Developing teachers’ knowledge of students as learners of mathematics through structured interviews

A structured interview process is proffered as an effective means to advance prospective teachers’ understandings of students as learners of mathematics, a key component of pedagogical content knowledge. The interview process is carried out in three phases with the primary objective of developing listening skills for accessing students’ mathematical thinking. The interviews adhere to clinical interview procedures for discovering cognitive activities and, accordingly, are initiated by presenting an open-ended mathematics task. Three rounds of interviews were completed by undergraduates enrolled in a middle school mathematics methods course. Anecdotal data generated by their interview reports suggest that the structured interview process engenders an interpretive orientation to listening to students and furthers awareness of how students make sense of mathematics. Features of the interview process that may limit its potential benefits are discussed; recommendations for further study are proposed.     

Emerging Considerations for Professional Development Institutes for Science Teachers

This paper describes two professional development institutes in project-based science. We collected data from these institutes in the form of structured questionnaires, individual written reflections by the teachers, and focus-group interviews. An analysis of the data revealed three factors that had been underrepresented in previous research: comfort, technology, and balance. In terms of comfort, the teachers expressed a need for both physical and psychological comfort for them to learn. The technological emphasis in our institutes caused teachers to stress in their comments our developing software. We found that, depending on teachers' previous knowledge, technology could be a barrier or a support to the success of institutes. Finally, we found a necessity to balance elements within the institute and a need to balance cognitively demanding time on task with less demanding opportunities for informal interaction.     

Convergent validity of group tests of cognitive development

This study was designed to investigate the convergent validity of individual clinical task interviews as presented by Piaget and Inhelder paired with three widely used group tests of cognitive development. These tests are designed to assess the acquisition of cognitive abilities. The three group test raw scores paired with summed raw scores on four concrete-formal task interviews yielded the following Pearson product-moment correlations: Reasoning Test (Ankney and Joyce), 0.43; Logical Reasoning Test (Burney), 0.61; Classroom Test of Formal Operations (Lawson), 0.37. The raw data was then ranked into cognitive level groups and presented on contingency tables. The following contingency coefficients were determined: Logical Reasoning Test, 0.52; Logical Reasoning Test (adjusted), 0.61; Classroom Test of Formal Operations, 0.50. This study reflects that the Reasoning Test tends to indicate lower cognitive levels of subjects when paired with summed scores on the clinical task interviews, whereas the Logical Reasoning Test and the Classroom Test of Formal Operations tend to indicate higher cognitive levels of subjects when paired with summed scores on the clinical task interviews. In each case the correlations do not appear to be sufficiently strong to warrant selection or categorization of an individual student based on his/her test performance.     

The role of temperament in children's affective and behavioral responses in achievement situations

Although students' affects and behaviors in achievement situations have been shown to be influenced by their previous learning experiences, less is known about how they relate to students' dispositional characteristics, such as temperament. This study examined to what extent children's temperament is related to their affective and behavioral responses in achievement situations. Teachers rated first-graders' (n = 153) temperamental characteristics in the Fall semester. Children's active task avoidance, anxiety, and helplessness were rated in test situations in the Fall and Spring semesters. The results showed that the more easily distracted the children were, the more task avoidance they showed, and the more their task avoidance increased during the first grade. Moreover, children's high level of inhibition was related to high levels of anxiety and helplessness. The findings suggest that characteristics that are related to students' behavioral regulation and inhibition are particularly important for their affective and behavioral responses in achievement situations.     

Triadic interaction in clinical task-based interviews with mathematics teachers

A clinical task-based interview can be seen as a situation where the interviewer–interviewee interaction on a task is regulated by a system of explicit and implicit norms, values, and rules. This paper describes how documenting and mapping triadic interaction among the interviewer, the interviewee, and the knowledge negotiated can be used to increase procedural replicability of the interview and accuracy of drawn conclusions about the interviewee’s thinking process. Excerpts from interviews with 25 inservice mathematics teachers working on a task to make up a problem whose solution requires division of two fractions are discussed. The excerpts illustrate the relationship between methodological decisions taken by the interviewer during the interview and the applicability of the interview output to the research questions. A divergent analysis of the interviews with these teachers, which spanned over two years and were conducted by four interviewers, is used to offer a framework for analyzing data collected in clinical task-based interviews.     

