Inquiry-based science education: towards a pedagogical framework for primary school teachers

Inquiry-based science education (IBSE) has been promoted as an inspiring way of learning science by engaging pupils in designing and conducting their own scientific investigations. For primary school teachers, the open nature of IBSE poses challenges as they often lack experience in supporting their pupils during the different phases of an open IBSE project, such as formulating a research question and designing and conducting an investigation. The current study aims to meet these challenges by presenting a pedagogical framework in which four domains of scientific knowledge are addressed in seven phases of inquiry. The framework is based on video analyses of pedagogical interventions by primary school teachers participating in open IBSE projects. Our results show that teachers can guide their pupils successfully through the process of open inquiry by explicitly addressing the conceptual, epistemic, social and/or procedural domain of scientific knowledge in the subsequent phases of inquiry. The paper concludes by suggesting further research to validate our framework and to develop a pedagogy for primary school teachers to guide their pupils through the different phases of open inquiry.     

Episodic Memory: A Neglected Phenomenon in the Psychology of Education

Contemporary educational psychology has employed models of procedural and semantic (or declarative) memory, but generally it has ignored a third form of memory (i.e., episodic memory) thought by some (e.g., Tulving, 1983,1985) to be especially important for explications of human functioning. Tulving's (1983,1985) ternary theory of memory is presented, with emphasis given to the acquisition, representation, and expression of knowledge in episodic memory. I argue that studies of pupils' episodic memories, their characteristics, and their functions may enhance the power and relevance of educational psychology with respect to understanding how pupils learn from instruction in classroom contexts. A conceptual framework and possible strategies for the conduct of instructional research are described that consider pupils' episodic memories as important mediating variables in learning from teaching.     

Educating teachers about managing classrooms and students

The author defines instruction, classroom management, student socialization, and disciplinary intervention as functions commonly performed by teachers, and suggests guidelines for educating teachers in the latter three functions. A knowledge base reflecting established scientific findings exists to inform teacher education concerning classroom management. No such knowledge base exists concerning student socialization and disciplinary intervention, but principles reflecting a consensus of expert opinion can be identified. The author argues for sustained focus on a single integrated approach, taught as an action system that includes attention not only to propositional knowledge (concerning principles of effective management) but also to procedural knowledge (of how to implement these principles) and conditional knowledge (of when and why to implement them). Other recommended elements include conceptual change teaching designed to confront and correct inappropriate attitudes or beliefs that students may bring with them; emphasizing the basics by concentrating on the most commonly occurring classroom teaching situations; and developing skills as much as possible through the apprenticeship approach (modeling, coaching, scaffolding/fading) but supplementing this as needed with didactic instruction in basic concepts and skills, structured classroom observation and student teaching experiences, and use of case materials and simulation exercises as substitutes for field experiences that cannot be included in the program.     

The contribution of domain-specific knowledge in predicting students' proportional word problem-solving performance

This study explored the extent to which domain-specific knowledge predicted proportional word problem-solving performance. We tested 411 seventh-grade students on conceptual and procedural fraction knowledge, conceptual and procedural proportion knowledge, and proportional word problem solving. Multiple regression analyses indicated that all four domain-specific knowledge variables (i.e., conceptual and procedural fraction knowledge, conceptual and procedural proportion knowledge) significantly predicted proportional word problem-solving performance. Conceptual fraction and procedural proportion knowledge contributed the most unique variance (10.0 and 6.7%, respectively, of the total variance) to proportional word problem solving. Procedural fraction and conceptual proportion knowledge each also contributed significant unique variance to proportional word problem solving explaining 5.6 and 2.8%, respectively. The results support the notion that both conceptual fraction and proportion knowledge and procedural fraction and proportion knowledge play a major role in understanding individual differences in proportional word problem-solving performance to inform interventions.     

