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

Gregory Schraw and David W. Brooks

Department of Educational Psychology and Center for Curriculum and Instruction, University of Nebraska-Lincoln, Lincoln, NE 68588

Abstract: Self-regulation refers to students' ability to understand and control their learning, and is important for success in chemistry courses. We describe the "will" and "skill" components of self-regulation, and how instructors can enhance these components in their classes. Chemistry teachers most often focus on developing their students' chemistry knowledge bases. Self-regulation deals with more general skills that make one a more efficient and effective learner. In this article we focus on improving self-efficacy, attributions, strategy use, and effective use of metacognitive knowledge. We conclude with guidelines for integrating self-regulation skills into the chemistry classroom.



We all want our students to succeed in chemistry. The purpose of this paper is to provide an integrated approach to promoting self-regulation in the chemistry classroom that achieves this end. We focus on developing student skills and self-awareness in three main areas, including motivation, strategy use and metacognition. Previous articles in this Journal have addressed a number of teaching strategies to improve comprehension in the classroom and laboratory. These include the use of concept maps (1, 2), critical thinking skills (3), cooperative learning groups (4), and creating a "science culture" in the classroom (5). These articles focus on active teaching rather than active learning. A number of other articles have focused on teaching specific learning strategies to students to promote deeper learning (6, 7). These articles focus on student skills without addressing motivational concerns that may prevent students from using newly acquired skills.

Students learn best when they possess an integrated package of skills and beliefs that support learning. We emphasize two general aspects of student learning from contemporary self-regulated learning theory: the skills necessary to think critically and solve problems, and the will to use these skills (8, 9, 10). We begin by defining a number of terms central to self-regulated learning theory. We next describe the relationships among these, suggest ways to help students learn such skills in the chemistry classroom, as well as ways to promote self-monitoring. We conclude by discussing a set of realistic goals for a one-semester chemistry class.

Understanding Self-Regulation

Self-regulation refers to students' ability to control their learning (8, 9, 10). Learners become self-regulated using both knowledge and strategies we refer to as skills and the motivational desire to use these skills that we refer to as will. Figure 1 shows a graphic representation of will and skill sub-components. We begin with two aspects of will (i.e., self-efficacy and attributions) because both are known to affect initial engagement and persistence in important ways. We then describe three sub-components of skill: knowledge base, strategies and metacognitive awareness.

Figure 1. Self-Regulation


Motivation is a process whereby goal-directed effort is initiated and sustained. Research on the role of motivation has mushroomed over the past decade (10, 11). Researchers once believed that motivation had little impact on how students learned. This view has changed dramatically; now it is believed that motivation not only prepares a student to learn, but also changes the learning process itself. A number of different types of motivational beliefs have been studied recently, including self-efficacy (12), attributions (13), goal orientations (14), intrinsic motivation (15), hope (11), and perceived control (16). We focus on self-efficacy and attribution theories because each has been researched extensively for at least ten years, and teachers at all levels have a significant impact on these beliefs.

Self-efficacy refers to the degree to which individuals possess confidence in their ability to achieve a specific goal. For example, a student might be confident about her ability to make appropriate computations and then prepare dilute solutions from concentrated stock solutions, or to conduct a systematic library search for synthetic methods for preparing gamma-lactones. 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 (17).

Four factors affect the relative strength of one's self-efficacy judgments (18):

Modeling with explicit feedback from slightly more competent peers appears to be the most important of these factors with respect to improving efficacy (17, 19).

As self-efficacy increases, so do the student's willingness to engage and persist in challenging tasks (18), and the quality and quantity of information processing (17). Teacher efficacy also plays an important role in the classroom (20). Teachers with higher levels of teaching efficacy set broader curricular goals, provide greater student challenge, and invest more time helping students (21, 22). Highly efficacious teachers plan better by using their knowledge about course content, pedagogy and student development.

Of course, it is possible to have too much of a good thing. During interviews with college science students near the end of a semester, Horn (23) found that many students continued to expect final grades of C even though, for this to occur, they would need to earn 300 points on a 250 point final. She observed that this problem appeared to be most prevalent among student athletes, and suggested that this might reflect the propensity of these students to never relinquish hope. As far as we know, there is no strategy supported in the literature for chemistry teachers to deal effectively with this problem.

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 (13), 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).

Effective teachers help their students understand that classroom success is attributable to many factors in addition to ability. The most important of these is effort, in the form of deliberate practice, that develops a knowledge base and procedural automaticity. Teacher help, but especially modeled demonstrations, is a second crucial factor. Strategy use and monitoring constitutes a third factor. In general, student motivation and performance improve whenever they shift their success attributions from external, uncontrollable causes to internal, controllable ones. We offer several guidelines for attributional retraining later in this paper.



