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The effects of explicit self-regulated learning strategy instruction on mathematics achievement

ProQuest Dissertations and Theses, 2009
Author: Janet Sings Jenkins
Self-regulated learning includes the use of a set of strategies for planning, monitoring, and self-evaluating students' efforts toward reaching specific learning goals. This study examined the extent to which explicit self-regulated learning strategy instruction impacted regular eighth grade students' learning behaviors and mathematics achievement. The study was a quasi-experimental design using a control and treatment group which consisted of eighth grade general mathematics students. The treatment was explicit instruction of ten self-regulated learning strategies. Data were gathered using a researcher-designed survey and standardized mathematics test scores. Findings indicated that the treatment group reported a significantly higher level of self-regulated learning strategy use, earned significantly higher mathematics test scale scores, and showed significantly greater academic growth than the control group. Additionally students' use of self-regulated learning strategies was statistically significant in explaining the variance in students' mathematics test scores and academic growth.




TABLE 1: Gender of participants 45 TABLE 2: Race of participants 46 TABLE 3: Economic status of participants 46 TABLE 4: English language proficiency status of participants 47 TABLE 5: Parent education status of participants 47 TABLE 6: Skewness and standard error of skewness (ses) 54 TABLE 7: Alignment of survey items based on self-regulation phase 55 TABLE 8: Coefficient alpha values for the survey 56 TABLE 9: MANOVA means and standard deviations 59 TABLE 10: Total survey means and standard deviations 61 TABLE 11: Total survey means and standard deviations for gender 63 TABLE 12: Total survey means and standard deviations for race (1 st administration)

64 TABLE 13: Total survey means and standard deviations for race (2 nd and 3 rd


65 TABLE 14: Total survey means and standard deviations for economic status 67 TABLE 15: Total survey means and standard deviations for English language proficiency

68 TABLE 16: Total survey means and standard deviations for parent education (1 st and 2 nd administrations)

71 TABLE 17 : Total survey means and standard deviations for parent education (3 rd administration)

72 TABLE 18: Phase 1 means and standard deviations for economic status 73 TABLE 19: Regression means and standard deviations for eighth grade EOG scores 77


TABLE 20: Correlation coefficients for eighth grade EOG 77 TABLE 21: Unstandardized regression coefficients (B) and intercept, the standardized regression coefficients (β), semipartial correlations (sr), t-values, and p-values for eight grade EOG

78 TABLE 22: Regression means and standard deviations for ABC growth 79 TABLE 23: Correlation coefficients for ABC growth 79 TABLE 24: Unstandardized regression coefficients (B) and intercept, the standardized regression coefficients (β), semipartial correlations (sr), t-values, and p-values for ABC growth 80


FIGURE 1: Interaction for parent education level 69


Statement of problem and sub-problems Although researchers define self-regulation in a variety of ways, most are similar to Zimmerman’s (2002, p. 65) definition, which states that self-regulation is the “self- generated thoughts, feelings and behaviors that are oriented to attaining goals.” Self- regulated learning strategies are those skills and behaviors that students use independently to enable them to reach the learning goals they have set for themselves. The problem is that all students are not knowledgeable about a variety of strategies, how to determine which strategies are most effective for a given task, or how to monitor their progress based on the strategies they have decided to utilize. In most middle grades and high school mathematics classes, the focus of instruction is on mathematics content, as it should be, but without including explicit instruction on the use of self-regulating learning strategies, students may not have all the skills needed to be successful, independent, self- regulated learners. There are several sub-problems associated with including instruction on the use of self-regulated learning strategies in middle grades mathematics classes, which is the setting for this study. First, teachers are not generally aware of self-regulated learning strategies. There doesn’t appear to be a finite list of strategies that should be included along with mathematics instruction. Professional development for mathematics teachers does not usually focus on how to incorporate explicit instruction on self-regulated

