University students’ grasp of inflection points

This paper describes university students’ grasp of inflection points. The participants were asked what inflection points are, to mark inflection points on graphs, to judge the validity of related statements, and to find inflection points by investigating (1) a function, (2) the derivative, and (3) the graph of the derivative. We found four erroneous images of inflection points: (1) f ′ (x)?=?0 as a necessary condition, (2) f ′ (x)?≠?0 as a necessary condition, (3) f ″ (x)?=?0 as a sufficient condition, and (4) the location of “a peak point, where the graph bends” as an inflection point. We use the lenses of Fischbein, Tall, and Vinner and Duval’s frameworks to analyze students’ errors that were rooted in mathematical and in real-life contexts.     

Relationships between teachers’ metacognitive knowledge and students’ metacognitive knowledge and reading achievement

The study examined the relationships between teachers’ metacognitive knowledge of reading strategies and their students’ metacognitive knowledge and reading comprehension. The study was carried out among language art teachers (N?=?34) and their students (N?=?534) in the last year of primary school (ninth grade) in Estonia. Multilevel modeling was used to test the hypotheses of relationships between students’ metacognitive knowledge and reading comprehension, while controlling for students’ previous reading comprehension (in eighth grade) as well as the relations between teachers’ metacognitive knowledge of reading strategies and students’ metacognitive knowledge and comprehension. The results showed that students’ metacognitive knowledge of reading strategies related to their reading comprehension, concurring with previous findings. The main finding was that teachers’ metacognitive knowledge of reading strategies significantly related to their students’ metacognitive knowledge, but not to reading comprehension. These results indicate that students’ reading comprehension may be supported by improving their metacognitive knowledge of reading strategies. In addition, the findings highlight the importance of teachers’ metacognitive knowledge in students’ metacognitive knowledge.     

Developing preschool teachers’ knowledge of students’ number conceptions

This article describes a study that investigates preschool teachers’ knowledge of their young students’ number conceptions and the teachers’ related self-efficacy beliefs. It also presents and illustrates elements of a professional development program designed explicitly to promote this knowledge among preschool teachers. Results indicated that teachers’ knowledge of students’ number conceptions improved and that their related self-efficacy increased. Furthermore, prior to participating in the programs, a significant negative correlation between knowledge and self-efficacy was reported. However, no significant correlation was found after the program.     

University students’ success: A psycho-sociological approach

The aim of this paper is to propose a basic model to analyse processes of change in educational institutions taking into account both individual and contextual variables. It aims to identify the basic factors of change in order to contribute to reduce the dispersion of research projects, both from close subjects and one subject alone within human sciences, in order to make scientific accumulation easier and to guide social practice better. This proposal is based on Cryer and Elton’s (Studies in Higher Education, 1: 75–86, 1990) contributions, in this case applied to the learning processes of university students. They may account for static and dynamic aspects. To prove its coherence, it has been statistically compared with the data of a survey carried out among university students in Catalonia (Spain).     

Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge?

This research analyses preservice teachers’ knowledge of fractions. Fractions are notoriously difficult for students to learn and for teachers to teach. Previous studies suggest that student learning of fractions may be limited by teacher understanding of fractions. If so, teacher education has a key role in solving the problem. We first reviewed literature regarding students’ knowledge of fractions. We did so because assessments of required content knowledge for teaching require review of the students’ understanding to determine the mathematics difficulties encountered by students. The preservice teachers were tested on their conceptual and procedural knowledge of fractions, and on their ability in explaining the rationale for a procedure or the conceptual meaning. The results revealed that preservice teachers’ knowledge of fractions indeed is limited and that last-year preservice teachers did not perform better than first-year preservice teachers. This research is situated within the broader domain of mathematical knowledge for teaching and suggests ways to improve instruction and student learning.     

University students’ conceptions of learning across multiple domains

Research on students’ conceptions of learning is a growing and complex area of interest in the field of psychology of education. Even though much of the investigation addressed to explore conceptions of learning at the university level, still less research has considered how naïve (i.e. ‘learning as reduction of deficit knowledge through individual effort’) and sophisticated (i.e. ‘learning as opportunity and self-efficacy’) conceptions of learning are related to personal and contextual factors. This research investigated how gender, academic area, and level of study influence university students’ conceptions of learning. Three hundred forty-six university students participated in the study. They were either from humanities (240) or technical-scientific (106) areas of study and they were attending either a Bachelor (140) or Master’s degree (206) course. Conceptions of learning were explored using a self-report instrument (Learning Conceptions Questionnaire; LCQ). A MANOVA revealed that females show conceptions of learning more related to social and motivational aspects of learning with a greater personal involvement, compared with males. No typical pattern of conceptions of learning was found for humanities students or for technical-scientific students. Increasing with the level of study, students showed both naïve and sophisticated conceptions of learning increased, since both ‘learning as reduction of deficit knowledge through individual effort’ and ‘learning as opportunities and self-efficacy’ were more likely. Implications of these results and future lines of research will be discussed.     

