A comparative analysis of the relationship between learning styles and mathematics performance

Learning styles

In our ever-evolving society, it has become increasingly apparent that ‘each student plays an integral role in his individual learning experience’ (Weinstein and Hume 1998, p. 6). While teachers prepare lessons and present information, it is ultimately the student who interprets, understands, and retains such information in a way that permits facile retrieval and recall for application. In order to perform these tasks, students employ different preferences for and habits of sense making. A learning style is defined as the way in which a person ‘begins to concentrate on, process, internalize, and remember new and difficult academic information’ (Hall 2008, p. 6). Learning styles therefore indicate how the student ‘perceives, interacts with, and responds to the learning environment’ (Hall 2008, p. 6).

Although the concept of learning styles appeared as late as the 1970s, there have been many different ways to approach this concept. Nevertheless, it is fairly reasonable to classify learning styles from two main perspectives. One pertains to individual processing of information (e.g., auditory, visual, and kinesthetic; see Pashler et al. 2009); the other pertains to individual relationship with other learners (i.e., competitive and cooperative; see Johnson and Johnson 1989). Competitive and cooperative as learning styles are the focus of the present research.

In a classroom setting, the competitive learner implements an individualistic personal learning plan and employs learning strategies that enable the learner to achieve learning goals (Johnson and Johnson 1989). Competitive learners often see all students in the class as working towards the same goal of learning. However, the competitive learner wants to not only become the first in achieving that goal but also achieve that goal in a more outstanding manner than the peers (Montgomery and Groat 1998). Consequently, competitive learners often see academic performance as a system of few winners and many losers. The chief benefit of the competitive learning style is the motivation that stimulates great learning effort (e.g., Burguillo 2010). On the other hand, some educational psychologists have argued that competitive learning may not be desirable because it produces high stress, low self-concept (in the case of failure), cheating, and aggression in the classroom (Johnson and Johnson 1989).

A composite variable was constructed in PISA that measures competitive learning style. The composition of the competitive learning variable includes the following: (a) I would like to be the best in my class in mathematics; (b) I try very hard in mathematics because I want to do better on the exams than the other students; (c) I make a real effort in mathematics because I want to be one of the best; (d) in mathematics, I always try to do better than the other students in my class; and (e) I do my best work in mathematics when I try to do better than others. This composite appears to sufficiently catch the essence of the competitive learning style (see Montgomery and Groat 1998).

A foil to the competitive learner, the cooperative learner tends to enjoy working in a group or team setting. Cooperative learners, in an effort to achieve a certain goal of learning, often break down tasks into specific roles which are then assigned to members of the group (Murphy and Alexander 2006). Individual members subsequently accomplish their specific tasks and then share their findings with the whole group. The cooperative learner is far less concerned with ‘being number one’ than the competitive learner, and cooperative learning puts significant emphasis on the group dynamic and on the progress of the group as a whole. Many educational psychologists have praised the enhanced exchange of information, knowledge, and skills as well as the interdependence and individual accountability, all forged and fostered by a cooperative learning environment (e.g., Slavin 1980; Weinstein and Hume 1998). As its chief disadvantage, the cooperative learning environment is difficult to establish and many teachers struggle with the implementation in their classrooms (e.g., Gillies and Boyle 2010).

A composite variable was constructed in PISA that measures cooperative learning style. The composition of the cooperative learning variable includes the following: (a) in mathematics, I enjoy working with other students in groups; (b) when we work on a project in mathematics, I think that it is a good idea to combine the ideas of all the students in the group; (c) I do my best work in mathematics when I work with other students; (d) in mathematics, I enjoy helping others to work well in a group; and (e) in mathematics, I learn most when I work with other students in my class. Arguably, these variables are sound indicators of the cooperative learning style (see Murphy and Alexander 2006).

In general, cooperation is more effective for higher-order tasks (e.g., problem solving), whereas competition is more effective for lower-order tasks (e.g., rote learning) (e.g., Johnson et al. 1981; Johnson et al. 1980). These researchers concluded in their meta-analyses that students completing academic tasks under cooperative conditions tend to outperform students completing academic tasks under competitive conditions. Later on, another meta-analysis replicated this conclusion (Qin et al. 1995).

Johnston (1997) argued that, to promote academic success, educators need to understand how students differ in their approaches to learning tasks and use that understanding to create strategies for learning. Johnson et al. (2000) examined eight cooperative learning methods and found that all of them indicate significantly positive effects on academic achievement. Specific to mathematics education, Bell (1989) asserted that, to increase mathematics performance, how students learn in mathematics must be analyzed. Hall (2008) also asserted that learning styles are a significant determinant of mathematics performance. In general, review of educational research has indicated a positive relationship between learning styles and mathematics achievement (Middleton and Spanias 1999). Overall, it is important to investigate learning styles as a critical variable in explaining mathematics performance.

