An investigation of undergraduates' transformational problem solving strategies: cognitive/metacognitive processes as predictors of holistic/analytic strategies

Recent years have seen increasing interest in the role of metacognition in mathematical problem solving. The study described in this paper explored problem solving strategies used by undergraduates. Furthermore, cognitive/metacognitive processes are predicted each of holistic and analytic strategies. Educational sciences students (n=178) were asked to talk/think aloud while solving two constructed response transformational problems. The protocols were transcribed and analysed, revealing that the cohort used nine strategies. The results showed that a holistic strategy was predicted by five cognitive/metacognitive processes, two of which were suppressors; whilst an analytic strategy was predicted by four cognitive/metacognitive processes, three of which were suppressors.     

Do it this way! Metacognitive strategies in collaborative mathematical problem solving

Recent years have seen increasing interest in the role of metacognition in mathematical problem solving, and in the use of small group work in classroom settings. However, little is known about the nature of secondary students' metacognitive strategy use, and how these strategies are applied when students work together on problems. The study described in this paper investigated the monitoring behaviour of a pair of senior secondary school students as they worked collaboratively on problems in applied mathematics. Analysis of verbal protocols from think aloud problem solving sessions showed that, although the students generally benefited from adopting complementary metacognitive roles, unhelpful social interactions sometimes impeded progress. The findings shed some light on the nature of individual and interactive metacognitive strategy use during collaborative activity.     

An Explanation for the Difficulty of Leading Conceptual Change Using a Counterintuitive Demonstration: The Relationship Between Cognitive Conflict and Responses

Bringing successful teaching approaches for stimulating conceptual change to normal classrooms has been a major challenge not only for teachers but also for researchers. In this study, we focused on the relationship between cognitive conflict and responses to anomalous data when students are confronted with a counterintuitive demonstration in the form of a discrepant event. The participants in this study were 96 secondary school students (9th grade) from S. Korea. We investigated students?? preconceptions of motion by administering a written test. After the exam, we presented a demonstration that may have conflicted with the ideas held by students. We then investigated the relationship between students?? cognitive conflict and responses to anomalous data by using a Cognitive Conflict Level Test (CCLT). Results showed that cognitive conflict initiated the first step in the process of conceptual change. Anxiety was an especially crucial component of cognitive conflict, affecting the relationship between cognitive conflict and students?? responses. In addition, superficial conceptual change was found to be the most common response.     

Motivation and metacognition when learning a complex system

Our cognitive-motivational process model (Vollmeyer & Rheinberg, 1998) assumes that motivational factors (i.e., mastery confidence, incompetence fear, interest, and challenge) affect performance via mediators. Previous studies (Vollmeyer, Rollett, & Rheinberg, 1997) found that strategy systematicity and motivational state during learning mediate the impact of initial motivation on the learning of a complex system. Potential mediators could be other cognitive (e.g., hypothesis testing) and metacognitive aspects, in that more motivated learners (high mastery confidence, low incompetence fear, high interest) analyse more deeply. Verbal protocols from 44 students who learnt to control a complex dynamic system were collected. We measured their initial motivation (on the four factors specified), then during learning we assessed their strategy systematicity and motivational state. Additionally, we analysed the verbal protocols to obtain indicators of learners’ cognitive and metacognitive processes. Performance measures were levels of knowledge acquisition and application. The cognitive-motivational process model was replicated. Qualitative cognitive aspects were added as mediators, however, the results for metacognition were problematic, partly because participants gave relatively few clearly expressed metacognitive statements.     

Addressing student misconceptions concerning electron flow in aqueous solutions with instruction including computer animations and conceptual change strategies

The effects of both computer animations of microscopic chemical processes occurring in a galvanic cell and conceptual change instruction based on chemical demonstrations on students' conceptions of current flow in electrolyte solutions were investigated. Preliminary results for verbal conceptual questions suggest that conceptual change instruction was effective at dispelling student misconceptions that electrons flow in aqueous solutions of electrochemical cells. Computer animations did not appear to have an effect on students' responses to visual or verbal conceptual questions. An animation/conceptual change interaction for verbal conceptual questions suggests that animations may prove distacting when the questions do not require students to visualize. Data from this study also suggests that lecture attendance and recitation participations helped students answer visual questions.     

