Epistemic profiles and self-regulated learning: Examining relations in the context of mathematics problem solving

Relations were examined between epistemic profiles, regulation of cognition, and mathematics problem solving. Two hundred sixty-eight students were sampled from undergraduate mathematics and statistics courses. Students completed inventories reflecting their epistemic profiles and learning strategies, and were profiled as rational, empirical, or both. Based on their profiles, 24 students participated in two problem-solving sessions. Episodes were coded for planning, monitoring, control, use of empirical and rational argumentation, and justification for solutions. For both self-reported metacognitive self-regulation and regulation of cognition during problem solving, students profiled as rational had the highest self-reported mean and actual frequency of regulation of cognition compared to students profiled as predominantly empirical. Moreover, students profiled as predominantly rational correctly solved more problems than the other two groups. Finally, students’ approaches to problem solving were consistent with their epistemic profiles. Relations are discussed in the context of various theoretical frameworks.     

Consistent results with the consistency hypothesis? The effects of epistemic beliefs on metacognitive processing

We explored relations between students’ epistemic beliefs, metacognitive monitoring and recall performance in the context of learning physics through metaphor. Eighty-three university undergraduate students completed questionnaires designed to measure their epistemic beliefs and prior knowledge about Newtonian physics. Students were epistemically profiled as rational, empirical, or metaphorical in their approaches to knowing. Using a think-aloud protocol, students read a text on Newton’s First and Third Laws. The text included metaphors as examples of the various laws described. Results revealed that students profiled as metaphorical engaged in more metacognitive processing compared to students profiled as rational or empirical. Moreover, path analyses revealed that metacognitive monitoring positively predicted recall performance. Results challenge Muis’ (2008) consistency hypothesis; the ways in which knowledge is represented in text may be the linking factor for relations between metacognitive monitoring and epistemic beliefs rather than the underlying epistemology of the domain.     

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.     

Strategic development of multiplication problem solving: Patterns of students' strategy choices

Low mathematics achievement is a persistent problem in the United States, and multiplication is a fundamental area in which many students manifest learning difficulties. This study examined the strategic developmental levels of multiplication problem solving among 121 elementary school students in Grades 3 through 5. A latent class analysis modeling was used to identify three valid groups representing different patterns of strategy choices for each of three types of multiplication problems. Findings indicated intra-group variability for problem-solving accuracy, for frequency of using different strategies, and for accuracy of executing direct retrieval/algorithm (DR/AG) strategies. Students demonstrated relative consistency in their strategy choices for solving the three problem types. Students who used DR/AG strategies most frequently showed the highest problem-solving accuracy and the highest accuracy of executing the DR/AG strategies. Students who most frequently relied on incorrect operations or who indicated they did not know how to solve problems demonstrated the lowest problem-solving accuracy among the three groups; the number of students in this group increased with problem difficulty levels. Implications are discussed in terms of identifying students' strategic developmental levels and providing differentiated instruction based on the identified levels.     

Metacognition in Mathematical Problem Solving

Metacognition is considered by most educationists as an element necessary for many cognitive tasks. In problem solving, it has been said that possessing knowledge alone is insufficient and problem solvers need to exhibit high level cognitive skills like “self-regulation skills” (also known as metacognitive strategies) for successful problem solving.

A study on students' metacognitive strategies was carried out with over a thousand secondary and pre-university students from 12 schools. A questionnaire adapted from Biggs (1987) was administered to students at various levels (Secondary 2, Secondary 4, Pre-University 1), from different academic tracks (General, Science, Arts) and academic streams (Special, Express, and Normal). They were required to self-report on their metacognitive beliefs; their use of metacognitive strategies in mental tasks involving memory, problem solving and comprehension; and their attitudes towards the learning of various academic subjects. 20 items from the questionnaire which were related to problem solving were categorized into four stages, namely, orientation, organisation, execution and verification and data from these items were analysed.

Some findings that emerged were:

• (a) Normal stream students exhibited a lower usage of metacognitive strategies as compared to students from the Express and Special streams.

• (b) Metacognitive strategies used by Normal stream students tended to be of the “surface” type.

