The effectiveness of using incorrect examples to support learning about decimal magnitude

Comparing common mathematical errors to correct examples may facilitate learning, even for students with limited prior domain knowledge. We examined whether studying incorrect and correct examples was more effective than studying two correct examples across prior knowledge levels. Fourth- and fifth-grade students (N = 74) learned about decimal magnitude in a brief tutoring session. Students were randomly assigned to two conditions: 1) comparing correct and incorrect examples (incorrect condition) or 2) comparing correct examples only (correct condition). The incorrect condition helped students learn correct procedures and key concepts more than the correct condition, including reducing misconceptions. Students’ prior knowledge of decimals did not interact with condition. Students’ explanations during the intervention revealed that those in the incorrect condition more frequently discussed correct concepts (e.g., the magnitude of a decimal and identifying misconceptions). Overall, contrasting incorrect examples with correct examples can help students learn correct concepts and procedures.     

The representation of fraction magnitudes and the whole number bias reconsidered

Two experiments investigated the whole number bias in the representation of fraction magnitudes with adults. A fraction magnitude comparison task was used where half of the comparisons were consistent with whole number ordering and the other half were not. Distance effects were found in Experiment 1 indicating that participants were comparing the magnitude of the whole fraction rather than just the parts. However, accuracy and response time also depended on the comparisons' consistency with whole number ordering. Experiment 2 manipulated the distance between the fraction pairs and showed that the whole number effect was strongest when the distance between the fraction pairs was very small. The results suggest that even skilled adults do not always have direct access to a fraction's magnitude on the number line. When the magnitudes are especially close together, adults may rely on alternative implicit or explicit strategies, such as examining the whole number parts, to evaluate the comparison.     

Kuhn and conceptual change: on the analogy between conceptual changes in science and children

This article argues that the analogy between conceptual changes in the history of science and conceptual changes in the development of young children is problematic. We show that the notions of ‘conceptual change’ in Kuhn and Piaget’s projects, the two thinkers whose work is most commonly drawn upon to support this analogy, are not compatible in the sense usually claimed. We contend that Kuhn’s work pertains not so much to the psychology of individual scientists, but to the way philosophers and historians should describe developments in communities of scientists. Furthermore, we argue that the analogy is based on a misunderstanding of the nature of science and the relation between science and common sense. The distinctiveness of the two notions of conceptual change has implications for science education research, since it raises serious questions about the relevance of Kuhn’s remarks for the study of pedagogical issues.     

Effectiveness of Conceptual Change Text-oriented Instruction on Students’ Understanding of Energy in Chemical Reactions

The aim of this study is to compare the effectiveness of conceptual change text instruction (CCT) in the context of energy in chemical reactions. The subjects of the study were 60, 10th grade students at a high school, who were in two different classes and taught by the same teacher. One of the classes was randomly selected as the experimental group in which CCT instruction was applied, and the other as the control group in which traditional teaching method was used. The data were obtained through the use of Energy Concept Test (ECT), the Attitude Scale towards Chemistry (ASC) and Science Process Skill Test (SPST). In order to find out the effect of the conceptual change text on students’ learning of energy concept, independent sample t-tests, ANCOVA (analysis of covariance) and ANOVA (analysis of variance) were used. Results revealed that there was a statistically significant mean difference between the experimental and control group in terms of students’ ECT total mean scores; however, there was no statistically significant difference between the experimental and control group in terms of students’ attitude towards chemistry. These findings suggest that conceptual change text instruction enhances the understanding and achievement.     

Profiles of algebraic competence

The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map algebraic symbols onto word problems was evaluated. Two weeks later, unassisted algebraic problem-solving tests were completed. Cluster analyses revealed four meaningful, relatively well-ordered, arithmetic/algebraic competence profiles reflecting partial knowledge states associated with the acquisition of algebraic understanding. The findings are discussed in terms of the conceptual changes associated with the acquisition of algebraic competence.     

Facilitating Conceptual Change in Gases Concepts

The aim of this study is to investigate the effectiveness of conceptual change oriented instruction (CCOI) over traditionally designed chemistry instruction (TDCI) on overcoming 10th grade students’ misconceptions on gases concepts. In addition, the effect of gender difference on students’ understanding of gases concepts was investigated. The subjects of this study consisted of 74 10th grade students from two chemistry classes. One of the classes was assigned as experimental group and the other group was assigned as control group. The experimental group was instructed with CCOI and the control group was instructed by TDCI. Gases Concept Test (GCT) was administered to both groups as pre- and post-tests to measure the students’ conceptual understanding. The results showed that students in the experimental group got higher average scores from Gases Concept Test. Also, a significant difference was found between the performance of females and that of males in terms of understanding gases concepts in favor of males.     

