Students’ images of mathematics

Students’ judgments about “what counts” as mathematics in and out of school have important consequences for problem solving and transfer, yet our understanding of the source and nature of these judgments remains incomplete. Thirty-five sixth grade students participated in a study focused on what activities students judge as mathematical, and how they make their judgments. Students completed a photo sorting activity; took, viewed, and captioned their own photos of mathematics; viewed and commented on classmates’ photos; and participated in a small group discussion. Across multiple sources of data, findings showed that students attended to two major features of photos and activities when making judgments: surface cues present in the photos, such as numbers and money, and the possibility for mathematical action. Some students looked for the possibility of mathematics, while others asked if mathematics was necessary. Students also gave higher ratings to activities with which they had personal experience. The article concludes with possible implications for practice.     

Students’ Views of Nature of Science

Science & Education - Nature of science (NOS) is considered an important aspect of scientific literacy. Despite efforts in guiding school students to develop more adequate NOS views, little is...     

Students’ conception of infinite series

This is a report of a study of students’ understanding of infinite series. It has a three-fold purpose: to show that students may construct two essentially different notions of infinite series, to show that one of the constructions is particularly difficult for students, and to examine the way in which these two different constructions may be built so that we may uncover ways to help students improve their understanding. The theoretical framework consists of action–process–object–schema theory and the specific model of conceptions in Balacheff’s theory of conception, knowing, and concept. Approaching the problem from these two different theoretical perspectives allows us to provide different and at the same time complementary explanations of observed phenomena. The two different infinite series constructions are, briefly stated, series as an infinite unending process of addition and series as a sequence of partial sums. Students are found to have difficulty building an understanding of series as a sequence of partial sums and thus tend to have difficulty in problem situations that require this interpretation. The study uses semi-structured interviews with 10 graduate students. The interviews explore situations that might give insight into students’ notion of the sequence of partial sums.     

University Students’ Understanding of Chemical Thermodynamics

This study explored undergraduate students’ understanding of the chemistry topic of thermodynamics using a 4-tier diagnostic instrument, comprising 30 questions, and follow-up interviews. An additional objective of the study was to assess the utility of the 4-tier instrument for use in studies on alternative conceptions (ACs) as there has been no study done on it since its introduction in the literature in the year 2010. A total of 296 students majoring in Chemistry at a university in Singapore participated in this study—88 students in the preliminary study, 102 students in the pilot study and 106 students in the main study. This article reports on the results obtained with students in the main study; their age ranges from 20 to 22 years. Comprising answer and reason tiers plus associated confidence ratings, the 4-tier diagnostic instrument enabled the eliciting of 34 ACs harbored by the undergraduates as well as the strengths of these ACs. Of concern to note is that even for questions which were answered correctly, the mean confidence was not very high. The results of this study reiterate the point that thermodynamics is a topic fraught with conceptual difficulties and ACs. Based on the results from this study, the potential of the 4-tier test for AC studies is further underscored. Some implications of the study are discussed.     

An Exploratory Study of the Supervision of Ph.D./Research Students’ Theses

Twenty-five faculty members were interviewed to determine how they supervised their Ph.D. students’ thesis preparation. A content analysis of the interview data indicated that the majority of them were task-focused. They supported their students intellectually, emotionally, and structurally. Some academics considered their students as colleagues, and a few developed research teams. Watching the students grow and develop and doing research with them as colleagues were the most enjoyable aspects of the supervision process. The integrated competing values framework (ICVF) was used to illustrate how most of the study participants were task-focused and were not able to deliver paradoxical roles; nor were they able to reflect on their supervisory capabilities and learn from those reflections.

Seven Years After the Call: Students’ and Graduates’ Perceptions of the Re-envisioned Ed.D.

Given continued confusion about the Ed.D.degree, universities affiliated with the Carnegie Project on the Education Doctorate (CPED) have re-envisioned it using a set of guiding principles and design features. In this study, we investigated why students and graduates chose to pursue the Ed.D., what and how they learned, how they viewed themselves, and whether they perceived their programs to be aligned with CPED’s principles. Data were collected from 296 participants at 14 CPED institutions using an online survey. Results indicated respondents agreed that their programs were aligned with CPED principles, helped them meet their professional and personal goals, and developed them as scholarly practitioners.     

