Methodology
المؤلف:
Steve Thornton & Sue Wilson
المصدر:
Enhancing Teaching and Learning through Assessment
الجزء والصفحة:
P132-C13
2025-06-25
616
Methodology
Journal writing (Artzt, 1999; Brown, 2001), case studies (Hammermas et al., 2001), professional conversations (Britt et al., 2001; Thornton & Blain, 2002) and the preparation and presentation of structured portfolios (Frid & Sparrow, 2003) are all recognized as valuable tools to promote pre-service teachers' capacity to be reflective practitioners.
In the study described below pre-service teachers were required to reflect on their knowledge and to see themselves as active researchers of their own teaching in the context of the Standards for Excellence described above.
One of the authors teaches a subject Secondary Teaching Studies (Mathematics) to students at the University of Canberra, Australia. This subject is a one-semester subject that forms part of either a one-year Graduate Diploma in Education or of the final year of a four-year Bachelor of Education degree. Students enrolled in this subject hope to teach mathematics to secondary students, aged 11 to 18, in the following year. For most of these students this subject of 36 hours is the only one in which they look specifically at how students learn mathematics, at mathematics curriculum, and at different approaches to teaching mathematics. All students also undertake a four-week period of Professional Experience, during which time they work full-time in a school under the guidance of an experienced teacher of mathematics.
Assessment for this subject typically involves three assignments: an exercise in micro-teaching, the development of a set of detailed lesson plans, and the accumulation and presentation of a portfolio of activities, resources, lesson plans and reflections during the semester and particularly during the period of Professional Experience. While these assessment tasks have immediate and obvious practical value, it is debatable to what extent they meet the criteria of sustainable assessment, nor to what extent they promote the development of teacher identity, as described above. Yet for these students, this is their only pre-service experience in mathematics education, hence it is critical that they are well positioned to become life-long learners of the art and craft of teaching mathematics.
It is noteworthy that many, but not all, of the students involved in this class were mature-aged students, who already had varied life experiences and a strong sense of personal identity. Two of the students had left extremely well-paid careers to become teachers, others had experience as parents and community leaders. These students had a strong sense of why they wanted to become teachers and what they hoped to achieve. In general they "wanted to make a difference". They were also very aware of their own experiences as students in mathematics classes, and while they had been successful, they felt that their school experiences had not engaged them, and had not promoted the development of deep mathematical understanding. In the words of one student, "I don't think I will make a very good maths teacher, because I have just begun to realize that I don't really understand anything I learned at school - I was just good at it."
One author, the lecturer of the subject, had been concerned for some time that the portfolio presented by students tended to be little more than an unfocused collection of resources, journal articles and lesson plans with only brief annotations, but no apparent coherence. While it told me something about the pre-service teachers' capacity to collect resources, it told me little about their capacity to thoughtfully weave these resources into the complex web of teaching mathematics, nor to make sense of their teaching experiences in the light of what they had read and discussed in their academic studies.
In an attempt to make the portfolio assessment more focused, it was decided to reframe it in line with the AAMT Standards for Excellence described above, and to add a 20-minute individual interview, during which time pre-service teachers were asked to explain their rationale for including parts of the portfolio, and to evaluate their knowledge of, practice of, and beliefs about teaching. Each pre-service teacher was asked to answer three questions, segments of which were:
1. The AAMT Standards for Excellence in the Teaching of Mathematics in Australian Schools list three aspects of being an excellent teacher: professional knowledge, professional practice and professional attributes. From your own Professional Experience describe a situation where one of these aspects was evident. Use your portfolio to provide concrete evidence to support your answer.
2. With reference to the readings discussed during the semester, describe the characteristics of a classroom in which high levels of engagement with mathematical ideas are likely to be present. Refer to a class that you taught during Professional Experience and describe how you attempted to create and/or sustain such an environment. Use your portfolio as evidence.
3. Discuss one of the quotations below. Refer to readings during the semester, a class you taught during Professional Experience, and your portfolio to support your answer.
"Of course setting is advantageous for instruction. It's just not advantageous to the students in the lower classes."
"(Children) are bored because the things they are given and told to do in school (mathematics) are so trivial, so dull, and make such limited and narrow demands on the wide spectrum of their intelligence, capabilities and talents." John Holt (1965)
Each student was then asked to bring their portfolio to an interview, to answer the three questions above, and to refer to their portfolio as evidence. Two mathematics educators interviewed the students, made notes during the interview, referred to the portfolio for any further clarification, and provided feedback within thirty minutes of the completion of the interview. Students were informed that the interview process was an experiment, and that it was being used as an attempt to make the portfolio more focused. Each student also agreed to have the interview taped for future reference.
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