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Studies were conducted to identify critical barriers which could impede the progress of Hispanic undergraduates enrolled in science and engineering programs. The underlying theme in most studies was the interplay of language in various problem-solving tasks. Studies examined: (1) predictors of academic achievement (as measured by grade point average); (2) ability of students to translate word problems into appropriate mathematical equations, with an emphasis on identifying errors caused by misinterpretations of the problem statement as opposed to errors caused by mathematical deficiencies; (3) extent to which students' academic, motivational, and socioeconomic characteristics mediated their performance in various cognitive measures; and (4) the ability of students to solve logical reasoning problems containing multiple negations. Findings indicate that Hispanic students are underprepared in comparison to Anglo students. Areas in which Hispanics displayed underpreparation are algebraic skills, language skills, and problem-solving skills requiring substantial amounts of linguistic processing. Differences in socioeconomic status between Hispanics and Anglos were also found. In addition, findings indicate that various errors committed by the Hispanics in solving mathematics and logics problems are the result of semantic difficulties and not necessarily the result of difficulties in the content area. (JN)

Minorities have for some time faced underrepresentation in the technical professions. However, recent statistics indicate that many more minorities are enrolled in higher education than ever before. This report centers on identifying the particular difficulties that bilingual Hispanic students majoring in technical subjects have in performing mathematics and physics-related tasks. Further, the research aims at separating the difficulties into those deriving from language deficiencies and those from conceptual ones. The findings cited investigate the relationship between grade point average, language proficiency, and performance on various mathematical tasks for a group of 60 Hispanic bilingual undergraduates majoring in technical subjects. The results indicate that language proficiency is strongly correlated with mathematics performance as well as grade point. This suggests that courses that attempt to raise the level of language proficiency of those Hispanics possessing low skills may improve pupil performance in mathematics or decouple somewhat the interdependence between language proficiency and mathematics performance. (MP)

Minorities have for some time been underrepresented in the technical fields, such as engineering and computer science. This development is known to be caused by a variety of factors, but the primary purpose of this report is to help identify those factors that adversely affect the cognitive development of the technical bilingual student in terms of which are language related and which are not. The results of two projects aimed at elucidating the interconnection between linguistic and mathematical cognitive development are presented. The first is a study of translational mathematics skills among bilingual Hispanic engineering and science students. In the second study, an attempt is made to determine the dependence of algebraic performance upon verbal context. Data were obtained using both written exams and clinical interview techniques. Results indicated several mathematical misconceptions unique to Hispanic students that may originate in linguistic factors. Possible causes and remedies for these misconceptions are discussed. (MP)

The spontaneous use of analogies in problem-solving occurs when a subject first spontaneously shifts his attention to a situation (B) which differs in some significant way from an original problem situation (A), and then tries to apply findings from B to A. This paper describes research on the process with 10 scientifically trained subjects (advanced doctoral students and professors in technical fields) who were interviewed (most were videotaped) on a variety of problems. Four processes were found to be fundamental in making an inference by analogy, indicating that many successful solutions by analogy are not "instant solutions." Two major processes involved in confirming analogy relations were identified: matching key features or relationships and forming a bridging analogy. Analysis of transcripts led to an hypothesis that at least three types of analogy generation mechanisms exist: generation via an abstract principle, generative transformations, and associative leaps, the latter two mechanisms being the primary methods observed so far. Since many solutions by analogy are not "instant solutions," but a more extended process of conjuncture and testing, it is suggested that some of these processes are learnable and that developing students' abilities to use generative transformations, leaps, and bridges may be possible and desirable. (JN)

This project had three major goals: (1) investigate the extent to which introductory physics students misuse or misunderstand formulas; (2) catalogue the typical ways in which they do this; and (3) begin the larger task of identifying key types of knowledge that successful problem solvers use to give formulas meaning. Exploratory interviews and group sampling studies were conducted. The interviews were conducted with approximately 25 freshmen and sophomore engineering students. As a result, the project was able to discover new misconceptions about qualitative concepts in physics, develop and refine more simple and elegant problems which would expose and isolate those misconceptions with a minimum of distraction from other possible difficulties, and form hypotheses about four levels of knowledge being used in successful problem solving. A series of three different 45-minute diagnostic tests were conducted with entering freshman engineering majors, using sample sizes of 150, 34, and 38 respectively. These each involved approximately 18 of the questions which had been pilot tested in interviews, including both algebra and physics questions. A parallel test was given to an older group of 24 engineering majors who had just completed a course in introductory mechanics. These tests allowed for the comparison of students before and after taking introductory physics to determine whether the students' learning had been formula-centered. Findings and comments on the research methodology are presented in this final report. (Author)

