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5 Indicators of Student Behavior STUDENTS AS KEY ACTORS At the very center of science and mathematics education lies the behavior of students. It is these behaviors that allow society to gauge and compare the extent to which the educational system is providing opportunities to learn and nurturing the attitudes important for a scientifically literate society. Moreover, a focus on what students do, assuming they have choices, offers a great advantage: student behaviors may be viewed as manifestations of a large number of hard-to-measure influences on the learning of and interest in science and mathematics. It is easier to design indicators that capture the combined effect of poorly understood influences than to assess those factors separately and directly. For example, it is relatively straight- forward to collect information on the number of students who choose to study physics. The decision to study physics is a clear behavioral event, an observable activity that sums up the effects of parental suggestions, guidance counselors' advice, college admission require- ments, the reputation of the local physics teacher, and the student's own interest in science. Similarly, it is possible to collect data on stu- dents' reactions to science as a career without fully understanding the variety of factors that are likely to affect those reactions. These influences are important to understand, and more research is needed to understand better their role in shaping behavior. Nevertheless, 73

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74 INDICATORS OF SCIENCE AND MATHEMATICS EDUCATION it is possible to design indicators of the important behaviors of stu- dents without completely understanding the influences that cause the behaviors or the personality characteristics that the behaviors represent. Recent research in cognitive science (Resnick, 1983) and the growing acceptance of generative or constructionist psychology (e.g., Osborne and Wittrock, 1983; Watts and Gilbert, 1983) further high- light the importance of the student in the learning process. The current view of the student learner is one who actively constructs his or her own meaning, rather than serving as a passive receptacle of the teacher's transmitted information. The constructionist view of the learner places great importance on the prior knowledge of the student and the nature of the learning activities in which the stu- dent engages. Because learners have some control over the nature and quality of their efforts, some of the responsibility for learning outcomes shifts from the teacher to the student. This gives added importance to the monitoring of student behaviors. Welch (1984) argues that the methods of effective scientific inves- tigation provide a model for effective science learning. The methods for learning science should follow the methods for doing science. The mode} consonant with our earlier definition of scientific literacy- suggests that successful students must participate in certain activi- ties, such as observation and experimentation; be guided by a number of beliefs about the process, such as objectivity and tentativeness; and possess certain personal traits, such as curiosity and commitment. This is not to argue that all science learning will easily and naturally flow from the Hanson activities that can be carried out successfully by students, given that they are also expected to learn complex scien- tific principles not easily derived from experiments that are possible in the school laboratory. It does imply that students learn much of the core of science and mathematics more effectively by emulating the behavior and habits of mind of scientists and mathematicians. If one accepts this assumption, the development and monitoring of in- dicators of these behaviors clearly is pertinent to assessing the health of science and mathematics education. The previous report of this committee (Raizen and Jones, 1985) adopted an input-output model to help categorize the various ele- ments of the domain of science education. In this model, student characteristics, such as motivation, are viewed as antecedent or input conditions. Student interactions with teachers, peers, and curricu- lum materials are viewed as transactions, while changes in student

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INDICATORS OF STUDENT BEHAVIOR 75 attitudes and achievement are seen as the outputs of the system. For example, a student with a strong interest in mathematics (an- tecedent) who does homework in algebra (transaction) is likely to develop an understanding of algebra (outcome). By contrast, a stu- dent with little prior knowledge of proportions who daydreams during half the chemistry class wiD be unlikely to become interested in a career as a chemist or learn much about the synthetic materials that make up much of the environment. Unfortunately, this mode! is limited in that cause-effect relation- ships are difficult to define. Do students daydream because they do not understand, or do they not understand because they daydream? Should strong interest be considered an antecedent to the process or an outcome of a prior learning situation? There is a circularity among antecedent, process, and outcome that is difficult to resolve. This is one of the reasons that the committee, in the course of debat- inz these matters, decided in this report to focus on the important behaviors of students and teachers as the major actors Involved in the process of learning and not be too concerned with the categoriza- tion of these behaviors in an input-output model. Taking an algebra course, a student activity, is a desired behavior whether it is viewed as evidence of an interest in mathematics or is seen as a precursor to achievement. Paying attention in class, once a course is selected, is another level of behavior that bears on achievement. . In order to highlight the importance of student behaviors in sci- ence and mathematics and provide some structure for recommending indicators, this chapter differentiates among three categories of be- haviors: (1) student activities, (2) altitudes toward science andmath- ematics, and (3) scientific and mathematical habits of mind. Student activities are the observable actions of students, or adults for that matter, that have been demonstrated to be important in attaining some modicum of scientific and mathematical literacy, whether or not one wishes to infer some underlying affective trait. An example is homework. Doing homework, when effectively administered and carried out, is important in student learning (Husen, 1967; Walberg et al., 1986) quite apart from its relationship to an attitude on the part of the student. So too is taking trigonometry courses or studying science an hour per week in fifth grade, particularly if the instruction is of high quality. Attitudes toward science and mathematics are emotional reac- tions to the various components of these enterprises. They are per- sonal response tendencies, developed through experience, that can

