Showing papers by "Alexander Renkl published in 1999"

Learning mathematics from worked-out examples : Analyzing and fostering self-explanations

Abstract: Recent research has shown that learning from worked-out examples is of major importance for initial skill acquisition in well-structured domains such as mathematics. However, only those learners who actively process the presented examples profit noticeably from this learning mode. Specifically, the learning outcomes depend on how well the learners explain the solution steps presented in the examples to themselves (‘self-explanation effect”). In a series of studies on learning mathematics from examples, learners’ spontaneous self-explanations and instructional means used to encourage self-explanations were investigated. In this research, the following main findings were obtained. Most learners were rather passive with respect to their spontaneous self-explanations. Among the active and successful learners, two subgroups employing different self-explanation styles could be identified. With regard to the instructional means used to induce effective example processing, it turned out that to employ “learning by teaching” in order to stimulate explanation activities was of very limited use. Attempts to directly train for or elicit certain types of self-explanations were more successful. However, even in the latter case, self-explanations had inherent deficits (e.g., proneness to errors). Thus, we sought to design learning arrangements that try to integrate self-explanations with well-timed and well-adapted instructional explanations (e.g., from tutors) in order to enhance students’ problem-solving skills.

Was lernen wir in Schule und Hochschule: Träges Wissen?

Abstract: Empirical studies show that learning in school and university frequently results in inert knowledge (Inert knowledge is defined as theoretical knowledge which cannot be used for solving complex, realistic problems) Consequently, a gap between knowledge and action emerges in school and university Learning that is designed according to the proposals of situated instructional theories can overcome this gap However, the demand for constructive activity of learners called forth by these approaches must not be misunderstood as the demand for dismissing any instructional efforts In contrast, only the balance between construction and instruction allows for the acquisition of applicable knowledge which may lead to successful action This is exemplified in studies about learning of different domains conducted in schools and universities

Instruktionale Effekte einer kombinierten Lernmethode: Zahlt sich die Kombination von Lösungsbeispielen und Problemlöseaufgaben aus?

Abstract: Example-based learning environments have already proved to be effective in various domains. However, as examples represent convenient operational instructions, they invite a lot of learners to process the presented information only in a passive and superficial way, which results in negative consequences on the learning success. Problem-solving tasks do not have this undesirable "side effect". But learning by problem solving gives rise to other difficulties, especially a high burden on cognitive resources. This problem can be avoided by presenting worked-out examples. These considerations led to the hypothesis that a systematic combination of both learning methods makes effective learning possible. In order to test this hypothesis, instructional effects of a combined learning condition (n=15) and a "pure" example condition (n=15) were investigated experimentally in the domain of accountancy. The learners' (quantitative) activity of elaborating the learning materials, the quality of the elaboration generated, and the success in different transfer tasks were used as dependent measures. With respect to all these dependent measures, the experimental group was significantly better. As a consequence, it is recommended that problem-solving tasks should be integrated in example-based learning environments.

Kaufmännisches Rechnen: Lernen mit Lösungsbeispielen

Abstract: Sowohl im Alltag als auch im Berufsleben kommt man kaum ohne sie aus. Sie bevolkern nahezu alle Lehrbucher und sind aus der Welt des Lehrens und Lernens kaum wegzudenken: Losungsbeispiele. Ob es darum geht, den neugekauften Videorekorder zu programmieren oder eine Mathematikaufgabe zu losen — zumindest der Laie ist auf Losungsbeispiele angewiesen. Die Bedeutung, die Losungsbeispielen beim Lernen und Problemlosen beigemessen wird, konnte in einer Vielzahl von Untersuchungen bestatigt werden (Reimann, 1996). Inbesondere zu Beginn des Erwerbs kognitiver Fertigkeiten spielen Losungsbeispiele fur Lernende eine immense Rolle. Wenn die Wahl zwischen einem abstrakten Lehrtext und Beispielen gegeben wird, zieht es die uberwaltigende Mehrheit vor, sich beim Lernen an Beispielen zu orientieren, wie LeFevre und Dixon (1986) zeigten. Selbst die Verbesserung der Qualitat des Lehrtexts bei gleichzeitiger Verschlechterung der Beispielqualitat oder der Versuch, den Lernenden die Wichtigkeit des abstrakten Lehrtextes zu suggerieren, anderte nichts an der Beispiel-Praferenz: Die Lernenden blieben trotzdem den Beispielen treu. Auch in der formalen Domane Mathematik, von der man annehmen konnte, das die Vorgabe von Prinzipien allein genugt, um Probleme zu losen, spielen Losungsbeispiele eine wichtige Rolle (Reimann, 1996). Aus Arbeiten von Ross (z. B. 1990) geht hervor, das Anfanger selbst dann Beispiele nutzen, wenn sie das allgemeine Losungsprinzip, also etwa die entsprechende Formel, zur Verfugung haben. Ohne Beispiele scheinen zumindest Anfanger die Formel nicht verstehen und damit auch nicht anwenden zu konnen. Anderson und Kollegen zeigten, das zumindest Programmieranfanger verbale Beschreibungen von LISP-Prozeduren ignorieren und sich auf Beispiele verlassen (z.B. Pirolli & Anderson, 1985).