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This study aims to investigate the effects of the use of multiple geometry proof formats on Indonesian students' reading comprehension of geometry proof (RCGP). Four classes of prospective secondary mathematics teachers (N=125), aged 18 to 19 years, participated in this quasi-experimental study. While the experimental group was instructed in three proof formats (paragraph, two-column and flow-chart proof), the control group was instructed in only the two-column proof format. Similar pre- and post-tests, based on Yang and Lin's (2008) RCGP test, were administered to both groups. N-Gain scores were used to determine the improvement of both groups. The N-Gain scores showed significantly more improvement of students' RCGP in the experimental group. More detailed analysis indicated that the use of multiple proof formats supports the students' understanding of the facets of logical status of statements and the critical ideas in the proof. This study shows the benefits of offering multiple proof formats to support prospective mathematics teachers' RCGP.

Using multiple representations (MR) such as graphs, symbols, diagrams, and text, is central to teaching and learning in physics classrooms. While different studies have provided evidence of the positive impact of the use of MR on physics learning, a comprehensive overview of existing literature on the use of MR in physics education, especially at the undergraduate level, is missing. This manuscript addresses this gap in the literature by reporting on the outcomes of a systematic review study that aimed to provide an overview of the existing knowledge base, to identify gaps in the knowledge base, and to propose future research about the use of MR in the context of undergraduate physics education. For the purpose of this study, we reviewed 24 empirical studies published between 2002 and 2019 in scientific, peer-reviewed journals in the context of undergraduate physics education. The outcomes of this review study are discussed under these themes (a) In what ways does the use of MR in instruction support student learning? (b) What kinds of representations do students use? (c) What difficulties do students face in using MR? (d) What is the relation between students' use of MR and students' problem-solving skills? and, (e) What is the added value of technology integration in teaching with MR? We identify gaps in the existing knowledge base, and we propose future research directions in these three areas: (a) Exploring the use of MR in university physics textbooks; (b) Blending of different kinds of MR; and, (c) The use of virtual reality applications.

From literature, we know that making the connections between mathematics and physics is not trivial for most students, even at the advanced level. In the specific context of partial derivatives in thermodynamics, research suggests that making explicit connections between the mathematics and the physics is necessary to foster student understanding. In this paper, we investigate how graphical reasoning can help undergraduate students in making connections between the partial derivatives of temperature with respect to position and to time and their respective physical meaning in the context of one-dimensional systems modeled by the heat equation. We conducted task-based, think aloud interviews with four pairs of undergraduate students majoring in physics or mathematics and use dynamic conceptual blending diagrams to analyze their reasoning processes and the role of the graphs therein. The results in this paper indicate that stimulating graphical reasoning is a promising way to promote the blending of mathematical and physical knowledge. Specifically, our data shows that constructing graphs can be a catalyst which helps students to give physical meaning to the partial derivatives ?T/?t and/or ?T/?x. Therefore, in teaching/learning activities, actively promoting graph construction and reasoning based on those graphs offers perspectives to support the blending of mathematics and physics.

Identity-based research in physics education has been receiving increased attention in the past few years given the potential of identity in producing novel insights into the ways' students engage in physics. In this study, we examined the development of preservice physics teachers' physics identity through a specific instructional practice: a specially designed course incorporating the use of the multiple representations. Although specific programs and instructional practices have been found to influence the development of physics identity, there is no clear evidence about the kinds of instructional practices that might support its development. To examine the influence of multiple representations on each component of physics identity, we designed and implemented a physics course that used a multiple representation (MR)-based instructional approach with a group of 61 preservice physics teachers at a public university in Indonesia. Data were collected with a pre- and post-questionnaire on physics identity, a conceptual understanding test, and a post-test that examined differences between identity components before and after the course, conceptual understandings, as well as the participants' views about the use of the MR-based instructional approach. The findings revealed a significant improvement of two components of physics identity, namely, competence and interest, and point to the potential of MR-based instruction in physics courses.

