Using Variables in School Mathematics: Do School Mathematics Curricula Provide Support for Teachers?

This study employed content analysis to examine 3 popular middle-grades mathematics curricula in the USA on the support they provide for teachers to implement concepts associated with variables in school mathematics. The results indicate that each of the 3 curricula provides some type of support for teachers, but in a varied amount and quality. More specifically, whereas the University of Chicago School Mathematics Project (UCSMP) curriculum provides support for teachers on several aspects of using variables in school mathematics, the support found in the Connected Mathematics 2 and the Math Connects curricula focused mainly on one conception of variables—namely, the use of variables as quantity that varies in the Connected Mathematics 2 curriculum and the use of variables as specific unknowns in the Math Connects curriculum. Overall, the UCSMP curriculum provides the most support for teachers, followed by the Connected Mathematics 2 curriculum, with the Math Connects curriculum recording the least support for teachers to enact variable concepts. It is worth pointing out that, although the 3 curricula collectively provide guidance for teachers to implement variable ideas within meaningful real-world contexts, the supports identified in the respective curriculum were not sufficient in addressing all of the areas that are essential for teaching the many concepts associated with variables in school mathematics effectively. Recommendations for curriculum developers and for international researchers with interest in the roles of variables in school mathematics are provided.     

Teacher–child interaction in Chinese kindergartens: an observational analysis

The goals of this research were to describe the daily life of children and teachers in Chinese kindergarten programmes, to better understand how teacher–child interactions affect both teachers and children. The main assumption guiding this research was that teacher–child interaction is one of the most important processes in early childhood education. A clear understanding of typical teacher–child interactions may help to improve teachers’ support of children’s learning and development. In‐depth field observations of 12 Chinese teachers in six classrooms were conducted using a participant‐observer approach. Five hundred and eighty‐nine teacher–child interaction cases were observed and described. An inductive content analysis of the cases resulted in the creation of nine functional categories for teacher‐initiated interactive behaviours and nine functional categories for child‐initiated interactive behaviours. In this paper, we describe these functional interaction categories and report on their relative frequency in the Chinese kindergarten classrooms involved in this study. Teacher and child interactive behaviours are complementary, depending on the shared meaning of the interaction. Some differences were found in the interactive behaviours of older and younger children with their teachers. We discuss the results in the cultural context of China and conclude that careful and systematic observation and analysis of early childhood classroom interaction is essential for better understanding and improvement of teaching practices.     

Various ways to determine rational number size: an exploration across primary and secondary education

European Journal of Psychology of Education - Understanding rational numbers is a complex task for primary and secondary school students. Previous research has shown that a possible reason is...     

Reading Comprehension of Dutch Deaf Children

In this study, the reading comprehension of deaf children and adolescents in the Netherlands is examined along with their word identification. The reading comprehension of 464 deaf students and the word identification of 504 deaf students between 6 and 20 years of age was examined. The results show the reading comprehension scores of deaf children to be far below the scores of hearing children. On average, the deaf subjects scored at a level equivalent to a hearing child in the first grade. The word identification scores of the deaf children, however, were almost equivalent to the scores of hearing children. Although reading comprehension and word identification appear to be related, this relation does not completely explain the comprehension difficulties encountered by deaf children. Additional factors are required to explain deaf children’s difficulties with reading comprehension.     

Picking the winners by consensus: Grant-giving practice in the Netherlands

The Netherlands form a consensus democracy. In such a society the legitimacy of decisions is of great concern to all. An elaborate system of checks and balances tends to exist and the pressure to join an emerging consensus at meetings is both subtle and tremendously powerful. In the Dutch system of higher education and research the manifestations of the consensus ideal are numerous. This paper highlights them where appropriate. It reviews the Dutch research effort in an international perspective and concludes that R&D expenditure in the Netherlands, measured as a proportion of GDP, is declining. Fairly radical changes in science policy orientation since the 1960s are reviewed and the current frameworks for policy formulation, academic foresight and the organisation of support are sketched. After discussing NWO's different funding instruments, the practices of picking the winners are described in some detail. Three different peer review models are then discussed with special attention to their strengths and weaknesses. The paper's final section is focussed on the evaluation practices in force.     

Social IEP Objectives, Teacher Talk, and Peer Interaction in Inclusive and Segregated Preschool Settings

The purpose of this study was to examine: (a) the role of teacher talk in promoting peer interaction, (b) the adequacy of social IEP objectives to reflect children’s social functioning and guide provision of teacher talk, and (c) differences in children’s peer interaction and teacher talk in inclusive and segregated settings. Thirty children with disabilities and their teachers participated. Overall, we observed low rates of teacher talk thought to support peer interaction; however, when teachers verbally facilitated peer interaction, children were observed interacting more frequently with peers. Children’s social IEPs accurately reflected their current level of social functioning. However, the social IEPs appeared to fail to influence teacher intervention. Finally, children with disabilities in inclusive settings interacted with peers more than children in segregated settings, even though there was no significant difference in amount of teacher talk in the two settings.     

The Relationship Between Undergraduate Attendance and Performance Revisited: Alignment of Student and Instructor Goals

We revisit the relationship between attendance and performance in the undergraduate university setting and apply agency theory in the instructor–student context. Building on agency theory propositions in the educational setting advanced by Smith, Zsidisin, and Adams (2005) , we propose that the student and instructor must align goals to promote the student's achievement of performance learning outcomes, and attendance functions as a behavior‐based alignment mechanism to encourage the convergence of faculty and student interests. Further, we propose that attendance does not equally affect lower‐ and higher‐performing students and that absences are also negatively related to students' cumulative grade point average. We test these hypotheses with data from undergraduates enrolled in management courses at a state university in the southeast. Our results show that attendance is positively related to exam performance, there are more pronounced negative effects of an absence for lower‐performing students than for higher performers, and absences are negatively related to a student's cumulative grade point average. We discuss the implications of our findings for students, instructors, and universities as well as practice in teaching and learning.     

Two components of responding in Pavlovian lick suppression

The present research examined the temporal distribution of responding in a lick suppression paradigm. In Experiment 1, rats were trained with either a 30- or a 120-s conditioned stimulus (CS), which was followed either by a footshock (unconditioned stimulus [US]) or nothing. Licking during the CS was suppressed only in the former condition. Suppression was more pronounced early in the CS. In Experiment 2, rats were exposed to two 30-s or two 120-s CSs, with delivery of the shock being contingent on CS1 for half of the animals and on CS2 for the other half. For both the paired and the unpaired conditions, suppression at the beginning of CS1 was observed for all the groups. By discounting the possibility of generalization between CS1 and CS2, it appears that this initial suppression was not a conditioned response to the CS, but an unconditioned one due to mere exposure to the shock US.     

Some determinants of second-order conditioning

In a Pavlovian conditioning situation, an initially neutral stimulus may be made excitatory by nonreinforced presentations in compound with an established conditioned excitor [i.e., second-order conditioning (SOC)]. The established excitor may be either a punctate cue or the training context. In four conditioned suppression experiments using rats, we investigated whether SOC phenomena parallel other cue interaction effects. In Experiment 1, we found that the response potential of a target stimulus was directly related to the intertrial interval when SOC was mediated by a punctate cue, and inversely related to the intertrial interval when SOC was mediated by the training context. Experiment 2 demonstrated that punctate- and context-mediated SOC are oppositely affected by posttraining context extinction, and Experiments 3 and 4 demonstrated that context- and punctate-mediated SOC are differentially affected by conditioned stimulus (Experiment 3) and unconditioned stimulus (Experiment 4) preexposure treatments. These findings parallel phenomena in conditioned inhibition and cue competition situations.