Metacognitive Experiences: The Missing Link in the Self-Regulated Learning Process

The measurement of online self-regulation processes is a very important issue and in this rejoinder to Ainley and Patrick (this issue) I am arguing that including measures of metacognitive experiences, in conjunction with measures of other affective experiences, in various phases of task processing can increase the reliability and validity of online measures and our understanding of the self-regulation process. Furthermore, behavioral and performance measures as well as thinking aloud protocols can enrich not only the reliability and validity of our measures but also our awareness of the factors involved in the formation of the various facets of subjective experiences, be it affective or metacognitive.

Tracing the development of preservice teachers’ efficacy beliefs in teaching mathematics during fieldwork

This paper focuses on efficacy beliefs with respect to teaching mathematics; it aims at testing and validating an existing scale for measuring efficacy beliefs in the domain of mathematics, examining the development of preservice teachers’ efficacy beliefs in mathematics during fieldwork, and identifying factors that contribute to the development of these beliefs. Exploratory factor analysis applied to longitudinal data collected through a questionnaire administered to almost 90 preservice teachers elicited a two-factor model, reflecting efficacy beliefs in mathematics instruction and classroom management. Using cluster analysis, we found four patterns in the development of preservice teachers’ efficacy beliefs regarding these two factors. Our analysis of semi-structured interviews with eight participants representing these four patterns suggested that preservice teachers’ efficacy beliefs were mainly informed by experimentation with teaching and interaction with mentors, tutors, peers, and pupils. Based on our findings, we draw implications for mathematics preservice teacher education and provide suggestions for future research.

Mathematical belief change in prospective primary teachers

The development and influence of beliefs in teacher education has been a topic of increasing interest for researchers in recent years. This study explores the responses of a group of prospective primary teachers to attempts to facilitate belief change as part of their initial teacher education programme in mathematics. The students’ responses seemed to fall into three categories: non-engagement; building a new set of beliefs and; reforming existing beliefs. In this article the participants’ responses are outlined and illustrated with stories from three individuals. This study suggests that belief reform is complex and fraught with ethical dilemmas. Certainly there is a need for further research in this area, particularly given the pervasive influence of beliefs on teaching practice.

An international comparison using a diagnostic testing model: Turkish students’ profile of mathematical skills on TIMSS-R

This study illustrates how a diagnostic testing model can be used to make detailed comparisons between student populations participating in international assessments. The performance of Turkish students on the TIMSS-R mathematics test was reanalyzed with a diagnostic testing model called the Rule Space Model. First, mathematical and cognitive skills (‘attributes’) measured by the test were determined. One hundred sixty-two items were coded in terms of their attribute involvement, creating an incidence matrix—the Q-matrix. Using the Q-matrix and the student response data, each student’s attribute mastery profile was determined. Mean attribute mastery levels of Turkish students were computed and compared to those of their American peers. It was shown that Turkish students were weak in algebra and probability/statistics. They also demonstrated poor profiles in skills such as applying rules in algebra, approximation/estimation, solving open-ended problems, recognizing patterns and relationships, and quantitative reading.

Mexican-American Students’ Perceptions of Teachers’ Expectations: Do Perceptions Differ Depending on Student Achievement Levels?

This exploratory study examines the learning beliefs of high and low achieving, low-income Mexican-American students. Semi-structured interviews were conducted with 11 ninth grade students. The qualitative analysis shows that students’ perceptions of their teachers’ expectations of a “good” student or a “not so good” student did not differ along achievement lines. However, the students’ perceptions about what it means to be a good student differentiated the low-achievers from the high-achievers. This study’s findings may be used to inform educators about Mexican-American students’ orientation towards school and learning, in hopes for creating more equitable educational settings where all students achieve to their fullest potential.

Controlling split attention and redundancy in physical therapy instruction

In this study, we examined the effectiveness of instructional materials designed to control redundancy and split attention in the teaching of complex orthopedic physical therapy skills. Participants included 41 first-year physical therapy students. The modified instruction group received a modified unit of instruction designed to reduce cognitive load, while the control group received a traditionally designed unit of instruction. Four hypotheses were tested relating to achievement on cognitive and psychomotor tests, ratings of cognitive load, and task completion times. The multivariate analysis yielded significant results for three of the four hypotheses (ES = +0.52). As predicted, the participants receiving the modified instructional materials scored significantly higher on the written post-test and psychomotor tasks, while reporting a lower level of cognitive load on both tasks. These results suggest that designers can increase the germane cognitive load by reducing the extraneous cognitive load through good instructional and message design practices.

Lecturers on teaching within the ‘supercomplexity’ of Higher Education

While a vast literature exists on students and their learning, work on lecturers and their teaching continues to lag some way behind. This paper explores the notion that the complexity of Higher Education (HE) today significantly impacts upon what goes on in the classroom through a two-tiered study. Semi-structured interviews were conducted to explore lecturers’ perceptions and experiences of teaching a specific module. Interviewees raised issues pertaining to the wider departmental, institutional and socio-political context. Consequently, focus groups were run with key people in the University to explore their perceptions of teaching and learning within the current HE climate. The findings suggest that lecturers perceive numerous external factors to impinge upon their teaching and attempt to militate against these in various ways in order to achieve ongoing enhancement of learning for students.