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76 INDICATORS OF SCIENCE AND MATHEMATICS EDUCATION be characterized as favorable or unfavorable. However, these atti- tudes can be inferred only from the behaviors of people. Responding "yes" to the statement, "I would like to become a mathematician when ~ grow up," leads one to believe that that person has a positive attitude toward mathematics. The elements of the field as perceived by the individual become the stimuli that prompt the behavior. It is the behaviors rather than the attitudes that are observed and measured and that can become indicators of the state of science and mathematics education. The third category of behaviors derives from scientific attitudes or scientific habits of mind, as discussed in Chapter 2 in defining scientific and mathematical literacy. The behaviors involve a set of beliefs and assumptions about the natural world, certain ways of thinking, and techniques for confronting and solving problems. They are a code of ethics observed by the scientific community that has developed as part of the success pattern of science and that provides boundaries for the actions of scientists. The code includes certain characteristics of the process of doing science objectivity, skepticism, replication of results, parsimony and elegance of con- cepts, theories, and proofs. It also mirrors the characteristics of successful scientists and mathematicians, for example, curiosity and commitment. Again, one cannot measure these traits clirectly. One observes behaviors that are believed to be manifestations of the traits. As an example, a student who tests the accuracy of the weather predictions in the Farmer's Almanac by actually observing and recording tem- perature and precipitation each day over a period of time is believed to possess the scientific attitudes of skepticism and belief in the value of evidential tests. The traits are inferred from the behavior. Indicators reflecting how students behave and what they believe need to be gathered concurrently and integrated with the other indi- cators described by the committee. This is of particular importance to individuals at the state and local levels in a position to influence what happens in schools. Unless information about behavior and attitudes is known in addition to test scores for a reasonable sample of the student population, the focus for such policy makers remains blurry and decisions tentative. For example, even if students are performing well in their curricular areas in elementary school, early warning signs of negative attitudes or behavior could predict lessened interest in high school and college mathematics and science.

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INDICATORS OF STUDENT BEHAVIOR STUDENT ACTIVITIES 77 What students do is likely to have an impact on what they learn. Because of this relationship, it is important to develop and monitor regularly indicators of selected student activities, both those conducted within the science and mathematics classroom and those likely to occur outside the school. Concurrently, however, there is a need to continue to examine the relationships between the indicators suggested below and measures of student learning. Some research using national assessment data in science indicates linkages between student learning and indicators of such behaviors as doing homework, course taking, and out-of-school science experiences (hobbies and clubs, science projects, museum attendance, extracurricular reading) (HueftIe et al., 1983; Walberg et al., 1986~. However, this work needs to be updated and replicated using more recent information, for example, the new NAEP data currently being analyzed by the Educational Testing Service. Additional factors related to learning may also be discovered that may become important indicators in the future. In-Schoo] Activities The relationship between instructional time and student learning was discussed in the committee's earlier report, leading to recommen- dations on monitoring course enrollment for both science and math- ematics in secondary school and instructional time in elementary and middle school (Raizen and Jones, 1985, Chapter 4~. The com- mittee still considers these measures of student behavior whether courses and instruction are imposed on the students through school requirements or elected by them voluntarily to be important indi- cators of educational quality because of their well-established effects on student achievement. We also reiterate the caution raised in the earlier report that course enrollment data, to be meaningful, must include some sort of typology or descriptive information that allows classifying the courses as to level of subject matter covered. Course enrollment data should be obtained in enough detail to make it possible to describe the total number of pupils enrolled in specific mathematics and science classes, as well as to describe the amount of science taken by a typical student. This requires not only obtaining school-level data on science enrollments but also monitor- ing individual course-taking patterns. The data may be aggregated

