In the context of the critical role of self-efficacy in educational achievement, this present research examined students' and teachers' efficacy in use of learning strategies in mathematics, and the relationship with achievement. The second phase of a multi-method doctoral study, ninety-two students and ten teachers from a diverse secondary school were surveyed on efficacy in use of learning strategies, and the factors they perceived as facilitating or inhibiting the use of learning strategies in the classroom context. The findings are contextualised within a multi-method framework comprising two research projects. The cumulative findings bring to light illusory-efficacy in a sizeable number of student participants who did not achieve, highlighting the importance of true efficacy and learning strategies to reduce disparities and enhance achievement.
Self-efficacy differs from concepts such as self-concept and self-esteem. Self-concept is a composite view of oneself based on past environmental experiences, and oriented to the past. Self-efficacy is future-oriented and represents an individual's use of self-perceptions in successfully accomplishing a particular task with the target behaviour clearly specified (Skaalvik & Bong, 2003). Self-esteem involves emotional reactions to actual accomplishments (Linnenbrink & Pintrich, 2003). The "dynamic and malleable nature of self-efficacy perceptions render them more amenable to experimental procedures aiming at efficacy enhancement" (Bong & Skaalvik, 2003, p.30), and thereby enhancing the level of achievement. This distinction between self-efficacy and self-concept is significant in the education context. Research on self-related constructs for advancing achievement in New Zealand schools have focussed on the assessment of students' self-concept (Chamberlain & Caygill, 2002; Education Review Office, 2002; Nash & Harker, 1997; Hughes et al., 2000), and thereby undervalued by omission the role of self-efficacy in learning and achievement of students.
Research spanning two decades on use of learning strategies and self-efficacy, has been examined by Schunk (2001). He reports that for students who scored below grade-level in mathematics, use of cognitive modelling enhanced achievement. Elementary students with difficulty in subtraction, when provided exposure to mastery or coping models, performed well. Modelling, followed by monitoring and training in self-monitoring produced better performance, as compared to modelling without monitoring. Strategies underlying teacher-led motivated learning in students include (Pintrich & Schunk, 2002):
The present study explores the role of self-efficacy and learning strategies in students' achievement in mathematics. The learning strategies examined include: (a) strategies for self-regulatory learning, (b) resource management; and (c) motivation. These strategies were derived from factor analysis and multiple discriminant analysis of phase I of the research (Marat, 2003; 2005b), and developed into two survey questionnaires (Appendix I and II). Phase I of the research comprised 137 student participants from two culturally diverse schools in Auckland. Participants were assessed for self efficacy in achievement in mathematics. The major findings were: (a) Students are reporting relatively high levels of self-efficacy for achievement in mathematics which are not reflected in actual achievement; (b) Three major factors emerge as independent variables which impact on achievement in mathematics; (c) These factors are also seen to have predictive value in determining students' level of achievement in mathematics.
Kaupapa Maori approaches to research are based on the assumption that research that involves Maori people, as individuals or communities, should set out to make a positive difference for the researched. This does not have to be an immediate or direct benefit...The research approach also has to address seriously the cultural ground of respect, of working with communities, of sharing processes and knowledge. (Smith, 1999, p.191)From the initial stages of the research process, which involved formulation of the research problem, consultancy with practitioners and experts from the field of educational research led the present project. The emerging results of the first phase of the research was presented at the Joint New Zealand and Australian Association for Research in Education Conference (Marat, 2003), and audience feedback was integrated into the research-in-progress.
The choice of methodology and methods in the present study resulted from a synthesis of quantitative and qualitative approaches. The essential test was "[t]o ensure that the evidence obtained enables us to answer the initial question as unambiguously as possible" (de Vaus, 2002, p.9). While the framework of the research method was survey-based, correlational methods, and content analysis were used to analyse the data. Thus, this research comprising two phases was based on a framework comprising: (a) mixed method design, and (b) multimethod design. Morse (2003) explains mixed method design as incorporating both quantitative and qualitative strategies, and multimethod design as one inclusive project comprising two or more research projects, each complete in itself. What emerges is methodological triangulation described as "[t]wo or more subprojects, each of which exhibits methodological integrity. While complete in themselves, these projects fit to complement or enable attainment of the overall programmatic research goals" (p.190).