Real-world connections in secondary mathematics teaching

The mathematics-education community stresses the importance of real-world connections in teaching. The extant literature suggests that in actual classrooms this practice is infrequent and cursory, but few studies have specifically examined whether, how, and why teachers connect mathematics to the real world. In this study, I surveyed 62 secondary mathematics teachers about their understanding and use of real-world connections, their purposes for making connections in teaching, and factors that support and constrain this practice. I also observed 5 teachers making real-world connections in their classrooms and I conducted follow-up interviews; these qualitative data are used to illuminate findings from the survey data. The results offer an initial portrayal of the use of real-world connections in secondary mathematics classes and raise critical issues for more targeted research, particularly in the area of teacher beliefs about how to help different kinds of students learn mathematics.

Mathematical enculturation from the students’ perspective: shifts in problem-solving beliefs and behaviour during the bachelor programme

This study investigates the changes in mathematical problem-solving beliefs and behaviour of mathematics students during the years after entering university. Novice bachelor students fill in a questionnaire about their problem-solving beliefs and behaviour. At the end of their bachelor programme, as experienced bachelor students, they again fill in the questionnaire. As an educational exercise in academic reflection, they have to explain their individual shifts in beliefs, if any. Significant shifts for the group as a whole are reported, such as the growth of attention to metacognitive aspects in problem-solving or the growth of the belief that problem-solving is not only routine but has many productive aspects. On the one hand, the changes in beliefs and behaviour are mostly towards their teachers’ beliefs and behaviour, which were measured using the same questionnaire. On the other hand, students show aspects of the development of an individual problem-solving style. The students explain the shifts mainly by the specific nature of the mathematics problems encountered at university compared to secondary school mathematics problems. This study was carried out in the theoretical framework of learning as enculturation. Apparently, secondary mathematics education does not quite succeed in showing an authentic image of the culture of mathematics concerning problem-solving. This aspect partly explains the low number of students choosing to study mathematics.

Assessing Teachers’ Beliefs to Facilitate the Transition to a New Chemistry Curriculum: What Do the Teachers Want?

In this article, we describe the results of a study of chemistry high school teachers’ beliefs (N = 7) of the chemistry curriculum and their roles, their beliefs on the teacher as developer of materials, and their beliefs about professional development. Teachers’ beliefs influence the implementation of a curriculum. We view the use of a new curriculum as a learning process, which should start at teachers’ prior knowledge and beliefs. The results reveal that it is possible to develop a new curriculum in which teachers’ beliefs are taken as a starting point. Promising approaches to prepare teachers for a new curriculum is to let them (co)develop and use curriculum materials: It creates ownership, and strengthens and develops teachers’ pedagogical content knowledge (PCK).

Making the Hidden Explicit: Learning About Equity in K-8 Preservice Science Education

Preservice teachers in a K–8 science methods course used guided video reflection to examine their interactions with children during science teaching. This inquiry approach helped preservice teachers identify and respond to gaps between their beliefs and intentions about teaching all children and their enactment of those beliefs. The experience of teaching a science lesson and then viewing it multiple times through a critical framework provided an opportunity for preservice teachers to recognize hidden assumptions, unexamined behaviors, and the unintentional meanings they may have conveyed to children. This encouraged them to think more critically about their roles as teachers in creating spaces where all children have access to quality science learning experiences.

Clergy’s Views of the Relationship between Science and Religious Faith and the Implications for Science Education

Since many teachers and students recognize other kinds of knowledge (faith) based on other ways of knowing, consideration of these realities is appropriate for the science education community. Understanding the multitude of ways that clergy view relationships between science and faith (i.e. alternative ways of knowing) would assist in understanding various ways that people address complex issues arising from ideas about science and faith. We administered a questionnaire composed of multiple-choice and short answer items to 63 United Methodist ministers. Findings included (1) that formal, organized faith contexts (e.g. church services) serve as informal science education opportunities, (2) participants demonstrated considerable diversity regarding the types of relationships developed between science and faith, and (3) participants recognized a need exists for better understandings of science and its relationship to faith for them, their colleagues, and their congregations.

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Teachers’ Perspectives on a Professional Development Intervention to Improve Science Instruction Among English Language Learners

Our 5-year professional development intervention is designed to promote elementary teachers’ knowledge, beliefs, and practices in teaching science, along with English language and mathematics for English Language Learning (ELL) students in urban schools. In this study, we used an end-of-year questionnaire as a primary data source to seek teachers’ perspectives on our intervention during the first year of implementation. Teachers believed that the intervention, including curriculum materials and teacher workshops, effectively promoted students’ science learning, along with English language development and mathematics learning. Teachers highlighted strengths and areas needing improvement in the intervention. Teachers’ perspectives have been incorporated into our on-going intervention efforts and offer insights into features of effective professional development initiatives in improving science achievement for all students.

