Relationships among computational performance,pictorial representation,symbolic representation and number sense of sixth‐grade students in Taiwan

Twenty classes in ten schools with 627 sixth‐grade students in five cities in Taiwan participated in this study. The research provides information on the performance differences among written computation, pictorial representation, symbolic representation and number sense. The results of One‐way ANOVA analysis indicate that significant difference was found among WCT, PRT, SRT and NST tests, with F=536.327, p=0.000. The a posteriori comparisons show for each pair (WCT vs PRT, WCT vs SRT, WCT vs NST, PRT vs SRT and SRT vs NST) significant difference at the 0.001 level (p=0.000), except for the pair comparison between PRT and NST. This implies that these Taiwanese students were highly skilled in written computation but their written skills were not equally transferred to use of non‐computational paths that depended on symbolic representation, pictorial representation and number sense to solve similar problems.     

Modelling water systems in an introductory undergraduate course: Students’ use and evaluation of data-driven,computer-based models

ABSTRACT

Introductory undergraduate courses present an opportunity to use disciplinary concepts in solving authentic problems. Making complex natural systems accessible to students through computer-based models allows them to practice making evidence-based predictions and communicate understanding. Despite the importance of modelling tools in formal classrooms, gaps exist in our understanding of how post-secondary students engage in computer-based modelling. Introductory courses, particularly in the hydrosciences, typically do not use these tools. This mixed methods study examines students’ model-based reasoning about a water-related issue over two years in response to a flipped course model. Students in an introductory water course learned basic hydrologic content and used a computer-based water model to complete a project. Data came from a pre-/post-course assessment, student assignments, and student interviews. Results of quantitative and qualitative data analyses show that students in the revised version of the course (Year 2, n?=?53) increased their understanding of core hydrology concepts and performed better on their evaluation of a computer-based water model, than students in the initial course (Year 1, n?=?38). We tentatively attribute these observed changes to increased active learning opportunities surrounding computer-based modelling of water systems. Findings contribute to science literacy development, undergraduate science learning environment design, and undergraduate scientific modelling.     

Secondary students’ modelling conceptualisation in situations related to particle dynamics: a clinical perspective

This study investigates the modelling conceptualisation of secondary school students in two situations related to particle dynamics: pendulum’s motion and horizontal motion. We performed in-depth clinical interviews with secondary school students (N?=?10). Participants’ ideas about properties which are not ‘given’ in empirical observations were explored in order to investigate signs of abstractions and idealisations in their reasoning processes. We proposed contributions to modelling in science education based on Mario Bunge’s epistemology and we employed his basic concepts as the axis to analyse our results: (1) abstractions and idealisations, considered as thought processes required to build conceptual counterparts of concrete objects; (2) theoretical models, meaning hypothetico-deductive systems concerning those conceptual objects; and (3) general theoretical frameworks that allow us to derive those theoretical models. We developed our analysis viewing the ideas presented by participants as concepts-in-action and theorems-in-action as regarded by Gérard Vergnaud’s Theory of Conceptual Fields. Results indicated a gradation in the concepts-in-action mobilised in terms of levels of idealisation and showed that participants do not spontaneously recognise the use of a general theory as a possible way to obtain a theoretical model. These results suggest that science education practices must pay better attention to make abstractions and idealisations explicit in scientific concepts formation, as well as to the heuristic role of theories in model construction.     

Correct Interpretation of Chemical Diagrams Requires Transforming from One Level of Representation to Another

Volunteer non-major chemistry students taking an introductory university chemistry course (n = 17) were interviewed about their understanding of a variety of chemical diagrams. All the students’ interviewed appreciated that diagrams of laboratory equipment were useful to show how to set up laboratory equipment. However students’ ability to explain specific diagrams at either the macroscopic or sub-microscopic level varied greatly. The results highlighted the poor level of understanding that some students had even after completing both exercises and experiments using the diagrams. The connection between the diagrams of the macroscopic level (equipment, chemicals), the sub-microscopic level (molecular) and the symbolic level (equations) was not always considered explicitly by students. The results indicate a need for chemical diagrams to be used carefully and more explicitly to ensure learner understanding. Correspondingly, students need to interpret visual chemical diagrams using meta-visualization skills linking the various levels of representation, and appreciating the role of the diagrams in explanations need to be developed.     