• (c) There was no significant difference in the frequency of usage of metacognitive strategies between students from different academic tracks.

• (d) During the problem solving process, students spent most time on evaluation of answers rather than on monitoring their understanding.

• (e) Students from different levels (Secondary 2, Secondary 4 and Pre-University) exhibited similar frequency of usage of metacognitive strategies in problem solving.

• The implications of these findings on future research and development projects as well as the teaching of metacognitive strategies are discussed in the paper.

     

The Role of Students’ Scientific Epistemic Beliefs in Computer-Simulated Problem Solving

Research on how epistemic beliefs influence students’ learning in different contexts is ambiguous. Given this, we have examined the relationships between students’ scientific epistemic beliefs, their problem solving, and solutions in a constructionist computer-simulation in classical mechanics. The problem-solving process and performance of 19 tenth-grade students, with different scientific epistemic beliefs, were video recorded and inductively coded. Quantitative analysis revealed that different sets of epistemic beliefs were conducive to different aspects of students’ problem-solving process and outcomes. Theoretically sophisticated beliefs were in general associated with logical strategies and high solution complexity. However, authority dependence was associated with high degree of adherence to instructions. Hence, there might not be a universal relationship between the theoretical sophistication of students’ epistemic beliefs and quality of learning outcomes. We suggest that the conduciveness to desired outcomes is a better measure of sophistication than theoretical non-contextualized a priori assumptions.     

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.     

Schema-based instruction: Effects of experienced and novice teacher implementers on seventh grade students' proportional problem solving

This study examined the effects of a research-based intervention, schema-based instruction (SBI), implemented by experienced- (taught SBI in previous study; Jitendra et al., 2015) and novice-teacher implementers (taught SBI for the first time with professional development) on the mathematics outcomes of seventh-grade students. SBI is a multicomponent intervention that emphasizes the mathematical structure of problems through the use of schematic diagrams and incorporates problem solving and metacognitive strategy instruction. Results indicated that both experienced- and novice-teacher implementers delivered SBI with similar levels of fidelity; there was no SBI experience effect on the immediate and 10-week retention tests of proportional problem-solving, on a general measure of problem solving, or on the end of the year state mathematics achievement test. These results provide evidence that the effectiveness of SBI generalizes over time to different cohorts of teachers and that the impact of SBI on student mathematics outcomes is maintained over time without additional PD.     

非英语专业本科生英语阅读元认知策略使用情况的调查研究

对非英语专业本科生阅读元认知策略使用情况实证研究的结果表明,此类大学生使用阅读元认知策略的频率偏低,并且元认知策略使用水平与英语成绩呈正相关,成功学习者和不成功学习者在元认知策略使用水平上呈显著性差异。     

Middle school children's strategic behavior: Classification and relation to academic achievement and mathematical problem solving

Theories of problem solving (e.g., Verschaffelet al., 2000) hold strategic behavior centralto processing mathematical word problems. Thepresent study explores 80 sixth- andseventh-grade students' self-reported use of 14categories of strategies (Zimmerman &Martinez-Pons, 1986) and the relationship ofstrategy use to academic achievement,problem-solving behaviors, and problem-solvingsuccess. High and low achievement groupsdiffered in the number of different strategiesand categories of strategies reported but notin overall number of strategies, confidence inusing strategies, or frequency of strategy use.Students whose behaviors evidenced elaborationof the word problem's text reported moreself-evaluation; organizing and transforming;and goal setting and monitoring behavior.Implications for instructional practices thatsupport active stances toward problem solvingare discussed.     

合作写作促进元认知策略习得的实证研究

为探讨合作学习对促进写作元认知策略的习得以及提高学生写作水平的效果,在大学英语写作课堂进行实证研究。结果表明:合作写作促进学习者之间写作元认知策略的相互分享和自我反思,也提高了反馈的有效性,从而增强了他们写作元认知策略建构的广度和深度,大大提高了写作元认知策略的习得和写作水平。     

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.     

