Teachers’ conceptions of representation in middle school mathematics

Current reform efforts call for an emphasis on the use of representation in the mathematics classroom across levels and topics. The aim of the study was to examine teachers’ conceptions of representation as a process in doing mathematics, and their perspectives on the role of representations in the teaching and learning of mathematics at the middle-school level. Interviews with middle school mathematics teachers suggest that teachers use representations in varied ways in their own mathematical work and have developed working definitions of the term primarily as a product in problem solving. However, teachers’ conception of representation as a process and a mathematical practice appears to be less developed, and, as a result, representations may have a peripheral role in their instruction as well. Further, the data suggested that representation is viewed as a topic of study rather than as a general process, and as a goal for the learning of only a minority of the students—the high-performing ones. Implications for mathematics teacher education, prospective and practicing, are discussed.     

Learning biology as ‘Increase ones’ knowledge and understanding’: studying Taiwanese high school students’ learning strategies in relation to their epistemic views and conceptions of learning in biology

ABSTRACT

This study aimed to examine high school students’ learning strategies in relation to their epistemic views and conceptions of learning in the discipline of biology through a structural equation modelling technique. A total of 247 high school students (168 males) participating in this study completed 3 questionnaires, the Epistemic Views of Biology (EVB), the Conceptions of Learning Biology (COLB), and the Strategies of Learning Biology (SLB). The results supported the hypothesised model proposed in this study, and a new factor of ‘Increase one’s Knowledge and Understanding,’ reflecting the feature of high school students’ biology learning, and serving an important role in biology learning, was identified in this study. In addition, students’ epistemic views were associated with their conceptions of learning, which consequently correlated to their learning strategies. More specifically, the EVB of ‘Uncertainty’ negatively related to lower COLB, which consequently positively related to Surface Strategies, whereas the EVB of ‘Justification’ was positively correlated to higher COLB as ‘Increase one’s Knowledge and Understanding,’ which in turn was correlated to Deep Strategies. According to the research findings, theoretical and practical suggestions for future research are provided.     

An investigation of Taiwanese high school students’ science learning self-efficacy in relation to their conceptions of learning science

Background: Past studies have shown significant associations between students’ conceptions of learning science and their science learning self-efficacy. However, in most of the studies, students’ science learning self-efficacy has often been measured by a singular scale.

Purpose: Extending the findings of these studies, the present study adopted a multi-dimensional instrument to assess Taiwanese high school students’ science learning self-efficacy and investigate the relationships with their conceptions of learning science.

Sample: A total of 488 Taiwanese high school students (265 male and 223 female) were invited to participate in this survey.

Design and method: All the participants responded to the Conceptions of Learning Science (COLS) questionnaire regarding ‘Memorizing’, ‘Testing’, ‘Calculating and practicing’, ‘Increase of knowledge’, ‘Applying’ and ‘Understanding and seeing in a new way’ and the Science Learning Self-Efficacy (SLSE) instrument, including ‘Conceptual understanding’, ‘Higher-Order cognitive skills’, ‘Practical work’, ‘Everyday application’ and ‘Science communication’.

Results: The path analysis results derived from the structural equation modeling method indicated that, of all five SLSE dimensions, the ‘Understanding and seeing in a new way’ COLS displayed as a positive predictor, while the ‘Testing’ COLS was a significant negative predictor. The ‘Applying’ COLS item can only positively contribute to the SLSE dimensions of ‘Higher-Order thinking skills’, ‘Everyday application’ and ‘Science Communication’.

Conclusions: In general, students in strong agreement with learning science as understanding and seeing in a new way or the application of learned scientific knowledge are prone to possess higher confidence in learning science. However, students who consider learning science in terms of preparing for tests and examinations tend to hold lower science learning self-efficacy.     

First‐year secondary school mathematics students’ conceptions of mathematical proofs and proving

The aim of this study is to investigate students’ conceptions about proof in mathematics and mathematics teaching. A five‐point Likert‐type questionnaire was administered in order to gather data. The sample of the study included 33 first‐year secondary school mathematics students (at the same time student teachers). The data collected were analysed and interpreted using the methods of qualitative and quantitative analysis. The results have revealed that the students think that mathematical proof has an important place in mathematics and mathematics education. The students’ studying methods for exams based on imitative reasoning which can be described as a type of reasoning built on copying proof, for example, by looking at a textbook or course notes proof or through remembering a proof algorithm. Moreover, they addressed to the differences between mathematics taught in high school and university as the main cause of their difficulties in proof and proving.     

