ABC problem in elementary mathematics education: Arithmetic <Emphasis Type="Italic">before</Emphasis> comprehension

Mathematical habits of prospective teachers affect problem comprehension and success and expose their beliefs about mathematics. Prospective elementary teachers (PSTs) (n = 121) engaged in a problem solving activity each week in class. Data were collected from PSTs enrolled in an undergraduate elementary mathematics methods course at a Southeastern State University over multiple semesters (six semesters, seven classes). PSTs’ solution methods for one intentionally misleading mathematics problem were analyzed using a convergent parallel mixed methods content analysis. Two-thirds of PSTs misunderstood the problem scenario and directly translated numbers from the problem text. PSTs who answered correctly used a problem model strategy to comprehend the scenario and were more likely to use multiple models, draw a diagram, and draw a diagram before using another model. However, a large number of PSTs who answered incorrectly also used multiple models and drew diagrams. Self-correction was not common (8 of 121), because their equations did not provide feedback or support comprehension. Three kinds of imprecision also affected problem comprehension and were evident in both correct and incorrect solutions. Intentionally misleading problems helped PSTs see consequences of their mathematical habits and highlighted the importance of sense making and precision when creating problem models.     

Assessing the progress and the underlying nature of the flows of doctoral and master degree candidates using absorbing Markov chains

In this paper, absorbing markov chains are used to analyse the flows of higher degree by research candidates (doctoral and master) within an Australian faculty of business. The candidates are analysed according to whether they are full time or part time. The need for such analysis stemmed from what appeared to be a rather poor completion rate (as reported by the University concerned). However, this reported completion rate was a ‘macro’ figure that aggregated PhD and Master (by full time and part time) completions together. If there really was a problem, then the Faculty needed to know where in the system it was and what potentially might then be done to remedy the problem. The assembling of data into an appropriate database was difficult and required considerable care, but an adequate database was developed. The application of the absorbing markov chains to the problem resulted in an increase in the level of understanding associated with the long term underlying probabilities of completion and also expected durations of candidature. This information highlighted one area of concern. With the information gained from this study, appropriate strategies can subsequently be put in place for the rectification of some of the areas of concern discovered in the analysis. Areas for further research are also highlighted in this paper. Based on an earlier version of a paper delivered at the Western Decisions Sciences Institute 34th Meeting, Vancouver, Canada, 2005.     

Dyslexia as a limitation in the ability to process information

In an earlier paper (Miles and Wheeler 1975) it was reported that dyslexic subjects, aged over 13, were less able than suitably matched non-dyslexic subjects to respond correctly to arrays of tachistoscopically presented digits. A further experiment is now reported involving a younger age-group: 15 dyslexic subjects, average age twelve and one-half, were matched for spelling age with 15 non-dyslexic subjects, average age eight and one-half; and since the dyslexic subjects were appreciably less successful it is argued that “maturational lag” does not, on its own, fully account for the difference in performance between the two groups. A similar procedure was repeated with 41 dyslexic and 41 non-dyslexic subjects, all aged between 10.4 and 14.4, both with and without the introduction of a visual masking stimulus immediately after the test stimulus. Twenty undergraduate “fast-readers,” 20 undergraduate “slow-readers,” and four undergraduate dyslexic subjects were also compared both on their responses to tachistoscopically presented digits and on their performance in a visual search task. The results, taken in conjunction, suggest that dyslexia can be regarded as some kind of limitation in the ability to process information, perhaps affecting in particular the “visual code store” postulated by Posner et al. (1969). This paper was prepared for deliveryin absentia at the 27th Annual Conference of The Orton Society, in New York City, November 1976.     

Rorschach responses of dyslexic children

Fifteen dyslexic children between the ages of 8 and 16 were given the Rorschach ink blot test and their responses were compared with those of 12 suitably matched controls. It was found that they made very considerable use of the shape of the cards, but much less use of the other determinants (color, texture, etc.). Unlike the controls they seldom turned the cards around so as to obtain some fresh “view,” and the overall number of responses per person was considerably less, with many of them giving only one response per card. It is suggested that the educational and social pressures on a dyslexic child often make him reluctant to commit himself in a context where “playing safe” is socially acceptable.     

The role of fictive kinship relationships in mediating classroom competition and supporting reciprocal mentoring

Previous research has suggested that competitive classroom environments can play a role in perpetuating race and class inequalities. However, classroom competition can also promote learning, and eliminating it could do students a disservice. This paper draws on research literature and data from a qualitative study by Konstantinos Alexakos, Jayson K. Jones, and Victor H. Rodriguez on fictive kinship in order to explore the conditions under which classroom competition could benefit students from non-dominant groups. Based on their data, I argue that competition can support the learning of students from non-dominant groups, provided that it takes place in the context of strong emotional ties and successful interaction rituals. I also discuss the role of competition in facilitating reciprocal mentoring, as students seek knowledge and skills from each other in order to participate in solidarity-building classroom interactions. In addition, I show how their study challenges a perceived dichotomy between competition and cultural orientations towards communalism.     

Socialising principals: early career primary school principals in Trinidad and Tobago

This paper utilises an interpretivist framework and recent developments in practice theory to examine the conditions which influence practices of socialising into the role of school principal in Trinidad and Tobago. The results indicate that for the 11 early career primary school principals, role socialisation occurs within complex practice landscapes, where the practices of preparing classroom teachers for the principalship materialise within a context of contest. There is conflict between historical antecedents and the expectations and practices of socialising institutions such as the church, the school, the community and the Ministry of Education. This small-scale study has implications for leadership preparation practices and highlights principal socialisation as a challenge of context and history.     

Forum: structure, agency, and the development of students’ identities as learners

In this forum, we discuss the ways in which the culture of science has become conflated with categorical groupings of students according to race, class, and gender – so as to better understand how Black female students from economically disadvantaged backgrounds may become alienated from dominant school discourses that emphasize college and non-college bound trajectories. In addition, we examine the power and limitations of creating spaces inside and outside of science classrooms that value student discourses, goals, and ways of being. Specifically, we debate whether cogenerative dialogues can allow for (a) conscious critical conversations that cut across student, teacher and administration levels, (b) expanded possibilities for local action, and (c) the building of solidarity and respect amongst stakeholders.     

Disabled Learners in South Asia: lessons from the past for educational exporters

South Asia's historical heritage of ideas and practices for educating children with special needs contains many of the approaches that western teachers discovered independently in the past 150 years. These include close observation of children's current abilities, adjusting the curriculum to individual needs, valuing the social benefits even where intellectual progress is weak, allowing more time for learning, using specially designed materials, educating children with disabilities in ordinary schools, and providing role models of adult achievers who have disabilities. These approaches are here illustrated with stories from ancient India and educational documents from the British Raj. The cultural heritage has largely been ignored during the inflow of western educational ideas to South Asia. Some of the simpler approaches were displaced by the growing professionalisation of special education in the late 19th century. Casual integration of children with mild and moderate disabilities is still obscured in modern integration debates. To facilitate exchanges on a basis of mutual respect and reciprocity, the cultural and conceptual riches of South Asia's educational history must be rediscovered.