Learning Sequences in the Acquisition of Mathematical Knowledge: Using Cognitive Developmental Theory to Inform Curriculum Design for Pre-K–6 Mathematics Education

ABSTRACT—Using Central Conceptual Structure theory as an heuristic, learning sequences in the acquisition of number knowledge are described in three forms that bridge theory and practice: as a four-stage theoretical progression, as items on a developmental test created to test the theoretical progression, and as learning objectives in a curriculum designed to teach math concepts and skills implied in the theoretical progression. Other aspects of the theory that were used to create teaching methods and materials for the Number Worlds curriculum are also described, as are some of the outcomes of this theory-based program.     

Active learning in a constructivist framework

An important tenet of constructivism is that learning is an idiosyncratic, active and evolving process. Active learning, operationalized by cognitive, metacognitive, affective and resource management learning strategies, is necessary for students to effectively cope with the high level of demands placed on the learner in a constructivist learning environment. Case studies of two students detail contrasting passive and active learning behaviours. Examples of their strategic learning behaviours illustrate that having students involved in activities such as discussions, question answering, and seatwork problems does not automatically guarantee successful knowledge construction. The nature of students' metacognitive knowledge and the quality of their learning strategies are seen to be critical factors in successful learning outcomes.     

University and College Counselors as Athletic Team Consultants: Using a Structural Family Therapy Model

Increasingly, university and college counselors are sought out by their institution's sports coaches for assistance in achieving team goals. Traditional sport psychology models that have the individual athlete as their primary focus are insufficient frameworks for team‐level consultations. The authors believe that systemic approaches may provide an effective alternative. In this article, the authors offer and illustrate S. Minuchin's (1974) Structural Family Therapy as a heuristic model for conceptualizing and intervening with athletic teams.     

Linking pupil and teacher competence in reading and mathematics in Vietnam

This article reports results derived from the national study of Grade 5 in Vietnamese primary schools in which teachers and pupils took tests in reading and mathematics. The test data were calibrated so that teacher and pupil results could be mapped onto the same continuum. Results showed that the overlapping tests for teachers and pupils were appropriate for the pupils and easy for the teachers. Fit to the Rasch model indicated that the sets of items in both the reading and mathematics tests were each measuring a single domain. Teacher performances were predictably higher than those of the pupils. But there was a considerable overlap in scaled scores indicating that many Grade 5 pupils were out-performing a sub- sample of teachers. Of great concern were the analyses of aggregated results at provincial level. It was clear that the distribution of teacher competence in reading and mathematics was related to location of the provinces, and alarmingly so too was the distribution of pupil competence. The relationship between teacher and pupil competence was linear and indicated that pupil chances of improved learning were strongly linked to the competence of the teacher.     

Conceptions of water-related phenomena

Water is an important resource. Surprisingly, research into students' conceptions of water has been confined largely to studies of change of state. This paper reports the results of interviews about underground water, water pollution, the water cycle, and change of state). There were 45 students interviewed about these phenomena: all were in Year 9 or Year 10 in Western Australia from three schools, two country, on emetropolitan. In addition, 715 students in Years 9 and 10 in five government schools, three metropolitan and two country, completed a teacher-made, water topic test. Students appear to have a good understanding of some water-related phenomena, such as the water cycle, but have conceptions about other phenomena, such as the water table, which are not in accord with scientific views. As others have reported, interviews reveal that students often use scientific language without understanding. Specializations: educational technology and the teaching-learning process; public understanding of science and technology.     

Internationalisation of Business Education: Meaning and implementation

The internationalisation of business has been one of the most prominent features of the second half of the twentieth century, with its pace and breadth touching all elements of the value-adding network. In this environment, the higher education sector has been revising its aims and objectives to incorporate an international dimension to the skills and knowledge development of students. However, interpretation of the educational challenges posed by internationalisation in the form of guidelines that specify how the curriculum might be internationalised, is in its infancy. Despite early efforts, little work has been done to translate this trend into a developmental overview of curriculum delivery. This paper begins by synthesising the literature regarding globalisation, curriculum internationalisation and student learning in higher education. It seeks to bridge the gap between the aims of curriculum internationalisation and the subject curriculum. It applies well-accepted educational principles to the task by presenting a three-stage typology of business curriculum internationalisation. These stages are international awareness, international competence and international expertise. Directions for further research are also provided.     

Mathematics achievement of vietnamese grade 5 pupils

This article reports the results of a national survey of mathematics achievement at the end of primary school in Vietnam. A sample of more than 72000 students were assessed from 61 provinces. The items were matched to the Vietnam Mathematics curriculum for Year 5 students. Using a skills audit of the items, a variable of Vietnamese mathematics development was defined following an item response analysis of the data. Findings reveal that the levels of mathematics achievement were relatively high and that the mathematics curriculum was closely aligned with international trends in mathematics for primary school. There were some areas of concern in that lower achievement levels were persistently aligned with low socio economic groups and these were typically located in three regions of Vietnam, heavily populated by ethnic sub-groups. The views expressed in this paper are those of the authors and do not claim to represent the views of the Vietnamese Government in any way. The article is based on a World Bank project (in Vietnam) on achievement at the end of primary school.     

The affective lives of doubled-up Latinx youth: Influences of school experiences,familism, and ethnic identity exploration

Doubled-up Latinx youth experience many daily challenges associated with ethnic minority status and residential instability. Doubled-up youth share housing with noncustodial caregivers such as friends and/or extended family members primarily because of economic hardship and a breakdown in available parental support. Using data from baseline and 10 days of twice-a-day surveys, this study examined how in-school positive experiences, familism (i.e., a perspective that gives precedence to the family), and ethnic identity (i.e., affirmation, exploration, and resolution) influence after school positive (e.g., feeling joyful/happy) and negative (e.g., feeling stressed/anxious) affect among doubled-up Latinx youth (70% female; M_age = 16.5). Results indicate that in-school positive experiences were associated with more after school positive affect and less after school negative affect. In addition, youth with higher levels of familism reported experiencing less after school negative affect. However, gender moderated the relation of ethnic identity exploration and experiences of after school positive affect. Specifically, females with higher levels of ethnic identity exploration reported relatively lower levels of after school positive affect compared with males. Overall, study findings highlight the importance of both person-level and varying contextual influences on the affective lives of doubled-up Latinx youth.     

Una aproximación socio-histórica a la re-mediación

La adquisición de la lectoescritura plantea en nuestras sociedades numerosos problemas que tradicionalmente se le han achacado al individuo como portador de déficits específicos que estarían en la base de cualquier dificultad a la hora de enfrentarse a un texto escrito. Si tenemos en cuenta el origen socio-histórico del proceso lector, nos daremos cuenta de que al niño se le exige en los primeros años de escolaridad un esfuerzo que la humanidad realizó gradualmente y con el apoyo de sucesivos sistemas mediadores que hoy se han suprimido en el proceso de aprendizaje. En este artículo, los autores proponen recuperar esos sistemas mediadores tanto para la enseñanza de la lectoescritura como para la recuperación de los malos lectores.