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University of Georgia, 2020
Collective mathematical argumentation is powerful for student learning of mathematics and teachers’ questioning strategies are pivotal in orchestrating collective argumentation. Adapting Habermas’ (1998) construct of rational behavior, this study demonstrates how teachers’ questioning can be framed based on this construct a teaching method to regulate argumentative discourse.
The purpose of this study was to investigate how teachers use rational questioning to organize collective argumentation with respect to Habermas’ three components of rationality as a way to develop students’ awareness of the rationality requirements of argumentation.
The participants in this study were two beginning secondary mathematics teachers who have learned about supporting collective argumentation during their teacher education program as well as during professional development for several years. Four video-recorded lessons within a school year for each participating teacher were chosen to serve as the main data source for this study.
In this dissertation, I develop a Rational Questioning Framework from Habermas’ theory of rationality and integrated it with Toul min’s model for argumentation (1958/2003) as a more powerful analytic tool to investigate teacher questioning strategies concerning both rationality requirements of argumentation and fundamental components of argumentation. […]
Georgia State University - Department of Mathematics and Statistics, 2020
Over the past decade, research about students’ proof capabilities has been a prevalent topic in collegiate mathematics education. Also, while not as prevalent, there has been in- terest in research about the teaching practices of the introduction to proof and other proof– based collegiate mathematics courses.
To investigate the link between these two topics, this dissertation examined the assessment and teaching practices of Dr. Wyatt, a research mathematician who participated in mathematics education research alongside mathematics educators from multiple universities, utilized as the instructor of a Transition–to–proof course.
An analysis of responses of his former students, observations of his instruction, the examination of a variety of types of assessments used during the course, and an interview at the end of the semester are used to determine the impact his participation in mathe- matics education research had on his beliefs about teaching and the assessment of students’ mathematical understanding/knowledge.
This dissertation utilizes an assessment framework developed by Mejia-Ramos et al. (2012) (which focuses on students’ proof comprehension) and a framework about teaching practices at the collegiate level developed by Speer et al. (2010).
The findings in this dissertation indicate that Dr. Wyatt uses several types of assessment that focus on the foundational aspects of mathematical proof while providing targeted feedback to students’ responses. Further, Dr. Wyatt’s teaching practices have been enhanced through the use of a new assessment question type modeled on what he learned from the mathematics education research project.To know more…
D. Di Girolamo, M.A. Mariotti, F. Morselli, I. Rebella
26 marzo 2021 - 17:00-18:30
Corso di formazione per insegnanti “L’insegnamento della matematica tra ricerca didattica e prassi scolastica"
AIRDM e la CIIM - Commissione Italiana per l’Insegnamento della Matematica dell’UMI
University of Minnesota, 2020
Proof is considered foundational for mathematical understanding and has received increased attention in mathematics education over the last two decades. This mixed methods research study explores opportunities to develop mathematical knowledge for teaching proof during secondary mathematics teacher preparation. I used the mathematical knowledge for teaching proof framework (Lesseig, 2011) to develop a survey distributed to secondary mathematics methods instructors.
This survey provided data pertaining to each instructor’s learning goals around proof and instructional strategies they use to support opportunities to develop their teacher candidates’ mathematical knowledge for teaching proof. In addition, interviews were conducted with five participants to provide further details on their survey responses and their instructional strategies. The responses related to learning goals were often focused on providing opportunities to develop common content knowledge for proof.
The findings also indicated that factors such as educational level and departmental assignment were not associated with providing opportunities intended to support the development of mathematical knowledge for teaching proof. Instead, a teacher educator’s approach towards proof in their methods course(s) is influenced by their view of what counts as proof.
This view varied across all participants and is not unlike the variation discovered in previous research. Further research must explore reasonable expectations for what counts as proof at the secondary level and must identify specific strategies for drawing connections between common content knowledge for proof and the work of teaching.
Jorge Andrés Toro Uribe
Universidad de Antioquia, Facultad de Educación, Medellín, Colombia, 2020
The doctoral work Argumentation of the mathematics teacher during the discussion of tasks in classroom contributes to the research in Mathematics Education in the argumentation and proof, and communication and language lines, when it comes to understanding how the mathematics teacher's argumentation is like in usual class lessons where the discussion of a number of tasks takes place.
A theoretical perspective is adopted, which is based on the articulation of two theoretical considerations: argumentation and discourse in mathematics classroom. In this thesis, according to a qualitative interpretative approach based on the observation of two high school teachers, we sought to answer the question: how is the teacher's argumentation during the discussion of tasks in classroom? For this purpose, three auxiliary questions were raised to direct the data analysis:
(i) What the features of the mathematics teacher's argumentation are during the discussion of tasks in classroom?
(ii) What the purposes of the mathematics teacher’s argumentation are during the discussion of tasks in classroom? and
(iii) What the conditions that activate the mathematics teacher's argumentation are during the discussion of tasks in classroom?
The answer to the first auxiliary question took into account elements of discourse analysis and theoretical aspects, which allowed identifying features in three dimensions. In one of the dimensions, the communicative, statements, questions and gestures or expressions are recognized. In another dimension, interactional, participation, means and class rules, convincing and discussing are recognized. And in a last dimension, the epistemic one, the treatment of the mathematical object, concepts and definitions, retaking other lessons, treatment of errors, procedures and answers, and justifying and/or refuting are recognized. Each of the dimensions is accompanied by a series of teacher actions that allow identifying them in class lesson situations.
The answer to the second question required the inclusion of terms such as argumentative intervention and closure, which allowed identifying certain educational purposes in the teachers' argumentation in the different selected episodes for analysis.
The answer to the third question required the adaptation of a theoretical reference, in order to identify indicators within conditions that activate the teacher's argumentation.
The following are identified: questions and opportunities for participation in communicative and interactive strategies; argumentative interventions and closures in the lesson approach; type of task and task solution procedure in the task approach; and treatment of mathematical objects, retaking other lessons, anticipate future lessons and ways to justify and refute professional knowledge.
In addition to these answers, an extension to a theoretical reference regarding the typology of teacher reactions is proposed as an input of this research. A definition that could be useful in considering argumentation in the mathematics classroom is presented, a link between argumentation and opportunities for participation and therefore with learning is shown, and argumentation is included as part of the teacher's mathematical discourse.PDF