Unpacking students’ epistemic cognition in a physics problem-solving environment

It is a widely held view that students’ epistemic beliefs influence the way they think and learn in a given context, however, in the science learning context, the relationship between sophisticated epistemic beliefs and success in scientific practice is sometimes ambiguous. Taking this inconsistency as a point of departure, we examined the relationship between students’ scientific epistemic beliefs (SEB), their epistemic practices, and their epistemic cognition in a computer simulation in classical mechanics. Tenth grade students’ manipulations of the simulation, spoken comments, and behavior were screen and video-recorded and subsequently transcribed and coded. In addition, a stimulated recall interview was undertaken to access students’ thinking and reflections on their practice, in order to understand their practice and make inferences about their process of epistemic cognition. The paper reports on the detailed analysis of the data sets for three students of widely different SEB and performance levels. Comparing the SEB, problem solutions and epistemic practices of the three students has enabled us to examine the interplay between SEB, problem-solving strategies (PS), conceptual understanding (CU), and metacognitive reflection (MCR), to see how these operate together to facilitate problem solutions. From the analysis, we can better understand how different students’ epistemic cognition is adaptive to the context. The findings have implications for teaching science and further research into epistemic cognition.     

Do learning protocols support learning strategies and outcomes? The role of cognitive and metacognitive prompts

Although writing learning protocols is an effective follow-up course work activity, many learners tend to do it in a rather suboptimal way. Hence, we analyzed the effects of instructional support in the form of prompts. The effects of different types of prompts were investigated in an experiment with four conditions: cognitive prompts, metacognitive prompts, a combination of cognitive and metacognitive prompts, or no prompts (N = 84 undergraduate psychology students). We found that the prompts stimulated the elicitation of cognitive and metacognitive learning strategies. The provision of purely metacognitive prompts did not, however, improve learning outcomes. Only the groups who had received cognitive, or a combination of cognitive and metacognitive, prompts learned more than the control group. This effect was mediated by cognitive learning strategies. The learners in the successful groups did not perceive the prompted learning strategies as more helpful than the learners of the group without prompts. It can be concluded that cognitive prompts—alone or in combination with metacognitive prompts—are an effective means to foster learning. However, additional means should be employed in order to convince the learner of the usefulness of such prompts.     

Disabled readers' processing of prose: Do any processes change because of intervention?

A multiple baseline design was implemented to address the questions, “Do qualitative changes in reported strategies occur during treatment and does strategy instruction concurrently influence a conceptually related task?” The dependent measure for the prose recall task was the number of idea units recalled, while the number of facts comprehended during silent reading sessions assessed transfer effects. “Thinking aloud protocols” were used to identify cognitive processes during prose recall. The results suggested that a qualitative shift in verbal strategy reports occurred across training sessions. The introduction of cognitive training (visual and verbal mapping of idea units) increased the recall of prose compared to the baseline conditions, although concurrent effects on reading comprehension tasks were minimal. It was assumed that unstable cognitive processes during prose recall, as well as nonequivalent mental processes between the two tasks, accounted for the poor transfer of training effects.     

Metacognitive strategies that enhance critical thinking

The need to cultivate students’ use of metacognitive strategies in critical thinking has been emphasized in the related literature. The present study aimed at examining the role of metacognitive strategies in critical thinking. Ten university students with comparable cognitive ability, thinking disposition and academic achievement but with different levels of critical thinking performance participated in the study (five in the high-performing group and five in the low-performing group). They were tested on six thinking tasks using think-aloud procedures. Results showed that good critical thinkers engaged in more metacognitive activities, especially high-level planning and high-level evaluating strategies. The importance of metacognitive knowledge as a supporting factor for effective metacognitive regulation was also revealed. The contribution of metacognitive strategies to critical thinking and implications for instructional practice are discussed.     

Do cognitive and metacognitive processes set the stage for each other?

Cognitive and metacognitive learning processes might not only functionally complement but also set the stage for each other. To address potential stage-setting effects between these processes, we conducted two experiments in which we varied whether students were prompted to engage in the cognitive processes of organization and elaboration prior to using the metacognitive processes of comprehension monitoring and remediation planning as well as implementing their remediation plans (cognitive-first sequence), or vice versa (metacognitive-first sequence). As the medium for engaging in these processes we used learning protocols, which were performed as follow-up activity to a lecture or regular lessons. We consistently found that the learners in the metacognitive-first groups outperformed their counterparts regarding the quality of the executed organization and metacognitive processes. We conclude that cognitive and metacognitive processes can influence each other's quality; however, they do not necessarily set the stage but can also damage the stage for each other.     