Unintended knowledge learnt in primary science practical lessons

This study explored the different kinds of unintended learning in primary school practical science lessons. In this study, unintended learning has been defined as student learning that was found to occur that was not included in the teachers learning objectives for that specific lesson. A total of 22 lessons, taught by five teachers in Korean primary schools with 10- to 12-year-old students, were audio-and video recorded. Pre-lesson interviews with the teachers were conducted to ascertain their intended learning objectives. Students were asked to write short memos after the lesson about what they learnt. Post-lesson interviews with students and teachers were undertaken. What emerged was that there were three types of knowledge that students learnt unintentionally: factual knowledge gained by phenomenon-based reasoning, conceptual knowledge gained by relation- or model-based reasoning, and procedural knowledge acquired by practice. Most unintended learning found in this study fell into the factual knowledge and only a few cases of conceptual knowledge were found. Cases of both explicit procedural knowledge and implicit procedural knowledge were found. This study is significant in that it suggests how unintended learning in practical work can be facilitated as an educative opportunity for meaningful learning by exploring what and how students learnt.     

Pre-service Physics Teachers and Conceptual Difficulties on Temperature and Heat

In this article the ‘lesson preparation method’ was used to investigate pre-service teachers’ pedagogical content knowledge, in particular their knowledge of pupils’ conceptual difficulties on temperature and heat. A relation is found between the conceptual difficulties pre-service teachers expect their pupils to have and the conceptual difficulties they themselves have or have had. The discussion considers what pedagogical content knowledge teacher educators should include in the initial or inservice teacher education curriculum.     

Conceptual and procedural approaches to mathematics in the engineering curriculum: views of qualified engineers*

The research interest underpinning this paper concerns the type of mathematical knowledge engineering students may acquire during their specialised education in terms of the conceptual and procedural dimensions of doing and using mathematics. This study draws on interviews with 25 qualified engineers from South Africa and Sweden regarding their views on the role of mathematics in engineering education, with special focus on the conceptual and procedural aspects of mathematical knowledge. A thematic analysis of the interview data led to the identification of two main themes. According to the conceptual view a predominantly conceptual approach is needed and valued more than procedural skills, while the balanced view emphasises a balance of conceptual understanding and procedural fluency as well as links between them. It is suggested that the mathematical education of engineers would need to be more conceptually oriented to prepare for the demands at the workplace.     

Group work in primary school science: discussion,consensus and guidance from experts

Research suggests potential problems when group work is used in school science to support the integrated acquisition of conceptual understanding and testing procedures. Yet integrated acquisition is promoted by current policy, and is a popular classroom strategy. Work by Howe et al. (Learning and Instruction 10 (2000) 361) indicates that the problems may be overcome if pupils: (a) discuss conceptual material in small groups and reach consensus; (b) subject consensual positions to guided empirical appraisal. The present paper reports a study with 9–12-year old pupils, which tests the proposal of Howe et al. using heat transfer as its topic, in contrast to the shadow size of Howe et al. In broad terms, the results are consistent with what Howe et al. report, although there are subtle differences in both outcome and process. Nevertheless, the similarities are such as to indicate a robust technique, with clear relevance to classroom practice. To facilitate application, the paper outlines what the technique requires in terms of group organisation and teacher support, and suggests that in both cases there is consistency with current practice.     

Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge?

This research analyses preservice teachers’ knowledge of fractions. Fractions are notoriously difficult for students to learn and for teachers to teach. Previous studies suggest that student learning of fractions may be limited by teacher understanding of fractions. If so, teacher education has a key role in solving the problem. We first reviewed literature regarding students’ knowledge of fractions. We did so because assessments of required content knowledge for teaching require review of the students’ understanding to determine the mathematics difficulties encountered by students. The preservice teachers were tested on their conceptual and procedural knowledge of fractions, and on their ability in explaining the rationale for a procedure or the conceptual meaning. The results revealed that preservice teachers’ knowledge of fractions indeed is limited and that last-year preservice teachers did not perform better than first-year preservice teachers. This research is situated within the broader domain of mathematical knowledge for teaching and suggests ways to improve instruction and student learning.     

