Abstract
Mathematics has been a subject of study for hundreds of years. While the basic principles have not changed much, the style of teaching it has definitely evolved with time. This paper looks at how these teaching styles blended with the math teacher’s self-efficacy affect the achievement of students in elementary math. While self-efficacy stems from an individual’s belief that he or she is capable of succeeding and overcoming a particular challenge, teaching styles are more skills related and are not so dependent on the human ‘internal’ state. This paper attempts to bring the two together so as to establish their contribution to students’ achievement in math.
Introduction
While research has shown that teachers play the greatest roles in bringing about student achievement in any pedagogical program (Sanders, 1998, 2000; Goldhaber, 2002; Alexander & Fuller, 2005), there is still need to investigate the extent to which the teacher’s style of instruction and self-efficacy. Researchers agree that the individual teacher’s effort is most probably the greatest influence on student achievement. Sanders (1998) stated that the “single largest factor affecting academic growth of populations of students is differences in effectiveness of individual classroom teachers.”
Teaching styles are thus a very key part of math instruction. However, the new core standards in math are definitely going to affect the style math teachers employ in their instruction. The new standards lean more towards numbers, spatial relations, geometry and measurements (National Research Council, 2009). This is because previous math instruction has been faulted as being too ‘weak’ in a conceptual sense especially when compared to states like Hong Kong, Singapore and Korea (Ginsburg, Leinwand and Decker, 2009).
While there is now support for the notion that teaching styles as well as teachers’ self-efficacy influence positive student outcomes (Sanders, 1998, 2000; Goldhaber, 2002; Alexander & Fuller, 2005; Tschannen-Moran & Hoy, 2001; Good & Brophy, 2003), it is notable that this ‘acceptance’ is quite recent, stemming from the late 90’s to the present. This means that there are gaps in the research supporting the positive influence of teachers and those that find that teacher’s roles are not that important thus placing more emphasis on the role of students in their own achievement as a product of their efforts.
Theories on self-efficacy
Akbari, Naeeni, Kiany and Allvar (2009) state that a teacher’s sense of self-efficacy is a “judgment of his or her capabilities to bring about desired outcomes of student engagement and learning.” Self-efficacy has been found to play a vital role in enhancing student achievement in many research studies such as Bandura (1995), Bandura (1997), Zimmerman (1995) and Good & Brophy (2003). The concept of self-efficacy was popularized by Bandura (1977). Previously, self-efficacy was considered to be part of social learning theory.
Over time, several theories have come up attempting to define the concept of self-efficacy and its interaction with other dynamics such as student achievement. However, the concept of self-efficacy as laid down by Bandura remains the most popular. I shall now analyze this concept and its dynamics.
Bandura’s social cognitive theory
Bandura (1977) describe the theory of self-efficacy as one that deals with individual’s belief in his or her ability when confronted by various situations. The theory finds that people with different senses of efficacy behave differently when placed in similar situations. Usually, persons with a higher sense of efficacy set a higher standard for themselves and are more willing to take greater risks than their less efficacious counterparts (Akbari et al, 2009).
Good & Brody (2003) state that persons with a high sense of efficacy tend to be innovative and proactive. These efficacious people do not pass responsibility to other people. Instead, they come up with logical ways to face their daily challenges. These individuals are very persistent and will not give up easily when confronted by a tough situation. On the other hand, Bandura (1995) states that teachers with low self-efficacy “show weak commitment to teaching, spend less time in subject matters in their areas of perceived inefficacy, and devote less overall time to academic matters.”
Social learning theory
This theory is one of the earliest theories on behaviour. It deals with individuals’ acquisition of socially valuable skills that are mainly ‘learnt’ or developed from the individual’s interaction in a group. It mainly relates human qualities to their immediate environment. Akbari (2007) stated that social learning is dependent on group dynamics and an individual’s level of interaction. Self-efficacy as an aspect of social learning influences the level of interaction and learning from the group. Therefore in social learning theories, self-efficacy is necessary since an individual’s feeling of being efficacious in group will determine their level of interaction and eventually, social learning (Ormrod, 2006).
