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«Student Constructed Posters: A Tool for Learning and Assessment in Preservice Mathematics Education Robyn Zevenbergen C;rt01th lIniversity This paper ...»

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Mathematics Teacher Education and Development 1999, Vol. I, 72-83

Student Constructed Posters: A Tool for Learning

and Assessment in Preservice Mathematics


Robyn Zevenbergen

C;rt01th lIniversity

This paper reports on the implementation of a four-year project exploring effective

and alternative assessment items in a primary mathematics education course. The

paper provides a rationale for using posters in preservice education, then discusses the development of criteria for effective posters. It concludes with practical recommendations for the implementation of posters for assessment.

In the current context of teacher education, there is increasing pressure on teacher educators to do more with less, greater accountability, and increasing pressure from employing authorities to produce graduates with desired qualities.

The need for practices which produce and document learning outcomes is highly desired. This paper documents a four-year project aimed at developing assessment practices which are sustainable - both practically and economically - and meet the demands of the University, academics, students and employers. The focus of this paper is the evolution of student constructed posters in a preservice mathematics education course where the aim was to have successful assessment tools to document student learning and to provide a tool for effective teacher preparation.

Background Context In many countries, higher education has come under increasing challenge to ensure a high degree of personal transferability of skills from the university to the workplace (Stefani, 1994). Teacher education is not divorced from this movement and there is increasing pressure on higher education regarding the perceived poor preparation of teachers. In some countries, this has resulted in substantive changes in initial teacher preparation. Overall, such challenges are the results of employer groups who demand teacher education facilities be accountable for producing the teacher characteristics demanded by such employing authorities. In concert with these challenges are the changes within higher education where shrinking resources have forced substantial reductions in the number of staff employed in the sector, large classes and practices driven by economic imperatives rather than pedagogic ones. To this end, there is increasing pressure on teacher education staff to embrace practices which are sustainable yet produce teachers who are seen to have the characteristics desired by employer groups.

Within mathematics teacher education, this is critical given the need to expose students to practices that challenge many of the taken-for-granted practices dominating classroom life. By exposing students to the economically-driven prac

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within practices that legitimate the more traditional forms of pedagogy. and assessment which have dominated past practices in mathematics. In most cases, however, preservice mathematics education attempts to challenge the practices of the past and introduce new models of assessment. However, such practices are in danger of being ideologically over-ridden by the actual assessment regimes adopted within a preservice course. Hence, what is called for are assessment practices which are economically and practically sustainable and expose preservice mathematics teachers to exemplary practices. In so doing, such practices challenge widely-held,.conservative beliefs and practices.

In this context, it is essential to develop practices which are sustainable and produce desired learning outcomes for preservice teachers. This paper reports on a

project which had three very distinct aims:

(a) to develop skills in preservice teachers which enable them to produce stimulating resources for their students, (b) to develop the assessment skills of preservice teachers, and (c) to develop effective and innovative assessment tools within mathematics preservice teacher education.

These aims are undertaken within a context of shrinking resources and increasing workloads and as such, it is an overarching principle that the practice must be manageable and sustainable within such a work environment. This is particularly the case in teacher education where exemplary teaching and assessment practices must,be modelled to prospective teachers.

Posters in Higher Education Posters are a legitimate form of communication in professional arenas. They are valid forums for co~munic(ltion in conferences where short statements of research are expected. They offer a medium that stimulates concise communication and discussion. Gore and Camp (1987) and Baird (1991) have adopted the conference format in their undergraduate psychology courses with great success in terms of both student learning and enjoyment. Posters have been used across a range of disciplines including mathematics (Berry & Houston, 1995), psychology (Gore & Camp, 1987), nurse education (Fowles, 1992; Sorensen & Boland, 1991), and chemistry (Kennedy, 1985).. Where students have undertaken posters as a component of their assessment, it has been reported that they have a greater retention in the areas of their poster topic when performance, is measured on examinations (Lowry, 1992).

Posters are an excellent medium for developing communication skills particularly where short and concise communication is needed. This is of particular value in teacher education where teachers must be able to communicate across a ranges of mediums so as to include the various learning styles of students in their classrooms. Of even more importance, is that posters offer the potential for teachers to communicate kn0'Xledge in forms which differ substantially from the dominant modes of communication. In' mathematics, this is typically expository talk dominated by the teacher. Increasingly, it is obvious that such a teaching style does not cater for the diversity across classrooms. The short pithy statements conveyed 74 Zevenbergen through the poster may entice some learners to become involved in the active learning process. Similarly, visual learners are more likely to be stimulated by wellconstructed posters, and hence, motivated to learn.

Where posters have been developed in concert with other assessment techniques such as peer assessment (Zevenbergen, forthcoming; Freeman, 1995), students can be active participants in the assessment procedures. For teacher education students, this experience is invaluable in their professional development due to their restricted access to authentic assessment practices within the confines of the university. The practice of peer assessment of posters aids in learning more about the topic chosen by the student; more about other topics chosen by other students; and more about poster construction.

Berry and Houston (1995) found that posters promoted a very positive attitude in their students. They contend that this is due to the challenge to present work succinctly and the different medium for presentation as opposed to the more traditional forms of assessment used in their mathematics courses. They found that the posters stimulated a great deal of productive debate among the students. This they suggest was potentially due to the less formal settings in poster assessment than the formal oral presentations, thus encouraging students to communicate more effectively.