A method to investigate agricultural information use by small‐scale Mauritian cattle keepers

Summary

A study of whether, and how, small‐scale cattle keepers in a selected village in Mauritius were managing information was conducted with respondents in 59 households. A qualitative approach was followed using ethnography based on direct and participant observation, in‐depth semi‐structured interviews and grounded theory. Postulated structures of information were used as a starting point for data collection to identify the actual structures, and associated management practices. An ‘OPI’ approach to respondents was followed, involving an outside ('O'), periphery ('P') and inside (T) approach. These were a succession of interactions of increasing depth. Triangulation gave to the responses more validity and reliability. Recording of data was done after the interviews and away from the households. Content analysis of the data established patterns, concepts and categories of structures to show how the information was being managed. The outcomes included new findings about aspects of financial management by these small‐scale and part‐time cattle keepers, of use to extension programmes. The method is suggested as a structured, formal process to guide extension workers or consultants in their understanding of the situations in which they work.     

Assessment of Preschooler’s Scientific Reasoning in Adult–Child Interactions: What Is the Optimal Context?

In educational settings, continuous assessment of the child’s level of understanding is necessary to effectively utilize the principles of scaffolding and to create contexts that can advance the scientific reasoning of the child. In this article, we argue that a child’s performance is a dynamic notion that is created by all elements in an interaction, including the task. Therefore, we studied preschoolers’ levels of scientific reasoning varying different properties of the assessment context. Young children were interviewed about four scientific tasks using one out of four different protocols (varying in the degree of flexibility and adaptiveness) by an adult. In the first study, different task contents resulted in different performance levels. The second study indicated that the most structured protocol elicited the highest maximum level of reasoning in children and the highest percentage of correct predictions. The third study showed differences between the protocols in the adult’s verbal behavior. Adaptation in verbal behavior to different children by the adult did not result in higher scientific understanding by the children, whereas a higher degree of task structure did. Combined, the studies emphasize the importance of context, which has implications for assessment and teaching situations.     

President's Message

Counselor trainees' perceptions of inhibition while they were conducting interviews in differently monitored situations (audio-, video-, nonmonitor) were studied. The results clearly indicate that beginning counselors perceive monitoring to have an inhibiting effect upon their interview performance. Audio-monitoring was perceived as less inhibiting than video-monitoring. Implications concerning uses of video-monitoring in practicum situations are discussed.     

Moments of Intensity: Affect and the Making and Teaching of Art

Affect often arises unexpectedly within the process of making art (along with other creative activities). In this article I argue for affect as a necessary and constructive dynamic within educational processes specifically for art and design. After a consideration of its recent neglect within art education, I revisit the notion of affect with reference to a number of thinkers who provide different perspectives, but particularly through the lens of the US psychologist Silvan Tomkins. Through him and others I seek to understand how affect can be recognised and cultivated in pedagogic situations. I do so by reflecting on the making and teaching experiences of students following an MA in Art and Design in Education and a practice‐based PhD, as witnessed by me (supervisor/co‐tutor), as recounted by students and as discussed in post‐event conversation/semi‐structured interviews.     

Ethical leadership in schools: creating community in an environment of accountability and The cultural proficiency journey: moving beyond ethical barriers toward profound school change

The present study, which sought to analyse adolescent sportsmen's representations of responsibility, was mainly guided by the philosophical literature on this topic. A body of literature suggests that the contextual factors of sport practice, particularly regarding the rules that regulate play, may have a key role in the building of such representations. Semi‐structured interviews were conducted with two groups of 18 teenagers: one group of institutionalised athletes (who played soccer or basketball in a structured and official context) and one group of self‐organised athletes (who played the same sports in a self‐regulated context). The qualitative analysis showed that the institutionalised players described responsibility in functional terms; this result was explained by the rigid characteristics of their context of practice, which was based on task division and performance. In contrast, the self‐organised players described responsibility in moral terms; this result was explained by an open context of practice based on interaction. The overall results of our study raise questions about the educational capacity of institutionalised sport and the objective conditions that promote the social and moral development of young people.     