Middle and high school students’ conceptions of climate change mitigation and adaptation strategies

Both scientists and policy-makers emphasize the importance of education for influencing pro-environmental behavior and minimizing the effects of climate change on biological and physical systems. Education has the potential to impact students’ system knowledge – their understanding of the variables that affect the climate system – and action knowledge – their understanding of behaviors that can impact the system. Research on climate change education has largely focused on system and action knowledge that address mitigation while overlooking equally necessary adaptive responses. This study used a pre/post-test format to identify aspects of middle and high school students’ climate system knowledge and action knowledge of both mitigation of and adaptation to climate change. Results indicate that adolescents currently conflate climate change mitigation strategies with unrelated environmental problems far less than in previous surveys. However, students demonstrated limited understanding of adaptive responses to climate change. After engaging in an instructional unit on climate change, students expressed stronger system and action knowledge, but significant misconceptions remained that conflated mitigation of and adaptation to climate change.     

High school students’ acceptance and use of mobile technology in learning mathematics

The purpose of this research is to investigate factors affecting the acceptance and use of mobile technology in learning mathematics based on the Unified Theory of Acceptance and Use of Technology 2 (UTAUT2) model. The study group comprised of 1640 students attending different types of high schools and grade levels. The results of the study revealed both direct and indirect effects of exogenous variables on Behavioral Intention and Use Behavior in mobile technology acceptance of high school students in learning mathematics. It was also found that the theoretical model was confirmed adequately based on the regression coefficients, the significance of the regression coefficients, and the goodness of fit indices obtained from the SEM analysis. The strongest predictors of Behavioral Intention were Hedonic Motivation and Habit, respectively. Exogenous variables of the study together explained 76% of the variance in Behavioral Intention and 13% of the variance in Use Behavior.

     

Students’ conceptions and the learning of science

This introductory article to the Special Issue of the International Journal of Science Education attempts to review the theoretical contexts for research into children's conceptions in science and to identify future directions for research programmes in this field.     

Bridging home and school: understanding immigrant mothers’ cultural capital and concerns about play-based learning

This article explores immigrant mothers’ experiences and perspectives on early learning to identify the underlying principles of parents’ learning theories and their concerns about pedagogic practices at school. It employs data from interviews with nineteen immigrant mothers that reveal a discord between learning beliefs and practices at home and school. The paper argues that mothers’ cultural capital may shape their perspectives on learning, which may subsequently influence their children’s cultural capital and interests. Supporting children’s learning at school requires examining home learning beliefs so that teachers can establish a two-way exchange of knowledge, ideas and perspectives with common objectives of respecting differences and exploring possible reconciliation of differences. This paper urges educators to bridge home and school through engaging in dialogue with parents so that parents’ cultural capital and their understanding about play-based learning work to their children’s advantage.     

Primary school students’ conceptions about microorganisms. Influence of theoretical and practical methodologies on learning

Background: Microorganisms are very important in day-to-day life, but they are inadequately addressed in the Spanish educational system. It is essential that students are well informed about their characteristics and functions.

Purpose: The study aims to find out primary school students’ perceptions of microorganisms and to analyze whether theoretical or practical teaching interventions produce different levels in student’s learning about this topic.

Sample: The sample consisted of 199 primary students in 2nd (aged 7–8) and 6th (11–12) grades from two public schools in Albacete (Spain).

Design and method: This study uses a pre- and post-intervention questionnaire to evaluate the knowledge of students on the issue of microorganisms. We compare differences by age and two teaching–learning intervention methodologies: theoretical and practical.

Results: Results from the pre-test showed a poor understanding and several misconceptions. Children have a limited and negative view of microorganisms, mainly derived from non-formal learning. Both types of intervention provided an improvement in knowledge, but closed questions did not reveal clear statistically significant differences between methods. Open questions showed how the scientific use of the language and quality of verbalization is much better in the groups that received a practical intervention.

Conclusion: The findings can be a starting point for curriculum planners and for teachers interested in engaging students in science learning.     