Effect of cooperative learning strategies on student verbal interactions and achievement during conceptual change instruction in 10th grade general science

This study evaluated the effects of cooperative learning on students' verbal interaction patterns and achievement in a conceptual change instructional model in secondary science. Current conceptual change instructional models recognize the importance of student–student verbal interactions, but lack specific strategies to encourage these interactions. Cooperative learning may provide the necessary strategies. Two sections of low-ability 10th-grade students were designated the experimental and control groups. Students in both sections received identical content instruction on the particle model of matter using conceptual change teaching strategies. Students worked in teacher-assigned small groups on in-class assignments. The experimental section used cooperative learning strategies involving instruction in collaborative skills and group evaluation of assignments. The control section received no collaborative skills training and students were evaluated individually on group work. Gains on achievement were assessed using pre- and posttreatment administrations of an investigator-designed short-answer essay test. The assessment strategies used in this study represent an attempt to measure conceptual change. Achievement was related to students' ability to correctly use appropriate scientific explanations of events and phenomena and to discard use of naive conceptions. Verbal interaction patterns of students working in groups were recorded on videotape and analyzed using an investigator-designed verbal interaction scheme. The targeted verbalizations used in the interaction scheme were derived from the social learning theories of Piaget and Vygotsky. It was found that students using cooperative learning strategies showed greater achievement gains as defined above and made greater use of specific verbal patterns believed to be related to increased learning. The results of the study demonstrated that cooperative learning strategies enhance conceptual change instruction. More research is needed to identify the specific variables mediating the effects of cooperative learning strategies on conceptual change learning. The methods employed in this study may provide some of the tools for this research.     

Verbal and nonverbal behavior of ability-grouped dyads

In this study we describe the social interactions of ability-grouped dyads as they constructed knowledge of balance concepts to elucidate the relationship between interactions and conceptual growth. The verbal and nonverbal behaviors of 30 fifth-grade students were recorded as they completed three activities related to balance. These student interactions were examined within a framework of social cognition. For each dyad, characteristics of ability-grouped dyads were identified. Results revealed that high-achieving students effectively used prior experiences, maintained focus on the learning task, and were able to manipulate the equipment effectively to construct knowledge. Low-achieving students exhibited off-task behavior, lacked a metacognitive framework for organizing the learning tasks, centered on irrelevant features of the equipment, and were unable to use language effectively to mediate learning. Within low-high student dyads, high-achieving students typically modeled thinking processes and strategies for manipulating equipment. In addition, they focused the low-achieving students on the components of the tasks while verbally monitoring their progress, thus enabling low students to identify the critical features necessary for concept construction. These results highlighted the differences that students have in the use of language and tools. Low students' inefficient use of tools has implications for the ways science teachers structure lessons and group students for laboratory work.     

Conceptual change strategies and cooperative group work in chemistry

This study conducted at a suburban community college tested a method of conceptual change in which treatment students worked in small cooperative groups on tasks aimed at eliciting their misconceptions so that they could then be discussed in contrast to the scientific conceptions that had been taught in direct instruction. Categorizations of student understanding of the target concepts of the laws of conservation of matter and energy and aspects of the particulate nature of gases, liquids, and solids were ascertained by pre- and posttesting. Audiotapes of student verbal interaction in the small groups provided quantitative and qualitative data concerning student engagement in behaviors suggestive of the conditions posited to be part of the conceptual change process (Posner, Strike, Hewson & Gertzog, 1982). Chi-square analysis of posttests indicated that students in treatment groups had significantly lower (p < 0.05) proportion of misconceptions than control students on four of the five target concepts. Students who exhibited no change in concept state had a higher frequency of verbal behaviors suggestive of “impeding” conceptual change when compared to students who did change. Three factors emerged from qualitative analysis of group interaction that appeared to influence learning: (a) many students had flawed understanding of concepts that supported the target concepts; (b) student views towards learning science affected their engagement in assigned tasks, (c) “good” and “poor” group leaders had a strong influence on group success.     