University Students’ Understanding of Electromagnetic Induction

This study examined engineering and physical science students' understanding of the electromagnetic induction (EMI) phenomena. It is assumed that significant knowledge of the EMI theory is a basic prerequisite when students have to think about electromagnetic phenomena. To analyse students' conceptions, we have taken into account the fact that individuals build mental representations to help them understand how a physical system works. Individuals use these representations to explain reality, depending on the context and the contents involved. Therefore, we have designed a questionnaire with an emphasis on explanations and an interview, so as to analyse students' reasoning. We found that most of the students failed to distinguish between macroscopic levels described in terms of fields and microscopic levels described in terms of the actions of fields. It is concluded that although the questionnaire and interviews involved a limited range of phenomena, the identified explanations fall into three main categories that can provide information for curriculum development by identifying the strengths and weaknesses of students' conceptions.     

Students’ educational use of Facebook groups

The aim of the article is to explore educational use of student-managed Facebook groups in upper secondary education (in Denmark). Much research on educational potentials of Facebook has studied groups managed by teachers. However, there is a lack of in-depth research on Facebook groups managed by students and without participation from teachers. As this study shows, students’ use of student-managed groups differs from their use of teacher-managed tools such as learning management systems (LMSs). The article presents an empirical study based partly on a content analysis of 3139 posts and 15,018 replies within five Facebook groups, and partly on a questionnaire answered by 1463 students and 148 teachers. The results of the study show that whereas LMSs were seen by students primarily as institutional systems of the teacher, Facebook groups have an educational potential to be used by students for peer-to-peer learning.     

Cross-Grade Comparison of Students’ Understanding of Energy Concepts

The aims of this cross-grade study were (1) to determine the level of understanding of energy concepts of students at different academic grades and the differences in understanding between these grades and (2) to analyse the conceptual development of these students. Two hundred and forty-three students at 3 different levels (high school, undergraduate, and postgraduate) participated in this study. The students’ understandings of energy concepts were determined using a questionnaire, which requested them to define the concept verbally, and to represent it graphically. The most important findings of this study may be summarised as follows. Students from the different groups generally succeeded in defining ‘energy’ in a similar way, namely as the ‘ability to do work’. Nevertheless, some students (including those at university) also provided different alternative conceptions related to the energy concept. In addition, some students also found difficulty in visually analysing the relationships between different variables using graphs. This finding could help explain why attainment levels of all groups falls short in questions that involve the graphical representation of data.     

Diagnosing Students’ Understanding of the Nature of Models

Students’ understanding of models in science has been subject to a number of investigations. The instruments the researchers used are suitable for educational research but, due to their complexity, cannot be employed directly by teachers. This article presents forced choice (FC) tasks, which, assembled as a diagnostic instrument, are supposed to measure students’ understanding of the nature of models efficiently, while being sensitive enough to detect differences between individuals. In order to evaluate if the diagnostic instrument is suitable for its intended use, we propose an approach that complies with the demand to integrate students’ responses to the tasks into the validation process. Evidence for validity was gathered based on relations to other variables and on students’ response processes. Students’ understanding of the nature of models was assessed using three methods: FC tasks, open-ended tasks and interviews (N?=?448). Furthermore, concurrent think-aloud protocols (N?=?30) were performed. The results suggest that the method and the age of the students have an effect on their understanding of the nature of models. A good understanding of the FC tasks as well as a convergence in the findings across the three methods was documented for grades eleven and twelve. This indicates that teachers can use the diagnostic instrument for an efficient and, at the same time, valid diagnosis for this group. Finally, the findings of this article may provide a possible explanation for alternative findings from previous studies as a result of specific methods that were used.     

Students’ understanding of the structure of deductive proof

While proof is central to mathematics, difficulties in the teaching and learning of proof are well-recognised internationally. Within the research literature, a number of theoretical frameworks relating to the teaching of different aspects of proof and proving are evident. In our work, we are focusing on secondary school students learning the structure of deductive proofs and, in this paper, we propose a theoretical framework based on this aspect of proof education. In our framework, we capture students’ understanding of the structure of deductive proofs in terms of three levels of increasing sophistication: Pre-structural, Partial-structural, and Holistic-structural, with the Partial-structural level further divided into two sub-levels: Elemental and Relational. In this paper, we apply the framework to data from our classroom research in which secondary school students (aged 14) tackled a series of lessons that provided an introduction to proof problems involving congruent triangles. Using data from the transcribed lessons, we focus in particular on students who displayed the tendency to accept a proof that contained logical circularity. From the perspective of our framework, we illustrate what we argue are two independent aspects of Relational understanding of the Partial-structural level, those of universal instantiation and hypothetical syllogism, and contend that accepting logical circularity can be an indicator of lack of understanding of syllogism. These findings can inform how teaching approaches might be improved so that students develop a more secure understanding of deductive proofs and proving in geometry.     