Having an appropriate knowledge base is crucial for effective learning. Coppola et al. (4) describe a number of ways to organize the knowledge base to improve instruction. These include the use of concept maps, structured problems and opportunities for group-based learning. Effective teachers also emphasize the role of deliberate practice, including daily reading, completion of in-class projects, homework and expert modeling. One especially difficult problem is helping students to codify fragmented, tacit knowledge into organized, explicit knowledge (24). Research suggests that novices complete this process through practice and modeling from skilled experts.

Ericsson and colleagues (25, 26) have conducted a number of studies on the role of deliberate practice in the acquisition of expertise. These studies reveal a number of findings. The most important of these is that skill development and expertise are strongly related to the time and efficiency of deliberate practice. The more one practices, the better one gets, regardless of initial talent and ability. A second finding is that initial differences due to talent and ability decrease over time as a function of practice. This means that highly talented individuals lose their edge over time if they do not practice compared to less talented individuals.

Strategies refer to learning tactics used intentionally to accomplish a specific goal (27). They are essential to effective learning because they enable learners to use their limited cognitive resources more efficiently, approach problems more systematically, and increase positive motivational beliefs such as self-efficacy!

Two recent reviews (28, 29) support the following claims about strategy instruction:

1. Strategy instruction typically is moderately to highly successful, regardless of the strategy or instructional method. (See Pressley & Wharton-McDonald (30) for an excellent review.)

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

3. Programs that combine several interrelated strategies are more effective than single-strategy programs (28). Effective strategies, in order of importance, include 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.

4. Strategy instruction programs that emphasize when and where to use the newly acquired strategy are especially effective (i.e., promote conditional knowledge).

5. Teachers who incorporate strategy instruction into their classrooms should teach specifically for transfer by using the strategy in a variety of settings and unfamiliar domains (31). Research also indicates that the more automatic, well rehearsed a strategy is, the more likely it is to transfer (32).

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. This capability is called metacognition, or explicit knowledge of one's own cognition (see Figure 2). Metacognition includes two main components referred to as knowledge of cognition and regulation of cognition (33, 34). Knowledge of cognition consists of explicit knowledge of one's memory, knowledge base, and strategy repertoire, as well as what often is 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 2. Metacognition

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 (33). Another way is for teachers to model their own metacognition for students. When thinking out loud, teachers too often 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. Peer modeling of both strategies and metacognition not only improves performance, but increases self-efficacy as well (35).

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 (36). The checklist shown below provides an example:

Studies evaluating checklists report favorable findings, especially when students are learning difficult material (37, 38). 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.

Synergies Between Will and Skill

Students need both the will and the skill to succeed in chemistry courses. Many chemistry students struggle initially because they lack:

The will and the skill contribute to academic learning in several ways. One way is through a synergy 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 usage increases, students gain a better organized knowledge base and become more self-efficacious. A second way is through a synergy 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 synergy between skill components. For example, acquisition of new knowledge typically increases the efficiency of strategy use; effective strategy use leads to increased knowledge base.

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. Peer modeling appears to have a greater impact on self-efficacy than other variables (ref. 10, pp. 160-176). A second is that modeling can be incorporated into most forms of classroom and laboratory instruction quite readily.

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 (40). 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. For example, the synthetic strategy of building a ring molecule with two asymmetric centers in such a way that, when the ring is opened in a near final step, only two enantiomers will result. Peer modeling is among the strategies suggested by Coppola et al (4).

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 (17). Peer and teacher modeling also helps novices learn to think like expert chemists. In chemistry, for example, chemists think about systems in three ways: a macroscopic view, a submicroscopic view, and a symbolic view. When patients suffering from sickle cell anemia present at hospitals, they show symptoms characteristic of that disease. A chemist who understands the disease sees the 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 chemist’s symbolic representation of this situation is Glu --> Val, code for the replacement of the amino acid glutamic acid with 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 (39).

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 (38, 41). A variety of other methods have been described (42).

We offer the seven-step plan below as a general example of teacher-scaffolded 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. Why is learning this relevant?
  2. Model the procedure in its entirety while the students observe. For example, when teaching quantitative problem solving in science, identify the quantity sought together with its units. Then, determine what is given and/or available. Indicate how these are connected to one another. Next, perform any necessary calculations. Finally, check the answer to see if it makes sense.
  3. Model component parts of the task. If the task can be broken into smaller parts (e.g., identifying asymmetric atoms in a synthetic target molecule), model each part by using different problems or settings. In quantitative problem solving, stress the steps. The first step, determining the quantity that is sought, often is the most difficult for students.
  4. Make explicit the otherwise implicit strategies you use to solve problems (e.g., deciding whether water will appear as a liquid or a gas under a given set of conditions ). Students have a tremendous reluctance to writing reciprocals in quantitative problem solving. (Sometimes only implicit strategies seem to be 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. When planning syntheses, the student might be given several problems involving the protection of functional groups. A student might have various steps in laboratory work checked by the instructor.
  6. Allow students to practice the entire procedure under teacher guidance. Component steps eventually are merged into a single, smooth procedure that is performed intact.
  7. Have the student engage in self-directed performance of the task.