High school students' difficulties with quantum physics (QP) are partly due to their limited understanding of the nature of science (NOS). The essence of QP can only be understood with informed views about NOS aspects such as the role of models and the relevance of controversies between physicists. Inversely, QP is an ideal topic for teaching aspects of NOS. However, secondary school textbooks seldom support teachers to explicitly address NOS in QP. Drawing on a five year research program, including observations of students and teachers, we present teaching resources that link NOS aspects with QP. Our materials support active and reflective learning activities, while being adaptable to teachers' individual needs and affordances. We hope to inspire teachers to address NOS in their QP lessons.

This review study synthesises 28 empirical research articles emphasising the learning of morality aspects in the context of addressing socioscientific issues (SSI) in secondary science education. The key interrelated questions we seek to address in this study are how morality is conceptualised in the science classroom in the light of emerging sustainability issues and how it can be developed. We used the Four Component Model of Morality to create a knowledge base for how morality has been conceptualised in the literature on secondary science education and how it can be developed. The findings of this review study show that not all studies have used concrete, explicit conceptualisations of morality and that the role of sense of place and the situatedness of morality have often been neglected. It also emerged that studies focusing on students' moral character and action-taking were underrepresented. We recommend that further research be carried out on the interrelationships between moral character and enacted moral reasoning. The review also reveals a gap between morality research and teaching. Based on the outcomes of this review, we propose a set of recommendations aimed at guiding and encouraging students' morality within secondary science education.

Logical reasoning as part of critical thinking is becoming more and more important to prepare students for their future life in society, work, and study. This article presents the results of a quasi-experimental study with a pre-test-post-test control group design focusing on the effective use of formalisations to support logical reasoning. The participants were 163 pre-university secondary school students (11th and 12th graders). For the experimental group we designed a course in logical reasoning intending to develop students' use of formalisations in formal reasoning and everyday reasoning tasks. We show that students learned to use the intended formalisations. Overall, students from the experimental group had significantly better results on the post-test compared to the control group. Positive correlations were found between item scores and the use of Venn and Euler diagrams and scheme-based strategies. Our results support our hypothesis that the use of formalisations improves logical reasoning skills.

Combining mathematical and physical understanding in reasoning is difficult, and a growing body of research shows that students experience problems with the combination of physics and mathematics in reasoning beyond the introductory level. We investigated students' reasoning about boundary conditions (BCs) for the diffusion equation by conducting exploratory task-based, think-aloud interviews with twelve undergraduate students majoring in physics or mathematics. We identified several difficulties students experienced while solving the interview task and categorized them using the conceptual blending framework. This framework states that in reasoning, people draw from separate input spaces, in this case the mathematics and the physics input space, to form a blended space, where they make connections between elements from these spaces. To identify difficulties, we used open coding techniques. We observed few difficulties in the physics space. In the mathematics space, we identified several difficulties that we clustered in two main groups: findings about the mathematical meaning of BCs, and findings about reasoning with functions of two variables. Lastly, we identified four ways in which blending failed. Starting from our findings, we formulate recommendations for teaching and future research.

Due to growing interest in twenty-first-century skills, and critical thinking as a key element, logical reasoning is gaining increasing attention in mathematics curricula in secondary education. In this study, we report on an analysis of video recordings of student discussions in one class of seven students who were taught with a specially designed course in logical reasoning for non-science students (12th graders). During the course of 10 lessons, students worked on a diversity of logical reasoning tasks: both closed tasks where all premises were provided and everyday reasoning tasks with implicit premises. The structure of the course focused on linking different modes of representation (enactive, iconic, and symbolic), based on the model of concreteness fading (Fyfe et al., 2014). Results show that students easily link concrete situations to certain iconic referents, such as formal (letter) symbols, but need more practice for others, such as Venn and Euler diagrams. We also show that the link with the symbolic mode, i.e. an interpretation with more general and abstract models, is not that strong. This might be due to the limited time spent on further practice. However, in the transition from concrete to symbolic via the iconic mode, students may take a step back to a visual representation, which shows that working on such links is useful for all students. Overall, we conclude that the model of concreteness fading can support education in logical reasoning. One recommendation is to devote sufficient time to establishing links between different types of referents and representations.