People are not born to share a genetic predisposition in terms of the learning approach; instead, they learn how to conduct learning through a socialization process that is unique to each culture (Nelson 1995). Of course, some learning styles can be common to students around the world. For example, if tests require students mainly to reproduce knowledge, then memorization dominates their learning styles (Au and Entwistle 1999). But, other learning styles can be very culturally specific. Singleton (1991) stated that every culture has unstated assumptions about people and how they learn and these assumptions invisibly guide the educational process in that culture. According to Ma et al. (2013), the research literature that attempts to explain East Asian academic success is comprehensive, but with one weakness that speaks to the lack of attention to the way that East Asian students manage their learning in relation to their academic success. They argued that how students learn may hold important clues to the superior academic performance of East Asian students. Therefore, investigating learning styles in an international context has important implications for improving mathematics education in the USA.

East Asian success

Many researchers have attempted to examine student, family, teacher, and school factors salient in contributing to academic achievement in East Asia (see Ma et al. 2013). One popular perception is the amount of emphasis on effort over ability in East Asian cultures (Stevenson and Stigler 1992). Meanwhile, other researchers have attributed ability to academic success in East Asia (Eccles and Wigfield 1995). More recent studies have primarily focused on attitudes rather than behaviors, showing that students in East Asian countries have a significantly higher level of interest and motivation in learning than students in other highly developed countries (Bybee and McCrae 2011; Liu et al. 2006). Based on results from PISA and TIMSS, Watkins (2000) cautioned about the use of affective factors to explain disparities in mathematics performance between the USA and East Asia because students in some of the best-performing East Asian countries indicate low self-esteem and negative attitudes towards mathematics. Studies of mathematics performance among East Asian students also indicate parental education and expectation as primary determinants correlating positively to mathematics performance (Leung 2010).

Researchers who studied the high academic achievement of Japanese students claimed that important teacher and school variables should be considered when explaining East Asian academic success (Woodward and Ono 2004). East Asian schools are notable for large class sizes with a typical middle school class containing an average of 50 students. Watkins (2000) found that large classes in East Asian schools contribute to their students' superior performance in mathematics, reasoning that a large class size permits a widespread influx and circulation of ideas and insights that can facilitate deep understanding of mathematics. Superior performance in mathematics of East Asian countries has also been attributed to high national standards and expectations (Valverde and Schmidt 2000) and mathematics content that emphasizes depth rather than breadth (Kaya and Rice 2010). Some researchers noticed that East Asian students are very respectful toward teachers and maintaining an excellent relationship with teachers can be critical to learning (Stevenson and Stigler 1992), whereas other researchers warned that such an elevated level of respect can interfere with learning when students do not feel comfortable questioning what teachers say (Jeynes 2008).

In addition, a high societal expectation is always placed on teachers to be highly skillful in curriculum and instruction to help students learn and succeed in East Asian countries. Ma's (1999) influential study indicated that Chinese teachers have a much deeper understanding of mathematics content than American teachers. Other studies based on classroom videos have also shown that East Asian teachers present clearer lessons and engage students more in the learning process (Jacobs and Morita 2002; Leung 2005). Professional development may have played a central role in East Asian teachers' success (Fernandez et al. 2003).

The quality of instruction is considered as another prime contributor to the superior mathematics performance of East Asian students. Mathematics curriculum established by East Asian countries mandates that teachers do not simply place emphasis on the development of lower-level cognitive skills; instead of instructing students through the medium of rote memorization, East Asian mathematics teachers are expected to promote higher level critical and analytical thinking in their classes (Liu et al. 2006). This encouragement of higher-order thinking skills in East Asian mathematics classes may enable students to gain a more in-depth understanding of mathematics and apply their knowledge in more novel ways. East Asian mathematics teachers are also much more group-oriented than mathematics educators in other countries. In East Asian countries, it is not uncommon for a mathematics teacher from one school to observe and critique the teaching practice of a mathematics teacher from a different school, and this group teaching dynamic may have enabled East Asian mathematics educators to better refine their teaching practices and further tailor their teaching to the individual needs of their students (Watkins 2000). In the research literature, there are other accounts for East Asian success as the result of high levels of pressure to perform well on exit exams, additional outside schooling, and strong family support (e.g., Bray 2010; Cave 2001; Watanabe 2000).