Evolutionary Maps: A new model for the analysis of conceptual development,with application to the diurnal cycle

This paper presents a model of how children generate concrete concepts from perception through processes of differentiation and integration. The model informs the design of a novel methodology (evolutionary maps or emaps), whose implementation on certain domains unfolds the web of itineraries that children may follow in the construction of concrete conceptual knowledge and pinpoints, for each conception, the architecture of the conceptual change that leads to the scientific concept. Remarkably, the generative character of its syntax yields conceptions that, if unknown, amount to predictions that can be tested experimentally. Its application to the diurnal cycle (including the sun's trajectory in the sky) indicates that the model is correct and the methodology works (in some domains). Specifically, said emap predicts a number of exotic trajectories of the sun in the sky that, in the experimental work, were drawn spontaneously both on paper and a dome. Additionally, the application of the emaps theoretical framework in clinical interviews has provided new insight into other cognitive processes. The field of validity of the methodology and its possible applications to science education are discussed.     

Understanding metallic bonding: Structure,process and interaction by Rasch analysis

This paper reports the results of a survey of 3006 Year 10–12 students on their understandings of metallic bonding. The instrument was developed based on Chi's ontological categories of scientific concepts and students' understanding of metallic bonding as reported in the literature. The instrument has two parts. Part one probed into students' understanding of metallic bonding as (a) a submicro structure of metals, (b) a process in which individual metal atoms lose their outermost shell electrons to form a ‘sea of electrons’ and octet metal cations or (c) an all-directional electrostatic force between delocalized electrons and metal cations, that is, an interaction. Part two assessed students' explanation of malleability of metals, for example (a) as a submicro structural rearrangement of metal atoms/cations or (b) based on all-directional electrostatic force. The instrument was validated by the Rasch Model. Psychometric assessment showed that the instrument possessed reasonably good properties of measurement. Results revealed that it was reliable and valid for measuring students' understanding of metallic bonding. Analysis revealed that the structure, process and interaction understandings were unidimensional and in an increasing order of difficulty. Implications for the teaching of metallic bonding, particular through the use of diagrams, critiques and model-based learning, are discussed.     

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.     

Students’ misconceptions of statistical inference: A review of the empirical evidence from research on statistics education

A solid understanding of inferential statistics is of major importance for designing and interpreting empirical results in any scientific discipline. However, students are prone to many misconceptions regarding this topic. This article structurally summarizes and describes these misconceptions by presenting a systematic review of publications that provide empirical evidence of them. This group of publications was found to be dispersed over a wide range of specialized journals and proceedings, and the methodology used in the empirical studies was very diverse. Three research needs rise from this review: (1) further empirical studies that identify the sources and possible solutions for misconceptions in order to complement the abundant theoretical and statistical discussion about them; (2) new insights into effective research designs and methodologies to perform this type of research; and (3) structured and systematic summaries of findings like the one presented here, concerning misconceptions in other areas of statistics, that might be of interest both for educational researchers and teachers of statistics.     

Discussion, debate and dialog: changing minds about conceptual change research in science education

This paper provides a critical commentary on a suite of eight papers, which focus on conceptual change research in science education. Responses by Mercer, Smardon and Wells to a paper by Treagust and Duit are observed to reflect the backgrounds of the three authors with Wells focusing on issues of ontology and the affective domain. Mercer and Smardon focus on issues of identity and the role of dialog. Hewson’s, Vosniadou’s and Tiberghien’s responses to Roth, Lee and Hwang offer robust critique of what appear to be exploratory ideas. To what extent the authors of the response papers enter into dialog with the papers is discussed. How far research into learning in science has progressed since the 1980s is examined.

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 Impact of Field Trips and Family Involvement on Mental Models of the Desert Environment

This study examined the mental models of the desert environment held by fourth‐ and seventh‐grade students in the USA and whether those mental models could be affected by: (1) classroom field trips to a desert riparian preserve, and (2) interaction with family members at the same preserve. Results generally indicated that students in this study were resolute in their models and that field trips did not impact the types of models students adhered to. Twenty‐three seventh‐grade students who self‐selected to participate in a Family Science Club with their parents did demonstrate a shift in their mental models and developed significantly more sophisticated models over time. A critical implication of the study is that unless transformation of mental models of the environment is an explicit goal of instruction, simple exposure to the environment (even within the context of life science instruction) will not transform understandings of how organisms within an environment act and interact interdependently.     

Teacher help for conceptual level raising in mathematics

A field study with 16-year-old students in senior general secondary education was undertaken with the following research question: “Do students working in pairs on investigation tasks with the computer attain more conceptual level raising in mathematics when they are supported by a teacher who stimulates their interaction (process help) than when they are supported by a teacher who gives mathematical help (product help)?” Students in both conditions improved, but the two types of help showed no significant difference in level raising. Also, students in both conditions had serious problems with the learning materials, and wanted the teacher to explain and correct more. For students at this level of education, learning with investigation tasks in small groups appears to be very difficult.     

