Helping Students Self-Regulate
in Math and Sciences Courses:
Improving the Will and the Skill

Gregory Schraw and David W. Brooks

University of Nebraska-Lincoln, Lincoln, NE

Abstract: Self-regulation refers to students' ability to understand and control their learning, and is essential for success in college math and science courses. We describe the "will" and "skill" components of self-regulation, and how instructors can enhance these components in their classes. We focus on improving self-efficacy, attributions, strategy use, and effective use of metacognitive knowledge. We conclude with guidelines for integrating self-regualtion skills into the science classroom.

 


Helping Students Self-Regulate
in Math and Sciences Courses:
Improving the Will and the Skill
*

Gregory Schraw and David W. Brooks

University of Nebraska-Lincoln, Lincoln, NE

College math and science courses are never easy. Students can make steady incremental progress, however, if they follow the four-step plan outlined in this paper:

These four steps are illustrated in Figure 1.

Figure 1. Self-regulation.

Using the four-step plan above helps students become self-regulated because it gives them an explicit plan for improving their success in math and science courses, and helps them understand the integral relationship between knowledge, strategies and motivation. Without self-regulatory skills, students are at greater risk of dropping out or failing because they attribute their learning problems to lack of ability (Graham, 1991).

Throughout this paper, we emphasize the important role of effort in learning. We also examine how to increase the effectiveness of effort via motivational factors and strategy use in college-level math and science courses. We first define these constructs, then briefly review recent research from educational psychology that supports their inclusion in classrooms. We next provide suggestions for enhancing the motivational climate of classrooms and a six-step plan for improving strategy use. We emphasize the role of motivational beliefs and strategies for two reasons. One is that each plays a distinct and important role in learning. The other is that both are amenable to short-term classroom interventions -- meaning that you can have a measurable impact within the duration of your courses.

Coming to Terms with Self-Regulation

Self-Regulation refers to students' ability to understand and control their learning (Schunk & Zimmerman, 1994; Winne, 1995; Zimmerman, 1994). Students of all ages need to control their learning through productive motivational beliefs and use of cognitive learning strategies.

Motivation is a process whereby goal-directed effort is initiated and sustained. Research on the role of motivational beliefs in learning has mushroomed over the past decade (Pintrich & Schunk, 1996; Stipek, 1993). Researchers once believed that motivation had little impact on how students learned. This view has changed dramatically, in favor of the view that motivation not only prepares a student to learn, but changes the learning process itself. A number of different types of motivational beliefs have been studied recently, including self-efficacy (Bandura, 1997), attributions (Weiner, 1986), goal orientations (Dweck & Leggett, 1988), intrinsic motivation (Kohn, 1993), hope (Synder, 1995) and perceived control (Deci & Ryan, 1987). We focus on self-efficacy and attribution theories: each has been researched extensively for at least ten years, and teachers at all levels have a significant impact on these beliefs (Figure 2).

Figure 2. Components of motivation.

Self-efficacy

Self-efficacy refers to the degree to which an individual possesses confidence in his or her ability to achieve a specific goal. High efficacy in one setting does not guarantee high efficacy in another. Within a specific domain, however, high self-efficacy positively affects engagement, persistence, goal setting and various aspects of performance such as the type and amount of strategies used and the degree to which students monitor their learning (Schunk, 1989). Four factors affect the relative strength of one's self-efficacy judgments (Pajares, 1996):

Modeling with explicit feedback from slightly more competent peers appears to be the most important of these factors with respect to improving efficacy (Schunk, 1989; West & Welch, 1995).

Research reveals two important patterns regarding self-efficacy. One is that, as self-efficacy increases, so does the student's willingness to engage and persist in challenging tasks (Pajares, 1996). Self-efficacy increases the likelihood that students tough-out a difficult task that they might otherwise abandon. High self-efficacy appears to sustain students until they acquire the knowledge and strategies they need to succeed at a task. Second, increased self-efficacy directly increases academic performance by increasing the quality of information processing as well as the quantity. For example, research reviewed by Schunk (1989) and Pajares (1996) shows that high-efficacy students are more likely to use a broader array of strategies, use them more flexibly, monitor their comprehension better, and process information at a deeper level (i.e., generate important inferences about the material).