2 learning strategies into mathematics instruction. Second, the locus of control in the classroom environment can positively or negatively impact students’ use of self-regulated learning strategies. Eshel and Kohav (2003) found that teacher control and student control coexist in the classroom, but self-regulation is fostered in classrooms with strong student control, regardless of the level of teacher control. Purpose of the study This study was designed to examine how explicit instruction of self-regulated learning strategies impacted middle grades mathematics classes. Data was collected from students about their use of self-regulation and the strategies associated with self-regulated learning. Standardized test data was used to examine the impact on student achievement. Research questions There were two research questions for the study: 1. To what extent does the explicit instruction of self-regulated learning strategies in middle grades mathematics classes aid in developing independent, self-regulated learners? 2. To what extent does explicit instruction of self-regulated learning strategies in middle grades mathematics classes impact student achievement? Definitions of terms For this study self-regulated learning strategies refer to the set of specific skills students were taught to help them set learning goals, select appropriate strategies to accomplish assigned and self-identified tasks, manage their time, and to monitor and evaluate their progress toward reaching their learning goals. Being a self-regulated

3 learner refers to the level at which students are able to independently select, use and evaluate self-regulated learning strategies. Student achievement was determined by scores on North Carolina End-of-Grade Mathematics Tests. The literature does not seem to have a specific definition for explicit instruction as an instructional model. For their study on teacher effectiveness, Yates and Yates (1990, p. 229) define it as a set of practices that a student is offered that includes “direct cognitive guidance, supportive modeling, a relatively complete analysis of convert steps and attack strategies, error correction and extended opportunities for practice prior to being expected to think and perform at the level of a knowledgeable expert.” In a recent “Research Brief,” the National Council of Teachers of Mathematics (2007, p. 1) defined explicit instruction as “instruction that involves a teacher demonstrating a specific plan (strategy) for solving the problem types and students using this plan to think their way through a solution.” Their review of recent research indicated that using explicit instruction with exceptional and low-achieving students produced a moderate to large effect size on student achievement. Both of these definitions refer to the manner in which teachers provide students with the learning opportunities required to acquire specific skills and knowledge. For this study explicit instruction will refer to the methods teachers employed to include the use of self-regulated learning strategies in their regular mathematics lessons. Limitations Prior to beginning the study, several limitations were considered. The foundation of this study was the explicit instruction of self-regulated learning strategies in middle grades mathematics classes, and as such, may have been limited by the level of teacher

4 interest and willingness to include explicit instruction of self-regulated learning strategies in their lessons. The teachers may have felt that adding another component to their instruction would have detracted from the available instructional time allotted for teaching/learning mathematics. There was a concern that entrusting the explicit instruction to teachers who were not particularly knowledgeable about the use and instruction of self-regulated learning strategies may negatively have impacted the effects of the explicit instruction and consequently may have skewed the results of the study. There was a professional development component included in the study prior to and during the time when teachers begin their explicit instruction with students. Also, the level of implementation by each teacher, who included explicit self-regulated learning strategy instruction, was monitored to ensure fidelity to the treatment. There was a concern that other factors which were beyond the control of the researcher, such as teacher experience, variability of mathematics instructional technique, and school based programs may have influenced differences in outcomes for the control and treatment groups. A discussion of how the limitations may have impacted the study implementation and results is included in chapter five. Outline of the rest of report Following this introduction to the study, there is a literature review based on studies and articles by experts in the field of self-regulation. Overviews of the methods and procedures that were used in the study are included along with an explanation of the data collection process, statistical analyses and outcomes. Then there is a report of the study findings followed by a discussion of their implications, limitations, ethical considerations, and recommendations.