Metacognitive factors in scientific problem-solving strategies

The aim of this study on 42 seventh graders (ages 12–13) was to determine whether and to what extent students’ metacognitive level is linked to their conceptualization and performance in problem solving at school, especially science problems. This hypothesis is supported by a number of studies showing that metacognition is a factor in learning. Two indexes were devised for the study: an index of metaknowledge about classroom learning, and an index of metacognitive monitoring in relation to task difficulty on a non-academic problem. These two indexes were related to the students’ intelligence test scores and solving strategies on electricity problems. The results showed that (1) the metaknowledge level was more closely tied to crystallized intelligence (Gc), and (2) metacognitive monitoring was more closely associated with fluid intelligence (Gf). Moreover, both metacognitive indexes were strongly linked to scientific problem-solving strategies (correlations around .50).     

Relative effects of three questioning strategies in ill-structured,small group problem solving

The purpose of this research is to investigate the relative effectiveness of using three different question-prompt strategies on promoting metacognitive skills and performance in ill-structured problem solving by examining the interplay between peer interaction and cognitive scaffolding. An ill-structured problem-solving task was given to three groups. One group (Type QP) received instructor-generated question prompts that guided the problem-solving process; the second group (Type PQ) developed their own peer-generated questions; another group (Type PQ-R) developed their own question prompts first and revised them later with an instructor-generated question list. In this study, students in the QP group outperformed those in any other groups. The results revealed that providing instructor-generated question prompts was more effective than letting students develop their own questions, with or without revision, in ill-structured problem solving. Analysis of each of the four problem-solving stages revealed that the provided question prompts were more helpful in the stages of justification, and monitoring and evaluating than student-generated prompts. The difference between PQ and PQ-R groups is not statistically significant either overall or in any of the problem-solving stages.     

Reconsidering Personal Epistemology as Metacognition: A Multifaceted Approach to the Analysis of Epistemic Thinking

One of the central unresolved conceptual issues that concerns researchers of personal epistemology is the characterization of the intersection between personal epistemology and metacognition. The contested and diverse nature of both constructs makes untangling their connections a complex yet vital task. The purpose of this article is to advance the discussion regarding this intersection by offering a theoretical approach that may serve as a basis for analyzing epistemic thinking and aligning it with current views of metacognition. Based on a synthesis of theoretical and empirical studies, we argue that epistemic thinking is a multifaceted construct with both cognitive and metacognitive aspects. Furthermore, we propose that epistemic metacognition includes several aspects such as metacognitive skills; metacognitive knowledge about persons, strategies and tasks; and metacognitive experiences. The theoretical, methodological, and instructional implications of this approach are explored.     

Universals and specifics in learning strategies: Explaining adolescent mathematics, science, and reading achievement across 34 countries

We examined whether strategies of memorization, transfer through elaboration, and metacognition accounted for reading, science, and mathematics achievement across 34 countries. 158,848 fifteen-year-olds completed a reading literacy test and a questionnaire. Of these students, 88,401 completed a science test, and 88,590 completed a mathematics test. We analyzed the data using multi-level regressions of Rasch-estimated test scores and modeled differences across countries and across schools. Students who reported using memorization strategies often scored lower in all subjects. Transfer through elaboration was not significantly linked to any achievement scores. Lastly, students reporting greater use of metacognitive strategies often scored higher. Compared to students in individualistic societies, to achievement scores of students in collective cultures were linked more strongly to schoolmates' use of metacognitive strategies and less strongly to their own use of metacognitive strategies. These results highlight how cultural contexts can moderate the links between adolescents' learning strategies and their academic achievement.     

Problem solving in science and technology education

Both science and technology education have a commitment to teaching process; investigations or scientific method in science, design in technology, and problem solving in both areas. The separate debates in science and technology education reveal different curricular emphases in processes and content, reflecting different goals, and pedagogic and educational research traditions. This paper explores these differences and argues that each curriculum area can learn from the other. Despite the interest in processes, problem solving remains neglected in each area, particularly with respect to empirical accounts of student problem-solving activities and the supporting pedagogy. This paper draws on the situated learning and social constructivist literature to provide insights into problem solving in technology education. The research reported here, gives accounts of the problem-solving strategies of English secondary school students. These strategies represent their responses to technology activities and the learning environment created by teachers.