Self-explanation in the domain of statistics: an expertise reversal effect

This study investigated the effects of four instructional methods on cognitive load, propositional knowledge, and conceptual understanding of statistics, for low prior knowledge students and for high prior knowledge students. The instructional methods were (1) a reading-only control condition, (2) answering open-ended questions, (3) answering open-ended questions and formulating arguments, and (4) studying worked-out examples of the type of arguments students in the third group had to formulate themselves. The results indicate that high prior knowledge students develop more propositional knowledge of statistics than low prior knowledge students. With regard to conceptual understanding, the results indicate an expertise reversal effect: low prior knowledge students learn most from studying worked-out examples, whereas high prior knowledge students profit most from formulating arguments. Thus, novice students should be guided into the subject matter by means of worked-out examples. As soon as students have developed more knowledge of the subject matter, they should be provided with learning tasks that stimulate students to solve problems by formulating arguments.     

Task-dependent construction of mental models as a basis for conceptual change

Learning can be seen as a task-oriented process which often requires the reorganization of existing knowledge, usually referred to as conceptual change. This paper describes a theoretical framework for the analysis of conceptual change that considers conceptual knowledge as a generative cognitive tool for the creation of more specific mental representations — propositional symbolic structures and analog mental models. According to this view, conceptual change is based on a task-oriented interaction between these different kinds of mental representations. The assumption is made that it is possible to foster conceptual change by presenting to students well-defined tasks that stimulate the construction of elaborated mental models as well as an intensive interaction between these models and the corresponding propositional representations. In order to test this assumption an empirical study was conducted, in which subjects had to express their prior knowledge about a complex subject matter from the field of geography (time differences on the earth), which contained various conceptual deficits. The subjects were then randomly assigned to different groups who received the same learning material but had to solve different learning tasks requiring differently structured mental models. Afterwards, the subjects were asked to express their knowledge about the subject matter again and were tested for understanding with a comprehension test. The results support the view that a task-oriented interaction between propositional structures and mental models can help learners to evaluate the consistency of their conceptual knowledge. Accordingly, conceptual deficits result in the formation of mental models with an inadequate structure. Such deficits can be detected if the respective model is used in a sufficiently variable way, whereas they can remain unnoticed if it is used in a limited manner.     

The Effect of Guidance in Problem-Based Learning of Statistics

Contrary to classical problem-based learning, in guided problem-based learning, the learning goals are predetermined by the instructor—on the basis of a detailed decomposition of the subject matter to be studied—to activate prior knowledge and to structure self-study and subsequent group discussion. This study investigated the effects of classical problem-based learning and guided problem-based learning, for different prior knowledge levels, on perceived value and usefulness of the learning activity and on conceptual understanding of statistics. Participants randomly assigned 110 students to 10 problem-based learning groups, and subsequently, the 10 groups were allocated randomly to classical problem-based learning or guided problem-based learning. The results indicate that guided problem-based learning tends to enhance conceptual understanding of statistics more thanbreak; classical problem-based learning once students have some prior knowledge of the subject. Furthermore, guided problem-based learning tends to increase students’ awareness of the value and usefulness of the learning activity.     

Confidence in prior knowledge,self-efficacy,interest and prior knowledge: Influences on conceptual change

This study explored how confidence in prior knowledge, self-efficacy, interest, and prior knowledge interact in conceptual change learning. One hundred and sixteen college students completed an assessment of confidence in prior knowledge, self-efficacy, interest, prior scientific understanding, and prior misconceptions before reading a refutation text on seasonal change. Students’ misconceptions and scientific understanding of seasonal change was then assessed before and after reading a refutation text, and again at a two week delayed posttest. Three profiles of students emerged based on their confidence in prior knowledge, self-efficacy, interest, prior scientific understanding, and prior misconceptions. The profiles included: (1) Low (low confidence, self-efficacy, interest, and prior scientific understanding and high prior misconceptions), (2) mixed (high confidence, self-efficacy, and interest, but low prior scientific understanding and high prior misconceptions), and (3) high (high confidence, self-efficacy, interest, and prior scientific understanding and low prior misconceptions). Results indicated that the mixed profile appeared to be most productive for conceptual change and that learner characteristics most productive for conceptual change learning may differ from those most productive in other learning situations.     

