Epistemic quality for equitable access to quality education in school mathematics

This paper reports on a study that aims to address the challenges of UN Sustainable Development Goal 4 to ensure inclusive and equitable quality education for all. The study focuses on school mathematics in particular. With regard to ensuring equitable access to quality education, it is argued that there is a need to consider the epistemic quality of what students come to know, make sense of and be able to do in school mathematics. Accordingly, the aim is to maximize the chances that all pupils will have epistemic access to school mathematics of high epistemic quality. The study is based on the theoretical framework of Joint Action Theory in Didactics (JATD). Associated research questions focus on the quality of teacher-student(s) joint action and on the epistemic quality of the content. The paper draws on empirical research findings of the Developing Mathematical Thinking in the Primary Classroom (DMTPC) project (2010–12) and also on the findings of a parallel study of mathematics teachers’ assessment practices in Ghana. One teacher’s action research project is used as an exemplar to illustrate how mathematics can become more accessible and inclusive thus leading to an evolution in mathematical thinking and high-quality epistemic access for all.     

A Framework for Teaching Epistemic Insight in Schools

This paper gives the rationale and a draft outline for a framework for education to teach epistemic insight into schools in England. The motivation to research and propose a strategy to teach and assess epistemic insight followed research that investigated how students and teachers in primary and secondary schools respond to big questions about the nature of reality and human personhood. The research revealed that there are pressures in schools that dampen students’ expressed curiosity in these types of questions and limit their developing epistemic insight into how science, religion and the wider humanities relate. These findings prompted the construction of a framework for education for students aged 5–16 designed to encourage students’ expressed interest in big questions and develop their understanding of the ways that science interacts with other ways of knowing. The centrepiece of the framework is a sequence of learning objectives for epistemic insight, organised into three categories. The categories are, firstly, the nature of science in real world contexts and multidisciplinary arenas; secondly, ways of knowing and how they interact; and thirdly, the relationships between science and religion. Our current version of the Framework is constructed to respond to the way that teaching is organised in England. The key principles and many of the activities could be adopted and tailored to work in many other countries.     

Epistemic explanations for divergent evolution in discourses regarding students’ extended historical writing in England

In England, two concurrent but largely disconnected discourses have emerged whose representatives have promulgated initiatives relevant to students’ extended historical writing: genre theorists and the history teachers’ ‘extended writing movement’. Despite certain goals held in common, the two discourses have tended to talk past one another resulting in wastage, incoordination and replication in resourcing. One reason for these divergent discourses is that inter-discursive communication is difficult owing to epistemic differences regarding what the curricular goals regarding students’ extended historical writing should be. Using Bernstein’s model for the production of pedagogic knowledge as an interpretative framework, first I explain these discourses’ differing curricular conceptions by characterizing it as a tension between contrasting emphases on ‘recontextualization’ and ‘reproduction’ of academic knowledge. Second, as a representative of the extended writing movement, I offer a theoretical critique of genre theorists’ greater concentration on the field of reproduction. Third, I situate these developments in England in an international context by briefly comparing them to trends in the United States. Finally, I argue that these epistemic tensions regarding curricular goals matter and need to be resolved. Otherwise, the recommendations of the representatives of both discourses are destined to appeal to only limited audiences.     

TEACHERS’ KNOWLEDGE OF THE CONCEPT OF A FUNCTION: A THEORETICAL FRAMEWORK

In order to teach mathematics effectively, mathematics teachers need to have a sound mathematical knowledge, but what constitutes sound mathematical knowledge for teaching is subject to debate. This paper is an attempt to unpack what constitutes teacher knowledge of the concept of a function which is a unifying idea in the mathematics curriculum. The central components of the framework, which will be elaborated on in this paper, are: teachers’ subject matter knowledge, teachers’ pedagogical content knowledge, teachers’ technological pedagogical knowledge, technological content knowledge, and technological pedagogical content knowledge in relation to the concept of a function. The framework is informed by Shulman’s (Educational Researcher 15:4–14, 1986) Types of Teachers Knowledge Framework, Ball, Bass & Hill 29:14–17, 20–22, 43–46 (2005) Mathematical Knowledge for Teaching Framework, and Mishra & Koehler’s (Teachers College Record 108:1017–1054, 2006) Technological Pedagogical Content Knowledge (TPACK) framework.     

Teachers’ perceptions of effective teaching: a comparative study of elementary school teachers from China and the USA

This international study investigated Chinese and American elementary school teachers’ perceptions of effective teaching. The sample comprised Chinese (n?=?108) and US (n?=?110) participating teachers. The Effective Teaching Quality Survey (ETQS) was adopted for this comparative education research, an instrument that operationalized Stronge’s effective teaching theoretical framework. Research questions that guided this study were as follows: (1) what are the differences between the USA and China’s elementary school teachers’ perceptions regarding effective teaching? And (2) when comparing teaching experience, school location, and effective/ineffective teachers, what are the differences between the USA and China’s elementary school teachers’ perceptions on effective teaching? Statistically significant results were found when comparing nationality, teaching experience, school location, and effective/ineffective teaching. How these results related to the US and Chinese educational contexts with respect teaching and learning are discussed.     