Connecting Levels of Representation: Emergent versus submergent perspective

Chemical phenomena can be described using three representation modes: macro, submicro, and symbolic. The way students use and connect these modes when solving conceptual problems was studied, using a think‐aloud interview protocol. The protocol was validated through interviews with six faculty members, and then applied to four graduate and six undergraduate chemistry students. We used a ‘levels of complexity’ framework to analyse responses: the macro and symbolic modes were considered system‐level representations, and the submicro mode a component‐level representation. We found that faculty members thought of system‐level properties as emerging from mechanistic interactions between particles on the component level—an emergent perspective. In many cases, the students either failed to connect the system and component levels, or thought of system‐level properties as guiding the behaviour of particles on the component level—a ‘submergent’ perspective. Some students used their familiarity with a symbolic equation describing the behaviour of a substance as the starting point of a thought process that leads them to impose mechanistically unwarrantable behaviour upon its particles. We concluded that a submergent perspective inhibits students from confronting their misconceptions regarding particle behaviour, and explains why students are often able to correctly solve algorithmic problems while failing to solve conceptual ones. It is suggested that the directionality of connecting particle behaviour to system‐level properties should be emphasized in teaching.     

Learning Gene Expression Through Modelling and Argumentation

There is emerging interest on the interactions between modelling and argumentation in specific contexts, such as genetics learning. It has been suggested that modelling might help students understand and argue on genetics. We propose modelling gene expression as a way to learn molecular genetics and diseases with a genetic component. The study is framed in Tiberghien’s (2000) two worlds of knowledge, the world of “theories & models” and the world of “objects & events”, adding a third component, the world of representations. We seek to examine how modelling and argumentation interact and connect the three worlds of knowledge while modelling gene expression. It is a case study of 10th graders learning about diseases with a genetic component. The research questions are as follows: (1) What argumentative and modelling operations do students enact in the process of modelling gene expression? Specifically, which operations allow connecting the three worlds of knowledge? (2) What are the interactions between modelling and argumentation in modelling gene expression? To what extent do these interactions help students connect the three worlds of knowledge and modelling gene expression? The argumentative operation of using evidence helps students to relate the three worlds of knowledge, enacted in all the connections. It seems to be a relationship among the number of interactions between modelling and argumentation, the connections between world of knowledge and students’ capacity to develop a more sophisticated representation. Despite this is a case study, this approach of analysis reveals potentialities for a deeper understanding of learning genetics though scientific practices.     

The role of submicroscopic and symbolic representations in chemical explanations

Chemistry is commonly portrayed at three different levels of representation – macroscopic, submicroscopic and symbolic – that combine to enrich the explanations of chemical concepts. In this article, we examine the use of submicroscopic and symbolic representations in chemical explanations and ascertain how they provide meaning. Of specific interest is the development of students' levels of understanding, conceived as instrumental (knowing how) and relational (knowing why) understanding, as a result of regular Grade 11 chemistry lessons using analogical, anthropomorphic, relational, problem‐based, and model‐based explanations. Examples of both teachers' and students' dialogue are used to illustrate how submicroscopic and symbolic representations are manifested in their explanations of observed chemical phenomena. The data in this research indicated that effective learning at a relational level of understanding requires simultaneous use of submicroscopic and symbolic representations in chemical explanations. Representations are used to help the learner learn; however, the research findings showed that students do not always understand the role of the representation that is assumed by the teacher.     

