Conceptual change and the learning of history

This paper examines conceptual change as found in the domain of history. It is argued that while history does not have central concepts in the same manner as the physical sciences, history does have alterantive frameworks which are at different levels of explanation. Causal explanations and structural explanations are considered and student personalization of structures is emphasized. It is concluded that conceptual change in history is in part due to difficulties in determining to which theoretical context a concept belongs.     

Children's knowledge of astronomy and its change in the course of learning

This study examined the nature of 5-, 6-, and 7-year-old children's (n = 113) knowledge of astronomy and the process of knowledge change during learning. Children's pre-existing knowledge was assessed by questions and drawing tasks. About half of the children were taught elementary concepts of astronomy in small groups and afterwards all participants’ knowledge was assessed again. Most children could be categorized as having fragmented astronomy knowledge and the proportion of non-scientific models first proposed by Vosniadou & Brewer [Vosniadou, S., & Brewer, W. F. (1992). Mental models of the Earth: A study of conceptual change in childhood. Cognitive Psychology, 24, 535–585] was no greater than could be expected by chance. Children seemed to acquire factual information rather easily and therefore early instruction should introduce the core facts related to the topics. Some children over-generalized new knowledge very easily, indicating that the materials used in teaching may promote the development of non-scientific notions and that those notions must be addressed promptly to avoid the development of coherent non-scientific models.     

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.     

Student restraints to reform: Conceptual change issues in enhancing students' learning processes

Considerable research has been published on students' alternative conceptions of science concepts and the means of addressing those alternative conceptions. However, few studies have been reported on students' conceptions of learning and consequent learning processes and attempts to change such conceptions and processes. Recent research has shown that students' beliefs can act as barriers to the implementation of educational reforms that aim to alter students' learning processes. In this study an interpretive methodology was employed by a teacher participant-observer to investigate barriers to students' adoption of an alternative referent for learning and its consequent learning strategies in a Grade 11 chemistry class. Student narratives suggest that both “cold” and “hot” contextual factors influenced students' willingness to adopt an alternative referent. The consideration of “hot” factors, including students' beliefs, trust of the teacher, and ownership of the change process, is necessary if such change is to be understood more fully. The value and difficulties of a teacher adopting this researcher's perspective are also explored.     

Beyond Conceptual Change: Using Representations to Integrate Domain-Specific Structural Models in Learning Mathematics

ABSTRACT— Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for promoting representational change across cognitive development. I provide an example of an integrated structural model that highlights the underlying cognitive structures that connect numbers, mathematical operations, and functions. The model emphasizes dynamic multiple representations that students can internalize within the number line and which lead to developing a dynamic mental structure. In teaching practice, the model focuses on a counting task format, which integrates a variety of activities, specifically addressing motor, visual, and verbal skills, as well as various types of learning transfer.     

Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions

This article describes sixth-grade students’ engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students were also able to generalize the fraction model and transfer it to a new situation. Analysis of the students’ work demonstrates that they made use of four fraction constructs—part-whole, operator, quotients, and ratio. The activities also revealed difficulties in the students’ knowledge of fractions, some of which were overcome in the process of organizing and mathematizing the problem.     

Erratum to: Effect of Current Electricity Simulation Supported Learning on the Conceptual Understanding of Elementary and Secondary Teachers

This study examined the impact of computer simulation and supported science learning on a teacher’s understanding and conceptual knowledge of current electricity. Pre/Post tests were used to measure the teachers’ concept attainment. Overall, there was a significant and large knowledge difference effect from Pre to Post test. Two interesting interactions were observed during the data analysis. The first was the difference between Elementary and Secondary teachers. Both groups had significant gains, with large effect sizes, but the Elementary teachers (Pre-Mean = 3.70, Post-Mean = 7.51) started lower and ended higher exhibiting a significantly larger gain than the Secondary teachers (Pre-Mean = 4.96, Post-Mean = 6.71). The second interaction was the impact of gender. Both groups showed significant gains, with large effect sizes, but females (Pre-Mean = 3.90, Post-Mean = 7.21) gained significantly more than males (Pre-Mean = 5.13, Post-Mean = 7.01). These results confirm that computer simulation supported science learning can have a positive effect on concept attainment in teachers.     