Teacher-education students’ views about knowledge building theory and practice

This study investigated the effects of engaging students to collectively learn and work with knowledge in a computer-supported collaborative learning environment called Knowledge Forum on their views about knowledge building theory and practice. Participants were 24 teacher-education students who took a required course titled “Integrating Theory and Practice in Teaching.” Data mainly came from (1) student discourse recorded in a Knowledge Forum database, (2) a survey that examined students’ views about knowledge building, and (3) interviews with regard to students’ perceived barriers to implementing knowledge building theory in teaching. Findings suggest that with sustained discourse to construct their collective understanding of the relationships between theory and practice in teaching for a semester, the participants were able to attain more informed and practical views about knowledge building theory. In addition, students’ perceived barriers to implementing knowledge building in teaching were identified and strategies to help overcome these barriers discussed.     

University students’ use of motivational regulation during one semester

This study examined the interplay between university students' trajectories of motivational regulation and autonomous motivation across one semester, exploring both between and within person components. Participants (N = 193) from one large class reported motivation in two-week intervals over the course of one semester. Bivariate latent curve models with structured residuals revealed rates of change in motivational regulation and autonomous motivation were not linear, declining across the first ten weeks of the semester then bouncing back in the final month. Between-person effects of individual change demonstrated mirroring relationships of latent intercepts and slopes across the semester. Within-person findings revealed that autonomous motivation was a negative predictor of future motivation regulation. Students' grade point average only predicted students’ beginning level of motivational regulation. It appears that students with higher states of autonomous motivation view motivation regulation as unnecessary or even a potential threat to their learning pleasure and satisfaction.     

Effects of biology teachers’ professional knowledge and cognitive activation on students’ achievement

This study examined the effects of teachers’ biology-specific dimensions of professional knowledge – pedagogical content knowledge (PCK) and content knowledge (CK) – and cognitively activating biology instruction, as a feature of instructional quality, on students’ learning. The sample comprised 39 German secondary school teachers whose lessons on the topic neurobiology were videotaped twice. Teachers’ instruction was coded with regard to cognitive activation using a rating manual. Multilevel path analysis results showed a positive significant effect of cognitive activation on students’ learning and an indirect effect of teachers’ PCK on students’ learning mediated through cognitive activation. These findings highlight the importance of PCK in preservice biology teachers’ education. Items of the rating manual may be used to provide exemplars of concrete teaching situations during university seminars for preservice teacher education or professional development initiatives for in-service teachers.     

University faculty members’ and students perceptions of university academic systems

There are no provisions for routine evaluations or rankings of the universities in the Federal Republic of Germany. Consequently, it has become a matter of magazines to carry out inquiries into the opinions of students and faculty members in order to assess the quality of education at German universities. One of the first studies of this type was carried out by one of Germany's most respected magazines, Der Spiegel. The results of this study, particularly the questionnaires and validity of the given response categories, were subject to vehement criticism. In this context the exploratory study described in this chapter was conceived. Students and faculty were asked to give their personal and individual views about the academic system at their given universities. In order to guarantee the subjectivity of each individual's frame of reference, the responses of students and faculty were recorded, analyzed, and compared by means of computer-assisted content analysis. The results will be used to validate quantitative instruments of inquiry and to formulate proposals for their improvement.     

Managing reading and related literacy difficulties: University students’ perspectives

This study explored the experiences of university students who identified as always having had reading difficulties. Thirty-three participants, all from one Australian university, were surveyed and 10 were also interviewed. Findings revealed that many shared academic challenges related to studying, along with a belief that their difficulties were not well understood by staff or peers. While participants disclosed many similar personal struggles related to completing their studies, positive attributes such as determination and time management strategies were frequently mentioned as instrumental in allowing them to reach university. Experiences were more variable regarding awareness of, access to, and satisfaction with university-based support and academic adjustments. To facilitate optimal inclusive educational practices, this study supports the need for greater awareness among staff about challenges faced by these university students along with a more individualised and targeted approach to providing them with academic supports and accommodations.     

Distinguishing between knowledge and beliefs: students’ epistemic criteria for differentiating

“I believe that he/she is telling the truth”, “I know about the solar system”: what epistemic criteria do students use to distinguish between knowledge and beliefs? If knowing and believing are conceptually distinguishable, do students of different grade levels use the same criteria to differentiate the two constructs? How do students understand the relationship between the two constructs? This study involved 219 students (116 girls and 103 boys); 114 were in 8th grade and 105 in 13th grade. Students had to (a) choose which of 5 graphic representations outlined better the relationship between the two constructs and to justify their choice; (b) rate a list of factual/validated, non-factual/non-validated and ambiguous statements as either knowledge or belief, and indicate for each statement their degree of truthfulness, acceptance and on which sources their views were based. Qualitative and quantitative analysis were performed. The data showed how students distinguish knowledge from belief conceptually and justify their understanding of the relationship between the two constructs. Although most students assigned a higher epistemic status to knowledge, school grade significantly differentiated the epistemic criteria used to distinguish the two constructs. The study indicates the educational importance of considering the notions of knowledge and belief that students bring into the learning situation.     