Logical reasoning is of great societal importance and, as stressed by the twenty-first century skills framework, also seen as a key aspect for the development of critical thinking. This study aims at exploring secondary school students' logical reasoning strategies in formal reasoning and everyday reasoning tasks. With task-based interviews among 4 16- and 17-year-old pre-university students, we explored their reasoning strategies and the reasoning difficulties they encounter. In this article, we present results from linear ordering tasks, tasks with invalid syllogisms and a task with implicit reasoning in a newspaper article. The linear ordering tasks and the tasks with invalid syllogisms are presented formally (with symbols) and non-formally in ordinary language (without symbols). In tasks that were familiar to our students, they used rule-based reasoning strategies and provided correct answers although their initial interpretation differed. In tasks that were unfamiliar to our students, they almost always used informal interpretations and their answers were influenced by their own knowledge. When working on the newspaper article task, the students did not use strong formal schemes, which could have provided a clear overview. At the end of the article, we present a scheme showing which reasoning strategies are used by students in different types of tasks. This scheme might increase teachers' awareness of the variety in reasoning strategies and can guide classroom discourse during courses on logical reasoning. We suggest that using suitable formalisations and visualisations might structure and improve students' reasoning as well.

In this qualitative case study we examined the impact of a specially-designed classroom intervention for a group of 15–16-year-old Dutch biology students' use of values in contemplating five socioscientific issues in the human-nature context. The students worked in small groups to support various aspects of their morality. An ethical matrix was used as a heuristic to explore different arguments and moral values from different perspectives. The collected data consisted of written assignments, group conversations, and individual interviews. The results show that students' use of values differed from one issue to another. The values they used in their moral decision-making indicated that the influence of the intervention activities, aimed at enhancing a relationship between moral agent (student) and moral object (topic), was limited. The study provides evidence that the intervention positively conduced to students' cognition of the values that are personally relevant. Recommendations for further theorization, research and practice are discussed. [ABSTRACT FROM AUTHOR]

Conjecturing has been considered to inspire the need for proof, enhance the understanding of proofs, and construct a valid proof. This study describes students' processes of formulating a Euclidean geometry conjecture in the form of a conditional statement through constructing a geometric figure and using measuring and dragging modalities of a dynamic geometry system (DGS). To accomplish this aim, we adapted the existing conjecturing model by Baccaglini-Frank and Mariotti ([2010]. Generating conjectures in dynamic geometry: The maintaining dragging model. International Journal of Computers for Mathematical Learning, 15(3), 225–253. https://doi.org/10.1007/s10758-010-9169-3) and used it to analyse students' conjecturing processes. Our participants were prospective mathematics teachers (PMTs) during their first year at an Indonesian university, but the findings can be useful for secondary school students in other countries. We selected and categorized episodes from task-based interviews with eight PMTs a week after a teaching intervention. We interpreted their identification of robust invariants during constructing, dragging, and measuring. Our findings indicated that the adapted model was appropriate to describe PMTs' processes of conjecturing, which emerged through an exploration that involved robust invariants. We found that PMTs determined these invariants as premises or conclusion of the conjecture by observing the measure of parts of the constructed figure during dragging. The findings indicated that the measuring and dragging modalities of DGS supported PMTs in conjecturing. [ABSTRACT FROM AUTHOR]