Conceptual change within dyadic interactions: the dance of conceptual and material agency

We offer a new approach to emergent knowledge in processes of conceptual change in dyadic interaction by drawing on Pickering’s (The Mangle of Practice, The University of Chicago Press, London, 1995) Mangle of Practice theory, which theorizes the emergence of new scientific knowledge as occurring due to material resistance and human accommodations to such resistance. We use Commognition (Sfard in Thinking as communicating, Cambridge University Press, New York, 2008), which conceptualizes learning as a change in discourse, and conceptual change as change in meta-discursive rules, to examine the interaction between several dyads working on proportional reasoning tasks. These dyads were selected for close scrutiny based on a large previous experimental study designed to examine the most productive constellation for pairing students of different levels with or without a hypothesis testing device. The Mangle helps us theorize the emergent, unpredictable aspects of learning and conceptual change. We provide three criteria for examining the productivity of the interaction: Availability of an alternative discourse (proportional vs. additive), Resistance of material/disciplinary agency and Positioning of students to make meta-discursive shifts. We discuss this model as an aid for monitoring and designing learning situations that enhance conceptual change.     

Conceptual change and anomalous data: A case study in the domain of natural sciences

Cognitive conflict has been proposed as a strategy to promote conceptual change. The history and philosophy of science have shown the importance of anomalous data to change scientific theories and to the progress of science. Often, scientists use anomalous data to develop new interpretations that lead to new conceptualizations and finally, to a deep conceptual change. To be aware of contradiction seems to be a first step in the process of conceptual change. A study to explore novice students responses to anomalous data has been carried out. Sixty nine ninth graders, fifty seven eleventh graders and sixty three twelfth graders participated in the study. A paper and pencil task about the origin of life on the Earth was designed. Subjects were divided into two conditions. In condition “A” only anomalous data were presented to the subjects. In condition “A+B”, both anomalous and confirmatory data were presented. Results indicated that younger students were less aware of contradiction than older students when both anomalous and confirmatory data were presented. However, no differences have been found among them when just anomalous data were presented (condition A). Twelfth graders were aware of contradiction in both conditions. Some students’ epistemological beliefs influenced their response to anomalous data. Although no conceptual change (weak or strong restructuring) was achieved, as it could be predicted by the low domain-specific knowledge of the subjects and the complexity of the topic, presenting anomalous data facilitated the achievement of the first steps of the conceptual change process.     

Working (and studying) day and night: Heterogeneous effects of working on the academic performance of full-time and part-time students

A growing number of students are working while in college and to a greater extent. Using nationally representative data from the 1997 National Longitudinal Survey of Youth, I analyze the effect of working on grades and credit completion for undergraduate students in the United States. Strategies to identify the causal relationship between working and academic performance include student-level fixed effects to control for permanent, unobserved characteristics that may affect both work and study intensity, and system GMM models to account for potentially endogenous relationships between working and academic performance that vary over time. I examine the consequences of working for heterogeneous subgroups, with a particular focus on differences between full-time and part-time students. I find no evidence that students’ grades are harmed by marginal work hours, but that full-time students complete fewer credits per term when increasing work.     

Conceptual change and killer whales: constructing ecological values for animals at the Vancouver Aquarium

Changes in the mode of presenting the killer whales within the aquarium required both marine mammal and interpretation staff to change their conceptions of the role and value of killer whale ‘performances’. The process of change that staff underwent is similar to, and can be facilitated by understanding of, conceptual change processes among learners of science. Similar constructivist strategies of conceptual challenge can guide the staff's interaction with visitors, as an attempt is made to help visitors see the ecological relationships of wild and captive killer whales.     

The Mechanism of Vision: Conceptual Similarities between Historical Models and Children’s Representations

James Wandersee asked in 1986: ‘Can History of Science help science educators anticipate students’ misconceptions?. This paper aims to answer the same question by attempting a comparative bibliographical study between the assumptions of early philosophers and the conceptions of children relating to the roles of light and the eye in the process of vision. The results indicate remarkable similarities, which are analysed as to their nature and origin. The conclusions underline the significant role of the history of science as a rich bank of ideas for the design of educational material. Additionally, implications for educational research are discussed.