Chapter overview Prior to designing this study, a review of the literature was conducted to ensure that the study was based on a sound philosophical foundation and other previously conducted research. This chapter provides information from the current literature beginning with a brief introduction to self-regulation, followed by sections that address self-efficacy and its relationship to self-regulation, a more in-depth discussion of self- regulation, instructional models, and concluding statements that summarize how the literature informed the present study. Self-regulation introduction Zimmerman (2002) defines self-regulation as “self generated thoughts, feelings, and behaviors that are oriented to attaining goals (p. 65).” He states, “…self-regulation of learning involves more than detailed knowledge of a skill; it involves the self-awareness, self-motivation, and behavioral skill to implement that knowledge appropriately (p. 66).” He explains that self-regulation is a collection of skills that include specific, reachable goal setting, strategy adoption, self-monitoring, restructuring behaviors to meet goals, time management, self-evaluation, task ownership and adapting for the future (Zimmerman, 2002). Self-efficacy and its relationship to self-regulation The theoretical framework for using self-regulated learning strategies is based on

6 Bandura’s theory of self-efficacy. He defines self-efficacy as “a judgment of one’s capability to accomplish a certain level of performance (Bandura, 1986, p. 391).” Further he explains that one’s belief in one’s own abilities has an effect on the choices one makes. For example, people tend to avoid situations they believe require capabilities beyond the ones they possess. Similarly, people are more willing to engage in tasks that they feel they will be able to complete successfully. This willingness to engage in an activity contributes to the individual’s competency with respect to the skills required to complete the activity. According to Bandura, a person’s belief in how likely he/she is to be successful at a task has an influence on the level of effort the individual is willing to expend. An individual is more likely to put forth greater effort and persist toward the completion of the task if the person feels he/she is capable of successfully completing the task (1986). These ideas have implications for how students should be supported in their efforts to learn new skills and concepts and the importance of providing explicit self- regulated learning strategy instruction. Bandura’s theory of self-efficacy is rooted in social-cognitive theory, which holds that behavioral, environmental and personal factors interact to determine and define human actions (Schunk & Zimnmerman, 1997). Bandura includes both social constructionist elements that address how cognitive development occurs and it also includes elements of self-determination theory, which addresses motivational factors (Schunk & Zimmerman, 1997; Sullivan, 1998). Social constructivists fall into two groups. First are those who base their beliefs on Piaget’s work. They believe that human learning is an internal function that addresses the disequilibrium created within the individual when confronted with a conflict between

7 experience and what one believes he/she knows (Sullivan, 1998). In the second camp are those who base their beliefs on Vygotsky’s theory, which maintains that learning occurs as the result of human interaction in social settings (Sullivan, 1998). Bandura’s use of social cognitive theory is compatible with both perspectives (Martin, 2004, Schunk & Zimmerman, 1997; Sullivan, 1998). Schunk and Zimmerman (1997) describe a process for self-regulation development that begins with social interaction and modeling and eventually becomes an internal set of processes that are revised and monitored based on an individual’s interaction with new experiences and tasks. They suggest that Vygostky’s theory explains cognitive features of self-regulation and Piaget’s theory explains the self-motivation component that is inherent in those who are successfully able to self-regulate their own learning. In other words social cognitive theory as Bandura uses it to support his theory of self-efficacy blends social learning behaviors (Vygotsky) with motivational factors and personal monitoring (Piaget) to explain how self-regulating behaviors combine to increase self-efficacy (Harrison, Rainer, Hochwarter, & Thompson, 1997). According to Bandura’s theory of self- efficacy, as students take control of their own learning and engage in behaviors that they self-evaluate as beneficial, their understanding of their own ability to successfully accomplish future tasks increases and this thereby increases self-efficacy (Bandura, 1986). Self-efficacy is determined by four factors. The first factor which may contribute to self-efficacy is previous success. If one is successful at completing a task, he/she develops a greater confidence that he/she can successfully complete future tasks (Bandura, 1986); i.e. success breeds success. The second factor that may contribute to