Ninety-two students from Form VII and ten teachers from a culturally diverse secondary school participated in this research. Purposive-theoretical sampling was used to invite participants, after lack of response from a probability based random sample of secondary schools invited to participate in the research. In the present study, culture is considered as a contextualised, dynamic, and evolving construct, and much more diverse than dichotomous categorisation of individuals into individualistic or collectivistic cultures. This is to accord for the multicultural nature of New Zealand society, and the intra-ethnic and intra-individual diversity within the cultural groupings. Culture although a significant variable, has not been considered in analytical interpretation in the present research. While no comparisons are drawn between cultural groups, the distinct cultural identities of participants are valued and acknowledged. The decision to desist from using culture as a variable for analyses was based on an underlying ideology of considering culture as seamless construct, and the inappropriateness to compartmentalise participants and their responses into narrow categories based on cultural affiliations. As stated by Bandura (2002):
[A] selected cultural factor that yields a small difference in group averages is generalized to all individuals in the cultural grouping as though they all believed and behaved alike as dichotomously classified. ... Human behaviour is socially situated, richly contextualized and conditionally expressed. (p.276)However, since there is substantial body of work which highlights disparities in achievement grounded in the history and culture of New Zealand (Simon, 2000; Jenkins & Jones, 2000, Ministry, 2001), and initiatives which target achievement of specific cultural groups and 'achievement of all' (Ministry, 1998; Minister of Education, 2003), the literature reviewed encompasses culture as a construct having important bearing on self-efficacy and achievement. The purpose is two-fold: (a) to ensure that the present research has relevance for the diverse learning context in New Zealand schools, and (b) to highlight the links, if any, between historically grounded disparities, self-efficacy and achievement.
The conceptualisation of teacher efficacy in the present research is narrow, since the purpose of this research was to explore student efficacy comprehensively. Although teacher beliefs have been investigated, it is suggested that in-depth investigation on the role of teacher efficacy as a construct which impacts on student achievement will have to be considered in future research.
The students' survey tool (Appendix I) sought information on efficacy in the use of thirteen learning strategies in mathematics (Alpha 0.77). The term self-belief was used to explain the construct of self-efficacy to aid easy comprehension by participants. An open-ended statement at the end of each item sought information on how students used the learning strategy, and factors perceived as facilitating or inhibiting the use of these strategies in the classroom. To assess the relationship between students' efficacy and achievement, consent to access achievement scores was sought from students. The achievement results of only 40 students could be used for inferential analysis. Some of the students did not clearly write their names in the survey precluding use of their achievement grades. Teachers' survey included seven items on efficacy in use of learning strategies in the classroom context (Appendix II). An open-ended statement at the end of each item sought recall of instances in the past year when the teacher guided students in use of specific strategies, and factors which facilitated or inhibited use of strategies.
Questions | Response (%) | |
Yes | No | |
Deliberately set goals | 63 | 37 |
Deliberately made time-plan | 26 | 74 |
Deliberately took control over any negative thinking | 51 | 48 |
Deliberately praised oneself when successful | 62 | 38 |
Felt motivated when others succeeded | 66 | 34 |
Practised mathematics to learn | 79 | 21 |
Regulated the environment to facilitate learning | 51 | 49 |
Monitored progress | 71 | 29 |
Reviewed set goals | 39 | 60 |
Sought guidance | 65 | 32 |
Used resources provided by the school | 82 | 17 |
Used online resources | 72 | 27 |
Felt increase in confidence in capability to perform successfully in mathematics | 62 | 36 |
n= 92 Missing data ranged from 1.1% to 3.3% |
Emerging themes | Response (Frequency count) |
a) Goal setting | |
Goals set to achieve better grades Day-to-day goals set No goals | 13 5 6 |
Lead Statement: When I worked in mathematics this year I deliberately set goals. Comments from a selective number of participants: To pass everything - every internal; I really wanted to pass my internals, especially the first one so I made sure I worked on it; I set goals but they change constantly and only kept in my head; Set goals to get high marks in assessment; A goal to achieve well in maths; Goals are mostly short-term; I wanted to achieve excellence and merit; I don't set goals. | |
b) Time plan | |
No plan | 10 |
Lead statement: When I worked in mathematics this year I deliberately made a time plan Comments from a selective number of participants: I do not plan I do; I didn't really set a certain timetable of study; I don't have a plan; I try, but don't follow it; Do not make time-plan; I made a rough plan but did not necessarily keep to it; Because I can do no more; Too restrictive; No I did not place any time deliberately aside for maths; I just did the work when I had to do it until it was done. | |
c) Deliberately praised oneself when successful | |
No | 7 |
