep and strategic approach is associated with higher academic performance (Diseth & Martinsen, 2003). There is a little research about the relation between the studying approaches and the mathematics performance. Crawford, Gordon, Nicholas and Prosser (1998) concluded that "...fragmented conceptions of mathematics are associated with surface approaches to learning mathematics". On the other hand, cohesive conceptions of mathematics are associated with deep approaches to learning mathematics when students holding cohesive conceptions of mathematics adopt deep approaches to learning mathematics, and have very different interpretations of learning mathematics.
Statistically, the high number of educational fall-off in mathematics is a common problem of Iranian students. The findings of the third international mathematics and science study (TIMSS, 2003) emphasize the weak performance of Iranian students in the mathematics fields. The results of these researches indicate that Iran ranks 34th in mathematics of the third grade in secondary education among 46 countries and 22th among 25 countries of fourth grade. Therefore, it is necessary to inquiry the reasons for the students failure and to determine the variables which can be inquired for the students studying approaches. The studying methods of successful individuals are one of the influential ways to find the best method of studying and learning. Identifying the studying procedures of successful individuals and teaching these procedures to other students can play an important role in promoting the national culture and improving the education quality.
The studies which were carried out on the relationship between studying approaches and the mathematics performance indicated some measure of correlation between mathematics performance with studying approaches or learning methods. However, these studies do not particularly indicated the type of individuals with specific studying approaches in relation to mathematical skills. Thus the aim of this study is to compare students' mathematics skills based on the different studying approaches. Accordingly, two research questions are formulated:
1) How many clusters of studying approaches do we have among university students?
2) Do the basic mathematic skills differ significantly by the different studying approaches adopted by the university students?
2. Methodology
Participants of this research are all students from Ahwaz University who had been studying at the second semester of 2009 academic year, and the sampling method is cluster method. A number of classes are picked out randomly from students of computer, accounting, and banking major. Total sample includes 139 students (35 males and 109 females) and their age ranges from 18 to 39 years old, and the mean is 22.47 years old and standard deviation is 2.71 years old. To measure their basic mathematical skills, we used a five-choice test of 15 items which was used in Johnson & Kuennen (2006). To measure the students studying approach, the short version of the list scale of Approaches & Study Skills Inventory for Students (ASSIST) was used. This instrument was adopted from Entwistle (2008). This scale has three factors and each factor has 6 items with 5 point Likert scale (1=disagree to 5=highly agree) The sum of each factor values indicates the amount of strategic, deep and surface approaches. Cronbach alpha's reliability coefficient was 0.67, 0.51 and .062 for strategic, deep and surface approaches respectively.
Data analysis is carried out through two stages. In the first stage in order to answer the first question and to determine either the numbers of the studying approaches among the students or the number of groups which can be sorted by ASSIST scale, we use Bayesian Information Criterion (BIC). After that we determine the numbers of groups by use of two step cluster analysis with the maximum likelihood criterion in order to classify the students in groups and to identify the studying approaches. Then through the second stage, to answer the second question, we use the One-way Analysis of variance with dependent variable of the basic mathematic skills and independent
variable of the studying approaches. The post hoc test, the least significant differences (LSD), is used to study the significant differences of approaches in the basic mathematic skills. To analyze the data and answer the research questions we use SPSS Software, Version 13.
3. Findings
Table 1 illustrates the correlation between students' basic mathematic skills scores and each sub-scale of ASSIST studying approaches. As you can see, basic mathematic skills have a significant negative relationship with the surface studying approaches(r=-0.23, p<0.01). On the other hand, with the decrease in the surface studying approaches, there is an increase in the basic mathematic skills. Also there is a direct relationship between the basic mathematic skills and the deep studying approach, but this relationship is not significant (r=0.126, p>0.05). The basic mathematic skills has a significant positive relation with the strategic studying approaches(r=0.226, p<0.01). On the other hand, with the increase in the strategic studying approaches, there is an increase in the basic mathematic skills.