Research also indicates that teacher efficacy plays an important role in the classroom (Calderhead, 1996). Teachers with higher levels of teaching efficacy set broader curricular goals, provide greater student challenge, and invest more time helping students (Bandura, 1993; Woolfolk & Hoy, 1990). Teacher efficacy is due in part to the breadth of the teacher's knowledge base, the amount of graduate courses in education and content courses, and perhaps most importantly, to the amount and quality of long term strategic planning. Highly efficacious teachers plan better by using their knowledge about course content, general pedagogy and student development. This often is referred to as pedagogical content knowledge (van Driel, Verloop, & de Vos, 1998), illustrated in Figure 3. We argue that some general skills should be included in this mix for teachers, as in Figure 4.

 

Figure 3. Pedagogical content knowledge (Schulman, 1986).

 

Figure 4. Pedagogical content knowledge taking generic strategies and management into account (Schraw & Brooks, this work).

Attributions

Attributions are causal interpretations students provide themselves to explain their academic success and failure. For example, many college students who struggle in calculus attribute their failure to low ability rather than lack of relevant knowledge, strategies, or practice. Attributional responses vary along three causal dimensions (Weiner, 1986), including locus of control (i.e., internal vs. external causes), stability (i.e., short vs. longstanding effects), and controllability (i.e., controllable vs. uncontrollable). Different attributions elicit a variety of distinct emotions in learners. For example, attributing failure to a teacher (i.e., an uncontrollable, external, unstable cause) is less debilitating than attributing failure to low ability (i.e., an uncontrollable, internal, stable cause).

A number of studies have examined the kind of attributions that students make and why they make them. One of the most important findings from this literature is that different students make very different kinds of attributions. Some of these differences are gender related. For example, females in math and science settings are much more likely to attribute failure to ability (rather than effort) compared to males (Stipek, 1993). However, all students make frequent ability-related attributions (e.g., 'I'm not smart enough'). A review by Peterson (1990) found that negative attributional styles (e.g., attributing failure to ability and teachers) are related to low grades, less help seeking, vaguer goals, poorer use of learning strategies, and lower performance expectations. Fortunately, when students are aware of their attributions and guided by knowledgeable teachers, negative attributions can be changed.

Strategies

Strategies refer to learning tactics used intentionally to accomplish a specific goal or purpose (Dole, Duffy, Roehler, & Pearson, 1991). They are essential to effective learning for several reasons. They enable learners to use their limited cognitive resources more efficiently, approach problems more systematically, and increase positive motivational beliefs such as self-efficacy!

Research on strategy instruction has been an important part of educational research over two decades. Two recent reviews by Hattie, Briggs and Purdie (1996) and Rosenshine, Meister and Chapman (1996) support the following claims:

1. Strategy instruction typically is moderately to highly successful, regardless of the strategy or instructional method. This means that students usually benefit from instruction (See Pressley & Wharton-McDonald, 1997, for an excellent review).

2. Strategy instruction appears to be most beneficial for younger students, as well as low-achieving students of all ages. One reason may be that younger and lower-achieving students presently know fewer strategies and therefore have far more room for improvement.

3. Programs that combine several interrelated strategies are more effective than single-strategy programs (Hattie et al., 1996). One reason may be that no single strategy is enough to bring about a substantial change in learning. A repertoire of four or five strategies, however, may be quite effective in this regard. Interested readers are referred to the work of Brown, Pressley, Van Meter and Schuder (1996) for a more detailed description of a typical (and highly successful) cognitive strategy program.

