Constructivism in Mathematics Classrooms: Listening to Ghanaian Teachers’ and Students’ Views

One of the challenges of implementing a new curriculum is how to bridge the gap between the underlining principles of the curriculum and the cultural and social orientations of the society which includes teachers and students. This article reports on a study that explored how the cultural and social orientations of teachers and students can influence the implementation of a constructivist curriculum in mathematics classrooms. The data for the study came from 250 students and 41 mathematics teachers, using questionnaires, observations, and interviews. The results showed that inasmuch as mathematics teachers and their students acknowledge the importance of student’s active participation and teamwork, these practices have not been fully conceptualised into the Ghanaian mathematics classroom due to some cultural factors. Two main cultural factors were discovered from the analyses of the results. Firstly, the culture of acknowledging only correct answers in class has a negative impact on individual students’ confidence and participation during mathematics lessons. Also, the culture of teamwork is not fully accepted within Ghanaian classrooms as most students find it difficult working in groups and accepting and appreciating each other’s view. It was evident in all lessons that students were ridiculed by their peers when they provide a wrong answer to a question and this affected individual students’ participation in the classroom. Therefore, we suggested that teachers should be pro-active in promoting a classroom environment which is free from fear and intimidation to motivate students to be actively involved in the classroom discourse.     

Spontaneous partitioning: Pre-schoolers and discrete items

This study addresses the question of whether a dealing strategy that is widely used by young children in clinical interviews occurs in less structured situations. Our findings are that it did not in the setting we examined, namely the performance of a routine counting task, by pre-schoolers with the opportunity of sharing sweets when the task was completed. We discuss reasons for the apparent discrepancies between the results for clinical interviews and less structured situations.     

Are You Satisfied? PhD Education and Faculty Taste for Prestige: Limits of the Prestige Value System

This paper empirically evaluates Caplow and McGee??s (The academic marketplace, 1958) model of academia as a prestige value system (PVS) by testing several hypotheses about the relationship between prestige of faculty appointment and job satisfaction. Using logistic regression models to predict satisfaction with several job domains in a sample of more than 1,000 recent social science PhD graduates who hold tenure-track or tenured faculty positions, we find that the relationship between prestige of faculty appointment and job satisfaction is modified by PhD program prestige. Graduates of high prestige PhD programs value prestige more highly and graduates of low prestige programs value salary more highly. We explain our findings by incorporating reference group theory and a theory of taste formation into our model of the academic PVS, which identifies PhD programs as sites of socialization to different tastes for prestige (a process of cultural transmission) in addition to their well recognized role in transmission of human and social capital. We discuss practical and theoretical implications of our findings in relation to efforts to measure PhD program quality and to understand the structure of academic labor markets.     

The effect of illustrations in arithmetic problem-solving: Effects of increased cognitive load

Arithmetic word problems are often presented accompanied by illustrations. The present study examined how different types of illustrations influence the speed and accuracy of performance of both good (n = 67) and poor arithmeticians (n = 63). Twenty-four arithmetic word problems were presented with four types of illustrations with increasing information value. The results show that illustrations can have a detrimental effect on performance on arithmetic word problems, produced by irrelevant, redundant or interacting sources of information. Principles from cognitive load theory are used to explain the results, in particular in relation to (poor) working memory ability.     

Mathematical induction: A pedagogical discussion

It is observed that many students have difficulty in producing correct proofs by the method of mathematical induction. The notion of a correct proof by this method is analysed mathematically. Subsequently, the topic is analysed into behavioural skills and subjected to a conceptual analysis. Common misconception of induction are considered, with recommendations for their remediation. Finally, criteria for the analysis and evaluation of textbook treatments of induction are evolved and applied to a selection of texts.     

Efficacy of using non-linear pedagogy to support attacking players’ individual learning objectives in elite-youth football: A randomised cross-over trial

ABSTRACT

The present study examined the efficacy of a coaching curriculum, based on non-linear pedagogy, on improving attacking players’ individual learning objectives (ILOs) in elite-youth football. Participants included 22 attacking players (i.e., centre-forwards, wide-players and attacking midfield players) from a professional football academy in England. The players were randomly appointed to both control (CON) and intervention (INT) periods following baseline measures. The INT (non-linear) and CON (linear) periods were both designed to support the ILOs provided to each player as part of the elite player performance plan. The study adopted a randomised cross-over design and ILOs considered important for attacking players (i.e., strong foot finishing, weak foot finishing, 1-v-1 and decision-making) were evaluated using the Loughborough Shooting Skill Test. The results showed significant differences for INT in 1-v-1 (P< 0.02) and decision-making (P< 0.01). However, there were no significant differences for strong foot finishing, weak foot finishing or time taken. These results support non-linear pedagogy in developing 1-v-1 game play and decision-making but not for technical shooting proficiency.     

The foresight SAGA: Predicting future numbers of students

Recent attempts at predicting the numbers of studentsin Britain likely to seek places in higher education in the future are briefly described and their methods of prediction analysed. The author argues that future numbers cannot be reliably predicted since in recent years there has been no identifiable regular pattern from which a sound prediction might be made. Ways of improving the figures are suggested but the author proposes that these figures be used in the context of flexible planning, i.e., plans that incorporate the possibility of substantial modification at any stage.     

The role of two reading strategies in text comprehension: An eye fixation study in primary school children

This study examined whether 10–12‐year‐old children use two reading strategies to aid their text comprehension: (1) distinguishing between important and unimportant words; and (2) resolving anaphoric references. Of interest was the question to what extent use of these reading strategies was predictive of reading comprehension skill over and above decoding skill and vocabulary. Reading strategy use was examined by the recording of eye fixations on specific target words. In contrast to less successful comprehenders, more successful comprehenders invested more processing time in important than in unimportant words. On the other hand, they needed less time to determine the antecedent of an anaphor. The results suggest that more successful comprehenders build a more effective mental model of the text than less successful comprehenders in at least two ways. First, they allocate more attention to the incorporation of goal‐relevant than goal‐irrelevant information into the model. Second, they ascertain that the text model is coherent and richly connected.