The increasing availability of the computer in the classroom has created a need for informed and creative instructional software. Two areas of cognitive research in mathematics and science learning have implications to instruction and, consequently, to educational software design. These are research on misconceptions and on differences between expert and novice problem solvers. This paper treats these areas in two major sections. The first section provides a broad overview of the misconception literature and of the instructional implications associated with this body of research. Also included in the first section is a description of a computer-based approach designed to teach students how to translate algebraic word problems into equations. The second major section provides an overview of the differences between experts and novices and discusses a computer-based approach in which students are constrained to analyze physics in expert-like ways. The computer-based example used relates to the analysis of classical mechanics problems. A 31-item list of references concludes the document. (TW)

Described is a computer tutor designed to help students gain a qualitative understanding of important physics concepts. The tutor simulates a teaching strategy called "bridging analogies" that previous research has demonstrated to be successful in one-on-one tutoring and written explanation studies. The strategy is designed to remedy misconceptions by appealing to existing correct intuitions, and extending these intuitions by encouraging analogical thinking. The strategy was motivating and successful for some learning situations. Analysis of the data indicates those situations in which the strategy worked well and those where alternatives are needed. Implications for improving the tutor using artificial intelligence technology to incorporate a representation of student beliefs and intelligent sequencing of example presentations are outlined. (Author/RH)

Weaknesses in educational software currently available in the domain of mathematics are discussed. A technique that was used for the design and production of mathematics software aimed at improving problem-solving skills which combines sound pedagogy and innovative programming is presented. To illustrate the design portion of this technique, a "storyboard" for a sample problem from elementary algebra is presented. (Author/PK)

Numerous studies indicate that performance in solving single step multiplicative word problems is influenced by both problem structure and the types of numbers involved in the problem. For example, including numbers less than one often increases the difficulty of a problem. What remains unclear is how problem structure and number type interact in influencing difficulty. This study systematically investigated these two factors with math-proficient and remedial college students. Findings indicate that it is the role played by fractions in word problems that influences difficulty rather than simply the number of fractions in the problem. Pedagogical strategies for improving students' ability to perceive and represent multiplicative word problems are discussed. (Author)

The world presented to our senses is essentially continuous in space and time. The simplest observations of children have shown that we are not born with ways of "breaking up" the world. The structures of our knowledge must be developed, and the major issue this paper considers is how those structures develop. The discussion focuses on Jean Piaget's position and how it compares to several alternative positions. The alternative positions discussed hold in common that the structures of knowledge are copies of other structures. B. F. Skinner and Eleanor Gibson state that the structures of knowledge are copies of the structures of the world. Benjamin Whorf and the logical positivists believe the structures of knowledge to be taken from the structures of language. The Gestaltists tried to reduce the structures of knowledge to the structures of perception. It is concluded that Piaget provides a theory in which structures of knowledge grow from previous structures of knowledge through action, disequilibrium, and equilibration. It is argued that further research is needed, however, for "equilibration" to become an explanatory rather than just a descriptive term. (TW)

The idea that cognitive science can provide useful guidance to the teaching of physics has been met by some with skepticism. One argument is that the current understanding of cognition is too crude to be helpful; another, that any scientific approach to education stifles the art of teaching. Some feel that art and science need not be incompatible. This paper offers several illustrations of ways in which cognitive science can be used to refine the art of physics teaching. For a theory to be pedagogically useful it should help teachers see things they might not otherwise have noticed, provide an overall organizing scheme for instruction and suggest specific activities that can improve instruction. This paper focuses on the physics problem. Examples have been drawn from introductory level college physics classes. (CW)