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78 INDICATORS OF SCIENCE AND MATHEMATICS EDUCATION in different ways to answer such questions as: What is the aver- age number of mathematics courses taken by graduating boys and girls? What percentage of 12th-grade students are presently enrolled in a first-year physics course, and how many of these are minority students? At the elementary- and middIe-schoo! level, information on in- structional time plays a somewhat different role in mathematics than in science. Since mathematics has an established place in the cur- riculum, the question of interest concerns variations in time among classrooms and schools (see, e.g., Berliner, 1978), whereas for science, particularly in grades Key, the more important question is whether science is taught at all. Data (e.g., minutes of instruction per week) may be gathered for individuals or at the school level. The former provides such statements as: "The average third grader received 34 minutes of instruction in science each week," while the latter yields such information as: "The average school allocated 41 minutes per week to instruction in science.n The latter number is likely to be larger because of student absenteeism or being out of the class (e.g., at the library or in a special reading group) when the science instruc- tion is offered. This is particularly a problem for specific groups. For example, children from low-income homes may receive less actual instruction as a result of missing school. Another problem to which time surveys must be sensitive is the possible double-counting of homework time as both homework and instructional time when homework is done during school time rather than at home. Such time-based measures of exposure to subject matter, though informative, are a mere beginning, however. We have argued above that, in order to learn science or mathematics, one must be engaged in the process of actually doing science or mathematics. From that proposition, it follows that the quality of students' classroom ex- periences is as important if not more so than the amount of time spent on a subject (Brophy, 1986; Brophy and Good, 1986; Good and Weinstein, 1986; Stevenson et al., 1986~. Therefore, information should also be gathered on students' use of class time, that is, on what they actually do during the time periods reported as instruc- tion. In mathematics, systematic procedures have been developed for recording observations and identifying the cognitive levels of cIass- room instruction and behavior (Burkhardt, 1986~. In science, we have argued, quality entails the modeling of the behaviors of success- ful scientists. For example, how much time is devoted to hands-on scientific activities, how often do students exhibit curiosity about

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INDICATORS OF STUDENT BEHAVIOR 79 their world or are given opportunity to do so, and how meaningful to them are the problems that they are asked to solve? The construct to be investigated is the extent to which students are participating in the processes of science. Studies of how students use class time should be conducted by trained observers. The observers should assess the extent to which students are engaging in laboratory activities or similar hands-on ex- periences that entail making observations and taking measurements of natural phenomena, doing experiments or exercises that pose prom lems that capture students' imagination, working alone and in teams seeking answers to questions they themselves have formulated about the world around them, communicating the results of their investiga- tions by the written and spoken word, and questioning their findings and seeking verification by gathering additional evidence. Information on course enrollment and instructional time and on student use of time should be collected in regular four-year intervals. The suggestion for a four-year cycle is based on several considera- tions: a study usually requires two years for data to be gathered, analyzed, and reported; one study should be completed before the next one on the same subject is planned; and studies conducted every four years will be frequent enough to be useful to policy makers while keeping costs and response burden within bounds. The four-year cy- cle also matches that proposed for testing in Chapter 4, making it possible to investigate the relationships between student behaviors and achievement. Gathering data simultaneously on teacher behav- iors, student behaviors, curriculum, and achievement (see Appendix E) would provide a rich source of information for conducting research on how to improve science and mathematics education. For example, the influence of student, teacher, and curriculum on student learning could be exarn~ned in addition to exploring in some depth the vari- ation in the effects for various subgroups based on ethnicity, race, gender, and type of community. Out-of-Schoo] Activities Recent research (Fraser et al., 1986) suggests that out-of-school activities are more highly correlated with science learning than are in-school activities. Hence, it is important to consider such activities when monitoring the status of science education. In mathematics, with its hierarchical structure, out-of-school activities participation