Promoting elementary students’ epistemology of science through computer-supported knowledge-building discourse and epistemic reflection

This study examined the role of computer-supported knowledge-building discourse and epistemic reflection in promoting elementary-school students’ scientific epistemology and science learning. The participants were 39 Grade 5 students who were collectively pursuing ideas and inquiry for knowledge advance using Knowledge Forum (KF) while studying a unit on electricity; they also reflected on the epistemic nature of their discourse. A comparison class of 22 students, taught by the same teacher, studied the same unit using the school’s established scientific investigation method. We hypothesised that engaging students in idea-driven and theory-building discourse, as well as scaffolding them to reflect on the epistemic nature of their discourse, would help them understand their own scientific collaborative discourse as a theory-building process, and therefore understand scientific inquiry as an idea-driven and theory-building process. As hypothesised, we found that students engaged in knowledge-building discourse and reflection outperformed comparison students in scientific epistemology and science learning, and that students’ understanding of collaborative discourse predicted their post-test scientific epistemology and science learning. To further understand the epistemic change process among knowledge-building students, we analysed their KF discourse to understand whether and how their epistemic practice had changed after epistemic reflection. The implications on ways of promoting epistemic change are discussed.     

Dialogical argumentation in elementary science classrooms

To understand students’ argumentation abilities, there have been practices that focus on counting and analyzing argumentation schemes such as claim, evidence, warrant, backing, and rebuttal. This analytic approach does not address the dynamics of epistemic criteria of children’s reasoning and decision-making in dialogical situations. The common approach also does not address the practice of argumentation in lower elementary grades (K–3) because these children do not master the structure of argumentation and, therefore, are considered not ready for processing argumentative discourse. There is thus little research focusing on lower elementary school students’ argumentation in school science. This study, drawing on the societal-historical approach by L. S. Vygotsky, explored children’s argumentation as social relations by investigating the genesis of evidence-related practices (especially burden of proof) in second- and third-grade children. The findings show (a) students’ capacity for connecting claim and evidence/responding to the burden of proof and critical move varies and (b) that teachers play a significant role to emphasize the importance of evidence but experience difficulties removing children’s favored ideas during the turn taking of argumentative dialogue. The findings on the nature of dialogical reasoning and teacher’s role provide further insights about discussions on pedagogical approaches to children’s reasoning and argumentation.     

An alienation-based framework for student experience in higher education: new interpretations of past observations in student learning theory

This article orients a recently proposed alienation-based framework for student learning theory (SLT) to the empirical basis of the approaches to learning perspective. The proposed framework makes new macro-level interpretations of an established micro-level theory, across three levels of interpretation: (1) a context-free psychological state (alienation), (2) a context-bound psychological state (student alienation), and (3) sociological processes from which these psychological states arise. Evidence for the viability of this macro–micro framework is, however, lacking, as is a clear path to seeking such evidence due to the framework’s complexity. The dichotomy of state and process implied by the framework reflects a recognised ‘dual interpretation’ of alienation, by which micro-level experiences are linked to behaviours through mediating macro-level psychological states. We use this dual interpretation together with Seeman’s (Ann Rev Sociol, 1975) six variants of alienation to construct a clear and well-ordered overall framework, and to hypothesize comprehensive explanations for the correlations observed between surface approaches to learning and five dimensions of learning experience emphasized in SLT. These five hypotheses are presented as succinct if…then statements, and assessed according to established qualitative criteria. Overall, the article prepares the way both for empirical verification of what is a complex theoretical structure, and for other future research in this vein.     

Ready,steady, learn: school readiness and children’s voices in English early childhood settings

Internationally, school readiness is increasingly the rationale for early childhood education and care (ECEC). This is the case in England, yet the statutory English Early Years Foundation Stage framework for children 0–5 years also requires practitioners to listen to children’s voices: discourse indicates dissonance between school readiness and listening to children’s voices so this paper discusses an intrinsic case study that investigated beliefs and practices of 25 practitioners in the English midlands regarding school readiness and listening to children’s voices. In survey responses and semi-structured interviews, practitioners indicated they listen to – and act on – children’s voices but are confused about school readiness; their beliefs and practices align more strongly with social pedagogy than pre-primary schoolification. Findings carry messages for policy-makers regarding the need for coherent policy concerning the purpose of ECEC, with practitioner training and a framework aligned fully with that policy. A larger study is indicated.     