According to Ma et al. (2013), the research literature on East Asian academic success, even though comprehensive, lacks attention to whether academic success of East Asian students correlates with how they manage their learning process. They began this important line of inquiry by exploring the success of six top-performing East Asian countries (regions) in PISA 2009 (Hong Kong, Japan, Korea, Shanghai, Singapore, and Taipei). Their search for reasons for success concerned about student academic behaviors such as the use of learning strategies and meta-cognitive skills among students and school climatic attributes such as disciplinary climate among schools. They found striking total consistencies across all academic areas (reading, mathematics, and science) and across all countries (regions) that highly successful students were skillful users of advanced learning strategies in their learning and knew how to utilize meta-cognitive skills in the process of their learning. They reported that these positive effects are not only comprehensive but also the strongest among all statistically significant student academic behaviors. In line with Ma et al. (2013), the present research aims to examine the relationship between learning styles, another important aspect of how students manage their learning, and mathematics performance among American and East Asian students.

Samples

Data used to answer the research questions were obtained from the 2003 PISA database. As one of the latest databases accessible for data analysis of secondary education, PISA has been appraised as a valuable means to examine student literacy in reading, mathematics, and science. PISA shifts its focus from one subject to another, allotting specific student evaluation to one subject for each cycle of assessment. When the present research was conducted, PISA 2003 was the most recent source of comprehensive (student) data concerning mathematics performance. To fulfill the comparative perspective, the present research incorporated PISA samples from Hong Kong (4,478 students from 145 schools), Japan (4,707 students from 144 schools), Korea (5,444 students from 149 schools), and the USA (5,456 students from 274 schools) to generate statistical models.

Variables

Variables for the present research came from the PISA database that contains student achievement test data as well as responses of students and principals to surveys. The dependent variable was performance in mathematics literacy defined in PISA as the ability to ‘identify and understand the role that mathematics plays in the world, to make well-founded judgments and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned, and reflective citizen’ (Organization for Economic Co-operation and Development 2006, p. 24). Specifically, mathematics literacy covers quantity, space and shape, change and relationships, and uncertainty.

Independent variables came from students and schools (principals). At the student level, the independent variables included gender (coded as 1 = male and 0 = female), age (a continuous variable in years), father socioeconomic status (SES) (a continuous composite variable), and mother SES (a continuous composite variable). The key independent variables were competitive and cooperative learning styles at the student level¹. Both were continuous composite variables as discussed earlier. In PISA, each composite variable is standardized based on data from all participating countries (regions). Therefore, each value descriptive of, say, competitive learning is a score in reference to the grand average value of using competitive learning worldwide.

At the school level, some independent variables measured school context, including student-teacher ratio (a continuous variable), school mean father SES (a continuous variable aggregated from father SES of students within a school), school mean mother SES (see school mean father SES), proportion of certified teachers (a continuous variable), and quality of school educational resources (a continuous composite variable)². Other independent variables measured school climate, including school disciplinary climate (a continuous composite variable), teacher-student relationship (a continuous composite variable), student behaviors (a continuous composite variable), teacher behaviors (a continuous composite variable), school autonomy (a continuous composite variable), teacher participation (a continuous composite variable), and ability grouping (for all core school subjects) (coded as 1 = yes and 0 = no). Additional file 1 shows the construction of school-level composite variables.

The present research, with variables descriptive of both students and schools to model the relationship between learning styles and mathematics performance, falls into the research field of school effects; thus, the selection of variables at both student and school levels was based on the theoretical framework of school effects that emphasizes characteristics of student background as well as school context and school climate (see Ma et al. 2008). These categories were captured sufficiently with the above student-level and school-level variables (see Additional file 2 for descriptive statistics).

Analyses

To answer our first research question that concerns about differences in students' use of learning styles across countries, we produced descriptive statistics to indicate the average use of each learning style among students in different countries. To test whether the observed difference across countries is statistically significant, we performed one-way ANOVA. When one-way ANOVA indicated statistically significant results, we applied post hoc analysis (Scheffe) to ‘rank order’ the countries in students' use of a learning style.

where γ₀₀ is the grand national mean score in mathematics and u_0j is the error term at the school level. Coefficients γ_0p (p = 1, 2,…12) are associated with school-level variables. Therefore, the level 2 model functioned to control for school context and climate characteristics in the present research.