Attribution theory
This theory deals with ‘cause’ and ‘effect’. It deals with how individuals explain/attribute the cause of an event. The theory suggests that this attribution is related to the individual’s internal perception of himself/herself. This theory was laid down by Heider and Fritz in 1958 states that every ‘cause’ has three elements; locus, stability and controllability. Locus has more to do with the location of the ‘cause.’ If it is internal, it affects the individual’s self-efficacy and self esteem depending on whether the event is positive or negative.
Stability deals with the individual’s perception of the ‘cause’ as being dynamic or stationary. Where the individual perceives the cause as stationary, their self-efficacy is lowered since they feel that they will not succeed. The reverse is true where one perceives the cause as dynamic. Controllability on the other hand depends on the individual’s feeling of being in or out of control of the cause. If the individual feel that he or she is in control, then their self-efficacy improves since they feel that they can still achieve success and vice versa (Heider & Fritz, 1958).
If we consider the attribution theory in terms of teachers’ self-efficacy, the elements of locus, stability and controllability come into play. First, locus, which has to do with location of the cause, influences a teachers feeling of efficacy where he or she either perceives the mathematical challenge in an internal or external mother. If the teacher perceives the challenge as internal, then efficacy is low and vice versa. If the teacher thinks that the teaching problem is static, then they will feel less efficacious. Finally, controllability influences efficacy in that, teachers who feel that they are in control of the teaching process will feel more efficacious.
Research Analysis
Teaching styles and strategies
As we had earlier seen, teaching styles are very influential on student achievement. However, it is noteworthy that the styles employed in the teaching of math vary from all other styles used for other subjects, obviously because of the inherent nature of the subject. Teaching styles may also vary from instructor to instructor since they are heavily influenced by the instructor’s personal qualities, philosophy in life, educational philosophy and attitude (Beyond Crossroads, 2006). However, teaching styles in mathematics can be classified into:
- Student-centered approach versus Teacher-centered approach
- Thematic approach versus Topic-based approach
There are many other categories of teaching styles such as visual, kinesthetic, auditory, group, informal, formal, traditional, open and many others (Gray & Ross, 2006). I shall discuss the two categories above;
Student-centered approach versus Teacher-centered approach
As the words may suggest, a student centered approach is one that emphasizes more on the student. In their 2006 publication, Beyond Crossroads state that the understanding of the process through which students learn mathematics should inform the design of classroom instruction. In a student-centered approach, the student attempts to explore the subject on his/her own taking charge of the learning process and relying on the teacher only for guidance purposes. Springer, Stanne & Donovan (1999) found that where a student –centered approach takes an active and constructivist approach, then there is a high chance of success especially among students not used to the traditional learning methods.
In a teacher-centered approach, the teacher takes active control of the entire process of instruction. This is the most common method employed in public schools in the US. Normally, the teacher prepares lesson plans before class which they use to guide the teaching of math throughout the class term or year. The teacher constantly assesses the performance of students and may constantly assign work for the student to do independently.
While the teacher-centered approach is more common, its success is much more dependent on the teacher’s individual style. As Jarvis (2004) aptly puts it, the teacher’s style is “the totality of one’s philosophy, beliefs, values, and behaviors, and it includes the implementation of this philosophy; it contains evidence of beliefs about, values related to, and attitudes toward all the elements of the teaching-learning exchange.” Akbari et al (2009) describe these characteristics as ‘pervasive’, holding out even with changes in situational conditions.
Brown (2003) states that due to the diverse needs of students in mathematics instruction, there is need for math teachers to be sensitive to the students learning style. This is definitely a prudent approach since one can only achieve results if the students learn at their own pace. However, Brown states that matching of the teaching and learning styles is not a guarantee for success. There is thus need for caution when deciding to change teaching styles.
Thematic approach versus Topic-based approach
There has been a raging debate between scholars on which between the thematic and topic-based approach is the most effective teaching style. However, a Handal & Bobis (2006) study found that most teachers preferred to teach by topics rather than in themes. Nevertheless, both approaches to math teaching have been shown to yield successful results depending on the manner in which they were applied (Handal, Bobis & Grimison, 2001).