An Analysis of Teacher Discourse that Introduces Real Science Activities to High School Students

Most academic science educators encourage teachers to provide their students with access to more authentic science activities. What can and do teachers say to increase students’ interests in participating in opportunities to do real science? What are the discursive resources they draw on to introduce authentic science to students? The purpose of this ethnographic and discourse-analytic study is to investigate the ways in which the activities of scientists are discursively presented to high school students in a biology/career preparation course. Data sources were collected by means of observation, field notes, interviews, and videotaped lessons in an eleventh-grade biology/career preparation course. Drawing on discourse analysis, we investigate the discursive resources—or, more specifically and technically, the interpretative repertoires—teachers used to explain and promote opportunities to engage students in real science activities. Our analysis identifies and characterizes six types of interpretative repertoires: specialized, a-stereotypical, relevant, empirical, emotive, and rare-opportunity. To better understand the “big picture” of how these discursive resources are drawn on in the classroom, we also report on the frequencies of the repertoires in the discourse and the ways in which repertoires changed in the course of teacher-student interactions. The findings of this case study offer teachers and researchers with a better understanding of how specific forms of discourse—i.e., the repertoires—can serve as resources to enhance teacher-introduction of authentic science to students and provide students a bridge between school and authentic science.     

Identifying Essential Epistemic Heuristics for Guiding Mechanistic Reasoning in Science Learning

Mechanistic reasoning, or reasoning systematically through underlying factors and relationships that give rise to phenomena, is a powerful thinking strategy that allows one to explain and make predictions about phenomena. This article synthesizes and builds on existing frameworks to identify essential characteristics of students’ mechanistic reasoning across scientific content areas. We argue that these characteristics can be represented as epistemic heuristics, or ideas about how to direct one’s intellectual work, that implicitly guide mechanistic reasoning. We use this framework to characterize middle school students’ written explanatory accounts of two phenomena in different science content areas using these heuristics. We demonstrate evidence of heuristics in students’ accounts and show that the use of the heuristics was related to but distinct from science content knowledge. We describe how the heuristics allowed us to characterize and compare the mechanistic sophistication of account construction across science content areas. This framework captures elements of a crosscutting practical epistemology that may support students in directing the construction of mechanistic accounts across content areas over time, and it allows us to characterize that progress.     

Children’s epistemic reasoning about social inclusion of aggressive peers in a culturally diverse school

Moral reasoning in values education can promote a democratic way of life. It involves addressing behaviour expectations in responses to violence or bullying. There is increasing interest in how children make moral judgments about social inclusion within diverse cultural settings. Critical research highlights the relationship between epistemic cognition (views about the nature of knowledge and knowing) and reasoning. In this paper, we argue that this relationship is likely to be important in reasoning about moral values for inclusion in culturally diverse schools. However, we know little about how children in diverse educational settings reason about and enact school values for inclusion. Our study addresses this gap by examining primary school children’s epistemic reasoning about the social inclusion of peers with a focus on justifications for inclusion/exclusion of aggressive peers. Twenty-six children (10–11 years old) from one culturally diverse school community in Australia were asked to illustrate (drawings) and reflect on (15–20 minute interviews) a conflict situation involving exclusion from play. The findings showed that most children reasoned about including/excluding others based on a ‘one right answer’ pattern which reflected an explicit focus on following the school rules. Fewer children moved ‘beyond right answers’ to show transition towards perceiving multiple perspectives in their reasoning about inclusion/exclusion. Implications for values education are discussed.     

A theoretical framework towards understanding of emotional and behavioural difficulties

Children’s emotional and behavioural difficulties are the result of multiple individual, social and contextual factors working in concert. The current paper proposes a theoretical framework to interpret students’ emotional and behavioural difficulties in schools, by taking into consideration teacher–student relationships, students’ social and emotional skills and classroom context. Based on Bronfenbrenner’s bioecological model, according to which process, person and context are the main sources of children’s development, the current paper combines three theoretical approaches: firstly, in terms of process, the systems communication approach referring to teacher–students’ relationships; secondly, in terms of person, the Social and Emotional Learning, which refers to children’s social and emotional competences and skills; and thirdly, in terms of classroom context, the achievement goal theory, with emphasis on mastery classroom goal structure. The derived framework provides a means to capture the dynamic multidimensional process through which emotional and behavioural difficulties arise. This perspective provides educators with a comprehensive theoretical and practical preventative tool for emotional and behavioural difficulties.     