4. Strategy instruction programs that emphasize the role of conditional knowledge are especially especially effective. One explanation is that conditional knowledge enables students to determine when and where to use the newly acquired strategy.

5. Newly acquired strategies do not readily transfer to new tasks or unfamiliar domains. Teachers who incorporate strategy instruction into their classrooms should teach specifically for transfer by using the strategy in a variety of settings (Mayer & Wittrock, 1996). Research also indicates that the more automatic a strategy, the more likely it is to transfer (Cox, 1997).

Another question of interest is what kinds of strategies are most important to teach. Hattie et al. (1996) compared rank orderings for approximately 25 different learning strategies across three cultures (i.e., Japanese, Japanese-Australian, and Australian). Results indicated that a handful of general learning strategies were rated as most important among all cultures. These included in order of importance self-checking, creating a productive physical environment, goal setting and planning, reviewing and organizing information after learning, summarizing during learning, seeking teacher assistance, and seeking peer assistance. Not surprisingly, most of the commonly used strategy instruction program incorporate these skills (Pressley & Wharton-McDonald, 1997).

Collectively, self-efficacy, attributions and strategies play an important role in the extent to which college students self-regulate their learning. Having described each of these terms, we turn to a brief discussion of how motivational beliefs and strategies are interrelated. Afterwards, we describe in more detail ways to improve motivation and strategy use in the college classroom.

The Relationship between Motivation and
Strategy Use in the Self-Regulation Process

Motivation and strategies each contribute to academic success at all age levels. Motivational variables often are referred to as the will component of learning; strategies are referred to as the skill component. Students need both the will and the skill to succeed in math and science courses. Many students struggle initially in math and science because they lack:

The will and the skill contribute to academic learning in several ways. One way is through a reciprocal interchange between will (i.e., self-efficacy) and skill (i.e., strategy instruction) components. As self-efficacy increases, students are more apt to use strategies. As strategy instruction increases, students become more self-efficacious. A second way is through a reciprocal interchange between will components. For example, higher self-fficacy is related to adaptive attributional responses such as increased effort and strategy use. A third way is through a reciprocal interchange between skill components. For example, acquisition of new knowledge typically increases the efficiency of strategy use.

Improving Self-Efficacy and Attributions

Three generic strategies for improving student motivation include modelling, the use of informational feedback, and attributional retraining. We focus on modeling for two reasons. One is that peer modeling appears to have a greater impact on self-efficacy than other variables (Pintrich and Schunk, 1996, pp. 160-176). A second is that modeling can be incorporated into most forms of classroom and laboratory instruction quite readily. Similarly, informational feedback can be incorporated in most forms of classroom instruction. We also describe attributional retraining because it has shown itself to be effective and can be incorporated into most learning environments with only a minimal effort and without detracting from regular course content.

Modeling refers to the process of intentionally demonstrating and describing the component parts of a skill to a novice student. Modeling works because it provides a great deal of explicit information about a skill and raises the novice's expectations that a new skill can be mastered (Schunk, 1991). Not all models are the same, however. Peer models are usually the most effective because they are most similar to the individual observing the model. Teacher models are important as well. Often, the teacher is the only person in the classroom who adequately can model a complex procedure.

Research suggests that modeling is a highly effective way to improve simple and complex skills learned in the classroom. Modeling increases strategy use and self-efficacy (Schunk, 1989). In chemistry, for example, chemists think about systems in three ways: a macroscopic view, a submicroscopic view, and a symbolic view. When a patient suffering from sickle cell anemia presents at a hospital, he or she shows symptoms characteristic of that disease. A chemist who understands the disease sees their problems in terms of "sticky" hemoglobin molecules, ones in which particular genetic information has been changed such that two sites on adjacent molecules which typically carry negative electric charges lose these charges, become electrically neutral, and can attract or bond (i.e., become sticky). Part of the chemists symbolic representation of this situation is Glu --> Val, code for the replacement of the amino acid glutamic acid with the amino avid valine. Whether we're speaking about sick persons in hospitals, tank cars on railroad sidings, modern food labels, or whatever -- chemists will develop a macro, a micro, and a symbolic view of the situation. Thinking this way is a large part of being a chemist. The more explicit a chemistry teacher can be about this way of thinking in their instruction, the sooner students are likely to begin thinking like chemists.