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80 INDICATORS OF SCIENCE AND MATHS TICS EDUCATION in mathematics contests, computer work, jobs that require mathe- matics skills-appear to be relatively less important. For exam- ple, differential course taking among high school students accounts for more than a third to over half of the variance in mathematics achievement as currently measured (Welch et al., 1982; Jones et al., 1986~. An important out-of-school behavior is the amount of homework time spent on science and mathematics. There is an accumulation of research evidence that supports the value of homework in learning a subject, particularly if homework is checked and discussed (for a summary, see Raizen and Jones, 1985:89-91~. For example, Fraser et al. (1986) found that, for science test scores of 13-year-olds, and with other factors held constant, an increase of one hour per day in the time spent on homework is associated with a 7 percent increase in number of test questions answered correctly; the gain increases to 10 percent for 17-year-olds (Walberg et al., 1986~. However, most research on homework deals with general amount of homework done; data on the amount of homework devoted to such specific subjects as science have seldom been systematically gathered. Data need to be gathered and analyzed not only for specific subjects but with course-taking held constant, since the amount of homework done will probably vary with the number of courses taken. Other out-of-school behaviors that have been hypothesized to affect student learning include exposure to or involvement in (1) in- formal science learning situations at zoos, museums, science fairs, and the like; (2) time spent applying the content and processes of science and mathematics to one's daily life, for example, deciding on over-the-counter medication, taking certain health measures or risks like exercising or smoking, judging the veracity of a television commercial, or checking a restaurant or grocery bill; and (3) ac- tive participation in using knowledge of science and mathematics to address recurring societal problems, even in a limited way, for ex- ample, turning off lights when leaving a room or limiting the length of a shower during water shortages (conservation), maintaining a reasonable speed limit (safety and conservation of energy resources), picking up litter or turning down the volume on the radio (combat- ting pollution), or emptying the ashtray of the car on the street when stopped at an intersection (pollution).

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INDICATORS OF STUDENT BEHAVIOR Recommendations 81 The following three types of measures should be used as key indi- cators of students' in-school behavior. Data on each of the measures should be gathered and reported for gender, ethnicity, race, type of community (urban, rural, suburban), and grade level as well as by district, state, region of the country, and nationally. If discrepan- cies among groups continue to be found, as they have in the past, they will have important policy implications for achieving scientific and mathematical literacy for all students. The three types of mea- sures have to do with course enrollment, time devoted to science and mathematics, and quality of instruction. Key Indicator: The committee recommends that data on secondary school course enrollment be gathered on a four- year cycle for both mathematics and science. The specific data to be gathered are the number of semesters of science and mathematics taken by students and total enrollment in the variety of science and mathematics courses offered in secondary schools. Courses should be identified as to level of difficulty (e.g., for eighth-grade mathematics: remedial, typical, enriched, algebra). The indicators to be constructed from these data are the average number of mathematics and science courses taken and the percent- age of students enrolled in specific courses. Key Indicator: The committee recommends that the data to be gathered at the elementary- and middle-school level, equivalent to course enrollment data, be the number of min- utes per week devoted to the study of science and mathemat- ics. The indicator should also be expressed both as a ratio of all instructional time and of total time spent in school. At each policy level national, state, and local experts may wish to define the minimum amount of class time necessary in each grade, particularly for science. However, care needs to be taken not to countervene, through efforts to mandate or log instructional time, the potential benefits of integrating mathematics and science instruction to some extent.

