A problem-posing intervention in the development of problem-solving competence of underachieving, middle-year students

This study reported on the issues surrounding the acquisition of problem-solving competence of middle-year students who had been ascertained as above average in intelligence, but underachieving in problem-solving competence. In particular, it looked at the possible links between problem-posing skills development and improvements in problem-solving competence. A cohort of Year 7 students at a private, non-denominational, co-educational school was chosen as participants for the study, as they undertook a series of problem-posing sessions each week throughout a school term. The lessons were facilitated by the researcher in the students’ school setting. Two criteria were chosen to identify participants for this study. Firstly, each participant scored above the 60th percentile in the standardized Middle Years Ability Test (MYAT) (Australian Council for Educational Research, 2005) and secondly, the participants all scored below the cohort average for Criterion B (Problem-solving Criterion) in their school mathematics tests during the first semester of Year 7. Two mutually exclusive groups of participants were investigated with one constituting the Comparison Group and the other constituting the Intervention Group. The Comparison Group was chosen from a Year 7 cohort for whom no problem-posing intervention had occurred, while the Intervention Group was chosen from the Year 7 cohort of the following year. This second group received the problem-posing intervention in the form of a teaching experiment. That is, the Comparison Group were only pre-tested and post-tested, while the Intervention Group was involved in the teaching experiment and received the pre-testing and post-testing at the same time of the year, but in the following year, when the Comparison Group have moved on to the secondary part of the school. The groups were chosen from consecutive Year 7 cohorts to avoid cross-contamination of the data. A constructionist framework was adopted for this study that allowed the researcher to gain an “authentic understanding” of the changes that occurred in the development of problem-solving competence of the participants in the context of a classroom setting (Richardson, 1999). Qualitative and quantitative data were collected through a combination of methods including researcher observation and journal writing, video taping, student workbooks, informal student interviews, student surveys, and pre-testing and post-testing. This combination of methods was required to increase the validity of the study’s findings through triangulation of the data. The study findings showed that participation in problem-posing activities can facilitate the re-engagement of disengaged, middle-year mathematics students. In addition, participation in these activities can result in improved problem-solving competence and associated developmental learning changes. Some of the changes that were evident as a result of this study included improvements in self-regulation, increased integration of prior knowledge with new knowledge and increased and contextualised socialisation.

Statistical literacy in the elementary school: Opportunities for problem posing

This chapter addresses opportunities for problem posing in developing young children’s statistical literacy, with a focus on student-directed investigations. Although the notion of problem posing has broadened in recent years, there nevertheless remains limited research on how problem posing can be integrated within the regular mathematics curriculum, especially in the areas of statistics and probability. The chapter first reviews briefly aspects of problem posing that have featured in the literature over the years. Consideration is next given to the importance of developing children’s statistical literacy in which problem posing is an inherent feature. Some findings from a school playground investigation conducted in four, fourth-grade classes illustrate the different ways in which children posed investigative questions, how they made predictions about their outcomes and compared these with their findings, and the ways in which they chose to represent their findings.

Prospective elementary school teachers' ways of making sense of mathematical problem posing. 'Modos en que futuros profesores de primaria dan sentido a la invención de problemas matemáticos'.

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Exigencies for engaging undergraduates in rhetorical problem solving : insights from engineering managers and A3 report analyses

Undergraduate education has a historical tradition of preparing students to meet the problem-solving challenges they will encounter in work, civic, and personal contexts. This thesis research was conducted to study the role of rhetoric in engineering problem solving and decision making and to pose pedagogical strategies for preparing undergraduate students for workplace problem solving. Exploratory interviews with engineering managers as well as the heuristic analyses of engineering A3 project planning reports suggest that Aristotelian rhetorical principles are critical to the engineer's success: Engineers must ascertain the rhetorical situation surrounding engineering problems; apply and adapt invention heuristics to conduct inquiry; draw from their investigation to find innovative solutions; and influence decision making by navigating workplace decision-making systems and audiences using rhetorically constructed discourse. To prepare undergraduates for workplace problem solving, university educators are challenged to help undergraduates understand the exigence and realize the kairotic potential inherent in rhetorical problem solving. This thesis offers pedagogical strategies that focus on mentoring learning communities in problem-posing experiences that are situated in many disciplinary, work, and civic contexts. Undergraduates build a flexible rhetorical technê for problem solving as they navigate the nuances of relevant problem-solving systems through the lens of rhetorical practice.

Promoting Statistical Literacy Through Data Modelling in the Early School Years

This chapter addresses data modelling as a means of promoting statistical literacy in the early grades. Consideration is first given to the importance of increasing young children’s exposure to statistical reasoning experiences and how data modelling can be a rich means of doing so. Selected components of data modelling are then reviewed, followed by a report on some findings from the third-year of a three-year longitudinal study across grades one through three.

Modelación como estrategia de enseñanza en un curso con orientación en ciencias naturales

Con la presente comunicación se pretende describir y analizar una experiencia de Modelación llevada a cabo con alumnas de 16-17 años. En ésta, se exponen brevemente: etapas seguidas, temas escogidos por las alumnas, descripción y análisis de un trabajo de problem posing y otro de Modelación propiamente dicha. Es de destacar el interés que en general mostró este grupo de alumnas por temas centrados en el estudio de la dinámica poblacional de diversas especies, fenómeno que se manifestó en ambas actividades. Finalmente se presentan un análisis y discusión de algunas observaciones de la implementación en aula.

Designing problems : what kinds of open-ended problems do preservice teachers pose?