Differently structured advance organizers lead to different initial schemata and learning outcomes

Does the specific structure of advance organizers influence learning outcomes? In the first experiment, 48 psychology students were randomly assigned to three differently structured advance organizers: a well-structured, a well-structured and key-concept emphasizing, and a less structured advance organizer. These were followed by a sorting task, a text study phase, and a posttest. The results indicated that differently structured advance organizers lead to different proto-schemata before and different learning outcomes after the text study phase. The second experiment replicated and extended these findings with 53 mathematics students. As in experiment 1, three differently structured advance organizers were used; but to rule out alternative explanations, the sorting task between the advance organizer and the text study phase was omitted. The results showed strong beneficial effects of well-structured advance organizers on near and far transfer tasks. Taken together, both experiments support the claim that the structure of advance organizers has an effect on preliminary schemata and learning outcomes. On a general level, the results indicate that advance organizers can support the generation of proto-schemata and thus can be more than the activation of “existing” concepts in long-term memory. With regard to education, this implies that educators should not only think about whether prior domain-specific knowledge is present, but also about how to scaffold the generation of proto-schemata at the beginning of instruction.     

Finnish students’ reasons for their achievement in classroom activities: focus on features that support self-regulated learning

The aim of this study was to investigate how finnish students explain factors that contribute to their achievement in classroom learning activities and whether these factors are related to support of self-regulated learning (SRL) in classroom. Over seven weeks, 24 primary school students were videotaped during their typical classroom activities in 28 lessons to capture moments when they succeeded in learning tasks. From the video observations, 62 episodes were edited and used in stimulated recall interviews in which students were asked to report the reasons they related to their achievement in learning situations. Data-driven content analysis was used to analyse the open-ended interview data. The video observation data were analysed and sorted into theory-driven categories in order to find out how SRL was supported in classrooms. The results showed that students describe achievement through the actions that they took in the learning situations, such as being able accomplish the task. The reasons given for their achievement dealt with ability to accomplish the tasks or doing academic activities in order to achieve in the task. Furthermore, the students recognised classroom activities that support SRL, acknowledging their contribution to their achievement, mostly through the support that they received from their teachers and peers.     

Coping mechanisms of part‐time students

A characteristic shared by the majority of adult students is that they are undertaking part‐time study. For these adult learners one of the major difficulties is how to find time for their study. This paper reports the coping mechanisms that part‐time adult students adopt to meet the additional demands that study puts on their existing commitments to work, family and social lives. Data were collected from 53 part‐time students in eight universities in Hong Kong through semi‐structured interviews. A model featuring three coping mechanisms (sacrifice, support and negotiation of arrangements) within four domains (self, work, family and social life) was used for the analysis. Whether or not these coping mechanisms are operationalized to a sufficient extent can have a significant impact upon the students' progress with their courses. The analytical grid provides a framework for counselling and advising adult learners. Part‐time adult students can also use the model to evaluate their own situations and determine which coping mechanisms will work for them to deal with time management issues.     

Being taught to learn together: an ethnographic study of the curriculum in two Chinese kindergartens

This paper reports the findings of a pilot study which adopted an ethnographic approach to investigate the cultural features of the Chinese kindergarten curriculum by means of ‘semi‐participant’ observations, semi‐structured interviews, daily conversations and open‐ended questionnaires in two Chinese kindergartens. The paper first introduces the debate over teaching and learning in the early years in Western contexts. It then demonstrates that the curriculum in Chinese kindergartens is mainly implemented by means of teachers' formal collective teaching. Children seem to be taught to learn; their spontaneous learning interests are welcomed but seldom developed in depth. The preference among teachers for this formal collective teaching, coupled with their perception that this teaching is required in their particular situations, creates a tension between teaching and children's learning. The shift in parents' views of education, from an over‐emphasis on children's knowledge‐based study to support for children's harmonious overall development, also contributes to this tension.     

Parental teaching styles in an open-ended teaching-learning environment

The present study extends earlier work on parental teaching style by making the task to be completed less structured, extending parent-child interaction over a 2 week time period, and equalizing the expertise of the parent relative to the child. Additionally, the study examines the effects of parental intrusiveness on a subsequent task. Subjects were 22 Caucasian middle class parent-child dyads. Audiorecordings were taped over a 2-week period while dyads were learning aspects of Logo computer programming. Even in this prolonged nonspecific learning situation, in which parents were encouraged to proceed at the child's pace, parents were overwhelmingly directive. Additionally, children of directive parents performed best on a subsequent generalization task.     

