Prospective Elementary School Teachers’ Ways of Making Sense of Mathematical Problem Posing

The study tackled prospective teachers’ sense-making of mathematical problem posing and the impact of posing different contextual problems on their learning. Focus was on the generation of new problems and reformulation of given problems. Participants were 40 prospective elementary teachers. The findings provide insights into possible ways these teachers could make sense of problem posing of contextual mathematical problems and the learning afforded by posing diverse problems. Highlighted are five perspectives and nine categories of problem posing tasks to support development of proficiency in problem-posing knowledge for teaching

Modos en que futuros profesores de primaria dan sentido a la invención de problemas matemáticos

The study tackled prospective teachers’ sense-making of mathematical problem posing and the impact of posing different contextual problems on their learning. Focus was on the generation of new problems and reformulation of given problems. Participants were 40 prospective elementary teachers. The findings provide insights into possible ways these teachers could make sense of problem posing of contextual mathematical problems and the learning afforded by posing diverse problems. Highlighted are five perspectives and nine categories of problem posing tasks to support development of proficiency in problem-posing knowledge for teaching.El estudio indagó sobre los modos en que futuros profesores de primaria dan sentido a la invención de problemas matemáticos y el impacto de plantear diferentes problemas contextualizados en su aprendizaje. El foco fue la invención de nuevos problemas y la reformulación de otros dados. Los participantes fueron 40 futuros maestros de primaria. Los resultados proporcionan elementos sobre posibles modos en que estos maestros dan sentido a la invención de problemas matemáticos y el aprendizaje que ofrece plantear diversos problemas. Se destacan cinco perspectivas y nueve categorías de tareas en la invención de problemas para apoyar el desarrollo de la competencia de plantear problemas en la enseñanza

POST-SECONDARY STUDENTS’ LEARNING OF DESCRIPTIVE STATISTICS THROUGH STORY-BASED TASKS

This paper reports on one aspect of a larger project that investigated the use of inquiry-oriented, story-based tasks in teaching statistics. Specifically, its focus is on identifying levels of understanding of descriptive statistics concepts that students in a first-year university business statistics course were able to develop through their engagement in a story-based task. Understanding was framed by Skemp’s (1976) theoretical perspectives of instrumental and relational understanding. Data sources consisted of students’ written responses to the story-based task during the course. Findings indicated that most of the students were able to develop instrumental understanding and a partial level of relational understanding of the concepts. In general, findings suggest that learning statistics through stories has the potential to have a positive impact on students’ understanding of concepts in areas that previous research suggests is difficult for students to learn

Problem-Based Learning, Assessment Literacy, Mathematics Knowledge, and Competencies in Teacher Education

Problem-based learning could have a great impact in teacher education not only to support prospective teachers’ learning, but also to help them to design and implement learner-centered experiences to satisfy requirements of reform-based curriculum. In this paper, we discuss the nature and role of problem-based learning to support authentic learning opportunities in an undergraduate teacher education program. We address its use in an educational assessment course aimed at developing prospective teachers’ assessment literacy and competencies. We focus on two sections of the course for elementary school prospective teachers in which students were also engaged in activities involving assessment in teaching mathematics and share examples of the content of the course. A study of the impact of the course on the students’ knowledge is in progress.

Researching the expertise of mathematics teacher educators in initial teacher education settings

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Mathematics Teachers’ Learning Through Inquiry

Inquiry-based teaching strives to engage students in learning mathematics with understanding in the classroom. Therefore, there is great interest in supporting teachers to meet this pedagogical challenge by developing practices that promote such an educational environment at different school levels. A powerful way for teachers to learn and transform their teaching is through teacher inquiry. This paper presents a model for inquiry into mathematics teaching based on the perspectives of theorists directly associated with teacher education. This model is described as an overarching inquiry cycle in which teachers begin with practice, pose a pedagogical problem, understand a key construct in the problem, hypothesize an inquiry-teaching model, test/apply it, and finally revise/apply this model. This approach is illustrated with a self-directed professional development process aimed at helping elementary teachers to develop understanding of inquiry-based teaching of mathematics

Commentary on the special issue: Seeing self-based methodology through a philosophical lens

A mathematics teacher educator’s (MTE) use of self-based methodologies goes beyond developing MTE professional knowledge by contributing scholarly inquiry into MTE work. Existing discussions of MTEs’ use of self-based methodologies have provided descriptions of the methodologies and examples of their use by MTEs to unpack their practice. What is less clear is why MTEs elect to use self-based methodologies. Yet central to understanding and validating self-based methodologies as a means of developing knowledge in mathematics teacher education is understanding the aims of MTEs who use such methodologies. On the basis of author interviews, drafts, and final papers for this special issue, we illustrate and describe MTE assumptions about ontology, epistemology, and ethics of research. Our interpretations through these lenses led to findings about the philosophical underpinnings of self-based methodologies. Using these findings, we argue that the philosophical underpinnings of self-based methodologies as utilized by MTE authors in this special issue are efforts to conduct research in ways that align with views of self in different contexts

Commentary on Thematic Special Issue: Seeing Self-Based Methodology Through a Philosophical Lens

A mathematics teacher educator’s (MTE) use of self-based methodologies goes beyond developing MTE professional knowledge by contributing scholarly inquiry into MTE work. Existing discussions of MTEs’ use of self-based methodologies have provided descriptions of the methodologies and examples of their use by MTEs to unpack their practice. What is less clear is why MTEs elect to use self-based methodologies. Yet central to understanding and validating self-based methodologies as a means of developing knowledge in mathematics teacher education is understanding the aims of MTEs who use such methodologies. On the basis of author interviews, drafts, and final papers for this special issue, we illustrate and describe MTE assumptions about ontology, epistemology, and ethics of research. Our interpretations through these lenses led to findings about the philosophical underpinnings of self-based methodologies. Using these findings, we argue that the philosophical underpinnings of self-based methodologies as utilized by MTE authors in this special issue are efforts to conduct research in ways that align with views of self in different contexts