Lead statement: When I worked in mathematics this year I deliberately praised myself when successful. Comments from a selective number of participants: Don't want to get big-headed; No this leads to overconfidence; Do not praise myself; It's something I should do; Because if I did I would get overconfident; I am not like that | |
d) Felt motivated on seeing others succeed | |
Wanted to succeed like them | 9 |
Lead statement: When I worked in mathematics this year I felt motivated when I saw others like myself succeed. Comments from a selective number of participants: I felt that if I can do it so can I and worked towards it; Made me realise I could achieve too; I wanted to achieve just as well others did. | |
e) Practised mathematics to learn | |
To do well in examinations | 18 |
Lead statement: When I worked in mathematics this year I made myself practice so that I could learn. Comments from a selective number of participants: It's the only way to improve in mathematics; Before exams I studied; I bought study guides and got help from my dad; Every time I have time I would practice and revise my work; Did homework; I usually concentrate my effort on solving merit and excellence questions; Going over and over problems to ensure I knew the material (yet I failed damn it!!!) | |
f) Monitoring progress | |
Checking grades No, don't care | 8 8 |
Lead statement: When I worked in mathematics this year I made sure I was aware of my progress. Comments from a selective number of participants: Mark down what grades I have got so far; I also like to see how I can do in relation to the class; Keep tabs on my achievement; I don't really keep up-to-date on where I am; No I don't; Was not aware of my progress. | |
g) Reviewed goals | |
Did not review, no goals set Went over results, keeping in mind what was done | 11 4 |
Lead statement: When I worked in mathematics this year I reviewed my mathematics goals after I had set them. Comments from a selective number of participants: I didn't set any goals; Don't have goals; Have not changed them; No I never review; To see what I have to work on; I always keep my goals in mind; Day to day goals so they don't really need reviewing rather I just tried to complete the goal; I never had any as from starting the subject I was bored stiff. | |
h) Sought guidance / help | |
From text books Maths tutor Maths teacher | 3 4 6 |
Lead statement: When I worked in mathematics this year I sought guidance and help. Comments from a selective number of participants: Revision books; Maths tutoring both in school and out of school; From parents and my tutor; Get all the help I need from teacher and friends; From my dad; Asked the teacher questions and used text books; I sought help from teachers but haven't really received it; As no one ever explains it properly it may well be Arabic. | |
i) Resources provided by the school | |
Text books | 10 |
Lead statement: When I worked in mathematics this year I used resources provided by the school. Comments from a selective number of participants: Text book; Teacher and text books; My maths text book; Bought extra text books; Sigma mathematics; Old exam papers and text books; Test papers and library books; Work books and text books. | |
j) Online Ministry resources | |
Download exemplars from NZQA, TKI websites | 17 |
Lead statement: When I worked in mathematics this year I used online Ministry resources. Comments from a selective number of participants: It is very useful; Yes, I use online exemplars; Downloaded practice exams; Visited TKI for studying; NZQA website; NZQA website exemplars. | |
k) Confidence to succeed in examinations | |
Feel increase in confidence Not confident/ worried | 6 5 |
Lead statement: When I worked in mathematics this year I feel increasing confidence in my capability to succeed in mathematics Comments from a selective number of participants: It's quite difficult; No I feel less confident than ever at this point in time; I feel I am getting better; Because I don't succeed; Or so I thought until I found out my marks, then life seemed pointless...; As the system is corrupt and obsessed with making the subject as boring as possible. God if you really want to help maths students, get rid of the subject completely as it is demoralising; When I got a good mark; I feel I know how to study well for a maths exam now; I got 1 E and 2 M in recent exams. I believe I can do better in external exams; I'll get there.... |
Grade | Frequency (%) |
Excellence | 5 |
Merit | 25 |
Achieved | 37.5 |
Not achieved | 30 |
Did not sit | 2.5 |
n=40 |
Questions | Correlation | Approx. significance |
Practised mathematics to learn | .296 | .027 |
Used resources provided by the school | .347 | .009 |
Felt increase in confidence in capability to perform successfully in mathematics | .341 | .010 |
n = 40 |
Figure 1: Cross tabulation: Practised mathematics with achievement
Figure 2: Cross tabulation: Used school resources with achievement
Figure 3: Cross tabulation: Increase in confidence in capability to succeed mathematics with achievement
Questions | Response (Frequency count) | |
Yes | No | |
Guided to work towards setting goals | 8 | 2 |
Assisted to override negative thinking | 9 | 1 |
Provided guidance on time management | 9 | 1 |
Provided models on successful use of learning strategies | 6 | 4 |
Provided opportunities for mastery learning | 4 | 6 |
Guided students to revisit their goals | 8 | 2 |
Provided in-class opportunities to use school and Ministry online resources | 1 | 9 |
n= 10 |
Items and Comments | |
a) | Guided to work towards setting goals Comments of teacher participants: Encourage to use a study time-table when preparing for exams; Students were given practice papers for revision; Students were updated on the credits they have or not obtained and what they should now direct themselves to achieve; What does this mean? |