Determinism and Underdetermination in Genetics: Implications for Students’ Engagement in Argumentation and Epistemic Practices

In the last two decades science studies and science education research have shifted from an interest in products (of science or of learning), to an interest in processes and practices. The focus of this paper is on students’ engagement in epistemic practices (Kelly in Teaching scientific inquiry: Recommendations for research and implementation. Sense Publishers, Rotterdam, pp 99–117, 2008), or on their practical epistemologies (Wickman in Sci Educ 88(3):325–344, 2004). In order to support these practices in genetics classrooms we need to take into account domain-specific features of the epistemology of genetics, in particular issues about determinism and underdetermination. I suggest that certain difficulties may be related to the specific nature of causality in genetics, and in particular to the correspondence between a given set of factors and a range of potential effects, rather than a single one. The paper seeks to bring together recent developments in the epistemology of biology and of genetics, on the one hand, with science education approaches about epistemic practices, on the other. The implications of these perspectives for current challenges in learning genetics are examined, focusing on students’ engagement in epistemic practices, as argumentation, understood as using evidence to evaluate knowledge claims. Engaging in argumentation in genetics classrooms is intertwined with practices such as using genetics models to build explanations, or framing genetics issues in their social context. These challenges are illustrated with studies making part of our research program in the USC.     

Concept Formation in Biology: The Concept ‘Growth’

Summaries

English

A concept is understood here as a logic core, which is surrounded by an associative framework, to which also the name of the concept belongs. The logic core is a pattern of properties of a class of things, which is invariant to individual objects of the class as well as to the observer. The pattern is determined by logic relations, which are constituents of the epistemic structure of the learner.

In this article an analysis of the situation concerning the concept ‘growth’ is carried out. The logic core of the concept is theoretically investigated by means of systems theory and is empirically tested by means of free definitions. The associative framework, however, is determined by means of free association tests.

It is shown that in the course of school education a marked shift takes place in the logic core as well as in the associative framework from a ‘growth in terms of geometric dimension’ towards a ‘growth in terms of particle numbers’.     

A Role for Epistemic Insight in Attitude and Belief Change? Lessons from a Cross-curricular Course on Evolution and Creation

This paper presents findings from a quasi-experimental study evaluating future teachers’ attitudes and beliefs in response to a cross-curricular university course on evolution and creation bridging biological and Christian theological perspectives. Based on previous findings, we hypothesized that a course providing learning opportunities for epistemic insight within this multidisciplinary arena might have effects on attitudes and beliefs relevant to the field. Hence, the main research question was the following: To what extent do student teachers’ attitudes and beliefs change by attending a cross-curricular course on evolution and creation intended to develop student teachers’ epistemic insight into the nature of science and into the relationship between science and theology? The answer from this quasi-experimental evaluation study (pre–post-design; test group n =?26, control group n =?24) is as follows: It depends upon the variable investigated! Pre–post-analysis using a repeated measures ANOVA revealed that the cross-curricular course integrating epistemic insight induced changes in creationist beliefs, in students’ perception of conflict, and in acceptance of evolution. In contrast, there was no effect on attitudes toward evolutionary theory, on attitudes toward the Biblical accounts of creation, or on scientistic beliefs. However, when student responses were analyzed individually, case-based evidence for belief change in students with scientistic positions emerged. Among the reasons for those different effects, we discuss conceptual differences between attitude and acceptance, features of the student teacher sample, and the particular content of the course explicitly addressing creationism but not scientism. In conclusion, the paper corroborates the role of epistemic insight in the multidisciplinary field of evolution and creation and provides initial evidence that epistemic insight possesses a particular potential concerning positions at both ends of the spectrum.     

The Elusive Slope

In understanding upper secondary school students’ interpretations of information in graphical representations of a distance–time graph and an ECG graph, little attention has been paid to the analysis of the condition of the conceptual development related to their utterances. Understanding this better can help improve the teaching of interpretations of information in graphical representations of different situations. This paper integrates results from 2 studies and 3 theoretical perspectives: Tall and Vinner’s theoretical perspectives on learning, Chi’s ontological perspectives on conceptual development and Friel’s theoretical perspectives on interpretation of graphical information. The findings provide evidence to support the conjecture that iconic interpretations could be stimulated and generated as a result of student categorisation of a distance–time graph as an event, when in fact the graph is being used to describe and communicate a process. The outcome further indicates that students found a resemblance between the ECG diagram and the periodic function of f(x) = sin(x).     

Feelings on feedback: Children’s emotional responses during mathematics problem solving

Theories of learning emphasize the importance of both the cognitive and affective state of the learner. The current study focused on children’s affective reactions to corrective feedback during mathematics problem solving. Eighty-seven elementary school children (M age = 7.6 years, 41% female, 68% White) solved mathematical equivalence problems during an online video call and received trial-by-trial feedback on their answers. Trained researchers used children’s facial expressions, tone of voice, and verbal statements to quantify their positive and negative affect on each trial. Overall, children tended to express more positive affect than negative affect. However, negative affect was more prominent when the child was incorrect and received negative feedback, and higher negative affect was associated with lower accuracy and lower persistence on the task. These results provide novel empirical evidence for the role of emotions during children’s STEM learning in a non-evaluative context.