Teachers’ assessments of students’ learning of mathematics

This paper reports a study of the classroom assessment practices of 12 sixth form college mathematics teachers in Malta. It explores the extent to which these teachers are knowledgeable about their students’ learning of mathematics and the implications that this has for their classroom practices. It reveals that these teachers’ knowledge of their students’ understanding of certain mathematical concepts is fairly limited. It then goes on to discuss this phenomenon in terms of a process that can hinder rather than promote learning. The research illuminates the position of teachers who appear to lack certain detailed information about their students which, it can be argued, could inform more effective teaching strategies. The paper concludes by exploring possible implications for similar situations where learning could be enhanced by more effective classroom assessment strategies and their use to inform future teaching and learning activities.     

Paragons of Virtue: teachers’ conceptual understanding of high ability in an egalitarian school system

Recent research suggests that teachers are useful in identifying high ability, provided they have some advance guidelines on how such identification should be operationalized and why. But how do teachers in an egalitarian school system, with neither specific knowledge nor guidelines, conceptualize and make provision for highly able pupils? A total of 232 teachers, representing all levels of the Swedish comprehensive school system, were questioned on different aspects of their conceptual understanding of talented pupils. Answers were given as brief written statements, and the data submitted to a content analysis which resulted in four cluster matrices. This showed that teachers can identify high ability fairly accurately with regard to cognitive attributes and personality characteristics, but fail to understand the socio‐emotional dynamics. Thus, highly able pupils appeared to have been regarded as ‘paragons of virtue’ possessing the social attributes of the teachers ‘ideal pupil’.     

Exploring intrinsic and extrinsic motivational aspects of middle school students’ aspirations for their mathematics learning

Middle school students have been pervasively described in the research literature as exhibiting disaffection, disengagement, and a lack of interest in mathematics classrooms. This study investigated this notion empirically using students’ own voice on their wishes for mathematics learning to see if they characterise themselves in this way in their self-reports. Over 3500 Australian middle school students responded to a free-format prompt and reported diverse but overwhelmingly positive aspirations related to intrinsic motivational features inherent in their disposition and to extrinsic factors in their environment, such as the learning context and activities provided. Evidence of all four goal orientations was found in the students’ responses but most noticeably for the productive mastery-approach orientation. When these students described what they wish for in their mathematics classrooms, they mentioned challenging work, interesting work, and opportunities to collaborate.     

Graduate students’ conceptions of university teaching and learning: formation for change

The paper introduces a framework concerning conceptions of teaching and learning of advanced graduate students and the trajectory of change in their conceptions following a formal course on course design and teaching. Students were enrolled in six sections of this graduate course, two offered in a 6-week format and 4 in a 13-week format. The courses were taught by three different instructors. Data were obtained from 88 doctoral students before and after the course using four questions pertaining to the meaning of effective teaching, effective learning, role of the teacher, and role of the learner. Using an open coding procedure, four conceptions were identified. These were transmitting knowledge, preparing context/managing instruction, promoting course learning, and promoting life-long learning. The generalized linear model procedure was used to conduct within and between group pre and post course comparisons. Overall, there was a significant change in response frequency ratios in all four categories across all courses, indicating a decrease in the responses in the first two categories and an increase in the frequency of responses in the last two categories. No significant differences were attributed to course type or instructor.     

High school students’ approaches to learning physics with relationship to epistemic views on physics and conceptions of learning physics

Background and purpose : Knowing how students learn physics is a central goal of physics education. The major purpose of this study is to examine the strength of the predictive power of students’ epistemic views and conceptions of learning in terms of their approaches to learning in physics. Sample, design and method : A total of 279 Taiwanese high school students ranging from 15 to 18?years old participated in this study. Three questionnaires for assessing high school students’ epistemic views on physics, conceptions of learning physics and approaches to learning physics were developed. Step-wise regression was performed to examine the predictive power of epistemic views on physics and conceptions of learning physics in terms of their approaches to learning physics. Results and conclusion: The results indicated that, in general, compared to epistemic views on physics, conceptions of learning physics are more powerful in predicting students’ approaches to learning physics in light of the regression models. That is, students’ beliefs about learning, compared with their beliefs about knowledge, may be more associated with their learning approaches. Moreover, this study revealed that the higher-level conceptions of learning physics such as ‘Seeing in a new way’ were more likely to be positively correlated with the deep approaches to learning physics, whereas the lower-level conceptions such as ‘Testing’ were more likely to positively explain the surface approaches, as well as to negatively predict the deep approaches to learning physics.     