Feedback (explicit information provided about the process and products of work) plays an important role in learning (43). 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 (44). Taking the time to provide students with timely and informative feedback significantly improves instruction (10, 43).

Attributional retraining refers to helping individuals better understand their attributional responses and develop responses that encourage task engagement. A review by Försterling (45) 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 and reinforced in class..

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.

Improving Strategy Use and Metacognition

Researchers have identified over 50 different general strategies (e.g., taking notes, asking for help) that aid classroom learning. In addition, chemistry classrooms often use numerous specialized strategies (such as adding the concentrated reagent to water, or drawing lines, dashes, and wedges so as to represent the configuration of groups connected to an atom). Teaching the chemistry-specific strategies is considered to be a part of the chemistry teacher's job; teaching general strategies usually 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 (27, 44).

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 (46).

Due to students' high degree of dependence on domain-specific strategies in math and science, chemistry strategy instruction should be an integral part of every chemistry course and probably each and every class (30). For example, in science and engineering, dimensional analysis has a rich history in problem solving (47, 48), 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 teacher or more advanced students.

Teachers should consider how to sequence general strategy instruction. 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.

1. Discuss and explain the value of strategies. Students should understand why they are being asked to learn strategies, what instruction will be like, and how they will use them. For example, you might suggest that students begin their reading of a chapter by looking at the problems found at the end of a chapter.

2. Introduce only a few strategies. The best chance of teaching students general strategies that are useful to them is to limit the number taught to two or three over an eight- to ten-week period of instruction. This time affords students a chance to acquire the strategy, practice it, and become somewhat automatic.

3. Continue practice over an extended period. Plan on six to ten weeks for instruction, modeling, and practice of a new strategy. Periodic follow-ups are helpful to ensure that the strategy is being maintained.

4. Model strategies extensively. Even when students understand why they are learning a strategy and how to use it, they need to see the strategy modeled by a teacher (or other expert). Modeling should include at least two components: (1) how the strategy is used in a variety of settings to accomplish different learning objectives, and (2) why the teacher uses the strategy. When solving quantitative problems, it always pays to speak out loud the final steps of whether or not the answer makes sense. Because an expert will use a variety of tests in different situations, this activity will be especially beneficial to your students.

5. Provide feedback to students about how, why, and when to use strategies (43).

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 (4). Furthermore, it is a good idea to mention late in the sequence about the strategies taught early in the sequence.

Realistic Goals for a Traditional Course

How much effective instruction related to self-regulation 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 is likely to enhance student efficiency by 10 percent or more. The hope is, of course, that these skills will transfer substantially to other math and science courses, and perhaps beyond. Thus far most research suggests that teachers must teach explicitly for transfer to occur.

The current evidence we cite suggests that devoting even a small amount of time to helping students appreciate the importance of self-regulation leads to noticeable, measurable performance improvements. 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 recommend that you incorporate our suggestions at a manageable pace, perhaps 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.

5. Enhance metacognitive awareness of their own learning

6. Provide practice using informational feedback



Literature Cited


1. Pendley, B. D.; Bretz, R. L.; Novak, J. D. J. Chem. Educ. 1994, 71, 9-15.

2. Regis, A.; Albertazzi, P. G.; Roletto, E. J. Chem. Educ. 1994, 1084-1088.

3. Wojciechowski, B. J.; Deal, S. T. J. Chem. Educ. 1996, 73, 85.

4. Coppola, B. P.; Ege, S. N.; Lawton, R. G. J. Chem. Educ. 1997, 74, 84-94.

5. Angel, S. A.; LaLonde, D. E. J. Chem. Educ. 1998, 75, 1437-1441.

6. Worrell, J. H. J. Chem. Educ.,1992, 69, 913-914.

7. Ross, M. R.; Fulton, R. B. J. Chem. Educ., 1994, 71, 141-143.

8. Zimmerman, B. J. In ., Self-regulation of learning and performance: Issues and educational applications; Schunk, D. H., Zimmerman, B. J., Eds.; Lawrence Erlbaum: Hillsdale, NJ, 1994, pp 3-22.

9. Schunk, D. H.; Zimmerman, B. J. Self-regulation of learning and performance: Issues and educational applications; Lawrence Erlbaum: Mahwah, NJ, 1994.