In recent years, there has been an increased interest in conceptual blending in physics and mathematics education research as a theoretical framework to study student reasoning. In this paper, we adapt the conceptual blending framework to construct a blending diagram that not only captures the product but also the process of student reasoning when they interpret a mathematical description of a physical system. We describe how to construct a dynamic blending diagram (DBD) and illustrate this using two cases from an interview study. In the interview, we asked pairs of undergraduate physics and mathematics students about the physical meaning of boundary conditions for the heat equation. The selected examples show different aspects of the DBD as an analysis method. We show that by using a DBD, we can judge the degree to which students integrate their understandings of mathematics and physics. The DBD also enables the reader to follow the line of reasoning of the students. Moreover, a DBD can be used to diagnose difficulties in student reasoning.

This study reports about biology undergraduates' writing in a course with genre-based writing instruction. The students read, analyse and synthesise research articles using the Scientific Argumentation Model (SAM), a tool to make explicit the characteristics of the research article genre. We explored to what extent 21 students make a synthesis when writing a review of two research articles and which research article's genre characteristics (rhetorical moves and qualifiers) they use. We defined a synthesis as a task in which students select, organise, and connect the articles' content. The analysis of students' reviews showed that most students made a synthesis of both articles. The articles' objective, supports and main conclusion were mostly reflected in the students' reviews. Most students did not use a qualifier in their final conclusion, and when they did use a qualifier it sometimes did not correspond to their main text, suggesting difficulties with understanding the rhetorical meaning of qualifiers. We suggest, supported by our interview and questionnaire data, that SAM could be useful for understanding, selecting, and organising research articles' content when writing a review. We conclude that the use of SAM could be a first step in synthesising research articles focused on supporting students' rhetorical consciousness.

One of the causes of the science teacher shortage is the low enrollment in science teacher education. In the Netherlands, science undergraduates can enroll in a half-year teaching course that leads to a teacher qualification for junior secondary education. The goal is that these undergraduates continue in teacher education to obtain a full qualification. The present study investigated how self-efficacy was related to continuing in teacher education, and to commitment, perceived workload, and stress. Moreover, we investigated how mastery experiences, vicarious experiences, social persuasions, and emotional states influenced self-efficacy. Findings based on 69 science undergraduates showed that self-efficacy was positively related to commitment and negatively to workload and stress, but unrelated to continuing in teacher education. Mastery experiences and positive emotional states explained variance in self-efficacy. We call for more research that investigates all sources of self-efficacy and for more attention to preservice teachers' emotional states in research and practice.

Grounded within literature pointing to the value of narrative in communicating scientific information, the purpose of this study was to examine the use of stories as a tool for teaching about natural selection in the context of school science. The study utilizes a mixed method, case study approach which focuses on the design, implementation, and evaluation of narrative-based curriculum materials. The data consisted of questionnaires, classroom observations, and interviews with the students and teachers. The analysis of the data showed that most of the students developed adequate scientific understandings about natural selection and they perceived the narrative as easier to comprehend than the textbook. The findings speak to the need for examining ways of blending narrative effectively into science lessons.

Due to changes in Dutch mathematics education, teachers are expected to use new teaching methods such as enquiry-based teaching. In this study, we investigate how teachers design, implement and evaluate new methods for statistics teaching for 7th-graders during a professional development trajectory based on peer collaboration. We monitored teachers' development in a network of four mathematics teachers from the same school. By using a mixed-methods approach in which we combined data from interviews, concept maps and classroom observations, we describe changes in teachers' practical knowledge. We found how the nature of these changes highly depends on teachers' personal concerns that emerge during the trajectory. Some teachers considered their concerns as challenges stimulating their learning, while other teachers experienced their concerns as a reason to fall back to previous teaching methods. Based on our results, we give some recommendations for organising teacher networks.

