Text editing in chemistry instruction

In two experiments, differential performance onchemistry problems was obtained for twotraining strategies: text editing andconventional problem solving. Text editingrequires students to scan the text of problemstatements and specify whether it providessufficient, missing or irrelevant informationfor solution. It was hypothesized that textediting, which emphasizes gaining familiaritywith schematic knowledge, would lead to higherachievement than conventional problem solving.Experiment one indicated that text editing wassuperior to conventional problem solving inlearning to solve molarity and dilutionproblems. In particular, students who weretrained in text editing skipped someintermediate steps while solving molarityproblems. In contrast, using stoichiometryproblems, experiment two showed that students whowere trained in text editing performed worsethan students given conventional problems tosolve. An error analysis suggested that becauseof its failure to direct students' attention tothe coherent problem structure in the firstinstance, text editing has no advantage overconventional problem solving in the domain ofstoichiometry problems. It was concluded thatthe suitability of a text editing trainingstrategy depends on the learning materials.     

Expertise and the organization of knowledge: Unexpected differences among genetic counselors,faculty, and students on problem categorization tasks

Chi, Feltovich, and Glaser (1981) observed that experts (physics faculty) organized problems into groups according to the underlying physics law or principle applicable, whereas the groupings of novice physics students focused on objects, literal physics terms, and physical configurations in the problems. Replication of these findings in a number of similar studies has led to the general acceptance of the proposition that the mental schemes used by experts to organize information within a content domain are organized according to the “deep structure” of the domain, whereas the schemes of novices are bound by “surface” dimensions. Categorizations of genetics problems produced by genetics counselor and faculty experts in comparison to student novices obtained in the present study, however, are inconsistent with a deep structure/surface structure dichotomy. As expected, faculty experts focused almost exclusively on conceptual principles, but student sorts focused primarily on problem knowns and unknowns. The expert counselor sortings unexpectedly resembled those of the students in this regard. Counselors also emphasized solution techniques to be used, whereas students emphasized the verbatim wording of the problem statement. These findings are consistent with the hypothesis that as expertise is attained, a person restructures his/her knowledge of the domain into a framework that is based on critical dimensions that facilitate the daily use of that knowledge. Implications for theoreticians, researchers, and teachers are drawn. Whenever possible, future studies of expertise should include noneducator experts; teachers should help students develop the ability to construct and reconstruct the organizational frameworks of their knowledge so as to facilitate the effective use of that knowledge in the face of change.     

Some Consequences of Prompting Novice Physics Students to Construct Force Diagrams

We conducted a series of experiments to investigate the extent to which prompting the construction of a force diagram affects student solutions to simple mechanics problems. A total of 891 university introductory physics students were given typical force and motion problems under one of the two conditions: when a force diagram was or was not prompted as part of the solution. Results indicated that students who were prompted to draw the force diagram were less likely to obtain a correct solution than those who were not prompted to solve the problem in any particular way. Analysis of the solution methods revealed that those students prompted to use a diagram tended to use the formally taught problem‐solving method, and those students not prompted to draw a force diagram tended to use more intuitive methods. Students who were prompted to draw diagrams were also more likely to depict incorrect forces. These results may be explained by two factors. First, novice students may simply be more effective using intuitive, situational reasoning than using new formal methods. Second, prompting the construction of a force diagram may be misinterpreted by the student as a separate task, unrelated to solving the problem. For instruction, the results of this study imply that ignoring students’ prior abilities to solve problems and their necessary developmental stages in learning formal problem‐solving techniques may lead to serious mismatches in what is taught and what is intended to be learned.     

How Can We Improve Problem Solving in Undergraduate Biology? Applying Lessons from 30 Years of Physics Education Research

If students are to successfully grapple with authentic, complex biological problems as scientists and citizens, they need practice solving such problems during their undergraduate years. Physics education researchers have investigated student problem solving for the past three decades. Although physics and biology problems differ in structure and content, the instructional purposes align closely: explaining patterns and processes in the natural world and making predictions about physical and biological systems. In this paper, we discuss how research-supported approaches developed by physics education researchers can be adopted by biologists to enhance student problem-solving skills. First, we compare the problems that biology students are typically asked to solve with authentic, complex problems. We then describe the development of research-validated physics curricula emphasizing process skills in problem solving. We show that solving authentic, complex biology problems requires many of the same skills that practicing physicists and biologists use in representing problems, seeking relationships, making predictions, and verifying or checking solutions. We assert that acquiring these skills can help biology students become competent problem solvers. Finally, we propose how biology scholars can apply lessons from physics education in their classrooms and inspire new studies in biology education research.     