One of the potential areas of concern with the use of posters is the display of incorrect content. Not only is this threatening to the ego of the student/s whose work is on display, but may impact on the misconstruction of incorrect knowledge for those students who are not familiar nor confident with the knowledge displayed.

Hence, it is suggested that discussion is an important component of the process so that misconceptions can be allayed (Berry & Houston, 1995).

In undertaking an analysis of peer assessment of various assessment items, Freeman (1995) found that where there was a high degree of subjectivity associated with marking, there was greater scope for varying interpretations of the criteria. In such cases, he strongly advocates that such pieces should be weighted lightly so as not to disadvantage students, particularly when issues of valid and reliable assessment are key components of accountability. In this case, where posters are visual displays and do have a subjective component, then it is necessary to consider how such assessment items will be weighted.

The Project Posters were introduced into the mathematics education suite of subjects in 1995 and continue to be implemented. An action research approach to their implementation is undertaken with student feedback and focus groups at the completion of each semester. This information is fed back into consecutive implementations so that the posters are continually refined and defined.

At the current stage of the project, the poster has been defined as being "a standalone resource containing a maximum of 25 words (excluding heading) which can be used in the classroom" as per the subject outline. A word limit has been imposed as an outcome of the excessive use of words on posters whereby they became more like a reader's digest than a poster. A series of topics has been identified from which students select. The topics are selected on the basis of the problems often posed to

preservice teachers. These include:

Student Constructed Posters 75 Area: The difference between area and perimeter Mass: What is mass? (the difference between mass and weight) Time: Using 24 hour clocks - representing 24 hour times Time: Using timetables"""" adding and subtracting times Space: The various types of angles [acute, obtuse, etc] Space: Geometry on a sphere.

Number: Subtraction with internal zeros Number: Operations with fractions Number: Equivalence of fractions Ratio: What is the difference between ratio and fractions?

Data: Graphs - using the appropriate graphs to represent data The current list of topics has arisen out of the students' evaluations and their expressed need for some suggestions for topics due to their early stage of professional development. Students identified that they were not conversant with the topics in mathematics education so early in their course. Topics are negotiable and students can identify other areas of study.

The intention of the poster is two-fold. In the first instance, it is to document the learning of the student. The student must display the selected concept in a concise, innovative and user-friendly manner that demonstrates the appropriate understanding of that concept. The topics are those which are often poorly understood by students and hence poorly taught. Second, through the construction of the poster, students will develop skills, techniques and knowledge about poster construction and effective communication.

A further dimension to the project has evolved, which is peer assessment. This is discussed in-depth in another paper (Zevenbergen, forthcoming), however, it is noteworthy that peer assessment has extended student learning - both in terms of the goals of the project, but also in terms of assessment. Furthermore, it has compelled students to become more critical and reflective about construction and content addressed in the posters. In the early years of the project students only constructed their own posters so their learning was restricted to the content they investigated. Although posters were displayed in common access areas, students did not examine them critically. Through the participation in peer assessment, students have gained substantially more knowledge due to the imposed need to critically reflect and evaluate their peers' posters.

The Posters For the project to be sustainable within the workloads of the academic staff and the restricted economic conditions of the students, the project has progressively evolved whereby criteria and conditions have been developed. All of the criteria and restrictions were negotiated with students throughout the project. Each year, progressive criteria are developed with the students as they encounter aspects of poster construction and display. These will be discussed in the following subsections.

Topics. The posters are the first assessment item in the subject so students have not encountered a significant amount of mathematics education content. Initial 76 Zevenbergen years of the project kept the topics open and students could self-select. However, they proposed th~ nomination of a number of key topics with scope for individual topics if so desired. This has worked satisfactorily.

Size ofposters. The posters currently are to be confined to the size of an A2 sheet.

This condition arose from a number of concerns. Firstly, practicality for display was a consideration. Posters which were large and cumbersome were difficult to display

- their sheer weight meant that they kept falling off walls. This often resulted in posters being wrecked as they lay crumbled and tramped on in the common areas.

As the posters were displayed in common areas and subsequently peer assessed, they needed to be allocated space. Where a consistent size was used, the nominated areas could be estimated and allocated. Secondly, many students assumed that bigger was better, constructing posters which were large but contained little content.

Students became distressed with their marks as they believed that their posters were expensive to construct, so therefore had to be good. Furthermore, for practical purposes, as teachers,· the equipment in schools (such as laminators and poster stands) will only take A2 cardboard, so it was in their best interests to learn to construct posters which matched the constraints of their future workplaces.

Durability. Restrictions on durability were imposed. As the posters were displayed in a common area - the hallways in the education building - they needed to be able to sustain abuse from other students from all Faculties across the campus.

For example, a student constructed a bar graph using chocolate bars - all of which were removed and eaten by other students. When marking occurred, the poster was not of a high standard. Similarly, posters investigating probability with coins often had the coins removed. A common theme for the notion of durability was whether the poster might be laminated so as to avoid being vandalised. This aspect was agreed to be important as in the classroom, similar acts of vandalism are likely to occur. Similarly, students felt that if they put a lot of work into their posters, they would like to preserve them for later lessons on the topics.

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