The ability to understand and use conceptual change pedagogy as a function of prior content learning experience

This research examined the relationship between content instruction and the development of elementary teacher candidates' understanding of conceptual change pedagogy. Undergraduate students (n = 27) enrolled in two sections of a science methods course received content instruction through either traditional or conceptual change methods, followed by instruction about conceptual change pedagogy. Candidates were interviewed pre- and postinstruction about their content and pedagogical knowledge and also wrote conceptual change lessons. Twelve of the 27 subjects were videotaped teaching in the field. Results indicate that prior to instruction, most candidates had weak content knowledge and held traditional pedagogical conceptions. After instruction, students in the conceptual change group had significantly larger gains in their content knowledge than those in the traditional group, gave qualitatively stronger pedagogical responses, and used conceptual change strategies more consistently in practice. These results indicate that personal experience of learning science content through conceptual change methods facilitated the development of understanding and use of conceptual change pedagogy in teaching practice. Thus if conceptual change methods are to be incorporated into teacher candidates' repertoire, science content courses that students take prior to teacher education should be taught using conceptual change pedagogy. In addition, courses in science education should use pedagogy more in line with that taught in methods courses.     

Online or face-to-face? Students' experiences and preferences in e-learning

Which aspects of e-learning courses do students experience as being favorable for learning? When do students prefer online or face-to-face learning components? These questions were the subject of a research study in a sample of 2196 students from 29 Austrian universities. The students completed a questionnaire on their experiences attending an e-learning course, on their perceived achievements, and on their preferences for online or face-to-face learning components. Students appreciated online learning for its potential in providing a clear and coherent structure of the learning material, in supporting self-regulated learning, and in distributing information. They preferred face-to-face learning for communication purposes in which a shared understanding has to be derived or in which interpersonal relations are to be established. An especially important result concerns students' perceptions of their learning achievements: When conceptual knowledge in the subject matter or skills in the application of one's knowledge are to be acquired, students prefer face-to-face learning. However, when skills in self-regulated learning are to be acquired, students advocate online learning.     

INVESTIGATING THE EFFECTIVENESS OF INQUIRY-BASED INSTRUCTION ON STUDENTS WITH DIFFERENT PRIOR KNOWLEDGE AND READING ABILITIES

This study examined the differential impacts of an inquiry-based instruction on conceptual changes across levels of prior knowledge and reading ability. The instrument emphasized four simultaneously important components: conceptual knowledge, reading ability, attitude toward science, and learning environment. Although the learning patterns and effect size analyses indicated that students from all subgroups demonstrated substantial gains on weather concepts, students from the low prior conceptual knowledge group demonstrated greater gains in conceptual knowledge than subgroups with more prior knowledge; and these gains remained stable 3 weeks after the instruction ceased. However, students from the low language proficiency group showed the least gains in conceptual knowledge. Students’ prior knowledge and reading ability were found to be positively and significantly associated to conceptual development. Recent perspectives on the role of language in science education and suggestions that support learning during instruction are briefly described.     

The challenges of developing disciplinary knowledge and making links across the disciplines in early years and primary humanities

ABSTRACT

This article argues that an understanding of disciplinary knowledge production helps to underpin a conceptual structure for the humanities curriculum. This is important as a conceptual curriculum more overtly supports knowledge production for both pupils and teachers than one that is solely focused on propositional knowledge. It can mean the difference between learning isolated bits of information for recall that hold little significance to the learner and engaging with new information for a purpose. A concept orientated curriculum places an emphasis on understanding transferable ideas and principles, one in which deeper understanding or improved capability is the focus.     

Experimentation in biology lessons: guided discovery through incremental scaffolds

Experimentation is a complex problem-solving process. In biology lessons, experiments involve creative thinking and open discovery; however, they still require some degree of instructional guidance. The right balance between discovery learning and instructional guidance depends substantially on students’ prior knowledge. Students with low prior knowledge in particular might have difficulties with conducting and understanding experiments. Incremental scaffolds might be a valuable tool to meditate between pure discovery and strong guidance while simultaneously taking learners’ individual knowledge and skills into account. In the current study, we examined the effects of incremental scaffolds (IncSc), no scaffolds (NoSc), and worked-out examples (WoEx) on students’ knowledge acquisition while doing inquiry-based experimentation with a special focus on students with low prior knowledge. In a pre-posttest design, 193 students (M_age?=?13.02?±?0.81 years) participated in a four-hour teaching unit on animals’ overwintering strategies. In the pre- and posttest, we assessed the students’ conceptual and procedural knowledge. Our results partially confirmed our hypotheses: Regarding the conceptual and procedural knowledge of all students, incremental scaffolds showed no additional benefit regarding students’ knowledge in the posttest when compared to working with no scaffolds or worked-out examples. For the students with low prior knowledge, working with incremental scaffolds led to higher conceptual and procedural knowledge after the teaching unit than working with worked-out examples.     