Bringing the Classroom to the Web: Effects of Using New Technologies to Capture and Deliver Lectures

Technology expands instructional options for faculty, and this study examines the differential learning effects of offering a lecture on physics to students in a traditional classroom versus internet video formats. Based on an experiment conducted in a natural educational context, results indicate enhanced transfer of lecture information in the video formats relative to the live condition, with students also responding more positively to personalized video presentation.

Assessing and tracking students’ problem solving performances in anchored learning environments

The purpose of this randomized experiment was to compare the performance of high-, average-, and low-achieving middle school students who were assessed with parallel versions of a computer-based test (CBT) or a paper-pencil test (PPT). Tests delivered in interactive, immersive environments like the CBT may have the advantage of providing teachers with diagnostic tools that can lead to instruction tailored to the needs of students at different achievement levels. To test the feasibility of CBT, students were randomly assigned to the CBT or PPT test conditions to measure what they had learned from an instructional method called enhanced anchored math instruction. Both assessment methods showed that students benefited from instruction and differentiated students by achievement status. The navigation maps generated from the CBT revealed that the low-achieving students were able to navigate the test, spent about the same amount of time solving the subproblems as the more advanced students, and made use of the learning scaffolds.

Correcting experience-based judgments: the perseverance of subjective experience in the face of the correction of judgment

Many of our cognitive and metacognitive judgments are based on sheer subjective experience. Subjective experience, however, may be contaminated by irrelevant factors, resulting in biased judgments. Under certain conditions people exert a metacognitive correction process to remedy such biased judgments. In this study we examine the proposition that even after a judgment has been corrected to avoid the biasing effects on subjective experience, subjective experience itself remains biased. We asked participants to judge the difficulty of anagrams for others. When they were aware of having been exposed to the solutions of some of the anagrams, they corrected their difficulty judgments for these anagrams. Despite this correction, their speeded choices in a subsequent task disclosed their biased subjective experience that these anagrams were easier to solve. Implications for the study of metacognition and for the educational domain are discussed.

How Much Have They Retained? Making Unseen Concepts Seen in a Freshman Electromagnetism Course at MIT

The introductory freshmen electromagnetism course at MIT has been taught since 2000 using a studio physics format entitled TEAL—Technology Enabled Active Learning. TEAL has created a collaborative, hands-on environment where students carry out desktop experiments, submit web-based assignments, and have access to a host of visualizations and simulations. These learning tools help them visualize unseen electromagnetic concepts and develop stronger intuition about related phenomena. A previous study has shown that students who took the course in the TEAL format (the experimental group) gained significantly better conceptual understanding than those who took it in the traditional lecture-recitation format (the control group). The present longitudinal study focuses on the extent to which these two research groups (experimental and control) retain conceptual understanding about a year to 18 months after finishing the course. It also examines students attitudes about whether the teaching format (TEAL or traditional) contributes to their learning in advanced courses. Our research has indicated that the long-term effect of the TEAL course on students’ retention of concepts was significantly stronger than that of the traditional course. This research is significant because it documents the long-term cognitive and affective impact of the TEAL studio physics format on learning outcomes of MIT students.

Implementing a Physical Activity Curriculum into the School Day: Helping Early Childhood Teachers Meet the Challenge

In Fall 2006, North Carolina kindergarten teachers were charged with the task of meeting the NASPE guidelines for providing daily physical activity to their kindergarten students. In turn, the teachers researched resources and consulted experts to design and develop a developmentally appropriate physical activity and physical play environment for their students. The purpose of this article is to disseminate useful information one group of kindergarten teachers believed would help other teachers in similar situations. The article discusses the planning process, suggestions for activities and necessary equipment for program implementation, and vignettes regarding the experiences the teachers and students have had during the physical activity and physical play program’s inaugural year.

What’s the problem? Meaning making and learning to do mathematical word problems in the context of digital tools

The general background of this study is an interest in how digital tools contribute to structuring learning activities. The specific interest is to explore how such tools co-determine students’ reasoning when solving word problems in mathematics, and what kind of learning that follows. Theoretically the research takes its point of departure in a sociocultural perspective on the role of cultural tools in thinking, and in a complementary interest in the role of the communicative framing of cognitive activities. Data have been collected through video documentation of classroom activities in secondary schools where multimedia tools are integrated into mathematics teaching. The focus of the analysis is on cases where the students encounter some kind of difficulty. The results show how the tool to a significant degree co-determines the meaning making practices of students. Thus, it is not a passive element in the situation; rather it invites certain types of activities, for instance iterative computations that do not necessarily rely on an analysis of the problems to be solved. For long periods of time the students’ activities are framed within the context of the tool, and they do not engage in discussing mathematics at all when solving the problems. It is argued that both from a practical and theoretical point of view it is important to scrutinize what competences students develop when using tools of this kind.