8 self-efficacy is vicarious experience. If an individual observes someone, who he/she perceives to be similarly capable, complete a task then the individual believes that he/she is also capable of completing the task (Bandura, 1986); i.e. if he can do it, so can I. Verbal persuasion is another factor that contributes to self-efficacy. If an individual is told that they are capable of completing a task by someone they trust they may decide that they are indeed capable. The influence of this factor is ultimately limited by the success one has when the task is attempted (Bandura, 1986). It does speak, however, to the power a teacher may have to motivate students to attempt new skills or problems. Finally, the general psychological state of the individual influences his/her self-efficacy. If the individual is highly stressed or agitated about attempting a new task, he/she may not feel as though he/she can successfully complete the task whereas under less stressful conditions, he/she may feel better about the situation in general (Bandura, 1986). Pajares (1997) has conducted a number of studies related to the influence of self- efficacy and mathematics performance. In one such study he wanted to determine if the type of mathematical assessment would influence students’ self-efficacy judgments. Three hundred twenty-seven middle school students were presented with both a multiple- choice assessment and an open-ended performance assessment of similar mathematics problems. Even though students performed better on the multiple-choice test, there was not a significant difference in their self-efficacy judgments. However, the findings did indicate that the higher performing students are better at identifying their level of self- efficacy than lower performing students. In another study, Pajares (1995) tested different levels of self-efficacy. Working with 391 college students enrolled in different universities, he found that students’

9 mathematical self-efficacy for completing specific mathematics problems was more reliable than their general confidence to perform mathematical tasks or their predictions of earning high grades in mathematics-related courses. The findings of this study differ to some extent from previous studies, which had indicated that students’ mathematical confidence was a strong indicator of problem-solving ability. The findings confirmed Bandura’s theory that there are different ways of assessing self-efficacy (Bandura, 1986). Pajares (1995) asserts that self-efficacy is more accurately related to specific tasks than to global views of generalized situations. As a result students could confidently predict their capability to complete specific problems, but were less able to accurately predict their capability to complete all mathematics problems of a particular type or to earn a high grade in a class. However, students generally are very aware of their capabilities, which is why teachers and counselors are advised to seriously consider students’ self-efficacy in the same way they consider test scores when making course placement decisions. In another study, Pajares (1999) explored the relationship between the mathematical self-efficacy, motivation and performance of 273 middle school students. He found that self-efficacy was a strong predictor of mathematical performance when the data were controlled for the effects of motivational influences. Additionally he found that students’ attitudes and achievement in mathematics decreased during the year the study was conducted. These findings are consistent with other studies in this area. However students’ mathematical confidence did not decrease during the same time period. The data collected for this study indicated that the decrease in performance and self-efficacy was greater for regular education students than for gifted students. Zimmerman (1990) has also studied the effects and influence of self-efficacy.

10 Most of his work seems to have been conducted with very young children, but in one particular study he explored fifth, eighth and eleventh grade students’ abilities to use self- regulated learning and estimate their mathematical efficacy. He found that students’ self- efficacy increased with age. High school students’ self-efficacy was greater than middle school students’, which was greater than the elementary school students. This seems contradictory to studies which indicate that students’ mathematical confidence decreases with age. It is important to note that confidence to complete a task may be low, but by being able to accurately predict one’s inability to successfully complete the task, self- efficacy is high. Self-efficacy is a measure of one’s ability to accurately predict their capability; it is not the same as one’s confidence level. Zimmerman (1990) found that students who more actively engaged in self- regulated learning strategies also had higher levels of self-efficacy than other students. It may be that students who are more actively engaged in the pursuit of learning are more aware of their strengths and limitations and thus their self-efficacy increases as their active involvement in learning increases. He provides an overview of the underlying beliefs and assumptions of self-regulated learning theory. He states, “self-regulated learning theorists view students as metacognitively, motivationally, and behaviorally active participants in their own learning process (Zimmerman, 1986, p. 308).” The metacognitive component recognizes student behaviors such as planning, organizing, self-instructing, self-monitoring and self-evaluating during the learning process. The motivational component examines the level at which students perceive themselves as competent, capable, and independent learners. The behavioral aspect of self-regulation refers to students’ abilities to recognize, select, and design appropriate learning strategies