Prospective teacher learning: recognizing evidence of conceptual understanding

This study examined prospective teachers’ (PSTs) ability to recognize evidence of children’s conceptual understanding of mathematics in three content areas before and after an instructional intervention designed to support this ability. It also investigates the role PSTs’ content knowledge plays in their ability to recognize children’s mathematical understanding. Results of content knowledge assessments administered at the beginning of the study revealed that content knowledge did seem to support PSTs’ analyses of children’s understanding when the child’s response demonstrated understanding or demonstrated a misconception. Content knowledge did not seem to support PSTs’ analyses of children’s procedural responses, as many PSTs with good content knowledge initially characterized procedural solutions as evidence of conceptual understanding. Similarly, content knowledge did not seem to support PSTs’ analyses of children’s responses with features commonly associated with understanding but not evidence of understanding. After the instructional intervention consisting of three multifaceted lessons in which PSTs examined many examples of student thinking, they showed improved ability to analyze responses with conceptual features and no evidence of conceptual understanding and responses demonstrating procedural knowledge. Results suggest that content knowledge is not sufficient for supporting PSTs’ analysis of children’s thinking, and that building activities such as the intervention into content courses may help develop this ability. Implications for teacher education programs and future research are considered.     

The Development and Evaluation of an Instrument to Assess the Attitudes of Public School Principals

This study examined the relationship among declarative, conceptual, and procedural knowledge in the acquisition of ruler measurement skills. Sixth-grade industrial arts students were taught how to use a ruler with one of two instructional methods; the fractional method was based on an understanding of fractions, whereas the line identification method required no understanding of fractions. Results indicated that the line identification method was superior overall to the fractional method, both for the initial acquisition as well as retention of skills. This superiority occurred for questions measuring understanding of fractions but not for ruler skills, indicating that students were able to use procedural knowledge to infer conceptual knowledge. Results are discussed in terms of several models of learning that address how declarative, conceptual, and procedural knowledge interact in the learning process.     

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’.     

Using manipulatives to support an embodied approach to learning trigonometry in a South African school: A case study

ABSTRACT

Multiple Intelligence Theory suggests that individuals perceive knowledge in eight different ways. This article reports on a study that explored the role of manipulatives in the teaching and learning of trigonometric ratios in grade 10. The approach attempts in addressing three domains of the Multiple Intelligence Theory (linguistic/verbal intelligence, logical/mathematical intelligence and spatial intelligence). The foundation of this research was a case study contained in the interpretative paradigm involving five grade 10 mathematics pupils at a high school in South Africa. The data was collected from: (1) activity sheet containing written responses of pupils; (2) observations; and (3) semi-structured interviews. The data was analysed and it was found that the use of manipulatives in teaching and learning mathematics played a positive role in leaners understanding of trigonometric ratios at grade 10 level. In general the findings of this study supported other research findings that confirm that manipulatives were important mediating tools in the development of conceptual and procedural understanding of mathematical concepts. Besides these pedagogical implications the study proved that the manipulatives effectively consolidated the features of Lesh's model.     

Examining the effects of writing on conceptual and procedural knowledge in calculus

It has been claimed that writing to learn mathematics (WTLM) may benefit students' conceptual understanding as well as their procedural ability. To investigate this claim, we collected data from students in two sections of an introductory calculus course. In one of the sections, students used WTLM activities and discussed the activities after completing the writing; in the other section, students used similar activities that did not involve writing but engaged them in thinking about the mathematical ideas and in discussing the activities. The errors from the in-class and final exams of both groups of students were categorized and analyzed for information about the students' conceptual and procedural understanding. We found no significant differences between the WTLM group and the non-writing group, which suggests that the real benefit from writing activities may not be in the actual activity of writing, but rather in the fact that such activities require students to struggle to understand mathematical ideas well enough to communicate their understanding to others. This revised version was published online in July 2006 with corrections to the Cover Date.     

Examining the relation between whole numbers and fractions: A meta-analytic structural equation modeling approach

With a Meta-Analytic Structural Equation Modeling approach, we investigated the role of whole-number knowledge on fraction performance, accounting for domain-general skills, age, and mathematics-difficulty status. We conducted analyses based on 6,096 students from 39 independent samples within 29 studies. Findings suggested conceptual whole-number knowledge emerged as a significant and stable predictor of conceptual and procedural fraction knowledge. More importantly, students experiencing mathematics difficulty demonstrated a distinct pattern of performance compared to typically-achieving students, including: conceptual whole-number knowledge had lesser impacts on conceptual fraction knowledge; procedural whole-number knowledge had greater impacts on procedural fraction knowledge; and working memory and fluid intelligence made fewer contributions to fraction knowledge.     