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82 INDICATORS OF SCIENCE AND MATNEMA TICS EDUCATION Because of the importance of possible differences among various groups ethnic and racial, gender, socioeconomic status, and so on- we recommend that the data be collected both at the level of the school and the individual student. Key Indicator: The committee recommends development of a time-use study involving external observers to obtain some indication of the quality of the science and mathemat- ics instruction being received. In science classes, this would include, in addition to the teaching of conceptual and fac- tual knowledge, the percentage of time spent by students involved in the processes of science (observing, measuring, conducting experiments, asking questions, etc.~. A similar study is recommended for mathematics classes; a panel of mathematics educators should determine the nature of stu- dent behaviors sought. Supplementary Indicator: The committee recommends the collection of information on minutes per week spent on science and mathematics homework. The frequency and detail necessary for gathering data on home- work are the same as for in-school activities that is, the information should be gathered every four years and allow analysis by ethnicity, race, gender, grade level, and size and type of community. Na- tional data are important for comparisons over time and with other countries; states and local districts may also wish to have this infor- mation. Care must be taken that homework done in school is not double counted as both homework time and instructional time. Research and Development: The committee recommends further research and development on possible supplementary indicators in the following three areas of out-of-school stu- dent behaviors, with the goal of clarifying their relationships to student mathematics and science learning: Amount of time (minutes) devoted to out-of-school sci- ence and mathematics activities, for example, going to

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INDICATORS OF STUDENT BEHAVIOR zoos and science museums, watching science programs on television, reading science books, playing with a computer at home, voluntarily doing science projects or mathematics puzzles. Percentage of students reporting that they use (apply) the concepts of science and mathematics from time to time in their own lives. One way to implement this in- dicator is to conduct a survey on the number of times students faced a personal decision and relied on some- thing that they learned in science or mathematics to help them make that decision. Percentage of students reporting that they use the con- cepts of science and mathematics to help them address some persistent societal problem. . 83 At the same time that the collection of information proceeds on the recommended indicators of in-school and out-oschoo! stu- dent behaviors, research should be pursued in three related areas. First, better understanding is needed of the linkages between student learning and such student behaviors as course-taking, doing home- work, and participating in extracurricular science or mathematics activities. The research should be designed not only to validate cur- rent findings on the linkages of these factors to learning but also to allow for the discovery of other student behaviors that strongly affect learning. Second, more work needs to be done to elaborate the constructs of student activities and how they might be measured in order to improve related indicators. Third, factors that influence student activities need to be examined, for example, who convinces children to avoid elective courses in science or what influences the amount of homework in science and mathematics that is done. If one assumes that the behavior of students inside and outside school affects learning, then it is important to understand what determines these behaviors. Research and Development: The committee recommends continued research on linkages between student learning and various student activities, on more effective ways of assess- ing activities that affect learning, and on the factors that influence individuals to engage in these activities.

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84 INDICATORS OF SCIENCE AND MATNEMA TICS EDUCATION ATTITUDES TOWARD SCIENCE AND MATHEMATICS Science and mathematics educators generally espouse as a goal that students acquire positive attitudes toward the various com- ponents of the scientific enterprise. These attitudes are seen to be important as outcomes of the schooling process and for their influence on the activities in which students choose to participate as students and in later life. Liking science or mathematics is an attitude to be learned in a science or mathematics class as an end in itself, as well as to facilitate further learning in science or mathematics and eventual career choices. Although we argue above that spontaneous behaviors are in gen- eral more trustworthy indicators than indicators of attitudes and feelings constructed from answers to questions posed by adults, at- titude questionnaires are not without some value. A multitude of attitude measures have been developed. For example, Gardner ref- erences more than 200 studies in a review he wrote in 1975. An ERIC search of science testing articles written between 1975 and 1985 (Welch, 1985) revealed that more than one-third of them were devoted to the measurement of attitudes. The last three NAEP assessments of science have included items on attitudes, and they will continue to be included in future national assessments. Approx- imately one-eighth of the 1986 science assessment was devoted to attitude items. Past attempts to obtain measures of attitudes toward science have focused on such topics as like or dislike of science classes, science teachers and scientists, and positive or negative judgments about the value of science, careers in science, and support of scientific research. Results are sometimes hard to interpret; for example, 49 percent of 17-year-olds in 1982 agreed or strongly agreed that their teacher makes science exciting, and 62 percent thought that their teacher was enthusiastic, yet less than 50 percent of this age group reacted positively to questions about their science classes. In general, the percentages of positive attitudes expressed by the nation's youth to- ward various components of science are disappointingly low (Hueftie et al., 1983~. In mathematics, the areas investigated include relationships be- tween attitude and achievement, the influence of parents and teachers on student attitudes, and other factors related to attitudes and at- titude change (Kulm, 1980~. More specifically, a sizable number of studies have investigated the effects of various attitudes on women's participation in mathematics courses and careers (Chipman et al.,