Effect of Eliciting Verbal Reports of Thinking on Critical Thinking Test Performance

Verbal reports of examinees' thinking on multiple-choice critical thinking test items can provide useful validation data only if the verbal reporting does not change the course of examinees' thinking and performance. Using a completely randomized factorial design, 343 senior high school students were divided into five groups. In four of the groups, different procedures were used to elicit students' thinking as they worked through Part A of a critical thinking test of observation appraisal (Norris & King, 1983). In the control group, students took the same test in paper-and-pencil format. There were no significant differences in test performance among the five groups nor in the quality of thinking among the four groups from whom verbal reports of thinking were elicited. These results are evidence that verbal reports of thinking can meet one of the necessary conditions of useful validation data—namely, that collecting the data does not alter examinees' thinking and performance. Some analyses found significant interviewer main effects and sex-by-interviewer and elicitation-level-by-interviewer-by-sex-by-grade interaction effects. Analysis of these interactions suggested that the role of the interviewer might limit the generality of the technique.     

Enhancing scientific discovery learning through metacognitive support

Using a virtual physics lab, we analyzed the impact of metacognitive support on simulation-based scientific discovery learning (SDL). The dependent variables for learning outcome were the immediate conceptual knowledge gain and the retained conceptual knowledge three weeks later. Additional dependent variables were the actual use of a domain-specific cognitive strategy, motivation, emotions, and cognitive load. To contrast the effects of metacognitive support with possible effects of goal specificity, the experimental study followed a 2 × 2 design with a sample of N = 129 ninth grade students and with metacognitive support (yes vs. no) and learning goals (specific vs. nonspecific) as factors. The results showed positive effects of metacognitive support on learning outcome, on actual cognitive strategy use, and on learning emotions. No interaction effect of metacognitive support and goal specificity on learning outcome was observed.     

Team-Based Learning: Moderating Effects of Metacognitive Elaborative Rehearsal and Middle School History Content Recall

Promoting Acceleration of Comprehension and Content through Text (PACT) and similar team-based models directly engage and support students in learning situations that require cognitive elaboration as part of the processing of new information. Elaboration is subject to metacognitive control, as well (Karpicke, Journal of Experimental Psychology: General 138(4):469–485, 2009)—successful learners use metacognitive elaborative rehearsal to process and make sense of incoming information even in the absence of structured opportunities or instructional prompts for elaborating. Levels of processing and cognitive load theories suggest that students in PACT classrooms may outperform students in comparison classes because PACT engages and supports deep cognitive processing (via elaboration and discussion) at the time of learning, allowing participants to better conserve and more consistently reallocate cognitive and metacognitive resources (compared to students in the non-treated group) for encoding content. In other words, PACT may moderate the relationship of metacognitive elaborative rehearsal and content retrieval. Extant data from years 1 (n?=?419) and 2 (n?=?704) of the PACT/RFU project suggests such an effect. As hypothesized, there were no mean differences in reported metacognitive rehearsal use across the groups because metacognitive elaborative rehearsal was not taught. However, regression coefficients for content recall on metacognitive elaboration were greater in the treatment group in both samples suggesting that an instructional emphasis on deep processing leads to better content recall. The findings are discussed in the context of the Common Core State Standards and the large-scale testing programs in place currently across the USA.     

Productive group engagement in cognitive activity and metacognitive regulation during collaborative learning: can it explain differences in students’ conceptual understanding?

This paper addresses the nature and significance of productive engagement in cognitive activity and metacognitive regulation in collaborative learning tasks that involve complex scientific knowledge. A situative framework, combining the constructs of social regulation and content processing, provided the theoretical basis for the development of a comprehensive coding scheme for interactive data analysis. An empirical study was conducted with two groups of university students working on two science-learning tasks. It examined the function of metacognitive regulation to control the flow of cognitive activity, and the extent to which group differences in cognitive and metacognitive regulation processes during collaborative learning could explain differences in the groups’ learning outcomes. The findings provide validation of the framework and its derived coding scheme. An example of a way in which a group engages in socially shared metacognitive regulation is presented to demonstrate how the coding scheme was applied to the data. Theoretical and empirical implications of the findings are discussed.