b) | Assisted to override negative thinking Comments of teacher participants: I do this all the time; Always mention about how mathematics is used in real life; Positive posters all around, positive words like "You can do it" It's not all bad; Explained the alternative methods in TRIG to overcome the application of Algebra in Year 11 mathematics alternative. |
c) | Provided guidance on time management Comments of teacher participants: Showed students how to revise; Too busy teaching mathematics; Devised a revision programme for students to achieve especially in Year 11; Diary/time management skills. |
d) | Provided models on successful use of learning strategies Comments of teacher participants: Probably; Most learning styles are covered in our schemes; What, like me? I model this on many occasions; Time constraints; Not aware of any models, used examples in text books to develop students thinking in order to solve problems. |
e) | Provided opportunities for mastery learning Comments of teacher participants: Going over questions not done well in class; What does this mean? It is a long time since I was at training College; Not common practice; Class-time one-on-one tutoring; Gave a number of repeated or similar examples of problems in order to achieve mastery of a concept in mathematics; Varied learning techniques used. |
f) | Guided students to revisit their goals Comments of teacher participants: Topic review at the end of topic for tests and exams; Students need to set their own goals where a majority of students did not realise the importance of this; Constantly updated students with their credits and asked them to evaluate where they were and how many credits they need etc. to complete their course; Termly reassessment. |
g) | Provided in-class opportunities to use school and Ministry online resources Comments of teacher participants: Big class, not enough computers in the lab; Too busy teaching; No computer times available; Computer rooms are always booked so it is not feasible as some other schools do; No IT resources or hardware available in the classroom to use online resources; Referred students to appropriate website which they could access from the school library or home. |
Analyses of teachers' reported use of learning strategies and comments reveal that while teachers use the strategies, it is not a deliberate and planned process (Tables 5 & 6). Eight out of ten teachers surveyed reported providing guidance in goal setting, however it emerges that the guidance were not specifically tailored for the topic or task. Comments included "encouraging use of a study-timetable, students given practice papers for revision". Four teachers reported providing guidance on mastery learning, and six teachers stated using modelling as a learning strategy. Comments on the mastery learning process revealed that it was usually teacher modelled problem solving, or going over questions in which students had not performed well. Cognitive modelling based on mastery learning has been recommended as an effective learning strategy in mathematics. Schunk (2001) provides a summary of research interventions in the use of learning strategies and self-efficacy spanning over two decades which aimed at enhancing student achievement in mathematics. In a study targeting students who scored below grade-level in mathematics, cognitive modelling produced enhancement in achievement. Elementary students with difficulty in subtraction, when provided exposure to mastery or coping modelling, performed well. In another study using multiple modelling strategies, in the initial stages, students observing coping-emotive models reported highest learning self-efficacy. With instructions and practice, all groups reported similar levels of self-efficacy and achievement. Modelling, followed by monitoring and training in self-monitoring produced better performance, as compared to modelling without monitoring. "Mastery learning enables 75 to 90 percent of the students to achieve the same high level as the top 25 percent learning under typical group-based instructional methods" (Block, 1971, p.3).In Phase I of this research project 42.7 percent of students did not achieve successfully, and 11 percent of students did not attempt the examinations, in Phase II 30% did not achieve, and 2.5% did not attempt the examinations.
Time and lack of access to resources such as computers and the Internet within the classroom were factors highlighted by teachers as impeding use of some of the learning strategies. While only one out of ten teachers reported providing in class guidance to students in use of resources, 72% of students reported efficacy in using online resources and 82% of students reported efficacy in using school resources. Efficacy in practising mathematics to learn was reported by 79% of student participants and 62% reported increase in confidence to perform successfully in mathematics. Inferential analysis reveals positive significant correlations between efficacy in use of three strategies, viz: practising mathematics to learn, using school resources, increase in confidence to perform successfully in examination and level of achievement (Table 4). Some of the participants who were in the achieved and the merit categories also reported lack of efficacy in use of learning strategies (Figures 1, 2, &3). While assessing the relationship between efficacy and achievement, it is important to consider the learning and performance self-efficacy distinction (Bandura, 2003). A high level of learning self-efficacy facilitates acquisition of skills, self-doubts about performance in challenging situations is conducive to achievement. A number of student participants who did not achieve also reported efficacy in use of learning strategies, and a sizeable number of students (30%) did not achieve in the examinations (Table 3).