11 and environments (Zimmerman, 1986). Pajares and Miller (1994) address the flaws in a number of studies that have previously attempted to determine if self-efficacy and self-concept are predictors of students’ problem-solving performance. They based their study on Bandura’s social cognitive theories of self-efficacy, which defines self-efficacy as “people’s judgments of their capabilities to organize and execute courses of action required to attain designated types of performances (p. 193).” The authors explain the difference between self-concept and self-efficacy. Although they admit that the two constructs are often used interchangeably by many researchers, they are inherently different. Self-efficacy “is a context-specific assessment of competence to perform a specific task, a judgment of one’s capabilities to execute specific behaviors in specific situations (Pajares & Miller, 1994, p. 194).” Self-concept is a more generic perception of one’s competence. Self-concept may be specific to a subject area, but is not specific to individual tasks. Example of self-concept: “Are you good at math?” Example of self-efficacy: “Can you solve this specific problem?” The authors remind us that measures of self-efficacy should occur immediately prior to performing the specified task. Many self-efficacy study designs are flawed by asking students to respond to self-efficacy instruments after task performance or an extended time prior to the task performance. A study conducted by Pajares and Miller (1994) found that “self-efficacy had stronger direct effects on (mathematics problem-solving) performance than did any of the (other) variables (p. 198)” examined in the study, such as mathematics self-concept,

12 perceived usefulness of mathematics, prior mathematics experience, and gender. Several aspects of the study supported Bandura’s theories. First, the overall findings indicate the power of self-efficacy. Second, most students’ overestimated the level of their performance. That is also consistent with social cognitive theory. Pajares (2002) states that Bandura’s social cognitive theory of human functioning is the framework for both self-efficacy and self-regulated learning. Pajares explains self- efficacy by stating, “Individuals engage in behavior, interpret the results of their actions, use these interpretations to create and develop beliefs about their capability to engage in subsequent behaviors in similar tasks and activities, and behave in concert with the beliefs created (Pajares, 2002, p. 116).” In the same journal, Zimmerman (2002) explains, “the self-motivated quality of self-regulated learners depends on several underlying beliefs, including perceived efficacy and intrinsic interest (p.66).” One of the most crucial of these beliefs is the students’ knowledge of their capabilities to successfully complete a task or activity, which is the essence of self-efficacy beliefs (Pajares, 2002). This is a compelling argument to substantiate the value of self-efficacy as a driving force for the use of self-regulated learning strategies. Pajares (2002) refers to a number of studies that indicate that gender may be a factor in students’ self-efficacy and use of self-regulated learning strategies. However, the differences vary by subject and grade span. He addresses several reasons why gender may appear to be a greater influence than it actually is. First he mentions that there is not a statistical difference between the self-efficacy of students with similar academic capabilities. He also indicates that differences seem to align to societal expectations that boys do well in mathematics and science and that girls do better in language arts. Pajares

13 hypothesizes that the methods used for measuring self-efficacy may also create differences among genders. Finally he mentions that boys and girls seem to respond to questions about self-confidence and capability differently. Girls tend to be more humble while boys tend to overestimate, exaggerate or brag (Pajares, 2002). Self-regulation Self-regulation is defined in several ways by various researchers. Zimmerman (1986) defines self-regulated learning strategies as the “actions directed at acquiring information or skills that involve agency, purpose (goals), and instrumentality self- perceptions by a learner (p. 615)” for the purposes of a study he conducted with 80 high school students, 40 from the high achievement track and 40 from the low achievement track. Fourteen categories of self-regulation strategies were identified from interviews with the students. Use of the strategies predicted with 93% accuracy the academic track of the students, thereby indicating that higher achieving students use a greater variety of self-regulated learning strategies and with greater consistency than lower achieving students. Zimmerman (1986) refers to 14 categories of self-regulated learning strategies that have been identified as contributing to academic achievement. The categories are identified as follows: 1. self-evaluation; 2. organizing and transforming; 3. goal-setting and planning; 4. seeking information; 5. keeping records and monitoring; 6. environmental structuring; 7. self-consequences; 8. rehearsing and memorizing; seeking social assistance from 9. peers, 10. teachers, and 11. adults; and reviewing records such as 12. tests, 13. notes, and 14. textbooks. Zimmerman also recognized learning behaviors that were initiated by someone other than the student, but did not include them as self-