This article reports on a longitudinal observation study about students' development in their use of procedures to calculate instantaneous rate of change. Different procedures for solving tasks on rate of change are taught in mathematics and physics classes, and together they form a repertoire. Our study took an actor-oriented perspective, which we operationalized as a search for students' personal constructions of relationships between (1) learning from mathematics and physics classes and (2) interview tasks. We followed 10 students for 2 years (from grade 10 to 12), during which we administered 4 task-based interviews. We analyzed the breadth and connectedness of students' repertoire of procedures and report on the long-term development thereof. We conclude that often procedures are not part of students' repertoire shortly after the first introduction of this procedure in class. Students need time to acquire single procedures, and much more time to develop a broad and connected repertoire. In the development of their repertoire, there are major differences between students. From an actor-oriented perspective, many personal constructions are visible between learning and interview tasks. Students often use procedures that differ from procedures that are most appropriate from an expert's perspective. We also observed from an actor-oriented perspective that words such as velocity, steepness, or slope act as bridge for creating relationships between situations and procedures.

The aim of this study is to evaluate a teaching strategy designed to teach first-year undergraduate life sciences students at a research university how to learn to read authentic research articles. Our approach--based on the work done in the field of genre analysis and argumentation theory--means that we teach students to read research articles by teaching them which rhetorical moves occur in research articles and how they can identify these. Because research articles are persuasive by their very nature, we focused on the rhetorical moves that play an important role in authors' arguments. We designed a teaching strategy using cognitive apprenticeship as the pedagogical approach. It was implemented in a first-year compulsory course in the life sciences undergraduate program. Comparison of the results of a pretest with those of the posttest showed that students' ability to identify these moves had improved. Moreover, students themselves had also perceived that their ability to read and understand a research article had increased. The students' evaluations demonstrated that they appreciated the pedagogical approach used and experienced the assignments as useful. On the basis of our results, we concluded that students had taken a first step toward becoming expert readers.

Primary scientific literature is one of the most important means of communication in science, written for peers in the scientific community. Primary literature provides an authentic context for showing students how scientists support their claims. Several teaching strategies have been proposed using (adapted) scientific publications, some for secondary education, but none of these strategies focused specifically on scientific argumentation. The purpose of this study is to evaluate a strategy for teaching pre-university students to read unadapted primary scientific literature, translated into students' native language, based on a new argumentation analysis framework. This framework encompasses seven types of argumentative elements: motive, objective, main conclusion, implication, support, counterargument and refutation. During the intervention, students studied two research articles. We monitored students' reading comprehension and their opinion on the articles and activities. After the intervention, we measured students' ability to identify the argumentative elements in a third unadapted and translated research article. The presented framework enabled students to analyse the article by identifying the motive, objective, main conclusion and implication and part of the supports. Students stated that they found these activities useful. Most students understood the text on paragraph level and were able to read the article with some help for its vocabulary. We suggest that primary scientific literature has the potential to show students important aspects of the scientific process and to learn scientific vocabulary in an authentic context.

In this qualitative study we used a case study approach to observe and analyse a mathematics teacher who was challenged to redesign her lessons during network meetings with colleagues. Changes in practical knowledge are described by means of concept maps and semi-structured interviews. We applied cycles of change from the Interconnected Model of Professional Growth to describe the teacher's professional development. We show that the teacher's practical knowledge changes in the domain of practical content knowledge, and that controlled experimentation and reflection are necessary conditions to learn a new teaching strategy and to develop a series of lessons for pupils. (Contains 3 figures and 4 tables.)

Learning to read and understand research articles (primary literature) is an important step in the enculturation of higher education students into the scientific community. We presume, based on ideas from the field of genre analysis, that it is important for the development of reading skills to become conscious of the rhetorical structures in research articles. So, we determined how well science students are able to identify 2 important elements of this rhetorical structure: conclusions and grounds. First-year undergraduate life science students who followed a course called "Biomedical Research" made assignments in which they had to identify these 2 elements. We analysed the answers of 20 students in detail and compared their answers with 2 expert readers. Furthermore, we conducted task-based interviews with 4 students to gain more insight into their reading strategies and to determine how they identify conclusions and grounds. Our results show that students and experts defined conclusions and grounds in different ways. Students and experts agreed on the most important conclusion of the articles. However, students identified a wide range of sentences which were not seen as conclusions by the experts. The grounds students mentioned mostly matched their conclusions. Students sometimes failed to mention important grounds for a particular conclusion. In conclusion, our study shows the differences between student and expert readers of primary literature. Based on our results, we formulated criteria for the design of a teaching strategy that aims to improve students' skills for reading primary literature. (Contains 1 figure and 6 tables.)