The general question examined by this study was whether the tendency of subjects to ignore the known score in giving the best guess for a sample mean was due to a descriptive heuristic such as representativeness or to a mechanistic one such as active balancing. Two experiments were conducted. In Experiment 1, subjects estimated: (1) the mean of a random sample of ten scores consisting of nine unknown scores and a known score that was divergent from the population mean; and (2) the mean of the nine unknown scores. The modal answer (about 40% of the responses) for both sample means was the population mean. The results extend the work of Tversky and Kahneman (1971) by demonstrating that subjects hold a passive, descriptive view of random sampling rather than an active balancing model. This result was explored further in in-depth interviews (Experiment 2), wherein subjects solved the problem while explaining their reasoning. The interview data replicated Experiment 1 and further showed (a) that subjects' solutions were fairly stable--when presented with alternative solutions including the correct one, few subjects changed their answers; (b) little evidence of a balancing mechanism; and (c) that acceptance of both means as 400 is largely a result of the perceived unpredictability of "random samples." (Author/AA)

The design and architecture of two user-controlled, computer-based problem analysis environments in classical mechanics are discussed. In the expert-like environment, the user analyzes problems according to a hierarchical concept schema consistent with how experts analyze novel problems in physics. In the second environment, the user searches a data-base of equations using novice-like, surface feature keywords in order to locate the appropriate equation(s) to use in solving a problem. Cognitive and pedagogical implications of the research are discussed. (Author)

Research findings that indicate the need for greater integration in the development of verbal and mathematical skills for college technical majors are presented in this paper. Although the project discussed was originally designed to isolate language-related difficulties that affect mathematical skills among bilingual Hispanic students, some problems shared by mainstream students were also uncovered. The tests used were designed to demonstrate the effect of verbal skills on logical ability and algebraic problem-solving ability. Patterns of thought manifested in the results of the written exams were then pursued further through clinical interviews. It is stressed that extant programs aimed at the preparation of minorities for technical education at college fall short by not including language skills as an integral part of the program. Such an integrated program, it is suggested, would enhance students' problem-solving performances. The tabulated results of the exams are appended. (RDN)

This report presents findings from a study of the cognitive processes and learning difficulties of ninth-grade students in Algebra I. A clinical interview approach was used with 14 students. A group of six Hispanic students and a group of five Anglo students were enrolled in the same algebra class; three Hispanic students were enrolled in an "advanced" class, since they had started algebra one-half year before the others. Probed were students' appreciation of algebra as an abstract logical system, command of the formal operations of algebra, ability to use algebra, and ability to solve problems. Performance in English vs. Spanish was compared, and students' teaching styles were analyzed as they taught peers. It was found that students preferred not to use algebraic techniques in solving problems, were poor at verbalizing definitions and procedures and at translating problem statements into equations, did not use their textbooks very much except as a place to find assigned problems, and treated algebra as a rule-based discipline, not as a concept-based one. Findings are discussed in relation to the effectiveness of the textbook, to instructional approaches, and to the interplay of language in cognitive processes. (MNS)

This document reports in detail an investigation of the cognitive processes and learning difficulties of ninth-grade students in Algebra I. A clinical interview approach was used with 14 students. A group of six Hispanic students and a group of five Anglo students were enrolled in the same algebra class; a group of three Hispanic students who had begun algebra one-half year earlier was also included. Probed were students' appreciation of algebra as an abstract logical system, command of the formal operations of algebra, ability to use algebra, and ability to solve problems. Performance in English vs. Spanish was compared, and students' teaching styles were analyzed as they taught peers. It was found that students preferred not to use algebraic techniques in solving problems, were poor at verbalizing definitions and procedures and at translating problem statements into equations, did not use their textbooks very much except as a place to find assigned problems, and treated algebra as a rule-based discipline, not as a concept-based one. Detailed descriptions of student performance are given, and findings are discussed in relation to textbooks, pedagogy, linguistics, and directions for future research. Nine recommendations for improved pedagogy and learning are also presented. Questions asked in eight interview sessions are appended, as is selected background information on student participants. (MNS)

Despite the fact that increasingly large percentages of Hispanic individuals are being admitted into college programs, the academic success of the students admitted is considerably lower than their non-minority peers. This study focused on the examination of possible causes for the differences in academic performance at the college level for pupils majoring in mathematics and science-related subjects. Forty-nine of the pupils selected were Hispanic bilinguals; the remaining non-minority 53 monolinguals served as a control group. The following three variables were investigated as possible causes for the different achievements of the two groups: (1) academic perparation; (2) motivational factors; and (3) social and economic status. Survey results indicated vast differences between the two groups in areas such as career counseling, role models, motivation, and traditional social and economic indicators. The key to solving the dilemma of improving the academic performance of Hispanic students is viewed as awareness of and compensation for academic deficiencies. (MP)