Analysing cognitive or non‐cognitive factors involved in the process of physics problem‐solving in an everyday context

Recently, the importance of an everyday context in physics learning, teaching, and problem‐solving has been emphasized. However, do students or physics educators really want to learn or teach physics problem‐solving in an everyday context? Are there not any obstructive factors to be considered in solving the everyday context physics problems? To obtain the answer to these questions, 93 high school students, 36 physics teachers, and nine university physics educators participated in this study. Using two types of physics problems—everyday contextual problems (E‐problems) and decontextualized problems (D‐problems)—it was found that even though there was no difference in the actual performance between E‐problems and D‐problems, subjects predicted that E‐problems were more difficult to solve. Subjects preferred E‐problems on a school physics test because they thought E‐problems were better problems. Based on the observations of students' problem‐solving processes and interviews with them, six factors were identified that could impede the successful solution of E‐problems. We also found that many physics teachers agreed that students should be able to cope with those factors; however, teachers' perceptions regarding the need for teaching those factors were low. Therefore, we suggested teacher reform through in‐service training courses to enhance skills for teaching problem‐solving in an everyday context.     

Physics Metacognition Inventory Part II: Confirmatory factor analysis and Rasch analysis

The Physics Metacognition Inventory was developed to measure physics students’ metacognition for problem solving. In one of our earlier studies, an exploratory factor analysis provided evidence of preliminary construct validity, revealing six components of students’ metacognition when solving physics problems including knowledge of cognition, planning, monitoring, evaluation, debugging, and information management. The college students’ scores on the inventory were found to be reliable and related to students’ physics motivation and physics grade. However, the results of the exploratory factor analysis indicated that the questionnaire could be revised to improve its construct validity. The goal of this study was to revise the questionnaire and establish its construct validity through a confirmatory factor analysis. In addition, a Rasch analysis was applied to the data to better understand the psychometric properties of the inventory and to further evaluate the construct validity. Results indicated that the final, revised inventory is a valid, reliable, and efficient tool for assessing student metacognition for physics problem solving.     

Structured Collaboration versus Individual Learning in Solving Physics Problems

The research issue in this study is how to structure collaborative learning so that it improves solving physics problems more than individual learning. Structured collaborative learning has been compared with individual learning environments with Schoenfeld’s problem‐solving episodes. Students took a pre‐test and a post‐test and had the opportunity to solve six physics problems. Ninety‐nine students from a secondary school in Shanghai participated in the study. Students who learnt to solve problems in collaboration and students who learnt to solve problems individually with hints improved their problem‐solving skills compared with those who learnt to solve the problems individually without hints. However, it was hard to discern an extra effect for students working collaboratively with hints—although we observed these students working in a more structured way than those in the other groups. We discuss ways to further investigate effective collaborative processes for solving physics problems.     

Characterising Learning Interactions: A Study of University Students Solving Physics Problems in Groups

The purpose of this article is to explore how a group of four university physics students addressed mechanics problems, in terms of student direction of attention, problem solving strategies and their establishment of and ways of interacting. Adapted from positioning theory, the concepts ‘positioning’ and ‘storyline’ are used to describe and to analyse student interaction. Focused on how the students position the physics problems, themselves, and each other, the analyses produced five different storylines. The dominant storyline deals with how the students handled the problem solving, whilst two other storylines characterise alternative ways of handling the physics problems, whereas the two remaining storylines are concerned with how students positioned themselves and others—as either funny and/or knowledgeable physics students—and constitute different aspects of the physics community. Finally, the storylines are discussed in relation to the pedagogical situation, with recommendations made for teaching practice and future research.     

