Department Mathematik



Mathematisches Kolloquium

Am Freitag, 1. Februar 2013, um 16 Uhr c.t. spricht

Prof. Dr. Wim Van Dooren
(Katholieke Universiteit Leuven)

im Hörsaal A027 über das Thema

Representational flexibility in linear function problems:
Conceptualization, relevant variables,
and implications for instruction

Zusammenfassung: The idea that it is important to encourage students to use multiple external representations (MER) of mathematical concepts is widely acknowledged in the literature (e.g., Kaput, 1992; Yerushalmy, 2006). The advantages and disadvantages of using MERs in problem solving and learning have been the focus of much research in the last four decades (e.g., Hollands & Spence, 1998; Panaoura et al., 2009). However, most studies have focused on a very specific facet of flexibility, i.e., students' ability to spontaneously translate across representations in order to solve tasks (e.g., McGowan & Tall, 1999). There is an important aspect of flexibility which has not received much attention, i.e., students' ability to choose representations to solve tasks.
Drawing from our research group's expertise in the field of strategy choice, this seminar will focus on students' ability to make flexible representational choices in order to solve linear-function problems.
Traditionally, being able to make a flexible representational choice was understood as students' ability to select the representation which better fits the characteristics of the task at hand, and many studies in the literature are designed with this task-based conceptualisation in mind (e.g., Vessey, 1991). However, recent studies concerning strategy choice (e.g., Verschaffel et al., 2009) have shown that students' strategy choices are dependent not only on the characteristics of the task at hand, but also on the characteristics of the students using the different strategies, and on the context in which the strategies are used, and we will show how this is also relevant for the representational choice literature.
We will present empirical studies relying on the choice/no-choice method (Siegler & Lemaire, 1997) to determine in what sense and to what extent secondary school students are flexible when solving linear function problems. We will present several conceptualisations of flexibility (purely task based, taking into account subject characteristics in a groupwise manner, and in an individual manner), and show how flexibility in representational choice predicts accuracy. Additionally, we will discuss results of an interview study about flexible representational choice, where we looked for students' reported reasons to make certain representational choices (referring to characteristics of the representation, task, subject and/or context).
Finally, we will show the results of a teaching intervention aimed at improving students' representational flexibility, in which an experimental group was exposed to a 1.5-hour session where they learnt how to fine-tune their choices to task and subject characteristics. The intervention aimed to improve students' flexibility by exposing them to their own representational choices and performance in different problems, and by presenting participants with examples of students who were asked to make similar choices in the past and who provided a detailed justification for their choices.

Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.

Treffpunkt zum Abendessen um 18.00 Uhr wird noch bekannt gegeben.