Bandura (1997) and Schunk (1994) attribute discrepancies between reported self-efficacy and achievement to the source of self-efficacy information, value of the task undertaken, and the presence or absence of skills required to accomplish the task. While efficacy can enhance motivation, students cannot produce 'new fangled performances' if the subskills for the exercise of personal agency are absent (Bandura, 1997). In a similar vein, Schunk (1994) states that high self-efficacy will not produce competent performances in the absence of requisite knowledge and skills. The explanation by Cramer (1998) on positive illusions is significant in this context. Reporting "positive illusions" about the self and giving responses which might be socially desirable are indicative of denial. These are coping strategies. Reviewing studies on the use of overly positive self-evaluations, and self-deceptive coping in college students, Cramer states that when the outcome measure is an external criterion and not self-reports, use of coping mechanisms such as these do not result in positive benefits.
It is arguable that students in the present study who report self-efficacy in use of learning strategies which were not reflected in achievement could be reporting illusory self-efficacy, rather than true self-efficacy. The nature of individual self-belief, if not based on self-awareness (Goleman, 1998) of true capability to undertake action, could be illusory, functioning only as a coping strategy or as a defense mechanism, leading to inflated levels of self-efficacy. Goleman defines self-awareness as "having a realistic assessment of our own abilities and a well-grounded sense of self-confidence" (p.318). According to Bandura (1991) "Perceived self-efficacy is concerned with people's beliefs about their capabilities to organise and execute courses of action" (p.158). The concerns voiced by Donnolley (2002), and Hames (2002) about the New Zealand educational system are significant in this context. Flexibility in the curriculum, while not providing assistance for teachers to effectively plan instructional strategies, and the stress on self-esteem by acceptance of low achievement levels appear to cost students the required knowledge and skills. Hames (2002), queries whether the emphasis on self-esteem, is not impacted adversely by poor performance, and might perhaps be fuelling egotism in students. The attribution of causes for failure, the role of culture, and perceptions of positioning the self in the wider socio-cultural context are other significant variables in this interplay between self-efficacy and achievement.
Strategies to promote mastery learning were not integral to the teaching-learning process as reported by teacher participants in the present research. Incorporating a cognitive-mediational approach to learning in the classroom requires teachers to have knowledge of instructional strategies that facilitate focus on students' thinking, understanding and self-regulated learning (Putnam & Borko, 1997). The authors suggest that teachers consider the concept of distributed cognition, the understanding that cognition is not solely an individual- oriented construct, but is distributed over the individual, others, and the environment, with all activities in the classroom having to be considered in the out-of-school context where activities are collaborative, and require resources which are beyond the capacity of individual members, but distributed among many individuals and requires a collectivistic orientation to be accomplished successfully. In the bicultural and multicultural New Zealand educational context, incorporating the concept of Akonga (Bishop et al, 2003) could be considered a parallel to this concept of distributed cognition. Finally, it is important to consider the perspective that fundamental changes in teacher beliefs and practices about students (and student learning and performance) can take place slowly, and requires considerable support mechanisms to guide teachers to the linkages between particular beliefs and practices in specific teaching learning contexts (Calderhead, 1996). "Teachers are expected to function in ways that acknowledge, and are in accordance with, the cultural practices, circumstances, and beliefs of their students. Their role as teachers in multicultural settings requires them to act as personal agents, proxy cultural agents, and collective cultural agents" (Gibbs, 2005, p.104). Teacher professional development practices in New Zealand should consider the role of teacher efficacy, agency, and use of learning strategies to facilitate positive outcomes in learning and performance for students and teachers.
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Author: Deepa Marat works as a Research Consultant at the Postgraduate Centre Matai Kahurangi Unitec Institute of Technology in Auckland. Her research interests include self-efficacy, self-related constructs, and agency. She is at present engaged in two collaborative research projects with a focus on student engagement and success in the tertiary sector. Underpinning each of these projects is a methodological framework led by indigenous research methodologies from Australasia. Email: dmarat@unitec.ac.nz
Please cite as: Marat, D. (2007). Students' and teachers' efficacy in use of learning strategies and achievement in mathematics. Issues In Educational Research, 17(2), 207-231. http://www.iier.org.au/iier17/marat.html |