10. Pintrich, P. R.; Schunk, D. H. Motivation in education: Theory, research, and applications; Prentice Hall: Englewood Cliffs, NJ, 1996.

11. Stipek, D. J. Motivation to Learn; Allyn and Bacon: Boston, 1993.

12. Bandura, A. Self-efficacy: The exercise of control; W. H. Freeman: New York, 1997.

13. Weiner, B. An attributional theory of motivation and emotion; Springer Verlag: New York, 1986.

14. Dweck, C. S.; Leggett, E. S. Psychological Review 1988, 95, 256-273.

15. Kohn, A. Punished by rewards; Houghton Mifflin: Boston, 1993.

16. Deci, E. L.; Ryan, R. M. Journal of Personality and Social Psychology 1987, 53, 1024-1037.

17. Schunk, D. H. Educational Psychology Review 1989, 1, 173-208.

18. Pajares, F. Review of Educational Research 1996, 66, 543-578.

19. Welch, D. C.; West, R. L. Developmental Review 1995, 15, 150-171.

20. Calderhead, J. In Handbook of educational psychology; Berliner, D. C., Calfee, R. C., Eds.; Macmillian: New York, NY, 1996, pp 709- 725.

21. Bandura, A. Educational Psychologist 1993, 28, 117-148.

22. Woolfolk, A. E.; Hoy, W. K. Journal of Educational Psychology 1990, 82, 81-91.

23. Horn, C.; Bruning, R. H. "Achievement in Biology: An exploration of the rolesof ability, motivation, and strategy use in the construction of knowledge and course achievement", April, 1995, American Educational Research Association.

24. Bereiter, C.; Scardamalia, M. Surpassing ourselves: An inquiry into the nature and implications of expertise; Open Court: Chicago, 1993.

25. Ericsson, K. A. In The road to excellence: The acquisition of expert performance in the arts, science and games; Ericssonn, K. A., Ed.; Lawrence Erlbaum: Mahwah, NJ, 1996, pp 1-50.

26. Ericsson, K. A.; Krampe, R. T.; Tesch-Römer, C. Psychological Review 1993, 100, 363-406.

27. Dole, J. A.; Duffy, G. G.; Roehler, L. R.; Pearson, P. D. Review of Educational Research 1991, 61, 239-264.

28. Hattie, J.; Biggs, J.; Purdie, N. Review of Educational Research 1996, 66, 99-136.

29. Rosenshine, B.; Meister, C.; Chapman, S. Review of Educational Research 1996, 66, 181-221.

30. Pressley, M.; Wharton-McDonald, R. School Psychology Review 1997, 26, 448-466.

31. Mayer, R. E.; Wittrock, M. C. In The handbook of educational psychology; Berliner, D. C., Calfee, R. C., Eds.; Macmillan: New York, 1996, pp 47-62.

32. Cox, B. D. Educational Psychologist 1987, 32, 41-45.

33. Schraw, G.; Moshman, D. Educational Psychology Review 1995, 7, 351-373.

34. Baker, L. Educational Psychology Review 1989, 1.

35. Schraw, G. In Adult learning and development: Perspectives from educational psychology; Smith, C., Pourchot, T., Eds.; Lawrence Erlbaum: Mahwah, NJ, 1998.

36. Schraw, G. Instructional Science 1998, 26, 113-125.

37. Delclos, V. R.; Harrington, C. Journal of Educational Psychology 1991, 83, 35-42.

38. King, A. Educational Psychologist 1992, 27, 111-126.

39. Kuhn, D. Psychological Review 1989, 96, 674-689.

40. Schunk, D. H. Learning theories: An educational perspective; MacMillan: New York, 1991.

41. Palincsar, A. S.; Brown, A. Cognition and Instruction 1984, 1, 117-175.

42. Schmuck, R. A.; Schmuck, P. A. Group processes in the classroom, 6th ed.; William C. Brown: Dubuque, IA, 1992.

43. Butler, D.; Winne, P. Review of Educational Research 1995, 65, 245-281.

44. Bruning, R. H.; Schraw, G. J.; Ronning, R. R. Cognitive psychology and instruction, 2nd ed.; Merrill: Englewood Cliffs, NJ, 1995.

45. Försteling, F. Psychological Bulletin 1985, 98, 495-512.

46. Runge, A.; Spiegel, A.; Pytlik Z., L. M.; Dunbar, S.; Fuller, R.; Sowell, G.; Brooks, D. W. Journal of Science Education and Technology 1999, 8, 33-44.

47. Bridgman, P. W. Dimensional Analysis; Yale University Press: New Haven, CT, 1922.

48. Hart, G. W. Multidimensional Analysis: Algebras and Systems for Science and Engineering; Springer Verlag: Heidelberg, 1995.

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