Implications of task structure on self‐regulated learning and achievement

School tasks interact with student motivation, cognition, and instruction to influence learning and achievement. Heeding calls for additional research linking motivational and cognitive factors in learning and instruction on specific tasks within authentic classroom settings we quantitatively and qualitatively track 90 tenth‐grade science students’ motivation, reported use of learning strategies, achievement, calibration, and task perceptions as they engage in a well‐structured task (WST) and an ill‐structured task (IST). Students achieved higher grades on, and reported more ease and value for, the WST whereas they utilised critical thinking and peer learning strategies more on the IST. Lower academic achievers calibrated their achievement less accurately on each task and experienced lower grades, interest, ease, and management capability on the IST. Conversely, higher academic achieving students reported more self‐efficacy and effort regulation and lower anxiety and elaboration on the IST. Motivation – notably less intrinsic goal orientation in low academic achievers and higher task value and self‐efficacy – predicted performance on the IST. The structure of tasks may provide prompts that illicit unique self‐regulated learning responses in students.     

I Am Sure There May Be a Planet There: Student articulation of uncertainty in argumentation tasks

We investigated how students articulate uncertainty when they are engaged in structured scientific argumentation tasks where they generate, examine, and interpret data to determine the existence of exoplanets. In this study, 302 high school students completed 4 structured scientific arguments that followed a series of computer-model-based curriculum module activities simulating the radial velocity and/or the transit method. Structured scientific argumentation tasks involved claim, explanation, uncertainty rating, and uncertainty rationale. We explored (1) how students are articulating uncertainty within the various elements of the task and (2) the relationship between the way the task is presented and the way students are articulating uncertainty. We found that (1) while the majority of students did not express uncertainty in either explanation or uncertainty rationale, students who did express uncertainty in their explanations did so scientifically without being prompted explicitly, (2) students’ uncertainty ratings and rationales revealed a mix of their personal confidence and uncertainty related to science, and (3) if a task presented noisy data, students were less likely to express uncertainty in their explanations.     

Involving Science Teachers in the Development and Implementation of Assessment Tools for “Science for All” Type Curricula

We describe a workshop in which 10 teachers from 10 schools, located in central Israel, participated in the development of alternative assessment tools in the context of implementing a new science curriculum for senior high-school students, namely “Science for All” (an STS type curriculum). In order to assist a group of teachers (who began teaching the “Science for All” program) in both teaching and assessment strategies, it was decided that the Department of Science Teaching at the Weizmann Institute of Science would sponsor a workshop for them. An evaluation study was conducted during the workshop and at its completion. The main goal of the study was to evaluate the outcomes of the workshop and to determine whether its objectives were attained. The research tools consisted of (a) an attitude questionnaire administered to participating teachers, (b) structured interviews with the teachers, (c) structured interviews with students, and (d) an attitude questionnaire administered to the students. Based on the results of the questionnaires and the interviews, it seems that all the teachers who participated in the workshop gained self-confidence in using the teaching strategies and assessment methods of this new interdisciplinary curriculum. The interviews with students revealed that their active involvement in their own assessment improved their sense of responsibility for their achievements. The variety of assignments enabled them to be at their best with certain assignments and to succeed less with others. In conclusion, we found that running a new interdisciplinary curriculum requires a professional development program that will stimulate teachers’ creativity and diversify the instructional strategies that they use in the classroom. Such skills should improve their ability to understand the goals, strategies, and rationale of the curriculum, as well as their students’ learning difficulties.     

Object Mastery Motivation in Pre-school Children with and without Disabilities

In this study the level of object mastery motivation between children with Down's syndrome and children without disabilities of matched mental age was investigated. Data were collected through structured observations of all the children playing with four different educational toys of increasing complexity. Four variables were examined: task pleasure, task persistence, success and off-task behaviour. A one-way ANOVA revealed both statistically significant and nonsignificant differences between groups. Participants from both groups displayed age-appropriate behaviour when playing with the toys. Those with disabilities interacted less than the comparison group with the effect-production and sensori-motor tasks (the easier tasks), whereas, with the more difficult problem-solving tasks, both groups persisted equally. It is suggested that successful attempts elicit persistence on less complex tasks, whereas on the more sophisticated ones this effect is obtained by the challenging nature of the task.