14 regulating strategies. In another article on attaining self-regulation, Zimmerman (2000) defines self- regulation as the “self-generated thoughts, feelings, and actions that are planned and cyclically adapted to the attainment of personal goals (p.14).” He goes on to describe the 3 phases of self-regulation: forethought, performance and self-reflection. The forethought phase includes goal setting, planning, and self-motivation to perform. Self-motivation is dependent upon one’s self-efficacy, or belief in one’s ability to perform effectively, one’s expectations, interest in the task, and goal commitment. The performance phase includes the use of self-control, focus and strategy implementation. The final phase, self- reflection, includes evaluation, self-satisfaction and self-reward. Self-regulating strategies are divided into three phases of a cyclical process. Forethought is the first phase. This phase includes task analysis, goal setting, planning and self-motivation. The second phase is the performance phase. This phase includes self-control and self-observation. This is the operational phase of completing a task. The third and final phase is the self-reflection phase. In this phase, students self-evaluate their efforts and develop a sense of satisfaction at their accomplishment. The final stage provides the motivation and impetus to tackle another task and so it is the basis for the forethought phase (Zimmerman, 2002). It is this stage that is enhanced by explicit instruction in self-regulated learning strategies. Students who have strategies that they have used to successfully complete previous tasks, will also have the confidence to approach future tasks with a better understanding of their capabilities and limitations. It is the self-awareness of one’s abilities that increases self-efficacy. Since the phases are cyclical, however, explicit instruction on strategies for other phases will ultimately

15 impact the whole process of self-regulation. Further Zimmerman (2002) concludes by stating, “Recent research shows that self-regulatory processes are teachable and can lead to increases in students’ motivation and achievement (p. 69).” Research indicates that attempts to teach problem-solving heuristics to mathematics students based on Polya’s method has not achieved the positive results expected. It seems that developing and successfully utilizing problem-solving strategies is both problem and solver specific. In numerous studies, teaching heuristics has not produced measurable differences when compared to control groups that did not receive specialized problem-solving instruction (Schoenfeld, 1985). However, teaching students to use heuristics as generalized strategies for problem-solving is different from teaching self-regulated learning strategies. The heuristics that are taught to students are generally thought processes, whereas self-regulated learning strategies are taught as learning behaviors, which are not situation or task specific. Zimmerman (2000) states that low levels of self-regulation are related to poor achievement in all aspects of life. He uses examples other than education, such as personal health care, to illustrate the point. He states that social learning experiences, or the lack thereof, contribute to the acquisition of self-regulation strategies. He states that individuals who have low levels of self-regulation grew up in “homes or communities where they (self-regulation strategies) are not taught, modeled, or rewarded (p.27).” This makes it important to include explicit self-regulated learning strategy instruction as a component of a complete instructional program. According to Pintrich and De Groot (1990), there are three motivational components linked to self-regulated learning. First is an expectancy component, which

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Abstract: Self-regulated learning includes the use of a set of strategies for planning, monitoring, and self-evaluating students' efforts toward reaching specific learning goals. This study examined the extent to which explicit self-regulated learning strategy instruction impacted regular eighth grade students' learning behaviors and mathematics achievement. The study was a quasi-experimental design using a control and treatment group which consisted of eighth grade general mathematics students. The treatment was explicit instruction of ten self-regulated learning strategies. Data were gathered using a researcher-designed survey and standardized mathematics test scores. Findings indicated that the treatment group reported a significantly higher level of self-regulated learning strategy use, earned significantly higher mathematics test scale scores, and showed significantly greater academic growth than the control group. Additionally students' use of self-regulated learning strategies was statistically significant in explaining the variance in students' mathematics test scores and academic growth.