Source: Studying Teacher Education, Vol. 11, No. 3, 294–311, 2015
(Reviewed by the Portal Team)
This article outlines the development of the author's professional eye as a teacher educator in mathematics education in Australia through the self-study process of initiating and evaluating task variations and describes how this process was used to generate interactions that supported teacher candidates’ assignment work.
This article focuses on one example of this research, where the intended object of learning is the construction of open-ended mathematics questions, which can be used by teachers for inclusive curriculum development.
Data were collected through the author's journal, notes from conversations with colleagues, teacher candidates’ work on the task and responses to online forums, and survey data.
The 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.
The impact of the feedback over time from multiple voices – teacher candidates and academic teaching staff – and the information gathered from the work samples of the assessment tasks have produced a task that is more educationally rich than its initial version.
Generally, the teacher candidates’ reactions to the task have remained very positive over the years, even though the variations to the assessment task have increased their workload.
Data show that variations to the task increased teacher candidates’ understanding of mathematics problem posing and generated pedagogical insights for task design.
Furthermore, reflecting on the inclusion of reasoning in the posed questions provided these teacher candidates with insights into how to access children’s thinking more readily.
In summary, with each year of self-reflection and reconstruction of this assessment task, variations have assisted in strengthening the opportunities for pedagogical growth in mathematics education, for teacher candidates and for the author as a teacher educator.
On-Going Reflections on the Task
Additionally, as part of the current task, the teacher candidates now write, after each question, three possible responses that children might offer. This inclusion has assisted many of the teacher candidates to focus on the defining aspect of open-ended questions: that they have multiple possible acceptable answers. However, while this added step in the assessment task has been successful in reducing the number of difficulties with the openness of problems, it has been noted by teaching staff and in analysis of submitted assignments that some teacher candidates have been presenting (say) one correct and two incorrect responses.
The problem pictures task forms only part of the assessment for the course Professional Practice and Mathematics: Designing an Inclusive Program, but it is sufficient for illustrating key aspects of the use of variation in studying teacher education.
Self-study has helped this process by underpinning the author's consideration of how to create and vary relevant spaces of learning that assist teacher candidates to (a) notice mathematics in the environment with a professionally critical eye, (b) understand how to focus on important aspects of their assessment tasks as well as strategies for pedagogy and curriculum development, and (c) work together in an online environment to develop and refine generally high-quality resources for teaching mathematics in primary schools.