Concept mapping in research on mathematical knowledge development: Background,methods, findings and conclusions

The theoretical background and different methods ofconcept mapping for use in teaching and in research on learning processes are discussed. Two mathematical projects, one on fractions and one on geometry, are presented in more detail. In the first one special characteristics of concept maps were elaborated. In the second one concept mapping allowed students' individual understanding to be monitored over time and provided information about students' conceptual understanding that would not have been obtained using other methods. Regarding the students' individual concept maps in more detail there were some additional findings: (i) The characteristics of the maps change remarkably from fourth grade to sixth grade; (ii) There is some evidence that prior knowledge related to some mathematical topics plays a very important role in students' learning behaviour and in their achievement; (iii) Concept maps provide information about how individual students relate concepts to form organised conceptual frameworks; (iv) Long-term difficulties with specific concepts are able to be traced. These findings are discussed with regard to results of other studies as well as to their implications for the teaching of mathematics in the classroom.     

The influence of prior knowledge on experiment design guidance in a science inquiry context

Designing and conducting sound and informative experiments is an important aspect of inquiry learning. Students, however, often design experiments that do not allow them to reach conclusions. Considering the difficulties students experience with the process of designing experiments, additional guidance in the form of an Experiment Design Tool (EDT) was developed, together with reflection questions. In this study, 147 pre-university students worked in an online inquiry learning environment on buoyancy and Archimedes’ principle. Students were randomly assigned to one of three conditions, each of which contained a different version of the EDT. Since students’ prior knowledge has been found to influence the amount and type of guidance they need, the versions of the tool differed with respect to the level of guidance provided. A pre- and post-test were administered to assess students’ conceptual knowledge. No overall differences between conditions were found. In a subsequent analysis, students were classified as either low, low-intermediate-, high-intermediate, or high prior knowledge students. For Archimedes’ principle we found that low-intermediate prior knowledge students gained significantly more conceptual knowledge than low prior knowledge students in the fully guided condition. It is hypothesised that students need at least some prior knowledge in order to fully benefit from the guidance offered.     

Conceptual change in mathematics: From rational to (un)real numbers

From an educational point of view, mathematics is supposed to have a completely hierarchical structure in which all new concepts logically follow from prior ones. In this article we try to show that there are also concepts in mathematics which are difficult to learn because of problematic continuity from prior knowledge to new concepts. We focus on the problems of conceptual change connected with the learning of calculus and the shift from rational to real numbers. We demonstrate the difficulty of this conceptual change with the help of historical and psychological evidence. In the empirical study 65 students of higher secondary school were tested after a 40 hour calculus course. In addition, 11 students participated in individual interview. According to the results the conceptual change from a discrete to a continuous idea of numbers seems to be difficult for students. None of the subjects had developed an adequate understanding of real numbers although they had learned to carry out algorithmic procedures belonging to calculus. We discuss how appropriate recent theoretical ideas on conceptual change are for explaining learning problems in this domain. Also some educational implications are presented.     

Fostering radical conceptual change through dual‐situated learning model

This article examines how the Dual‐Situated Learning Model (DSLM) facilitates a radical change of concepts that involve the understanding of matter, process, and hierarchical attributes. The DSLM requires knowledge of students' prior beliefs of science concepts and the nature of these concepts. In addition, DSLM also serves two functions: it creates dissonance with students' prior knowledge by challenging their epistemological and ontological beliefs about science concepts, and it provides essential mental sets for students to reconstruct a more scientific view of the concepts. In this study, the concept “heat transfer: heat conduction and convection,” which requires an understanding of matter, process, and hierarchical attributes, was chosen to examine how DSLM can facilitate radical conceptual change among students. Results show that DSLM has great potential to foster a radical conceptual change process in learning heat transfer. Radical conceptual change can definitely be achieved and does not necessarily involve a slow or gradual process. © 2004 Wiley Periodicals, Inc. J Res Sci Teach 41: 142–164, 2004     

Learning Using Dynamic and Static Visualizations: Students’ Comprehension, Prior Knowledge and Conceptual Status of a Biotechnological Method

The importance of biotechnology education at the high-school level has been recognized in a number of international curriculum frameworks around the world. One of the most problematic issues in learning biotechnology has been found to be the biotechnological methods involved. Here, we examine the unique contribution of an animation of the polymerase chain reaction (PCR) in promoting conceptual learning of the biotechnological method among 12th-grade biology majors. All of the students learned about the PCR using still images (n = 83) or the animation (n = 90). A significant advantage to the animation treatment was identified following learning. Students’ prior content knowledge was found to be an important factor for students who learned PCR using still images, serving as an obstacle to learning the PCR method in the case of low prior knowledge. Through analysing students’ discourse, using the framework of the conceptual status analysis, we found that students who learned about PCR using still images faced difficulties in understanding some mechanistic aspects of the method. On the other hand, using the animation gave the students an advantage in understanding those aspects.     