University students’ and teachers’ conceptions of teaching and learning in the biosciences

In this study we compare university teachers’ and first-year students’ conceptions of teaching and learning at the Faculty of Environmental and Biological Sciences. The conceptions were analysed using data from open-ended questionnaires. The results showed that at the beginning of studies the gap between teachers’ and students’ conceptions of teaching and learning is substantial. This finding has important implications for the educational process. In order to enhance successful studying from the beginning of students’ university careers, it is important for teachers to become aware of the differences between students’ and teachers’ conceptions of learning.     

From knowledge sharing to knowledge creation: A blended knowledge-management model for improving university students’ creativity

Creativity and knowledge management are both important competences that university students need to strive to develop. This study therefore developed and evaluated an instructional program for improving university students’ creativity based on a blended knowledge-management (KM) model that integrates e-learning and three core processes of KM: knowledge sharing, knowledge internalization, and knowledge creation. Moreover, this study investigated the underlying mechanisms that achieve the effectiveness of this model. A 17-week instructional program was conducted. The findings from both quantitative and qualitative analyses suggest the following. The blended KM model is effective in improving knowledge, dispositions, and abilities of creativity. The online sharing and evaluation of creative products, learning communities and discussions, and the practice of creativity strategies have substantial effects on all three aspects of creativity. The observation and peer evaluation of group assignments and creativity-related feedback enhance the learning of knowledge and dispositions. Finally, the creation of products and scaffolding of a teacher are critical to skill improvement.     

University students’ perceptions of summative assessment: The role of context

We report on a mixed-method study that compared students’ perceptions of summative assessment across two distinct disciplines – education and mathematics, at two research-intensive institutions in the UK. The disciplines chosen represent opposing positions in Biglan’s classification of academic disciplines, as well as having very different assessment practices. Results suggest that these education students prefer to be assessed by methods they perceive to discriminate on the basis of academic abilities. Moreover, they perceive the traditional closed-book examination as inadequate to assess the capabilities which are key to being successful in their subject, which fits some but not all of the general findings in the literature. However, comparing these results with those of an identical study with mathematics students, we find that the perceptions of summative assessment are very different. We account for that difference by suggesting that students’ epistemic beliefs play a role in shaping these perceptions and conclude that, in designing summative assessment in higher education, generalised and centralised forces for change need to be tempered by contextual and disciplinary factors.     

An instrument for assessing primary students’ knowledge of information graphics in mathematics

Information graphics have become increasingly important in representing, organising and analysing information in a technological age. In classroom contexts, information graphics are typically associated with graphs, maps and number lines. However, all students need to become competent with the broad range of graphics that they will encounter in mathematical situations. This paper provides a rationale for creating a test to measure students’ knowledge of graphics. This instrument can be used in mass testing and individual (in‐depth) situations. Our analysis of the utility of this instrument informs policy and practice. The results provide an appreciation of the relative difficulty of different information graphics, and provide the capacity to benchmark information about students’ knowledge of graphics. The implications for practice include the need to support the development of students’ knowledge of graphics, the existence of gender differences, the role of cross‐curriculum applications in learning about graphics, and the need to explicate the links among graphics.     

A boundary-crossing approach to support students’ integration of statistical and work-related knowledge

Vocational students and beginning professionals typically find it hard to integrate the mathematics and statistics that they have learned at school with work-related knowledge. To explore how such an integration process could be supported, we conducted an intervention in secondary vocational laboratory education. Our boundary-crossing approach was informed by the literature on boundary crossing and accompanying learning mechanisms (e.g., reflection in the form of perspective making and taking, and transformation in the form of hybridization). We hypothesized that reflection, as making and taking perspectives on school-taught and work-related knowledge, could lead to transformation, i.e., help students integrate these types of knowledge into a hybridized whole. Data collection included video and audio recordings of five 1-h meetings with three students, the data from their research projects, and interviews with the teacher and two workplace supervisors. The analysis of the students’ reasoning during the meetings revealed that their level of integrating school-taught statistics and work-related knowledge increased significantly and with a medium effect size. This suggests that a boundary-crossing approach can support students in integrating school-taught and work-related knowledge.     

Developing teachers’ knowledge of students as learners of mathematics through structured interviews

A structured interview process is proffered as an effective means to advance prospective teachers’ understandings of students as learners of mathematics, a key component of pedagogical content knowledge. The interview process is carried out in three phases with the primary objective of developing listening skills for accessing students’ mathematical thinking. The interviews adhere to clinical interview procedures for discovering cognitive activities and, accordingly, are initiated by presenting an open-ended mathematics task. Three rounds of interviews were completed by undergraduates enrolled in a middle school mathematics methods course. Anecdotal data generated by their interview reports suggest that the structured interview process engenders an interpretive orientation to listening to students and furthers awareness of how students make sense of mathematics. Features of the interview process that may limit its potential benefits are discussed; recommendations for further study are proposed.