Table 1. Correlation of basic mathematic skills with ASSIST sub-scales
Approach Math performance P-value N
Surface -0.23 0.007 139
Strategic 0.226 0.007 139
Deep 0.126 0.141 139
Figure 1 indicates the computed values of BIC criterion by their number cluster. The standardized values of ASSIST and the sub-scales of ASSIST are used to compute BIC. Figure 1 shows the value of BIC of the cluster and as it can be seen number 3 has the lowest (BIC=275.56).Therefore in order to answer the first research question, We must say that the number of the cluster which can be determined by ASSIST scale for the students studying approaches are 3 clusters.
CLUSTER
Figure 1: Value of BIC criterion by the ASSIST cluster
After determining the number of the cluster, the students are classified into clusters by two step cluster method and by use of the maximum likelihood criterion, and in order to determine the clusters' names and to identify the students studying approaches, we compare the mean of the clusters.
Figure 2: Error bar plot of the sub-scales standardized volume in each cluster
Figure 2 illustrates the plot of the means error bar standardized for each sub-scale. As observed, 47 students are classified into the first cluster. The mean middle bar indicates the group strategic approach as at a higher level in comparison to the means of other bars. The students who are included in this cluster are known as those using the strategic studying approach. Also 45 students are classified into the second cluster. Their surface studying approach sub-scale means is higher in comparison with other sub-scales. The students of this cluster have the surface studying approach and 47 students are in the third cluster, whom maybe categorized as having the deep studying approach.
Table 2. Mean and standard deviation of basic mathematic skills in each cluster
Approach Deep(n=47) Surface(n=47) Surface(n=45)
Mean 10.51 8.91 8.24
SD 2. 93 3.29 3.73
Table 2 indicates the mean and standard deviation of basic mathematic skill test for each cluster of the studying approach among students. In order to study the significance of means differences in basic mathematic skills between students studying approaches, one-way ANOVA was conducted. The independent variable is the students studying approach and dependent variable is the basic mathematic skills as shown in Table 3. As the table shows, basic mathematic skill mean has a significant differences in different studying approaches (F (2,136) = 5.6, p<0.01).
Table 3. One-way ANOVA for perfection the variable effect on math's performance
Source Sum of squares df Mean square F P-value
Between groups 125.45 2 62.72 5.6 0.005
Within groups 1523.71 136 11.2
Total 1649.16 138
Table 4 indicates the multi-comparison of the means in the basic mathematic skills using the LSD method. According to this table, there is not a significant difference between strategic and surface studying approaches
(p=0.339). The mean difference of the basic mathematic skills between the deep and surface studying is positive and significant (p<0.01), and between the deep and strategic approaches is positive and significant (p<0.05). On the other hand the students with deep studying approaches have higher basic strategic and surface studying approach.
Table 4. The summary of LSD test for comparing the mathematics skill mean of studying approach
Approach(I) Approach(J) Mean differences(I-J) Standard error P-value
strategic Surface 0.64 0.698 0.339
deep Surface 2.27 0.698 0.001
deep strategic 1.60 0.690 0.022
4. Conclusion
This study aims to compare the basic mathematic skills among different studying approaches of the university students. The correlation of the basic mathematic skills with studying approaches indicates that these skills have positive relation with the strategic approach and a negative significant relation with the surface approach. There is also a positive relationship between the basic mathematic skills and deep studying approach, although it is not significant. Consideration of the analysis of correlation indicates the occurrence of variables together while the analysis of correlation does not indicate which group of students scored higher than the others. The cluster analysis makes it possible to classify the students into three groups. The one-way ANOVA analysis and multi-comparison of LSD confirm that the students with deep studying approach have higher basic mathematic skills than the students with the surface and strategic studying approaches.