The diffusion of the learning pyramid myths in academia: an exploratory study

This article examines the diffusion and present day status of a family of unsubstantiated learning-retention myths, some of which are referred to as ‘the learning pyramid’. We demonstrate through an extensive search in academic journals and field-specific encyclopaedias that these myths are indeed widely publicised in academia and that they have gained a considerable level of authority. We also argue that the academic publishing of these myths is potentially harmful to both professional as well as political deliberations on educational issues, and therefore should be criticized and counteracted.     

Editorial: The changing face of academic development

“Quality teaching”, “curriculum change” and “innovative practice” are just a few of the common phrases used by university academics as a basis for defining and justifying their actions as educators and policy‐makers. Yet our analysis of 25 interviews with academics revealed differences in their conceptions of these terms. While the impact of such disparity upon the clarity of discussions across campus is not known, it is likely to be significant. We suggest there is a real need for academics and developers to work together to identify the meanings behind the language of higher education. By working collaboratively and contributing individual expertise, academics and developers can develop converging understandings and better shape the university curriculum. This paper explores ways in which we can work together to achieve this goal.

“Enseignement de qualité”, “changement de programme” et “pratique innovatrice” ne sont que quelques‐unes des expressions communément employées par les universitaires pour définir et justifier leurs actions en tant qu’éducateurs ou responsables de politiques. Toutefois, notre analyse d’entretiens effectués auprès de 25 universitaires révèle des différences en ce qui a trait aux conceptions entretenues à l’égard de ces expressions. Bien que l’impact d’une telle disparité sur la clarité des discussions à la grandeur du campus ne soit pas connu, celui‐ci est susceptible d’être significatif. Nous suggérons qu’universitaires et conseillers pédagogiques travaillent ensemble à identifier les significations sous‐jacentes au langage de l’enseignement supérieur. En collaborant et en fournissant une expertise individuelle, universitaires et conseillers pédagogiques peuvent parvenir à des compréhensions convergentes et, ainsi, mieux informer les programmes universitaires. Cet article explore quelques façons selon lesquelles nous pouvons travailler ensemble vers l’atteinte de cet objectif.     

“It’s the X and Y Thing”: Cross-sectional and Longitudinal Changes in Children’s Understanding of Genes

Studies from different theoretical traditions investigating children’s inheritance and genetics concepts have adopted a cross-sectional method. This paper is the first to examine both cross-sectional and longitudinal changes in children’s basic genetic concepts. It forms part of a larger investigation into the development of intuitive inheritance and genetics concepts in childhood. Four age cohorts (4–5 years, 7–8 years, 10–11 years, 14–15 years) were interviewed individually at two measurement occasions (T1, N = 182; T2, N = 164) separated by a 1-year interval. Cross-sectional analyses revealed an increase in children’s knowledge of genetics by 10 years. Between 10 and 14 years, there were fewer changes in the content of children’s knowledge, especially at the level of scientific genetic understanding. There was little evidence of longitudinal changes over the 1-year period. Overall, children may hold an understanding of genetics that is tied to knowledge of inheritance within families. This may pose challenges for acquiring more abstract and formal concepts of genes.     

Compatibility between cultural studies and conceptual change in science education: there is more to acknowledge than to fight straw men!

In this response, we attempt to clarify our position on conceptual change, state our position on mental models being a viable construct to represent learning, indicate important issues from the social cultural perspective that can inform our work on conceptual change and lastly comment on issues that we consider to be straw men. Above all we argue that there is no best theory of teaching and learning and argue for a multiple perspective approach to understanding science teaching and learning.

Conceptual Resources in Self‐developed Explanatory Models: The importance of integrating conscious and intuitive knowledge

This study explores the spontaneous explanatory models children construct, critique, and revise in the context of tasks in which children need to predict, observe, and explain phenomena involving magnetism. It further investigates what conceptual resources students use, and in what ways they use them, to construct explanatory models, and the obstacles preventing them from constructing a useful explanatory model. Our findings indicate that several of the children were able to construct explanatory models. However, of the six children interviewed multiple times (three third‐graders and three sixth‐graders), only one was consistently able to critique and revise her models to arrive at a consistent, coherent, and sophisticated explanatory model. Connecting intuitive knowledge and abstract knowledge was important in her construction of a coherent and sophisticated explanatory model. Students who relied only on intuitive knowledge constructed tentative and non‐sophisticated explanatory models. Students who relied only on verbal‐symbolic knowledge at an abstract level without connection with their intuition also did not construct coherent and sophisticated models. These results indicate that instruction should help students to become meta‐conceptually aware and connect their verbal‐symbolic knowledge and intuition in order to construct explanatory models to make sense of abstract scientific knowledge.