The thematic approach to math instruction involves a deeper focus on the application of mathematical concepts. It is from the application of these concepts that lessons and assignments are based. A thematic approach chooses to focus on a particular branch of mathematics and students are expected to understand the application of these concepts in a progressive manner (Bobis, 2006)
A topic-based approach is one where the teacher uses a particular textbook or curriculum guide from which he or she draws lessons and teaches according to the topics in the material. While, there is nothing wrong with this approach, the teacher’s coverage of all areas of the subject is likely to be hindered by the limitations in the teaching material.
Due to the new core standards in math in the US, a thematic approach would be more realistic since the mathematics curriculum is more practical and relevant (National Research Council, 2009). This is because the thematic approach allows the teacher to exhaust one theme before moving to the next. In this way, students are not ‘lost on the way’. However, research studies have shown that the topic-based approach is much simpler and it attempts to standardize the teaching of math (Handal & Bobis, 2006; Handal, 2000).
Teacher self-efficacy
Akbari et al (2009) state that the teacher’s sense of self-efficacy is considered as one of the most influential factors affecting teacher performance and student achievement. Good and Brophy (2003) had earlier stated that in mainstream education, it is apparent that there is a strong link between teacher efficacy and student achievement in all areas of study.
Ware & Kitsantas (2007) state that the reason why self-efficacy in teachers is important is because it affects the effort the teacher invests into instruction. They further state that a high sense of efficacy also leads to a higher feeling of inspiration in the teacher and this directly affects student morale. As Bandura (1995) earlier stated, lower self-efficacy means weaker commitment towards teaching and less time investment in the areas the teacher perceives himself/herself as being less efficacious.
Students are likely to be negatively affected in terms of cognitive development and sense of efficacy where a teacher is less efficacious. This is because teachers with lower self-efficacy give up easily when confronted by a challenging situation. This makes students feel that the area of study is particularly difficult thus causing the students to lack the right attitude needed to learn. This is especially true in math instruction since new concepts are introduced in almost every lesson.
Hoy (2000) found that these less efficacious teachers tend to project their inefficacy on students. They are more likely to resort to punishing students, creating a hostile and controlled classroom which undermines learning. They are also pessimistic towards students’ motivation and would rather rely on extrinsic methods of motivation. To hide their inefficacy, Akbari et al (2009) find that these teachers prefer to be in control and do not allow an open learning forum in their classes.
In contrast, highly efficacious teachers are more likely to adopt an open style of teaching where they allow students to contribute actively in the teaching process by asking questions or attempting to solve math problems with the teacher’s supervision. These teachers motivate students intrinsically and thus build a strong foundation for students to understand math and never shy away from a challenging problem.
In addition, these teachers go out of their way to ensure that rather than merely covering the curriculum, their students fully understand the concepts being taught. Tschannen-Moran & Hoy (2001) found that these teachers are highly innovative and are more inclined to take risks in their methods of instruction. Where these new techniques fail, the persistent characteristic of efficacious teachers enables them to try again.
High sense of efficacy in teachers has also been shown to be less critical of underperforming students. These teachers are more likely to help these struggling students to catch up with the rest. In summary, Akbari et al (2009) state that greater efficacy in teachers makes them more enthusiastic towards earning. They have lower stress levels and are much more likely to remain in the teaching profession for longer than their less efficacious counterparts.
Conclusion
As seen from the analysis of research studies, it is quite apparent that teaching styles and teacher efficacy play a big role in student achievement in mathematics. Akbari et al (2009) find that these two variables show a positive correlation with student achievement. This is why schools should ensure that they find out the levels of efficacy in teachers before they hire them. They should also inquire into the teaching styles that the teacher intends to employ in instruction.
Bandura (1995) states that self-efficacy is variable and individuals can therefore work towards increasing their sense of efficacy. Usually, the methods used to boost self confidence can also be used to increase efficacy. Schools should identify less efficacious teachers and place them in programs that would assist them to bolster their sense of efficacy. Additionally, they should identify the most successful teaching styles and recommend them to their teachers. However, caution should be taken since different teachers have different success levels when using a particular teaching style.
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