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INDICATORS OF STUDENT BEHAVIOR 85 1985~. Generally past studies have not succeeded in establishing a strong connection between positive student attitudes regarding the subjects themselves, teachers, classes, careers, and the like and student achievement. Three reviews of research on attitudes and performance in mathematics aD conclude that there is a positive cor- relation, although it is small (Aiken, 1970; Crosswhite, 1972; Kuhn, 1980; Bell et al., 1983~. Similar results have been found for science and other subjects (Welch, 1983; Wilison, 1983; Horn and Walberg, 1984~. These results may stem from difficulties in interpreting the meaning of attitude measures (Gardner, 1975~. Items used to assess attitudes have given inconsistent and ambiguous results (Munby, 1983), raising questions as to what is really being measured. In part because of the ambiguous findings to date, the committee suggests further work on national indicators of student attitudes toward science and mathematics. In the committee's view, it is time to examine carefully the purpose of the attitude assessments included in the NAEP, the IEA, and other major studies, to define the domain more precisely, and to develop better measures of the attitudes that are in themselves considered important outcomes of mathematics and science education or that have been demonstrated to have strong positive effects on student learning. Recommendation Research and Development: Given the importance at- tached by science and mathematics educators to the devel- opment of attitudes that will foster continuing engagement with science and mathematics, the committee recommends that research be conducted to establish which attitudes af- fect future student and adult behavior in this regard and to develop unambiguous measures for those that matter most. SCIENTIFIC AND MATHEMATICAL HABITS OF MIND In addition to developing in students cognitive competence in science and mathematics and favorable attitudes toward these fields, their education should also equip them with scientific and mathe- matical habits of mind, as defined in Chapter 2. These habits of mind evince themselves in behaviors that represent certain ways of thinking about the world. The behaviors themselves are thought to be manifestations of internalized personal traits that embody the

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86 INDICATORS OF SCIENCE AND ~4THEMA TICS EDUCATION scientific and mathematical world view. An example is fate control, discussed further below, a pattern of beliefs about one's relationship to events and of events to each other. Because scientific and mathematical habits of mind are an inte- gral part of scientific and mathematical literacy, indicators for them should be developed, monitored, and; the findings reported to ed- ucators and policy makers. We provide a brief overview of several constructs thought to be relevant and recommend that further re- search and development be undertaken in the area of scientific and mathematical habits of mind. Relevant Constructs Scientific habits of mind foster an extended milieu of beliefs about the world and one's place in it. The methods of science and the values attached to it have the power to shape an individual's sense of purpose and control over his or her own life. This sense is generally referred to as fate control. If one's sense of fate control is low, one may act as if one believed events to have few connections between them and that each event springs uninvited into one's life. The world-including one's own personal world is unpredictable, like a game of chance or a collage of happenings over which one has little control. As a rule, a person with these beliefs displays a rather primitive level of knowledge and understanding about science. If one's sense of fate control is high, one may act as if one believed that events have roots that evolve by processes one can discover and thereby possibly influence. People with this orientation are more keenly attuned to cause-and-effect relationships and to the structure of the relationship between events and ideas. The notion of fate control is given weight by a considerable body of research that connects children's attributions of their successes or failures to their persistence and performance in school (Seligman, 1975; Lefcourt et al., 1979; Stipek and Weisz, 1981~. The measurement of fate control or attribution of success is not nearly as well developed as the constructs themselves. Answers to items probing these constructs depend on the formats used (Stipek and Weisz, 1981~; there are cultural differences that may affect not only responses but also relationships between fate control, attribution of success, and student learning; attributions that are other-directed (i.e., may be interpreted to indicate low fate control) may in fact be quite realistic (e.g., "My teacher isn't very goody. At this stage, it

