Student perceptions of student perception of module questionnaires: questionnaire completion as problem solving

A sample of 202 students filling in a student evaluation of teaching (SET) questionnaire were asked to complete another questionnaire asking about the specific reasons for awarding a score to the specific SET questionnaire items. The aim was to find out what influenced students' judgements on those items. It was found that students' interpretation of some questions differed from the ‘expected’ interpretation. Several factors, such as the placing of questions and the salience of items retrieved from memory, could influence a score. It was also found that asking for an explanation improved scores overall. The conclusions were that questionnaire completion could be understood as a form of problem solving and judgement under uncertainty. The specific heuristics used led to variability in students' interpretation of the task.     

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.     

Worked Examples Versus Non‐goal‐specific Problems: a test of schema development in geometry

A multiple baseline across subjects experimental design was used to compare the effects of a teaching programme designed to enhance schemata acquisition with that of worked examples, traditionally used to teach geometry to high school students. In the first treatment, students were guided to form their own personal, independent schema through the use of non‐goal‐specific questions, that is, questions that did not ask to find a single, specific unknown. The second treatment introduced students to solved examples of problems asking for specific values. Following exposure to one or other of the treatments, measures were obtained of students’ success in problem solving, the time taken and the processes used. Results show that students in both groups had gains in the number of problems solved following intervention, with those exposed to the non‐goal‐specific procedure showing greater rates of improvement and greater efficacy in their problem‐solving strategies. These findings are discussed in terms of their implications for a schemata acquisition and problem‐solving hypothesis.     

Students’ Ability to Apply Their Knowledge in a Gaming Exercise: An Exploratory Study

This paper reports on a study exploring master students’ ability to apply their knowledge when solving an internal pricing problem in a supply chain. Analyses of 33 negotiation progress reports and 8 recordings of discussions demonstrate that most of the students were not able to apply relevant concepts and models to guide their handling of the task. The main reason for the variability in performance was the significant differences in the students’ general problem-solving abilities. Most students did not perform a thorough task analysis or develop a solution strategy before they met for negotiations, and they did not keep track of their task performance. The implications for teaching are highlighted, and directions for further research are proposed.     

Tower of Hanoi disk-transfer task: Influences of strategy knowledge and learning on performance

Tower of Hanoi has become a popular tool in cognitive and neuropsychology to assess a set of behaviors collectively referred to as executive functions. Substantial variability in performance on the Tower of Hanoi (TOH) disk-transfer task among normally functioning young adults, and potential contributions to these individual differences, were examined. In this expanded 60-problem version of the four-disk TOH, the degree to which problem administration (blocked vs. random) and strategy knowledge influenced overall performance and changes in accuracy across problems was examined. Eighty-seven college students were randomly assigned to a Blocked Group (problems given in ascending order of move-length) and a Random Group (problems given in a random order). After administration of the TOH task, participants described their problem solving and these verbal protocols were analyzed with regard to four elements of a strategic approach to problem solving. Problem administration order demonstrated no effect on task performance or on expressed strategy knowledge; however, strategy knowledge did predict performance on the TOH. An expected decrease in performance across trials was observed in the Blocked Group, and an increase in accuracy in the Random group indicated a learning effect. Strategy knowledge did not interact with these changes in performance across the items. These results suggest that external cues do not influence performance on the TOH to the same extent as individual differences in strategy induction relatively early in the problem solving process.     

Themes and Interplay of Beliefs in Mathematical Reasoning

Upper secondary students’ task solving reasoning was analysed with a focus on arguments for strategy choices and conclusions. Passages in their arguments for reasoning that indicated the students’ beliefs were identified and, by using a thematic analysis, categorized. The results stress three themes of beliefs used as arguments for central decisions: safety, expectations and motivation. Arguments such as ‘I don’t trust my own reasoning’, ‘mathematical tasks should be solved in a specific way’ and ‘using this specific algorithm is the only way for me to solve this problem’ exemplify these three themes. These themes of beliefs seem to interplay with each other, for instance in students’ strategy choices when solving mathematical tasks.     

Effects of different acquisition procedures on response variability

In three experiments with college students, the effects of different acquisition procedures on response variability were studied. The computer keypressing task involved learning a sequence with a minimum number of presses on a subset of the keyboard. Procedures differed in type of training and in the number, size, and sequence of training steps. Experiment 1 showed that instructions and shaping in three steps generated less variability in the number of responses made in each keypress sequence than shaping in six steps. Subsequent experiments showed that a large increase in the response requirement early in shaping increased variability. Postacquisition variability remained unchanged in the number of responses per sequence—the aspect of responding on which reinforcement was contingent—but declined in location and timing of keypressing. The results are discussed in terms of the implicit reinforcement of variability and how the acquisition of qualitatively different response strategies could influence variability.     

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.     

Patterns of Verbal Mediation During Problem Solving: A Sequential Analysis of Self-Explanation

The explanations that participants give themselves (self-explanations) while learning or solving problems have been shown to be positively associated with various performance measures. The major aim of this study was to identify patterns of self-explanation that distinguish between good and poor problem solvers. Thirty-two Grade 9 students were asked to solve 3 mixture problems—1 warm-up problem and 2 test problems—while thinking aloud. The problem-solving process was videotaped, protocols were transcribed, and 5 content categories were identified. Through a sequential analysis, patterns of self-explanation that differentiate between good and poor problem solvers were identified.     

Can Good Concept Mappers be Good Problem Solvers in Science?