Understanding Possibilities and Limitations of Abstract Chemical Representations for Achieving Conceptual Understanding

When learning with abstract and scientific multiple external representations (MERs), low prior knowledge learners are said to have difficulties in using these MERs to achieve conceptual understanding. Yet little is known about what these limitations precisely entail. In order to understand this, we presented 101 learners with low prior knowledge of abstract scientific MERs to see (a) how many, and what kind of ideas (propositions) learners remembered from these MERs and (b) what the impact of these ideas is on conceptual understanding of the content. Propositional analysis indicates that learners created flawed internal representations. The discussion analyses the potentials that the learners have in using abstract representations to increase their understanding of scientific information and possible effects of instruction.     

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.     

Development and application of a two-tier diagnostic test measuring college biology students' understanding of diffusion and osmosis after a course of instruction

This study involved the development and application of a two-tier diagnostic test measuring college biology students' understanding of diffusion and osmosis after a course of instruction. The development procedure had three general steps: defining the content boundaries of the test, collecting information on students' misconceptions, and instrument development. Misconception data were collected from interviews and multiple-choice questions with free response answers. The data were used to develop 12 two-tier multiple choice items in which the first tier examined content knowledge and the second examined understanding of that knowledge. The conceptual knowledge examined was the particulate and random nature of matter, concentration and tonicity, the influence of life forces on diffusion and osmosis, membranes, kinetic energy of matter, the process of diffusion, and the process of osmosis. The diagnostic instrument was administered to 240 students (123 non-biology majors and 117 biology majors) enrolled in a college freshman biology laboratory course. The students had completed a unit on diffusion and osmosis. The content taught was carefully defined by propositional knowledge statements, and was the same content that defined the content boundaries of the test. The split-half reliability was .74. Difficulty indices ranged from 0.23 to 0.95, and discrimination indices ranged from 0.21 to 0.65. Each item was analyzed to determine student understanding of, and identify misconceptions about, diffusion and osmosis.     

Students’ Perceptions of Their Science Teachers’ Pedagogical Content Knowledge

Pedagogical content knowledge (PCK) is a type of teacher knowledge to be developed by a teacher. PCK is said to contribute to effective teaching. Most studies investigated the development of PCK and its influence on students’ learning from the teachers’ perspectives. Only a limited number of studies have investigated the components of science teachers’ PCK that helped students’ learning from the perspective of students. Thus, it is the aim of this study to investigate the level of science teachers’ PCK from students’ perspective, in particular whether or not students of different achieving ability had different views of teachers’ PCK in assisting their learning and understanding. Based on the PCK research literature, six components of PCK have been identified, which were as follows: (1) subject matter knowledge, (2) knowledge of teaching strategies, (3) knowledge of concept representation, (4) knowledge of teaching context, (5) knowledge of students, and (6) knowledge of assessment in learning science. A questionnaire consisting of 56 items on a five-point Likert-type scale were used for data collection from 316 Form Four students (16 years old). One-way analysis of variance revealed that the differences in science teachers’ PCK identified by students of different achieving abilities were statistically significant. Overall, students of various academic achieving abilities considered all the components of PCK as important. The low-achieving students viewed all the components of PCK as being less important compared to the high and moderate achievers. In particular, low-achieving students do not view ‘knowledge of concept representation’ as important for effective teaching. They valued the fact that teachers should be alert to their needs, such as being sensitive to students’ reactions and preparing additional learning materials. This study has revealed that PCK of science teachers should be different for high and low-achieving students and knowledge of students’ understanding plays a critical role in shaping teachers PCK.     

Student Learning Through Participation in Inquiry Activities: Two Case Studies in Teacher and Computer Engineering Education

The two case studies reported in this article contribute to a better understanding of how inquiry tasks and activities are employed as resourceful means for learning in higher professional education. An observation-based approach was used to explore characteristics of and challenges in students’ participation in collaborative inquiry activities in two first-year introductory courses in teacher and computer engineering education. The findings highlight that the students’ activities varied with regard to focus and structure and were shaped by the types of inquiry tasks, i.e. case analysis and project-based work, by how the inquiry process was guided and supported and the way the domain-specific knowledge resources and practices were introduced. An exploratory strategy and rather confined use of resources characterised the teacher education students’ inquiry, while collaborative programming, a trial-and-error approach and extensive use of external resources that of the engineering education students’. For the teacher students, the main challenge was to construct meaning of conceptual knowledge and to integrate different forms of knowledge as a lens for analysing practice. The computer engineering students experienced challenges with unpacking the underlying principles and knowledge black-boxed in the widely available resources. The article suggests that future research and curriculum designs should depart from a more refined understanding of inquiry as a learning means, by connecting inquiry activities to the specific knowledge domains, the type of tasks most suited to explore each of this domains and the challenges that may arise for students.