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Mathematical Tasks from the Teachers’ Point of View. A Multiple Case Study of Teachers’ Goals in Norwegian Vocationally Oriented Classrooms

Linda Gurvin Opheim of the Faculty of Engineering and Science the University of Agder has submitted her thesis entitled «Mathematical Tasks from the Teachers’ Point of View. A Multiple Case Study of Teachers’ Goals in Norwegian Vocationally Oriented Classrooms» and will defend the thesis for the PhD-degree Wednesday 23 March 2022.

The teachers describe mathematical tasks that might help them resolve and change issues in their classrooms. They want mathematical tasks that will help them get their students to work, to be more motivated or to gain a better understanding. These are teachers’ rationales for initiating changes.

Linda Gurvin Opheim

PhD Candidate

The disputation will be held digitally and on campus. Spectators may follow the disputation on campus or digitally - link available below.

Linda Gurvin Opheim of the Faculty of Engineering and Science the University of Agder has submitted her thesis entitled «Mathematical Tasks from the Teachers’ Point of View. A Multiple Case Study of Teachers’ Goals in Norwegian Vocationally Oriented Classrooms» and will defend the thesis for the PhD-degree Wednesday 23 March 2022.

She has followed the PhD-programme at the Faculty of Engineering and Science at the University of Agder with specilisation in Mathematical Sciences, Scientific field Mathematics Education

Summary of the thesis by Linda Gurvin Opheim:

«Mathematical Tasks from the Teachers’ Point of View. A Multiple Case Study of Teachers’ Goals in Norwegian Vocationally Oriented Classrooms»

This study reports on the teachers’ perspectives when it comes to mathematical tasks, and changes teachers make in their everyday classroom.

Research within mathematics education is a complex field with many different factors, and there has been a huge effort by researchers to develop and improve teaching in mathematics. Still, it turns out that this is not easily transferred to the classrooms (Artigue, 2008; Breiteig & Goodchild, 2010).

Past experiences also reveal that new curriculums are not implemented as intended (Breiteig & Goodchild, 2010).

Disconnection between practice and research

There is a perceived disconnection between practice and research which has vexed education for a very long time (Silver & Lunsford, 2017).

To address these issues and understand the teachers’ perspectives, two research questions were formulated:

  1. What characterizes teachers’ descriptions of mathematical tasks they want to use in their classroom?
  2. What rationales do teachers express when they initiate changes to mathematical tasks during the collaboration?

The research is designed as a multiple case study (Stake, 2006), where the phenomenon to be studied is the teachers’ descriptions of mathematical tasks they want to use in their classrooms.

The cases are four teachers in the context of their classes and the schools they work at. Each case consists of a task design process, which include designing tasks, refining them, implementing, and evaluating the tasks.

Methodology

I have used techniques from grounded theory in the analysis process, and conducted open coding based on the ideas from Glaser and Strauss (1967).

Through the inductive analysis process, I have identified three different dimensions of how the teachers describe mathematical tasks:

  • Outcome of tasks
  • Characteristics of tasks and
  • Students’ reactions to tasks

The data was further analyzed with respect to the change sequences for each design process conducted with the teachers, using the Interconnected Model of Professional Growth developed by Clarke and Hollingsworth (2002).

The answers to the two research questions are clearly intertwined, because the teachers’ descriptions of mathematical tasks are linked to their rationales for initiating changes.

Motivation

According to the findings in this research project, teachers describe mathematical tasks mostly by the desired outcome of the tasks. These desired outcomes of tasks are related to their students and the need to resolve three types of classroom issues:

  • work
  • motivation and
  • understanding

However, there were also some aspects the teachers might struggle with that could hinder certain types of mathematical tasks. These were:

  • didactics
  • communication and
  • mathematics

The teachers describe mathematical tasks that might help them resolve and change issues in their classrooms. They want mathematical tasks that will help them get their students to work, to be more motivated or to gain a better understanding. These are teachers’ rationales for initiating changes.