Problem solving is an enduring issue in science education, ostensibly because science itself is basically concerned with problem solving—exploring the universe and seeking answers to intriguing phenomena in nature. Remarkable strides have been made in psychology about recording the minutiae of problem solving as a cognitive process. Concept mapping, a metalearning tool, is appearing on the scene as a potential pathway for promoting the acquisition of problem‐solving skills. Drawing 40 subjects from a pool of students who experienced cooperative and individualistic concept‐mapping experiences for six months and adjudged to be good concept mappers, this study found the concept‐, mapping group to be significantly more successful in solving three biological problems than 20 subjects who served as control. Written and think‐aloud procedures and interviews were conducted as part of the administration of the Biology Problem Solving Test. No statistically significant difference was found between students who mapped concepts cooperatively and those who mapped individually. There were mixed results for gender. The implications of the findings for further research and for improving problem‐solving abilities of students are drawn.     

Exploring individual and item factors that affect assessment validity for diverse learners: Results from a large-scale cognitive lab

A cognitive lab technique (n = 156) was used to investigate interactions between individual factors and item factors presumed to affect assessment validity for diverse students, including English language learners. Findings support the concept of access — an interaction between specific construct-irrelevant item features and individual characteristics that either permits or inhibits student response to the targeted measurement content of an assessment item. Access issues of 3rd and 5th grade students were explored at three stages during problem solving on mathematics items: 1) apprehension of task demands; 2) formulation of a solution; and 3) articulation of a solution. Adequacy of access at these levels appears to affect student performance. In particular, where students were able to experience increased apprehension in the first stage through the provision of item variations consistent with their individual access needs, they were more likely to formulate correct solution strategies. The implications of these findings are discussed and suggestions for future research are offered.     

The role of epistemic emotions in mathematics problem solving

The purpose of this research was to examine the antecedents and consequences of epistemic and activity emotions in the context of complex mathematics problem solving. Seventy-nine elementary students from the fifth grade participated. Students self-reported their perceptions of control and value specific to mathematics problem solving, and were given a complex mathematics problem to solve over a period of several days. At specific time intervals during problem solving, students reported their epistemic and activity emotions. To capture self-regulatory processes, students thought out loud as they solved the problem. Path analyses revealed that both perceived control and value served as important antecedents to the epistemic and activity emotions students experienced during problem solving. Epistemic and activity emotions also predicted the types of processing strategies students used across three phases of self-regulated learning during problem solving. Finally, shallow and deep processing cognitive and metacognitive strategies positively predicted problem-solving performance. Theoretical and educational implications are discussed.     

The development of flexibility in equation solving

This paper explores the development of students’ knowledge of mathematical procedures. Students’ tendency to develop rote knowledge of procedures has been widely commented on. An alternative, more flexible endpoint for the development of procedural knowledge is explored here, where students choose to deviate from established solving patterns on particular problems for greater efficiency. Students with no prior knowledge of formal linear equation solving techniques were taught the basic transformations of this domain. After instruction, students engaged in problem-solving sessions in two conditions. Treatment students completed the “alternative ordering task,” where they were asked to re-solve a previously completed problem but using a different ordering of transformations. Those completing alternative ordering tasks demonstrated greater flexibility.     

Representational systems used by graduate students while problem solving in organic synthesis

Graduate students taking a course in synthetic organic chemistry were asked to think aloud while solving several synthesis tasks. Analysis of the protocols indicated that subjects used different types of representations while problem solving. Subjects constructed solutions and communicated them through seven systems: Verbal, Pictorial, Methodological, Principles-Oriented, Literary, Laboratory-Oriented, and Economic. Beyond the Pictorial and Verbal systems, the most often used system was Methodological in nature—subjects believed the purpose of organic synthesis is to apply rules in a proper order until the task is solved. Subjects considered utilizing other systems of representation if they judged their results to be ambiguous when based on the Methodological system.     

Scaffolding a Complex Task of Experimental Design in Chemistry with a Computer Environment

When solving a scientific problem through experimentation, students may have the responsibility to design the experiment. When students work in a conventional condition, with paper and pencil, the designed procedures stay at a very general level. There is a need for additional scaffolds to help the students perform this complex task. We propose a computer environment (copex-chimie) with embedded scaffolds in order to help students to design an experimental procedure. A pre-structuring of the procedure where the students have to choose the actions of their procedure among pre-defined actions and specify the parameters forces the students to face the complexity of the design. However, this is not sufficient for them to succeed; they look for some feedback to improve their procedure and finally abandon their task. In another condition, the students were provided with individualized feedbacks on the errors detected in their procedures by an artificial tutor. These feedbacks proved to be necessary to accompany the students throughout their experimental design without being discouraged. With this kind of scaffold, students worked longer and succeeded better to the task than all the other students.     

Focusing attention to deep structure in math problems: Effects on elementary education students with and without attentional deficits

The purpose of this study was to examine the effects of actively categorizing math problems on the math problem solving performance of students with and without attention deficit disorder (ADD). To this purpose, 52 fifth and sixth grade students were involved in actively categorizing or noncategorizing (control) tasks followed by two problem solving activities. The results of this study indicated that students more frequently organize math problems by categories based on deeper structures (i.e., concepts or operations) when they were informed of the features to look for than students who organized math problems on their own. However, those students who actively organized the math problems and formed categories on their own had higher accuracy in an assessment of generality in a subsequent problem solving task than students who were earlier given categories. These effects were similar for both groups and provided generality to prior research on recall performance to assessing problem solving.