Knowing what you don't know makes failure productive

To progress from intuitive ideas to deep conceptual understanding, students need to become aware of gaps in their ideas. Attempting to solve problems prior to instruction may lead to a global awareness of knowledge gaps (i.e., awareness without being able to identify which specific component is lacking). These gaps may subsequently be specified by comparing students' solutions to the canonical solution. In our first experiment, the teacher highlighted specific gaps by comparing typical student solutions to the canonical solution before or after problem solving. The second experiment varied the factors form of instruction (with or without student solutions) and timing of instruction (problem-solving prior to or after instruction). Problem-solving prior to instruction triggered a global awareness of knowledge gaps. While this was beneficial for learning when combined with instruction with student solutions, our results indicate that comparing student solutions during instruction to specify the gaps is the most relevant factor.     

Assessing schematic knowledge of introductory probability theory

The ability to identify schematic knowledge is an important goal for both assessment and instruction. In the current paper, schematic knowledge of statistical probability theory is explored from the declarative-procedural framework using multiple methods of assessment. A sample of 90 undergraduate introductory statistics students was required to classify 10 pairs of probability problems as similar or different; to identify whether 15 problems contained sufficient, irrelevant, or missing information (text-edit); and to solve 10 additional problems. The complexity of the schema on which the problems were based was also manipulated. Detailed analyses compared text-editing and solution accuracy as a function of text-editing category and schema complexity. Results showed that text-editing tends to be easier than solution and differentially sensitive to schema complexity. While text-editing and classification were correlated with solution, only text-editing problems with missing information uniquely predicted success. In light of previous research these results suggest that text-editing is suitable for supplementing the assessment of schematic knowledge in development.     

The Missing Curriculum in Physics Problem-Solving Education

Physics is often seen as an excellent introduction to science because it allows students to learn not only the laws governing the world around them, but also, through the problems students solve, a way of thinking which is conducive to solving problems outside of physics and even outside of science. In this article, we contest this latter idea and argue that in physics classes, students do not learn widely applicable problem-solving skills because physics education almost exclusively requires students to solve well-defined problems rather than the less-defined problems which better model problem solving outside of a formal class. Using personal, constructed, and the historical accounts of Schrödinger’s development of the wave equation and Feynman’s development of path integrals, we argue that what is missing in problem-solving education is practice in identifying gaps in knowledge and in framing these knowledge gaps as questions of the kind answerable using techniques students have learned. We discuss why these elements are typically not taught as part of the problem-solving curriculum and end with suggestions on how to incorporate these missing elements into physics classes.     

Understanding student pathways in context-rich problems

This paper describes the ways that students’ problem-solving behaviors evolve when solving multi-faceted, context-rich problems within a web-based learning environment. During the semester, groups of two or three students worked on five physics problems that required drawing on more than one concept and, hence, could not be readily solved with simple “plug-and-chug” strategies. The problems were presented to students in a data-rich, online problem-based learning environment that tracked which information items were selected by students as they attempted to solve the problem. The students also completed a variety of tasks, like entering an initial qualitative analysis of the problem into an online form. Students were not constrained to complete these tasks in any specific order. As they gained more experience in solving context-rich physics problems, student groups showed some progression towards expert-like behavior as they completed qualitative analysis earlier and were more selective in their perusal of informational resources. However, there was room for more improvement as approximately half of the groups still completed the qualitative analysis task towards the end of the problem-solving process rather than at the beginning of the task when it would have been most useful to their work.     

The Role of Content Knowledge in Ill-Structured Problem Solving for High School Physics Students

While Physics Education Research has a rich tradition of problem-solving scholarship, most of the work has focused on more traditional, well-defined problems. Less work has been done with ill-structured problems, problems that are better aligned with the engineering and design-based scenarios promoted by the Next Generation Science Standards. This study explored the relationship between physics content knowledge and ill-structured problem solving for two groups of high school students with different levels of content knowledge. Both groups of students completed an ill-structured problem set, using a talk-aloud procedure to narrate their thought process as they worked. Analysis of the data focused on identifying students’ solution pathways, as well as the obstacles that prevented them from reaching “reasonable” solutions. Students with more content knowledge were more successful reaching reasonable solutions for each of the problems, experiencing fewer obstacles. These students also employed a greater variety of solution pathways than those with less content knowledge. Results suggest that a student’s solution pathway choice may depend on how she perceives the problem.     