What Teachers of Science Need to Know about Models: An overview

The purpose of this article is to provide an overview of the nature of models and their uses in the science classroom based on a theoretical review of literature. The ideas that science philosophers and science education researchers have in common about models and modelling are scrutinised according to five subtopics: meanings of a model, purposes of modelling, multiplicity of scientific models, change in scientific models and uses of models in the science classroom. First, a model can be defined as a representation of a target and serves as a ‘bridge’ connecting a theory and a phenomenon. Second, a model plays the roles of describing, explaining and predicting natural phenomena and communicating scientific ideas to others. Third, multiple models can be developed in science because scientists may have different ideas about what a target looks like and how it works and because there are a variety of semiotic resources available for constructing models. Fourth, scientific models are tested both empirically and conceptually and change along with the process of developing scientific knowledge. Fifth, in the science classroom, not only teachers but also students can take advantage of models as they are engaged in diverse modelling activities. The overview presented in this article can be used to educate science teachers and encourage them to utilise scientific models appropriately in their classrooms.     

Naming Block Structures: A Multimodal Approach

This study describes symbolic representation in block play in a culturally diverse suburban preschool classroom. Block play is multimodal and can allow children to experiment with materials to represent the world in many forms of literacy. Combined qualitative and quantitative data from seventy-seven block structures were collected and analyzed. The observed frequency of symbolism used for three levels of symbolism (1) pre-symbolism, (2) first level symbolism, and (3) second level symbolism was investigated. Results indicated significant differences for first level symbolism or real-world objects. Students reported making homes for Webkinz, indicating an ability to encode multimodally the Webkinz computer game played at home to their school block play. The implications from these findings suggest educators should consider both a sociocultural perspective on playing and children’s out of-school experiences on learning. A research agenda that includes multimodality as performance is critical to early childhood education.     

FORM AND STRUCTURE OF CHINESE CHARACTERS AND CHILDREN��S UNDERSTANDING OF SCIENCE

The written representation in Chinese can be considered as a pictorial or a symbolic representation which is very different from English where the pronunciation is related to how the word is spelt. Students face challenges of a very different nature when science is learnt in Chinese compared with English. In Hong Kong, students are making translations between the language they use in their daily lives, the science concepts and the scientific terms. The research team designed an interview protocol for primary school pupils in order to identify the pupils’ alternative concepts of science and if these alternative concepts are related to the structure of the Chinese language. The findings suggest that there are alternative conceptions related to (a) the form of the Chinese character—for example, the Chinese character for crocodile includes a radical meaning fish, and so pupils may take it that a crocodile is a fish; (b) the meaning of the Chinese character—for example, an electronic buzzer is a device used to attract bees as in Chinese, the character contains the word meaning “bees producing sound”. The findings provide important data for future endeavours aiming to compare the learning of science using different languages and on ways in which primary teachers may better facilitate their pupils in learning science.     

Dual representation and young children's use of scale models

To use a symbolic object such as a model, map, or picture, one must achieve dual representation; that is, one must mentally represent both the symbol itself and its relation to its referent. The studies reported here confirm predictions derived from this concept. As hypothesized, dual representation was as difficult for 2 1/2-year-olds to achieve with a set of individual objects as it was with an integrated model. Decreasing the physical salience of a scale model (by placing it behind a window) made it easier for 2 1/2-year-old children to treat it as a representation of something other than itself. Conversely, increasing the model's salience as an object (by allowing 3-year-old children to manipulate it) made it more difficult to appreciate its symbolic import. The results provide strong support for dual representation.     

The Relation between Students’ Epistemological Understanding of Computer Models and their Cognitive Processing on a Modelling Task

While many researchers in science education have argued that students’ epistemological understanding of models and of modelling processes would influence their cognitive processing on a modelling task, there has been little direct evidence for such an effect. Therefore, this study aimed to investigate the relation between students’ epistemological understanding of models and modelling and their cognitive processing (i.e., deep versus surface processing) on a modelling task. Twenty‐six students, working in dyads, were observed while working on a computer‐based modelling task in the domain of physics. Students’ epistemological understanding was assessed on four dimensions (i.e., nature of models, purposes of models, process of modelling, and evaluation of models). Students’ cognitive processes were assessed based on their verbal protocols, using a coding scheme to classify their types of reasoning. The outcomes confirmed the expected positive correlation between students’ level of epistemological understanding and their deep processing (r = 0.40, p = .04), and the negative correlation between level of epistemological understanding and surface processing (r = ?0.51, p = .008). From these results, we emphasise the necessity of considering epistemological understanding in research as well as in educational practice.     