There are a number of ways to model a new skill other than teacher-directed instruction. One method is reciprocal teaching, in which two to four students work in cooperative learning groups (King, 1992; Palincsar & Brown, 1984). A variety of other methods are described in Schmuck and Schmuck (1992).

We offer the seven-step plan below as a general example of effective modeling:

  1. Create a rationale for the new learning skill. Explain to students why acquisition of this skill is important. Provide examples of how, when, and where this skill will be used.
  2. Model the procedure in its entirety while the students observe. For example, when teaching quantitative problem solving in science, the factor-label method is used widely. In this method, the first goal is to identify the quantity sought together with its units. Then determine what is given and/or available. Finally, multiply the given quantities or their reciprocals in such a way that units cancel except for those found in the goal.
  3. Model component parts of the task. If the task can be broken into smaller parts (e.g., using the "integration by parts" method in a calculus class), model each part by using different problems or settings. In the factor label method, stress the steps. The first step, determining the quantity that is sought, often is the most difficult for students.
  4. Make explicit the otherwise tacit strategies you use to solve problems (e.g., how you conceptualize doing a mathematical proof). Students have a tremendous reluctance to writing reciprocals in the factor label method. [Sometimes experts do know why they do something; sometimes only implicit strategies are available, and we can't easily give a reason as to why we've chosen a procedure or approach at the outset. If you can't explain how to proceed to your students, you probably need to reflect on your own performance more carefully].
  5. Allow students to practice component steps under teacher guidance. For example, a music student may practice only the first eight measures of a piece of music, receiving feedback on each occasion from her piano instructor.
  6. Allow students to practice the entire procedure under teacher guidance. Component steps eventually are merged into a single, fluid procedure that is performed intact.
  7. Have the student engage in self-directed performance of the task.

Effective modeling is illustrated in Figure 5.

 

Figure 5. Effective modeling.

Feedback is an essential part of the modeling process. Feedback refers to explicit information provided to students about the process and products of their work. Feedback provided to students directly from the teacher improves both performance and self-efficacy. Students providing feedback to other students appears to be equally effective in many situations. Self-generated feedback also plays an important role in learning; it enables students to self-regulate their performance without teacher or peer-model assistance (Butler & Winne, 1995).

Previous research indicates that different types of feedback exert different influences on performance and self-efficacy. Outcome feedback provides specific information about performance and has little effect on initially correct or subsequent test performance. Cognitive feedback, which stresses the relationship between performance and the nature of the task, appears to exert a more positive influence on subsequent performance by providing a deeper understanding of how to perform competently. Of special interest, studies reveal that high quality cognitive feedback about poor performance improves self-efficacy and subsequent performance (see Bruning et al., for a review). Taking the time to provide students with timely and informative feedback significantly improves instruction (Butler & Winne, 1995; Pintrich & Schunk, 1996).

Attributional retraining refers to helping individuals better understand their attributional responses and develop responses that encourage task engagement. A review by Försterling (1985) found that the majority of attributional retraining programs are quite successful. The general sequence is as follows: (1) individuals are taught how to identify undesirable behaviors, such as task avoidance, (2) attributions underlying avoidant behavior are evaluated, (3) alternative attributions are explored, and (4) favorable attributional patterns are implemented.

Most retraining programs try to shift attributions such that learners attribute success to effort more than to ability. Effort is a controllable variable; ability is not. Programs adopting this strategy frequently report an increase in task engagement, persistence, and achievement levels. Generally, we recommend that instructors discuss early in the course the distinction between ability and effort, and emphasize the crucial role of effort. Students should understand that regardless of ability, effort is the lynch pin to increased knowledge, strategy use and effective problem solving.