However, some of the teachers are also making changes to improve one or more of the teacher aspects they might struggle with. This is evident when analyzing the change processes through the Interconnected Model of Clarke and Hollingsworth (2002).

This research project has shown that the Interconnected Model of Clarke and Hollingsworth (2002) also can be useful for analyzing change processes from the teachers’ perspective in the classroom when designing and implementing mathematical tasks.

However, I argue that such an analysis requires an expansion of the Interconnected Model, to include the student domain.

References

Artigue, M. (2008, April). Didactical design in mathematics education. Paper presented at the Nordic research in mathematics education, Copenhagen.

Breiteig, T., & Goodchild, S. (2010). The development of mathematics education as a research field in Norway: An insider's personal reflections. In The first sourcebook on Nordic research in mathematics education: Norway, Sweden, Iceland, Denmark and contributions from Finland (pp. 3-9). Charlotte, N.C.: Information Age Publishing.

Clarke, D. J., & Hollingsworth, H. (2002). Elaborating a model of teacher professional growth. Teaching and Teacher Education, 18(8), 947-967. https://doi.org/10.1016/S0742-051X(02)00053-7

Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: strategies for qualitative research. New York: Aldine de Gruyter.

Stake, R. E. (2006). Multiple case study analysis. New York: Guilford Press.

Disputation facts:

The trial lecture and the public defence will take place onlineregistration link below and in Auditorium B3 007, Campus Kristiansand

Head of the Department of Mathematical Sciences Ingvald Erfjord, University of Agder, will chair the disputation.

The trial lecture Wednesday 23 March at 10:30 hours
Public defence Wednesday 23 March at 12:30 hours

Given topic for trial lecture«Teachers’ perspectives, use and enactment of mathematical tasks: Synthesis of mathematics education research literature»

Thesis Title«Mathematical Tasks from the Teachers’ Point of View. A Multiple Case Study of Teachers’ Goals in Norwegian Vocationally Oriented Classrooms»

Search for the thesis in AURA - Agder University Research Archive, a digital archive of scientific papers, theses and dissertations from the academic staff and students at the University of Agder.

The thesis is available here:

https://uia.brage.unit.no/uia-xmlui/handle/11250/2984236

 

The CandidateLinda Gurvin Opheim: (1977, Ål i Hallingdal) General teacher Vestfold University College (2005) Masters degree in Mathematics Education UiA (2011) Master thesis: «Elevers kognitive engasjement i matematikkoppgaver» (English summary). Present position: Assistant Professor at the Department of Mathematical Sciences, University of Agder.

Opponents:

First opponent: Professor Ruhama Even, Weizmann Institute of Science, Israel

Second opponent: Professor Alf Coles, University of Bristol, UK

Associate Professor Niclas Larson, Universitety of Agder, is appointed as the administrator for the assessment committee.

Supervisors in the doctoral work were Professor John Monaghan, UiA (main supervisor) and Professor Simon Goodchild, UiA  (co-supervisor)

What to do as an audience member:

The disputation is open to the public, but to follow the trial lecture and the public defence digitally, transmitted via the Zoom conferencing app, you have to register as an audience member: (If you attend the didputation in the Auditorium, you do not need to register)

https://uiano.zoom.us/meeting/register/u5Ipf-mprj0iHtZCuHwbtXdFFoOHv29doAJc

A Zoom-link will be returned to you. (Here are introductions for how to use Zoom: support.zoom.us if you cannot join by clicking on the link.)

We ask audience members to join the virtual trial lecture at 10:20 at the earliest and the public defense at 12:20 at the earliest. After these times, you can leave and rejoin the meeting at any time. Further, we ask audience members to turn off their microphone and camera and keep them turned off throughout the event. You do this at the bottom left of the image when in Zoom. We recommend you use ‘Speaker view’. You select that at the top right corner of the video window when in Zoom.

Opponent ex auditorio:

The chair invites members of the public to pose questions ex auditorio in the introduction to the public defense, with deadlines. It is a prerequisite that the opponent has read the thesis. Questions can be submitted to the chair Ingvald Erfjord on e-mail ingvald.erfjord@uia.no