The PISA Tasks: Unveiling Prospective Elementary Mathematics Teachers’ Difficulties with Contextual,Conceptual, and Procedural Knowledge

The aim of this mixed methods study was to investigate the difficulties prospective elementary mathematics teachers have in solving the Programme for International Student Assessment (PISA) 2012 released items. A mathematics test consisting of 26 PISA items was administered, followed by interviews. Multiple data were utilized to provide rich insights into the types of mathematical knowledge that a particular item requires and prospective teachers’ difficulties in using these knowledge types. A sample of 52 prospective teachers worked the mathematics test, and 12 of them were interviewed afterwards. The data-sets were complementary: the quantitative data showed that PISA items could be categorized under contextual, conceptual, and procedural knowledge and indicated the most frequent difficulties in the combined contextual, conceptual, and procedural knowledge items. The qualitative data revealed that few prospective teachers could give mathematical explanations for conceptual knowledge items, and that their contextual knowledge was fragmented. Educational implications were discussed.     

A modified refutation text design: effects on instructional efficiency for experts and novices

Recently, cognitive load theory has been considered within conceptual change research. Although the effectiveness of refutation texts (RT) has been proven, the conceptual change process involved and the influencing factors remain unclear. To contribute to this research, we investigate the efficiency of pupils working with a modified RT design in which the alternative and scientific conceptions are not explicitly contrasted, and we examine the level of learner expertise as a possible influencing factor. We investigated the efficiency based on the scientific conceptions learned and the mental effort invested (reflecting cognitive load) during instruction (N = 195, 9th graders). Only pupils with high prior knowledge (experts) showed low efficiency and higher mental effort when dealing with alternative conceptions. Our results indicate that the experts did not profit from the mental effort they invested in the learning process, whereas the novices seemed to profit from their invested mental effort.     

Is There a Role for Executive Functions in the Development of Mathematics Ability?

ABSTRACT— This article examines the role of working memory, attention shifting, and inhibitory control executive cognitive functions in the development of mathematics knowledge and ability in children. It suggests that an examination of the executive cognitive demand of mathematical thinking can complement procedural and conceptual knowledge-based approaches to understanding the ways in which children become proficient in mathematics. Task analysis indicates that executive cognitive functions likely operate in concert with procedural and conceptual knowledge and in some instances might act as a unique influence on mathematics problem-solving ability. It is concluded that consideration of the executive cognitive demand of mathematics can contribute to research on best practices in mathematics education.     

Beyond Accountability and Average Mathematics Scores: Relating State Education Policy Attributes to Cognitive Achievement Domains

We found moderate correlations among four policy attributes (consistency, specificity, authority, and power), which suggest that in many states, at least in design, standards-based reform is working as advocates imagined—aligned content standards and assessments established, backed up by detailed guidelines and frameworks, incentivized by rewards and sanctions, and supported with extra resources and programs for struggling students and their teachers. Our findings suggest that specificity and authority may be related to improvements in procedural knowledge, and no change in problem solving or conceptual understanding, while power (accountability) may be associated with a small decrease in all types of learning. We found that disadvantaged students showed gains in procedural knowledge and did not lose ground in either conceptual understanding or problem solving. Implications for developing an improved theory of policy effects on achievement are discussed.     

概念隐喻和抽象思维

Ritchie支持概念隐喻理论,反对Vervaeke ＆ Kenney提出的批评。虽然Ritchie修正了概念隐喻理论,但他始终坚持抽象思维主要依赖体验经验的隐喻投射的观点。Ritchie的观点存在着简化论的危险,极为错误地表达了抽象思维．和不能解释概念隐喻理论通常预设的有意义的认知现象。我们提出了一个对普遍存在的映射（例如空间关系映射到其它领域）的更认知的解释,以代替依赖体验经验的解释。我们的解释非常符合Ritchie提到的程序知识和相似性。Ritchie主张把概念融合理论作为概念隐喻理论的基础,但概念融合理论并不能如他所愿产生足够的解释力。