How to Teach Strategies

Researchers have identified over 50 different general strategies (e.g., taking notes, asking for help) that aid classroom learning. In addition, math and science classrooms often use numerous specialized strategies (such as the quadratic formula, or hueristics for integrating functions in calculus). Teaching the discipline-specific strategies is usually considered to be a part of the teacher's job; teaching general strategies is not. Experts typically suggest teaching a few general strategies for as long as possible. Five that are frequently recommended are determining what is important in the text or lecture, summarizing, drawing inferences, asking questions before reading as well as afterwards, and comprehension monitoring. Discussions can be found in Dole et al. (1991) and Bruning, Schraw and Ronning (1995, especially chapters 4 and 11).

In the various science and mathematics disciplines it is traditional for a faculty to divide the material covered into content blocks. Teachers, especially those teaching in the early middle schools through early college years, would do well to consider dividing up the general strategies and teaching these explicity in their curricula.

Scientists often suggest that, in their professional work, they make use of sketches to help them organize information about problems. One form of sketch often advocated in science education is the concept map used to "represent meaningful relationships between concepts in the form of propositions" as in Figure 6 (Nowak & Gowin, 1984). In courses where such maps are thought to be particularly effective, an instructor might choose to include them systematically. Students might be encouraged to develop concept maps on their own, perhaps by including concept map creation and/or evaluation of predrawn maps as part of course assignments. In developing this article, the authors attempted to use concept maps frequently and systematically as a means of illustrating how one can approach explicit instruction with respect to the teaching strategies.

Figure 6. General concept map.

Strategy instruction appears to be equally effective in either student- or teacher-centered classrooms, and is effective for all students, even though it is most effective for lower-achieving students. In a typical chemistry course, leaving aside the content-specific strategies, it would be good to limit general strategy instruction. Such instruction often is not included at all (Runge et al, 1998). In departmental situations where students take courses in a sequence (such as biology, chemistry, physics, or general, organic, analytical, physical) it may help to introduce general strategies in a systematic, across-department fashion, and to develop a plan for introducing them throughout the multi-semester curriculum. Furthermore, it is a good idea to mention late in the sequence about the strategies taught early in the sequence. So, if concept mapping is taught early, it is fair game to bring it up throughout the later parts of a (multi-semester) curriculum, but without spending significant instructional time on this strategy.

Interest in strategy instruction has given rise to the concept of a good strategy user. Pressley, Borkowski, and Schneider (1987) described five characteristics of a good strategy user: (1) a broad repertoire of strategies, (2) metacognitive knowledge about why, when, and where to use strategies, (3) a broad knowledge base, (4) the ability to ignore distractions, and (5) automaticity (i.e., the ability to perform a task quickly and with minimal resources) in the four components just listed.

Due to students' high degree of dependence on domain-specific strategies in math and science, strategy instruction should be an integral part of every course and probably each and every class (Pressley & Wharton-McDonald, 1997). For example, in chemistry the factor label method is a general, powerful strategy, and it might receive considerable time during your instruction. Don't automatically discount simple strategies. Even graduate students in organic chemistry occasionally could profit from the rule -- count four bonds to every carbon atom. That's worth repeating nearly every class in organic chemistry. The teaching of strategies improves learner performance and increases self-efficacy and effort rather than ability attributions. We recommend that teachers observe highly self-regulated students to catalogue their strategies. One way to accomplish this is to use think aloud procedures during problem solving. These strategies are most appropriate for direct instruction by either the instructor or more advanced students.

Teachers should consider how to sequence strategy instruction as well. Generally, we recommend an approach in which teachers a) limit instruction to 3 to 5 strategies, b) embed strategy instruction as much as possible, and c) use peers and tutors whenever possible. We suggest this five-step sequence.