Polysemy in graph-related practices is the phenomenon that a single graph can sustain different meanings assigned to it. Considerable research has been done on polysemy in graph-related practices in school science in which graphs are rather used as scientific tools. However, graphs in science textbooks are also used rather pedagogically to illustrate domain-specific textbook content and less empirical work has been done in this respect. The aim of this study is therefore to better understand polysemy in the domain-specific pedagogical use of graphs in science textbooks. From socio-cultural and cultural-historical perspectives, we perceive polysemy as irreducible to either the meaning-making (semiotic) resources provided by the graph or its readers who assign meaning to it. Departing from this framework, we simultaneously investigated: (a) the meanings 44 pre-university biology students assigned to the Cartesian plane of a graph that is commonly used as a pedagogical tool in Dutch high school biology textbooks (an electrocardiogram); (b) the semiotic resources provided by this graph; and (c) the educational practices of which it is supposedly a part according to the actions constituted by the textbooks that were to be conducted by students. Drawing on this case, we show polysemy in the pedagogical use of graphs in science textbooks. In turn, we show how this polysemy can be explained dialectically as the result of both the meaning-making resources provided by the textbooks and the graph-related practices in which students supposedly engaged by using their textbooks. The educational implications of these findings are discussed.

Background and purpose: This study examines secondary-school students' opinions on participating in authentic science projects which are part of an international EU project on climate change research in seven countries. Partnerships between schools and research institutes result in student projects, in which students work with and learn from scientists about the global carbon cycle. This study focuses in particular on differences between male and female students, as female students normally like traditional school science less than male students. Sample and design: Data, drawn from 1370 students from 60 secondary schools across Europe, were collected through questionnaires taken at the end of the projects. The evaluated aspects were: organization; enjoyment; difficulty; and impact of the projects. Results: The findings suggest that authentic science education is appreciated very much by both male students and even more by female students. The projects had positive impacts on climate change ideas, in particular for female students. Female students felt that they had learned many new things more often than male students. Conclusions: Both male and female students have positive opinions about the authentic science projects. The results further point to positive effects of activities in which students have an active role, like hands-on experiments or presentation of results. The findings are placed in the international context of science education and their implications for policy are discussed. (Contains 4 tables.)

The Vietnamese curriculum reform which trends toward a student-centered approach requires Vietnamese teacher educators to prepare student teachers for teaching using this approach. In this article, we present a case study of three Vietnamese student teachers working in groups in a methods course to explore Freudenthal's theory of realistic mathematics education (RME). The course emphasized students' knowledge construction in meaningful contexts. Transcripts of class discussions and group discussions, interviews, student teachers' lesson plans, and journal writings were the main data sources that were used to investigate the development of student teachers' views on mathematics and mathematics education during the course. The deliberation about teaching strategies of three subjects working in a group to design lesson plans were also analyzed. The findings showed that the three student teachers explored new meanings of mathematics teaching that caused them to shift from their traditional point of view to a student-centered one. The student teachers were able to adapt the texts of their lessons to suit the student-centered approach. It is noted that among three subjects, there were two student teachers who questioned the realization possibilities of the student-centered approach in the Vietnamese educational context where the social and political conditions are not favorable for teaching with this approach.

The analysis of the undergraduate chemistry curriculum is presented. A new structure is proposed which helps the chemistry departments and students.