0000000000428646
AUTHOR
Unni Wathne
Imaginary Dialogues – In-service Teachers’ Steps Towards Mathematical Argumentation in Classroom Discourse
The purpose of this qualitative study was to explore in-service teachers’ first experiences with imaginary dialogues – a form of mathematical writing where students are introduced to a written and unfinished dialogue between two imaginary persons discussing a mathematical problem. Students are supposed to continue working with the problem and to complete the initial dialogue between these persons. In-service teachers were enrolled in a continuing university education mathematics course. They were given the task to try out imaginary dialogues in their classes from grades 4 to 10. Based on in-service teachers’ responses in open-ended self-evaluation forms, the study examined how the in-servic…
Third grade students’ multimodal mathematical reasoning when collaboratively solving combinatorial problems in small groups
The aim of this study is to investigate Norwegian primary school students’ multimodal mathematical reasoning when solving combinatorial problems. The data collection took place in four small groups of altogether thirteen 8–9 years old third-graders. Our study shows a variety of approaches used to solve the given combinatorial problems, such as count-all and grouping. These approaches were characterized by the students’ use of inscriptions that displayed all combinations and inscriptions that did not display all combinations. Moreover, the students used gestures such as pointing and sliding. The students’ multimodal reasoning was characterized by the ways their utterances, inscriptions, and …
Mathematics Video Podcasts as Integrated Elements of Online Lessons in Further University Education: In-Service Teachers’ Flow Experiences
This case-study examined in-service teachers’ perceptions of learning by means of online mathematic lessons consisting of a mix of text and video podcasts. The investigation is part of further university education directed at practicing teachers in lower secondary schools. The course was a distant education course, with in-service teachers learning online only. The research, based on a series of questionnaires and follow-up interviews, examined whether in-service teachers perceived that video podcasts embedded in online lessons fostered their learning compared to reading similar material. The study focused on efficiency, enjoyment, and concentration as perceived conditions for learning in c…
Designed Examples as Mediating Tools: Introductory Algebra in Two Norwegian Grade 8 Classrooms
A critical element in the introduction of algebra is to focus student attention on the basic ideas of algebraic reasoning including the use of concepts such as variable and algebraic expression. In the Norwegian classrooms, representing a student-centered instructional philosophy, the teachers utilized examples and problems that they themselves had designed, and the examples involved resources such as concrete objects and body movements in order to make algebra accessible to students. When designing these examples, teachers thus used their own previous experiences of teaching algebra in an attempt to articulate the passage from arithmetic to algebra.
Teachers' procedures when introducing algebraic expression in two Norwegian grade 8 classrooms
International audience; We investigate similarities and differences in two teachers’ way of introducing algebraic expressions by designed examples. One teacher moves from the specific to the general, and the other moves from the general to the specific. They both mediate the passage from the students’ real world and the school mathematics they know, to algebra.
Engaging Mathematical Reasoning-and-Proving: A Task, a Method, and a Taxonomy
This article is the second paper in a series of papers on studies focusing on teaching mathematical reasoning-and-proving in elementary mathematics classroom. Participants are in-service teachers enrolled in a continuing university education program in mathematics. Results from the first paper suggested the method of imaginary dialogues to have the potential to support in-service teachers in engaging their students in mathematical reasoning-and-proving, and Balacheff’s taxonomy of proofs to support in-service teachers in identifying students’ argumentation. This study is on the following years’ in-service teachers in the program. It examines their perceptions of the usefulness of two consti…
Developing further support for in-service teachers’ implementation of a reasoning-and-proving activity and their identification of students’ level of mathematical argumentation
This is the third in a series of papers focusing reasoning-and-proving. Participants were in-service teachers enrolled in a continuing university education programme in teaching mathematics for grades 5–10. Data were collected from a course assignment in 2018 and 2019, where the in-service teachers reported about their students’ work with a reasoning-and-proving task. Their reports included an identification of the levels the students’ written argumentation reached, based on Balacheff’s taxonomy of proofs. The course assignment’s instructions were expanded for the 2019-cohort. Comparing in-service teachers’ proof level identifications to the researchers’ by statistical analyses, indicated a…
In-Service Teachers’ Perceptions of the Design and Quality of Mathematics Videos in their On-Line Learning
This investigation is part of a continuing education program in mathematics, directed at in-service teachers in lower secondary schools holding teacher certificates. Online mathematics lessons, offered through a distant education course, consisted of a combination of text and video podcasts. University educators’ podcast development was guided by research-based design principles related to e-learning and multimedia instruction. The question arose as to whether in-service teachers enrolled in the course would perceive the podcast design as supportive for their learning. Using questionnaires, this study monitored how in-service teachers perceived podcast quality based on design dimensions. It…