Saif (2007) concludes that "...in measuring the students' performance, teachers should design items which
encourage understanding, judgment and critical thinking of learners, so that the learners understand the concepts and subjects through a deep approach. Beside the casual tests, teachers had better provide students with homework which need higher mental activities and ask the learners to do these activities for learning (p.629)". In mathematical instructions, the teacher should try to apply methods which promote the students problem-solving skills and its instructional the subject. This judgment ability and the review of the previous method could be raised in the students' minds and the teacher should avoid giving the homework which was explained completely in classes and those which don't require any creative mental activities. Unfortunately some teachers and mathematics lectures use the items in test which were answered during class sessions and this leads to the surface studying approaches among students.
In educational systems, there is a little emphases on training the appropriate studying method and it is believed that students would discover proper procedures of studying and learning automatically. But it is necessary for students to learn the proper methods, techniques and procedure of studying. There is considerable contemporary research to suggest a link between good teaching and a deep orientation to learning (Crawford et.al., 1998; Biggs, 2001). The use of active learning strategies in the classroom enables students to apply mathematical concepts and to foster meaningful learning (Crawford & White, 1999).
Based on the findings of this study, in which higher basic mathematics skills students were associated with deep studying approach, it is recommended that mathematics teachers need training into studying and learning approaches and how these approach are applied for learning and educational improvement. It is necessary to study the educational impact on such methods and studying approaches and mathematics performance by experimental methods. For example the studying method proposed by Danserau et. al., 1979 is one suitable method to increase learning and studying of mathematics. Other methods such as cooperative learning method can be probably suitable. Research findings suggest that cooperative learning strategies are typically associated with improved student achievement (Ma, 1996).
References
Bassant, K. C. (1995). Factors associated with types of mathematics anxiety in college students. Journal of Research in Mathematics Education, 26, 327- 345.
Biggs, J. (2003). Teaching for quality learning at university (2nd ed.). Berkshire, UK: Open University Press.
Crawford, K., Gordon S., Nicholas, J. and Prosser, M. (1998). Qualitatively different experiences of learning mathematics at university, Learning and Instruction, 8(5), 455-468.
Crawford, M., & White, M. (1999). Strategies for mathematics: Teaching in context. Educational Leadership, 57(3), 34-38.
Dansereau, D. F., Collins, K. W., McDonald, B. A., Holley, C. D., Garland, J. C.,Diekhoff, G., & Evans, S. H. (1979). Development and evaluation of a learning strategy program. Journal of Educational Psychology, 71, 64-73.
Diseth, A., & Martinsen, O. (2003). Approaches to learning, cognitive styles, and motives as predictors of academic achievement. Educational Psychology, 23, 195-207.
Entwistle, N. (2008) Taking stock: teaching and learning research in higher education. Review prepared for an international symposium on "Teaching and Learning Research in Higher Education",Guelph, Ontario, April, 25-26, 2008.
Jhonson, M., Kuennen, E.,(2006). Basic Math Skills and Performance in an Introductory Statistics Course. Journal of Statistics Education ,14(2), Retrieved June 11, 2009, from www.amstat.org/publications/jse/v14n2/johnson.html.
Ma, X. (1996). The effects of cooperative homework on mathematics achievement of Chinese high school students. Educational Studies in Mathematics, 31, 379-387.
Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for research in mathematics education, 30(5):520-540.
McCoy, L. (1992). Correlates of mathematics anxiety. Focus on Learning Problems in Mathematics, 14(2), 51-57.
Saif, A., A.(2007). Modern Educational Psychology: Psychology of Learning and Instruction. (6 rd ed.).Tehran: Dowran (In Persian).
Steen, L., A.,(1989). Teaching Mathematics for Tomorrow's World. Educational Leadership, 47(1) ,18-22.
TIMSS(2003). Timss 2003 International Mathematics Reports. Retrieved March 21, 2009, from http://timss.bc.edu/pdf/t03_m_front.pdf.