University students’ and teachers’ conceptions of teaching and learning in the biosciences

In this study we compare university teachers’ and first-year students’ conceptions of teaching and learning at the Faculty of Environmental and Biological Sciences. The conceptions were analysed using data from open-ended questionnaires. The results showed that at the beginning of studies the gap between teachers’ and students’ conceptions of teaching and learning is substantial. This finding has important implications for the educational process. In order to enhance successful studying from the beginning of students’ university careers, it is important for teachers to become aware of the differences between students’ and teachers’ conceptions of learning.     

Pre-service primary teachers’ conceptions of creativity in mathematics

Teachers in the UK and elsewhere are now expected to foster creativity in young children (NACCCE, 1999; Ofsted, 2003; DfES, 2003; DfES/DCMS, 2006). Creativity, however, is more often associated with the arts than with mathematics. The aim of the study was to explore and document pre-service (in the UK, pre-service teachers are referred to as ‘trainee’ teachers) primary teachers’ conceptions of creativity in mathematics teaching in the UK. A questionnaire probed their conceptions early in their course, and these were supplemented with data from semi-structured interviews. Analysis of the responses indicated that pre-service teachers’ conceptions were narrow, predominantly associated with the use of resources and technology and bound up with the idea of ‘teaching creatively’ rather than ‘teaching for creativity’. Conceptions became less narrow as pre-service teachers were preparing to enter schools as newly qualified, but they still had difficulty in identifying ways of encouraging and assessing creativity in the classroom. This difficulty suggests that conceptions of creativity need to be addressed and developed directly during pre-service education if teachers are to meet the expectations of government as set out in the above documents.     

Teachers’ and school administrators’ attitudes and beliefs of teacher evaluation: a preliminary investigation of high poverty school districts

This study examined attitudes and beliefs regarding teacher evaluation of teachers and their school administrators in the state of New Jersey, USA. The sample included 33 school administrators and 583 Pre-K through 12th grade teachers from four high-poverty urban school districts (22 schools). Participant attitudes and beliefs were assessed using the Teacher Evaluation Experience Scale (TEES; Reddy et al. in Educational Assessment, 21(2), 120–134, 2016). TEES is a multi-informant assessment designed to measure teachers’ and school administrators’ experiences with teacher evaluation through five scales (i.e., total and subscales of system, feedback, process, and motivation to change) and six open-ended questions. Based on the qualitative analyses, teachers identified collaborative communication and evaluation feedback as the most helpful aspects of their evaluation process. Based on the quantitative analyses, however, their average ratings did not exceed neutral on any of the four subscales. Overall findings suggest that school administrators’ experiences with teacher evaluation are more favorable than teachers’ experiences. Moderate correlations are found between participant characteristics and TEES scales. Implications for teacher evaluation are presented.     

The nature and development of middle school mathematics teachers’ knowledge

In this article, we report on the use of a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning programme. The instrument was designed to assess the aspects of teachers’ knowledge identified by Shulman (1987) refined by Ball et al. (2008) and extended to include teachers’ confidence to use and teach various topics in the middle school mathematics curriculum and their beliefs about mathematics teaching and learning. Based on a hierarchical coding of items, the application of the partial credit Rasch model revealed that the profile items were measuring a single underlying construct and suggested that the various facets of teacher knowledge develop together. We describe the characteristics of four levels of the hierarchical construct measuring teacher knowledge and understanding for teaching mathematics in the middle years of schooling, and discuss the unique affordances of a holistic view of teacher knowledge in contrast to considerations of multiple knowledge categories.     

Elementary-age children’s conceptions about mathematics utility and their home-based mathematics engagement

Integrating multiple theoretical frameworks, the authors examined rising first- to fourth-grade students’ mathematics utility conceptions—their knowledge and beliefs about the usefulness of mathematics, home-based mathematics engagement, and grade-level differences in mathematics utility conceptions and home engagement. Most children viewed mathematics as heavily focused on low-level mathematics operations and as learned and used primarily in school. Older children showed more awareness of mathematics as part of daily living, but still viewed mathematics as mostly school-based—more so than their younger counterparts. Results suggest that awareness of mathematics in daily life may be associated with children’s mathematics utility value (perceived usefulness of mathematics). Although children engaged in activities at home with the potential to foster mathematics development, the frequency of engagement was not related to their awareness of mathematics in daily activities. Thus, there may be untapped opportunities for young children to connect the mathematics they learn in school to their daily life.