From Students to Consumers: reflections on the marketisation of Portuguese higher education

A progressive attempt to replace traditional public administration values and concepts by others that are closer to private management can be observed in the replacement of the service user concept by that of consumer or client. This redefinition's more implicit or explicit intent is to increase consumers'/clients' status, their capacity to choose and make rational choices in the market, and, ultimately, to ensure that organisations fulfil their needs. Influenced by this tendency, higher education institutions (HEIs) also started to see students as clients or consumers and to influence their choices by trying to define HE demand. This is evident in the shift in their external communication strategies: ‘institutional information’, based on HEIs' prestige, is being progressively replaced by ‘marketed information’, based on economic consumer logic. In trying to understand how students are perceived by Portuguese HEIs, we undertook qualitative research based on the content analysis of undergraduate degrees' announcements in newspapers. Major findings evidence that their content: (1) can be classified in a continuum bounded by two poles: the use of ‘institutional information’ and the use of ‘marketed information’; (2) show the presence of a social representation of students as clients or consumers; (3) seems related to HEIs' nature (public vs. private), positioning in the HE system (universities and polytechnics) and ‘symbolic capital’ (traditional vs. new institutions).     

A STUDY OF SEMIOTIC REGISTERS IN THE DEVELOPMENT OF THE DEFINITE INTEGRAL OF FUNCTIONS OF TWO AND THREE VARIABLES

Tracing the path from a numerical Riemann sum approximating the area under a curve to a definite integral representing the precise area in various texts and online presentations, we found 3 semiotic registers that are used: the geometric register, the numerical register, and the symbolic register. The symbolic register had 3 representations: an expanded sum, a sum in sigma notation, and the definite integral. Reviewing the same texts, we found that in the presentation of double and triple integrals, not a single textbook continues to present the numerical register and the expanded sum representation of the symbolic register. They are implied and the expectation appears to be that students no longer need them. The omission of these representations is quite ubiquitous and correspondingly affects millions of students. Materials that present the missing numerical register representation and the expanded sum representation of the symbolic register throughout topics associated with double and triple integrals have been created. This paper presents the results of a clinical study on the improvement of student comprehension of multivariable integral topics when these representations are included.     

Learning Through Computational Modeling

Summary

When thinking of reasoning, problem solving, communication, and connecting related ideas, the tool of choice in nearly every discipline is the microcomputer. Furthermore, unlike the traditional calculator, the modern classroom computer has an unparalleled ability to implement both graphical and procedural components of mathematics understanding in a single unified object. By students' creation and utilization of mathematically relevant computer-based objects, this dual encapsulation provides them with a unique opportunity to see both the form of representation and their actions utilizing this representation simultaneously.

This paper suggests that the object-oriented environments that modern technology enables are ideally suited to parallel and facilitate the ability of students to take a broader variety of action upon objectsof a nature and kind hitherto unknown. These student-controlled actionsupon these mathematically powerful and computer-enabled objectshave the potential for creating classroom environments that both surpass the pale hopes of the integrated learning system and surprise those wedded to a conservative view of Piagetian developmental levels.     

Secondary teachers’ knowledge of elementary number theory proofs: the case of general-cover proofs

In light of recent reform recommendations, teachers are expected to turn proofs and proving into an ongoing component of their classroom practice. Two questions emerging from this requirement are: Is the mathematical knowledge of high school teachers sufficient to prove various kinds of statements? Does teachers’ knowledge allow them to determine the validity of an argument made by their students? The results of this study, in which 50 secondary school teachers participated, point to a positive answer to the first question in the framework of elementary number theory (ENT). However, the picture is more complex with respect to the second one. Results indicated that some teachers may over-value the generality of symbolic mode of representation and under-value the generality of verbal ones. Possibly, the verbal representation of an argument is less transparent and more difficult to understand.     