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INDICATORS OF STUDENT BEHAVIOR 87 would seem more promising, difficult as it is, to observe and assess overt behaviors that embody scientific habits of mind than to assess these through related attitudes about fate control and self-efficacy (Rowe, 1979; Blumberg et al., 1986; Educational Testing Service, 1987~. Research to clarify the unequivocal core of fate control that links to the development of a scientific world view should proceed. In mathematics, McLeod (1986) has found low positive correla- tions between fate control (or such related factors as locus of control, reflective/~mpulsive behavior, and field dependence/independence) and student achievement. Freudenthal (1983) has defined mathe- matical habits of mind as including the following attributes: ability to understand and use mathematical language, ability to visualize the data and the unknowns in a problem from different perspectives, grasping the degree of precision needed for a problem, knowing when and how to apply mathematics in a given context, and being aware of one's own mathematical activities. Much work on improved mea- sures will have to be done before it will be possible to assess the extent to which students are developing these attributes. One of the purposes of science and mathematics education is to enable and interest students in attending to these endeavors in some form throughout their lives. However, the motivation for individu- als to do so, inside and outside school, is in need of much research. If mathematics and science education succeed, then individuals will leave school understanding how to apply the knowledge and processes of science and mathematics to the questions and problems they face personally and as members of society. In that connection, four con- structs are advanced as relevant to consider in developing the desired attitudes, motivation, and curiosities in all students: engagement, expectations/autonomy, connectedness, and competence. While each of the constructs taken separately has a good deal of research underlying it, how they might act together to motivate attention to science and mathematics is not well understood. (For overviews, see Weiner, 1979; Malone, 1981; Connell and Ryan, 1984; Connell, 1985.) Which of these factors, linked in what patterns, make a difference in perceptions, motivations, and quality of involvement with scientific and mathematical ideas? And how might one go about obtaining indicators of the four constructs? Both of these questions will require considerable investigation before parsimonious indicators can be recommended that might be used routinely in the assessment of the condition of mathematics and science education.

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88 INDICATORS OF SCIENCE AND MATHEMATICS EDUCATION Engagement Engagement means the active, interested involve- ment in learning science and mathematics and making appropriate application to real problems or situations. The opposite of engage- ment is disaffection, which may be manifested by inattentiveness, avoidance, rebellion, or by resort to rote learning when one does not understand. The concept of discretion is relevant here. Tasks at work or school typically have two parts: prescribed and discretionary- aspects in which the person has some latitude to make choices (Jaques, 1956~. As the discretionary component increases, engage- ment seems to increase (e.g., Cavana and Leonard, 1985~. Expectations/Autonomy This construct encompasses the sense that one's own purposes, interests, and curiosity are being served by engaging in a particular set of activities and that, to some extent and on some occasions, one can choose from among options. The ratio of intrinsic to extrinsic motivation is high, as are performance, persistence in the face of difficulties, and sustained attention to science. For some people, science is intrinsically interesting; for others, it is not so interesting but is recognized as instrumental to other goals about which they care. Collectedness The theme of connectedness appears central. It is the degree to which students perceive that what they are doing and how they are doing it is connected to their everyday life-in career development, in health management, in their relationship to the community, and in their roles as citizens. They also need to see that ideas within the subject hang together in some fashion that makes sense rather than as a dictionary of facts; that is, there should be some thematic character to their learning. Science is always in a state of development and change, but for the most part there is coherence within the changes. The response of students to such changes could be expected to be different depending on whether they had a thematic or a discrete (dictionary-like) organization of knowledge. Competence Competence depends on having an accurate idea of what it takes to be a successful science or mathematics student. Success is a function in part of whether one knows what strategies are necessary to be successful and whether one possesses the strategies and the will to exercise them.

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INDICATORS OF STUDENT BEHAVIOR Recommendation Research and Development: The committee recommends research to identify and validate constructs related to the continuing involvement of students and adults with science and mathematics throughout their lives. In addition to the refinement of these constructs, strategies should be explored for obtaining indicators of the relevant constructs and asso- ciated behaviors. 89