Because competitive and cooperative learning are distinct (even though somewhat related) learning styles in the research literature, it is reasonable to analyze their utilizations separately in each country (OECD, 2010)³. In each case, because the key independent variable was the use of a particular learning style, statistical control was implemented at both student and school levels in order to ‘purify’ the relationship between that learning style and mathematics performance. As one of the major methodological decisions, student-level variables were defined as fixed (e.g., gender coefficient does not differ across schools) and the intercept was defined as random (i.e., average performance varies across schools) in all eight HLM models (two for each country). These treatments were in response to Thum and Bryk (1997) who suggested that, for example, if gender differences (across schools) are not a research question, it is appropriate to fix the gender variable. In addition, student-level and school-level variables were centered around their grand means for interpretative and analytical benefits (see Raudenbush and Bryk 2002). Finally, to determine statistical significance of a coefficient, the alpha level of 0.05 was used in the present research.

Summary of principal findings

The present research aimed to elucidate the mathematics performance disparities between American and East Asian students in terms of their use of learning styles. The findings are all situated in the backdrop that American students championed the use of both competitive learning and cooperative learning. The HLM models created for the USA, Hong Kong, Japan, and Korea all indicated that the competitive learning style was significantly and positively associated with mathematics performance. Students' drive to compete against one another to become the best thus mattered to mathematics performance among American and East Asian students. The point of difference between the USA and East Asia (Hong Kong, Japan, and Korea) was in the relationship between cooperative learning and mathematics performance. For East Asian students, increased use of cooperative learning was significantly associated with improved mathematics performance; while for American students, increased use of cooperative learning was not significantly associated with improved mathematics performance.

Common effects in using competitive learning

Table 2 indicates two important patterns concerning competitive learning. The first pattern pertains to the common effects of using competitive learning: competitive learning was significantly and positively associated with mathematics performance across all countries examined in the present research (the USA, Hong Kong, Japan, and Korea). Therefore, for students across the countries, increased use of competitive learning was associated with improved mathematics performance, even though effect sizes were small. The second pattern pertains to the ineffectiveness of competitive learning in the USA: competitive learning had a stronger positive relationship with mathematics performance in both Hong Kong (0.11 SD) and Korea (0.24 SD) than in the USA who had very similar positive results to those of Japan (0.08 SD for both countries). Therefore, from the educational perspective of improving their mathematics performance, East Asian students were able to use competitive learning either more effectively than or (at least) as effectively as American students.

In spite of the often negative views towards competitive learning in the USA (see Bergin and Cooks 2000; Good and Brophy 2008), this learning style demonstrated a consistent positive relationship with mathematics performance across countries. The USA has an inherently individualistic culture in which all individuals aspire to rise to the top. Such competitive spirit is clearly manifested in the learning of mathematics as American students championed the use of competitive learning among all students in the four countries (Table 1). If the pattern is that American students lead the way in competitive learning of mathematics but fall behind in using competitive learning for improved mathematics performance, American students may have applied competitive learning in an ineffective way as far as the improvement of their mathematics performance is concerned. We suspect that the support for American students to engage in competitive learning is inadequate even though they demonstrate the strongest determination to apply competitive learning. Most American educators endorse competition in a very limited way (see Good and Brophy 2008). Meanwhile, although the East Asian cultures do not explicitly promote individual excellence and achievement, the strong pressure to perform well so as to get into top colleges makes intensive academic competition among East Asian students nevertheless inevitable according to USA Today (August 4, 2013). Most East Asian educators recognize this reality and actually endorse competitive learning among students.

Unique East Asian advantage in using cooperative learning

Table 3 illustrates a striking pattern concerning cooperative learning. The pattern speaks to the unique finding of using cooperative learning among East Asian students: cooperative learning had a significant positive relationship with mathematics performance across all East Asian countries examined in the present research (Hong Kong, Japan, and Korea) but not in the USA. Therefore, for students in the East Asian countries, increased use of cooperative learning was associated with improved mathematics performance, even though effect sizes were small. Ironically, for American students who were stronger cooperative learners than their East Asian counterparts, increased use of cooperative learning was not associated with improved mathematics performance in the USA.

Similar to the case of competitive learning, a pattern occurs in which American students lead the way in cooperative learning of mathematics but fall behind in using cooperative learning for improved mathematics performance. This seemingly paradoxical phenomenon may indicate a flaw in the practice of cooperative learning in the USA. We suspect that two things are possible in regard to cooperative learning in the USA. First, many educators consider cooperative learning difficult to develop and implement (see Gillies and Boyle 2010). Students therefore may not have sufficient opportunities to apply cooperative learning to the study of mathematics, even though many students are in favor of this learning style.