 

 

Figure 7. Strategy Instruction

Metacognitive Awareness: Encore to Strategies, Prelude to Self-Regulation

Knowledge and strategies in isolation are not sufficient for self-regulation. Students must understand the strengths and limitations of their knowledge and strategies in order to be able to use them efficiently. Educational psychologists refer to this capability as metacognition, or explicit knowledge of one's own cognition. Metacognition includes two main components referred to as knowledge of cognition and regulation of cognition (Baker, 1989; Schraw & Moshman, 1995). Knowledge of cognition consists of explicit knowledge of our memory, knowledge base, and strategy repertoire, as well as what is often known as conditional knowledge, or knowledge about why, when and where to use strategies. Regulation of cognition consists of knowledge about planning, monitoring, and evaluation.

 

 

Figure 8. Metacognition.

Metacognition is important for two reasons. One is that it enables us to use our knowledge and strategies much more efficiently by being selective. Students with high levels of metacognition engage in deeper processing and learn more even though they do not allocate more time or effort to learning. Several studies have found this relationship even when ability is controlled (Schraw et al., 1995). A second reason is that metacognition compensates for average or low ability. Research shows that, when metacognitive awareness is high, students perform faster and more efficiently even when there ability is no higher than other students (Swanson, 1990).

Students need to understand the role of metacognition in self-regulation. To facilitate this understanding, teachers can discuss the importance of metacognitive knowledge and regulation. Ideally, such a discussion helps students construct an explicit mental model of the self-regulation process (Schraw & Moshman, 1995). Another way is for teachers to model their own metacognition for their students. Too often teachers discuss and model their cognition (i.e., how to perform a task) without modeling metacognition (i.e., how they think about and monitor their performance). A third way is to provide time for group discussion and reflection, despite time demands. Peer modeling of both strategies and metacognition not only improves performance, but increases self-efficacy as well (Schraw, 1998a).

Still another way to promote understanding is to help students develop a systematic approach to monitoring their learning. The use of monitoring checklists in which students check off component steps in monitoring this learning helps to systematize monitoring (Schraw, 1998b). The checklist shown below provides an example:

  1. What is the purpose for learning this information?
  2. Do I know anything about this topic?
  3. Do I know strategies that will help me learn?
  4. Am I understanding as I proceed?
  5. How should I correct errors?
  6. Have I accomplished the goals I set myself?

Studies that have used checklists report favorable findings, especially when students are learning difficult material (Delclos & Harrington, 1991; King, 1991). It is completely within bounds to print up and distribute checklists to students. When it comes to strategy instruction, it is hard to be too explicit.

What to Expect: Realistic Goals for a Traditional Course

How much can an instructor accomplish in a 10 to 14-week course? The answer to this question depends upon how much time and effort she or he devotes to promoting self-regulation. A wide variety of studies suggest that self-regulatory skills can be embedded comfortably into existing instruction without a substantial time loss. Depending upon the extent of peer modeling that is included, one might expect that 10 percent of course time is devoted to promoting self-regulation. This time is very well spent, however, when one considers that improved self-regulation will enhance student efficiency by 10 percent or more, and transfer to some extent to other math and science courses, and perhaps beyond.

Regardless of one's commitment, we believe that even a small amount of time invested in helping students appreciate the importance of self-regulation can lead to a noticeable improvement. Many students simply do not understand the full complexity of learning. Having a better grasp of how self-regulated students manage their learning gives less-regulated students a much greater sense of self-control.

We realize that some instructors reading this may have very little exposure to cognitive learning theory. We recommend that you incorporate our suggestions at a manageable pace over two or three semesters if necessary. Do only as much as you can do well. Strive for the ideal summarized in the following six benchmarks for promoting self-regulation.

  1. Make students aware of what it means to be self-regulated
  1. Foster an understanding of the knowledge base
  1. Enhance strategy repertoires
  1. Nurture appropriate motivational beliefs
  1. Provide practice using informational feedback

 

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