Students' mental load,stress, and performance when working with symbolic or symbolic–textual molecular representations

In science education, representations are necessary inter alia for the understanding of relationships between structures and systems. However, several studies have identified difficulties of students when working with representations. In the present study, we investigated students' responses (regarding their preference, test performance, mental load (ML), and stress) toward two kinds of representations: symbolic representations, which only use abstract symbols, versus combined symbolic–textual representations, which additionally comprise textual elements. Therefore, students were randomly assigned to one of two treatment groups: one group worked on test tasks accompanied by symbolic representations, and the others worked on the same tasks, but with symbolic–textual representations. Thereafter, the students' test performance and ML were assessed. The level of perceived stress and the salivary cortisol concentration were measured before and after the test and again a few minutes later. Additionally, heart rate variability parameters were assessed continuously. We found a strong preference of the test version with symbolic representations. Additionally, the students showed better test performance and lower ML when they worked with symbolic representations. However, the level of perceived stress was comparable between both groups and there was no strong physiological stress response: The cortisol concentration decreased in both groups and the heart rate was relatively similar. However, during the second half of the test, we observed a significantly higher ratio between low and high heartbeat frequencies in the group with symbolic–textual representations and we found an indirect influence of the kind of representation on test performance through its effect on ML. The poorer test performance and higher ML in connection with symbolic–textual representations confirm previous studies, which found that symbolic–textual representations pose major problems for students. Thus, teachers should enable students to understand symbolic–textual representations and consider carefully whether they can use symbolic representations instead, especially when they teach complex content.     

Pupils’ and Teachers’ Views on a British Science Magazine for Youth

This paper focuses on students' ability to transfer modelling performances across content areas, taking into consideration their improvement of content knowledge as a result of a model-based instruction. Sixty-five sixth grade students of one science teacher in an urban public school in the Midwestern USA engaged in scientific modelling practices that were incorporated into a curriculum focused on the nature of matter. Concept-process models were embedded in the curriculum, as well as emphasis on meta-modelling knowledge and modelling practices. Pre–post test items that required drawing scientific models of smell, evaporation, and friction were analysed. The level of content understanding was coded and scored, as were the following elements of modelling performance: explanation, comparativeness, abstraction, and labelling. Paired t-tests were conducted to analyse differences in students' pre–post tests scores on content knowledge and on each element of the modelling performances. These are described in terms of the amount of transfer. Students significantly improved in their content knowledge for the smell and the evaporation models, but not for the friction model, which was expected as that topic was not taught during the instruction. However, students significantly improved in some of their modelling performances for all the three models. This improvement serves as evidence that the model-based instruction can help students acquire modelling practices that they can apply in a new content area.     

Investigating the relationship between instructional practices and science achievement in an inquiry-based learning environment

ABSTRACT

This study investigates the discrete effects of inquiry-based instructional practices that described the PISA 2015 construct ‘inquiry-based instruction’ and how each practice, and the frequency of each practice, is related to science achievement across 69 countries. The data for this study were drawn from the PISA 2015 database and analysed using hierarchical linear modelling (HLM). HLMs were estimated to test the contribution of each item to students’ science achievement scores. Some inquiry practices demonstrated a significant, linear, positive relationship to science achievement (particularly items involving contextualising science learning). Two of the negatively associated items (explaining their ideas and doing experiments) were found to have a curvilinear relationship to science achievement. All nine items were dummy coded by the reported frequency of use and an optimum frequency was determined using the categorical model and by calculating the inflection point of the curvilinear associations in the previous model e.g. students that carry out experiments in the lab in some lessons have higher achievement scores than students who perform experiments in all lessons. These findings, accompanied by detailed analyses of the items and their relationships to science outcomes, give stakeholders clear guidance regarding the effective use of inquiry-based approaches in the classroom.