Second, even when cooperative learning is practiced in mathematics classrooms, it is likely applied to non-essential content lacking in intellectual depth and rigor. We present two observations from middle school mathematics classrooms in the USA. In both cases, the teaching is labeled as cooperative learning by the mathematics teachers. In one scenario, the teacher demonstrated as an example how to solve a mathematics problem on the board, and then assigned students a practice problem very similar to the one demonstrated but with different numbers. Students were instructed to work in groups of three to discuss and solve the problem. The discussion among students in each group encompassed whether the approach of problem solving demonstrated by the teacher was followed correctly and whether the numerical answer to the problem was correct. In the other scenario, the teacher prepared a stack of review packets that did not contain any new materials (they were basic problems over materials that students already learned). Students were told to work in groups to finish the review packets collaboratively. The discussion among students in each group concerned mainly about answers to problems and occasionally brief explanations of how certain answers were obtained.

In striking contrast, Cheng (2011) described the Chinese concept of cooperative learning in mathematics that emphasizes the ‘analysis and problem solving of complicated issues and knowledge that is of the nature of extensive coverage of the interconnected reasoning path’ (p. 75). Chinese mathematics educators see cooperative learning in mathematics as ‘suitable for topics involving large-scale conceptualization and multi-tiered reasoning’ (Cheng 2011, p. 79). To Chinese mathematics educators, ‘what is meant by ‘cooperativeness’ is the cooperativeness in the sense of mental activity rather than cooperation which is superficially just a form like people gathering’ (Cheng 2011, p. 81). We suspect that this difference in the practice of cooperative learning between East Asia and the USA is exactly what has produced the unique advantageous East Asian relationship between cooperative learning and mathematics performance that we have observed in the present research.

Competitive versus cooperative learning: which is more important?

Another notable pattern in Tables 2 and 3 is that where both competitive and cooperative learning showed significant results (i.e., in Hong Kong, Japan, and Korea), the relationship between competitive learning and mathematics performance was as strong as the relationship between cooperative learning and mathematics performance. Therefore, students in Hong Kong, Japan, and Korea employed both competitive and cooperative learning to the same advantage for the improvement of their mathematics performance. The East Asian experience is that to promote learning in mathematics, both individual excellence and group collaboration should be emphasized, as Cheng (2011) stated that even ‘under the circumstances of cooperative learning, thinking independently and cooperative communication intermingle and nurture each other’ (p. 80). Among other reasons, East Asian students outperform American students likely because East Asian students are encouraged and facilitated by educational practices that emphasize both types of learning styles.

Implications

The neat patterns concerning competitive and cooperative learning revealed in the present research can meaningfully inform American mathematics educators to think about the optimal balance between competitive and cooperative learning in the study of mathematics. We offer some implications to American mathematics education. First, as far as the improvement of their mathematics performance is concerned, even though the American culture honors individualist, it appears that American students have not been able to effectively translate this cultural advantage into competitive learning. It appears that the mainly negative attitudes of American educators towards competitive learning may need to be revisited. This suggestion may well be provocative to American educators, but the East Asian experience is so consistent: the drive for individual excellence turns out to be as important as the emphasis on collaborative effort as far as mathematics performance is concerned. American mathematics educators may need to encourage and more importantly facilitate individual efforts to aim higher, learn more, and perform better in mathematics.

Even in light of high pressure to perform and strong competition for success, East Asian students employed cooperative learning to the same results that they used competitive learning, in regard to their mathematics performance. American mathematics educators may need to change the way that cooperative learning is practiced in the study of mathematics. On this issue, American educators can learn from their East Asian counterparts. Intellectual depth and vigor may be lacking in cooperative learning in American mathematics classrooms but are pursued in cooperative learning in East Asian mathematics classrooms (see Cheng 2011). We suggest that professional development is an effective strategy for teachers to study and promote effective cooperative learning.

The complexity in understanding the importance of learning styles to the promotion of learning in mathematics may need to be underscored. From the educational perspective, learning styles fall under pedagogical concerns. We arise a question of whether it is possible that teachers' effective use of any pedagogy to a great extent depends on their content knowledge particularly in highly academic subjects such as mathematics. Cheng's (2011) study did demonstrate that mathematics teachers need to have a deep understanding of the mathematical intellectual work involved in cooperative learning. Ma (1999) also considered the understanding of fundamental mathematical concepts as the basis for any effective teaching and learning of mathematics. Therefore, it may not be adequate just to train teachers to use learning styles more effectively but also to understand the substantive mathematical intellectual work that they hope their students to gain from either individual or group learning.