The Accuracy of Students’ Judgments of Their Teacher’s Opinions

Monte Carlo methods were employed to evaluate the degree to which canonical function and structure coefficients may be differentially sensitive to sampling error. Sampling error influences were investigated across variations in variable and sample sizes, across variations in average within-set correlation sizes, and in across-set population correlation sizes. Sixty-four different research situations were investigated, and for each situation 1,000 random samples were drawn. Results suggest that both sets of coefficients are roughly equally influenced by sampling error, except perhaps when some intradomain correlation coefficients are quite large. Thus, the case for emphasizing interpretation of structure coefficients must be made on a psychometric basis rather than on the grounds that structure coefficients are less sensitive to sampling error influences, notwithstanding the positions previously taken by some theorists.     

Teachers’ and Students’ Conceptions of Good Science Teaching

Capitalizing on the comments made by teachers on videos of exemplary science teaching, a video-based survey instrument on the topic of ‘Density’ was developed and used to investigate the conceptions of good science teaching held by 110 teachers and 4,024 year 7 students in Hong Kong. Six dimensions of good science teaching are identified from the 55-item questionnaire, namely, ‘focussing on science learning’, ‘facilitating students’ understanding’, ‘encouraging students’ involvement’, ‘creating conducive environment’, ‘encouraging active experimentation’ and ‘preparing students for exam (PSE)’. Significant gaps between teachers’ and students’ conceptions on certain dimensions have been revealed. The inconsistency on the dimension ‘PSE’ is particularly evident and possible reasons for the phenomenon are suggested. This study raises the important questions of how the gap can be addressed, and who is to change in order to close the gaps. Answers to these questions have huge implications for teacher education and teacher professional development.     

A Critical Review of Students’ and Teachers’ Understandings of Nature of Science

Science & Education - There is widespread agreement that an adequate understanding of the nature of science (NOS) is a critical component of scientific literacy and a major goal in science...     

Students’ Preconceptions and Perceptions of Science-Oriented Studies

Do non-science, technology, engineering, and mathematics (STEM) students’ views about STEM studies correspond with how STEM students actually perceive these studies? This paper deals with this issue by comparing higher education students’ attitudes towards STEM studies between those who actually did a STEM study and those who did not. The attitudes of the first category of students have been referred to as perceptions and the attitudes of the second category as preconceptions. The study included 1,935 students in higher education. The results confirm both small and large differences between the preconceptions and perceptions, and show significant differences between suitably qualified students (i.e. eligible for STEM studies) and other students. At the end of this paper, we will discuss the implications of this study for future research and offer some suggestions for practice.     

Upper High School Students’ Understanding of Electromagnetism

Although electromagnetism is an important component of upper secondary school physics syllabuses in many countries, there has been relatively little research on students’ understanding of the topic. A written test consisting of 16 diagnostic questions was developed and used to survey the understanding of electromagnetism of upper secondary school students in Turkey (n = 120) and England (n = 152). A separate test consisting of 10 questions on the visualization of spatial rotation was used to investigate the hypothesis that students’ ability to visualize three‐dimensional situations from two‐dimensional representations might influence learning of electromagnetism. Many students’ responses showed misunderstandings and inconsistencies that suggested they did not have a coherent framework of ideas about electromagnetism. Common errors included confusing electric and magnetic field effects, seeing field lines as indicating a “flow”, using cause–effect reasoning in situations where it does not apply, and dealing with effects associated with the rate of change of a variable. Performance on the spatial rotation test was, however, only weakly correlated with performance on the electromagnetism questions. The findings suggest the need to develop teaching strategies that help students to visualize magnetic field patterns and effects, and assist them in integrating ideas into a more coherent framework.     

Cultivation of Students’Intercultural Awareness in CET

Language is the carrier of culture and it is also an integral part of culture. Therefore, learning English requires us not only master the English language knowledge and skills, but also understand t...