Manipulation of M demand of chemistry problems and its effect on student performance: A neo-piagetian study

It has been shown that student performance in chemistry problems decreases as the M demand of the problem increases, thus emphasizing the role of information processing in problem solving. It was hypothesized that manipulation (increase or decrease) of the M demand of a problem can affect student performance. Increasing the M demand of a problem would affect more the performance of subjects with a limited functional M capacity. The objective of this study is to investigate the effect of manipulation (increase) of the M demand of chemistry problems, having the same logical structure, on performance of students having different functional M capacity, cognitive style, and formal operational reasoning patterns. As predicted the performance of one group of students was lower after the manipulation (increase) in the M demand of the problem. This shows how even small changes in the amount of information required for processing can lead to working memory overload, as a consequence of a poor capacity for mobilization of M power.     

Exploring the Development of Conceptual Understanding through Structured Problem‐solving in Physics

A study on the effect of a structured problem‐solving strategy on problem‐solving skills and conceptual understanding of physics was undertaken with 189 students in 16 disadvantaged South African schools. This paper focuses on the development of conceptual understanding. New instruments, namely a solutions map and a conceptual index, are introduced to assess conceptual understanding demonstrated in students’ written solutions to examination problems. The process of the development of conceptual understanding is then explored within the framework of Greeno’s model of scientific problem‐solving and reasoning. It was found that students who had been exposed to the structured problem‐solving strategy demonstrated better conceptual understanding of physics and tended to adopt a conceptual approach to problem‐solving.     

The Mathematical Behavior of Six Successful Mathematics Graduate Students: Influences Leading to Mathematical Success

This study investigated the mathematical behavior of graduate students and the experiences that contributed to their mathematical development and success. Their problem-solving behavior was observed while completing complex mathematical tasks, and their beliefs were assessed by administering a written survey. These graduate students report that a mentor, most frequently a high school teacher, facilitated the development of their problem solving abilities and continued mathematical study. The mentors were described as individuals who provided challenging problems, encouragement, and assistance in learning how to approach complex problems. When confronted with an unfamiliar task, these graduate students exhibited exceptional persistence and high confidence. Their initial problem solving attempts were frequently to classify the problem as one of a familiar type, and they were not always effective in accessing recently taught information or monitoring their solution attempts, but were careful to offer only solutions that had a logical foundation. These results provide numerous insights into the complexities of using and extending one's mathematical knowledge and suggest that non-cognitive factors play a prominent role in a student's mathematical success.This revised version was published online in September 2005 with corrections to the Cover Date.     

THE EFFECTS OF TEACHING PROBLEM SOLVING ON ACADEMIC PERFORMANCE AND RETENTION

A study of the effects of explicitly teaching a problem‐solving strategy on problem‐solving ability, course average, course success, and student retention is reported. Two classes of microeconomics principles were involved in a quasi‐experiment. The experimental class was explicitly taught the problem‐solving strategy and this strategy was then used to solve microeconomic problems in class. The control class was assigned, solved, and discussed the same problems without being taught the problem‐solving strategy. Multiple regression and analysis of variance show that while teaching problem solving did not significantly affect course average, student success in passing the course or problem solving ability, it did result in significantly higher student retention. Results indicate that teaching problem solving only affects those students with low problem solving abilities who would have dropped out of class, and that teaching this strategy helps them remain in the class and succeed.     

Following the Template: Transferring Modeling Skills to Nonstandard Problems

This study seeks to analyze how students apply a mathematical modeling skill that was previously learned by solving standard word problems to the solution of word problems with nonstandard contexts. During the course of an experiment involving 106 freshmen, we assessed how well they were able to transfer the mathematical modeling skill that is used to solve standard problems to the solution of nonstandard ones that had an analogous structure. The results of our research show that students had varying degrees of success applying the different stages of modeling depending on whether they were solving a familiar problem (involving near transfer) or one that had an unfamiliar context (involving far transfer): in cases of near transfer, students applied the template formally even though it did not align with the text of the new word problem, which complicated further interpretation. In cases of far transfer, students chose to solve the problem by using an ordinary method of selecting a solution by trial and error in preference to the use of modeling. Thus, the application of the modeling skill as a multistage process is complicated when solving nonstandard problems involving either near or far transfer.