This paper describes preservice teachers' reported experience of problem posing based on self-selected original digital images. The 176 participants from Australia and Canada designed open-ended problems as part of their mathematics education course. Their 444 problems and accompanying photos have been analysed lo explore the types of problems posed and the focus of the mathematical connections. Findings indicate that preservice teachers are challenged when posing open-ended problems however, this process enables them to develop strategies for problem posing and to become more critically aware of the mathematical potential within their environment.

Exploring diverse community discourses : reflections from a local perspective

This paper represents some of the diverse discourses in the social sciences that are not often known by, or considered relevant to, those people interested in community development. On the contrary, I argue that these discourses may in fact be vitally pertinent to understanding the divergent predicaments facing us in our present moment.
After working in the field for twenty years, I am in the final stages of a PhD case study on one of the Victorian 'Community Building Demonstration Projects', based in Melbourne's North. This discussion is therefore based on the intersections between working in a community, traditionally accepted discourses of community development, and 'alternative' discourses that often appear unrelated.
In particular there are seven taken-for-granted cultural stories I will examine: problem posing, holism, social research, post colonial studies, critical social theory, public policy, and eco philosophy, in the hope that these might provide an 'other' story for community and development. Given this broad canvas, I will necessarily be breif on each topic.

The task of designing tasks for teacher education and development

Posing, adapting, and creating worthwhile tasks that support student learning are significant pedagogical practices of teachers. However in mathematics education, task design and curriculum development are not often the responsibility of practicing teachers. Textbooks can become the main source of mathematics problems and teachers often follow the text and its sequence of problems. Although mathematics teachers can benefit from access to research-based curriculum resources, limited opportunities to adapt and design tasks can make it challenging to meet the diverse needs and interests of their students. More opportunities for learning to create problems are needed for both practicing and beginning mathematics teachers. What then is involved in learning to pose, adapt and create worthwhile mathematics tasks? More specifically, how can teacher educators design tasks that support teacher candidates in learning to create mathematical tasks? As teacher educators we have, over the past few years, used our own courses as sites in Australia and Canada for investigating various contexts to support preservice teachers in their learning to adapt and create mathematical tasks. Our research includes both large scale and small qualitative studies to explore the perspectives of teacher candidates on learning to create and pose mathematical problems, the kinds of problems they pose, and the opportunities and challenges this offers us as teacher educators. Our work is inspired by Variation Theory that focuses on learning as the act of awareness and discernment of variation. We are exploring both how variation theory can be useful for preservice teachers in their designing, posing and adapting of mathematical tasks and for teacher educators in their design of such pedagogical tasks. The results of our work support the argument that tasks to design, adapt and pose mathematical problems enhance their pedagogical understanding and should be a feature of teacher education courses. This is a new area for research and practice; further exploration of the suitability of particular tasks in elementary mathematics teacher education is recommended.

Studying mathematics teacher education: analysing the process of task variation on learning

Self-study of variations to task design offers a way of analysing how learning takes place. Over several years, variations were made to improve an assessment task completed by final-year teacher candidates in a primary mathematics teacher education subject. This article describes how alterations to a task informed on-going developments in self-study of one assessment task employed in an online subject. Analysis of my journal, notes from conversations with colleagues, teacher candidates’ work on the task and responses to online forums, and survey data inspired variations focused on better exploration of key concepts involved in the task, raising of focal awareness, developing a stronger professional eye in the students and the author, adaptations for multiple curriculum levels, and explorations of dual teacher–student perspectives. The overall challenge has been to support teacher candidates to learn to design effective open-ended tasks with a critical professional eye. Descriptions of the changes made to the task and the development of my own professional eye as a consequence of the application of self-study are included. Data show that variations to the task increased teacher candidates’ understanding of mathematics problem posing and generated pedagogical insights for task design.

O processo de conscientização na sala de aula de língua espanhola

This article discusses the awareness process of students in a Spanish as a foreign language classroom, at a Centre of Language Studies in a city in the state of São Paulo, Brazil. The frame of reference is Paulo Freire's pedagogy (FREIRE, 1980, 1984, 1987, 1999, 2000), Wallerstein (1983) and Schleppegrell (1997)'s investigations which are important to the comprehension of the relation between Freirean's pedagogy and the language teaching. This is a qualitative research and it focuses on action research practice in a Spanish language classroom, in which a syllabus based on Paulo Freire's pedagogy was implemented in order to verify how the target language was used in the classroom (MENEGHINI, 2001). Data analysis and discussion are based on data triangulation and classroom interactions are taken on primary data. The implementation of this research suggests that the problem posing tasks on themes chosen from the student's realities are the way which leads to the awareness.

Negociações na formação de professores de Física: construções conjuntas e resolução de conflitos em problematização da prática educacional

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Física dos anos iniciais: estudo sobre a queda livre dos corpos através da metodologia da mediação dialética

The model used in Brazilian schools, based on both traditional and progressive education, transmits information without worrying to show the real meaning of things, and without taking into consideration the previous knowledge of the pupil. How to work with the contents of human knowledge in a meaningful way? One alternative way is the Methodology of Dialectical Mediation (MDM), which consists in four steps or pedagogical moments, rescuing, problem posing, systematizing and producing. This theoretical option considers the educational work as a relationship involving teaching, learning and contents, which are taken as independent moments tightly connected to the ongoing work, instead of isolated elements or static terms. The aim of the present work is to clarify the Methodology of Dialectical Mediation and develop a class proposal according to the MDM approach to the problem of the free falling bodies (gravity, material means and shape). To evaluate the methodology, questionnaires were applied after experiments, with the involvement of students at each predominant moment. The results suggested that the MMD, combined with experimental activity, is a tool that enhances the overcoming of immediate knowledge, allowing students to reach a better understanding of the scientific knowledge.

A problematização em educação em saúde: percepções dos professores tutores e alunos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)