Combining Exploratory Learning With Structured Practice to Foster Conceptual and Procedural Fractions Knowledge

Robust domain knowledge consists of conceptual and procedural knowledge. The two types of knowledge develop together, but are fostered by different learning tasks. Exploratory tasks enable students to manipulate representations and discover the underlying concepts. Structured tasks let students practice problem-solving procedures step-by-step. Educational technology has mostly relied on providing only either task type, with a majority of learning environments focusing on structured tasks. We investigated in two quasi-experimental studies with 8-10 years old students from UK (N = 121) and 10-12 years old students from Germany (N = 151) whether a combination of both task types fosters robust knowledge more than structured tasks alone. Results confirmed this hypothesis and indicate that students learning with a combination of tasks gained more conceptual knowledge and equal procedural knowledge compared to students learning with structured tasks only. The results illustrate the efficacy of combining both task types for fostering robust fractions knowledge

Combining exploratory learning with structured practice educational technologies to foster both conceptual and procedural fractions knowledge

Educational technologies in mathematics typically focus on fostering either procedural knowledge by means of structured tasks or, less often, conceptual knowledge by means of exploratory tasks. However, both types of knowledge are needed for complete domain knowledge that persists over time and supports subsequent learning. We investigated in two quasi-experimental studies whether a combination of an exploratory learning environment, providing exploratory tasks, and an intelligent tutoring system, providing structured tasks, fosters procedural and conceptual knowledge more than the intelligent tutoring system alone. Participants were 121 students from the UK (aged 8–10 years old) and 151 students from Germany (aged 10–12 years old) who were studying equivalent fractions. Results confirmed that students learning with a combination of exploratory and structured tasks gained more conceptual knowledge and equal procedural knowledge compared to students learning with structured tasks only. This supports the use of different but complementary educational technologies, interleaving exploratory and structured tasks, to achieve a “combination effect” that fosters robust fractions knowledge

Deutsch

Ein entscheidender Faktor für erfolgreiches Unterrichten und hohen Lernzuwachs ist die Anpassung des Unterrichts an die Lernvoraussetzungen der Schülerinnen und Schüler. Daher werden im Rahmen des adaptiven Unterrichtens unter anderem Aufgaben ausgewählt, welche den individuellen Voraussetzungen der Lerngruppe entsprechen. Die von den Lehrkräften hierfür benötigen Fähigkeiten beinhalten die Diagnose der Lernvoraussetzungen und der in den Aufgaben enthaltenen Anforderungen. Die Lehrkräfteausbildung kann den Grundstein für solche diagnostischen Fähigkeiten legen, aber auch bei erfahrenen Lehrkräften gilt es diese Kompetenzfacette in Lehrerfortbildungen weiterzuentwickeln. Die hier vorgestellte Studie beschreibt eine Maßnahme für die Förderung der diagnostischen Kompetenz im Bereich der Bruchrechnung bei Lehrpersonen aus der Praxis. Dabei wurden die teilnehmenden Personen im Bereich des fachdidaktischen Wissens hinsichtlich schwierigkeitsgenerierender Aufgabenmerkmale bei Textaufgaben mit konkreten Beispielen aus der Bruchrechnung fortgebildet. Die Kurzintervention verzeichnet große Effekte für die Experimentalgruppe im Vergleich zu einer Warte-Kontrollgruppe und kann somit als Hinweis für den Einfluss von Wissensfacetten bei Aus- und Fortbildungsmaßnahmen im Bereich der diagnostischen Kompetenz dienen. Die Urteilsakkuratheit der Einschätzung von Aufgabenschwierigkeit zeigt sich bei erfahrenen Lehrkräften stabil gegen den Einfluss von Zeitrestriktion. Dieses Ergebnis unterstreicht die Auswirkungen von Berufserfahrung auf Denkprozesse und wird als Facette professioneller Kompetenz gedeutet.Recent studies have found that adapting instruction to the prerequisite of students is a determinant factor of successful learning and teaching.   For adaptive teaching, teachers have to choose tasks that correspond for example in their difficulty to the individual prerequisite in a classroom and to the pedagogical aims. Thus, teachers need diagnostic competences to assess the prerequisites of their students and to judge the difficulties of possible tasks. The task difficulty is determined by features, which influence the solution rate. The teacher has to perceive and interpret these features. Prospective teachers can found these skills during their studies; in-service teachers should foster them in further trainings. The present study describes an intervention to foster diagnostic competence in the domain of fractions. The participants received instruction on pedagogical content knowledge about features that determines the task difficulty in the domain of fractions with concrete examples. Our study revealed large effects of this short intervention for the experimental group in comparison to a control group. The short intervention can therefore serve as an element in further teacher trainings in the field of diagnostic competence

Problem-solving prior to instruction

In Lernansätzen mit Aufgabenbearbeitung vor Instruktion generieren Lernende Lösungsansätze zu Aufgaben, deren Lösung sie noch nicht gelernt haben. In der Regel sind die generierten Lösungsansätze unvollständig oder fehlerhaft. Trotzdem zeigen Studien positive Lerneffekte dieser Ansätze. Unter den Namen "Productive Failure" (z.B. Kapur, 2012) und "Invention" (z.B. Schwartz & Martin, 2004) wurden die Lerneffekte vielfach repliziert, doch die zugrundeliegenden Lernmechanismen sind bislang unklar. Die vorliegende Dissertation versucht Lernmechanismen aufzuzeigen, welche die Effektivität dieser Ansätze erklären können. In quasi-experimentellen Studien werden Effekte des Zeitpunkts der Instruktion, der Form der Instruktion und der Unterstützung während der Aufgabenbearbeitung untersucht. Zudem wird aufgezeigt, wie die Befunde mit der Cognitive Load-Theorie in Einklang zu bringen sind. Ein theoretisches Rahmenmodell integriert die Ergebnisse der durchgeführten Studien mit weiteren Befunden.In Productive Failure (e.g., Kapur, 2012) and Invention approaches (e.g., Schwartz & Martin, 2004) learners first attempt to solve a problem and only afterwards, they receive instruction. This thesis aims at shedding light on the learning mechanisms underlying the effectiveness of such problem-solving prior to instruction approaches. It presents quasi-experimental studies that I conducted to investigate how the timing of instruction and the form of instruction interact to impact learning, and to investigate whether guidance during the problem-solving phase increases the quality of students solutions and, in turn, facilitates learning. I discuss how the seeming contradiction between the findings of problem-solving prior to instruction and the assumptions of cognitive load theory can be reconciled. I further aim to contribute to a unified theory of Productive Failure and Invention approaches by proposing three learning mechanisms and discussing the empirical findings in their light

Strategien der Binnendifferenzierung

Dass bei pädagogischen Entscheidungen die Heterogenität der Lernenden berücksichtigt werden muss,ist keine neue Erkenntnis. Viele unterschiedliche Strategien des Differenzierens werden schon seit Jahrzehnten diskutiert, in der täglichen Praxis umgesetzt und auch empirisch untersucht. Ein Überblick über wichtige Ansätze

Judgment bias in diagnosing misconceptions with decimal fractions

International audienceA prerequisite for remediating student misconceptions is their accurate diagnosis by the teacher. However, studies on judgment accuracy show that teachers differ substantially regarding their judgments even though little is known about the reasons so far. The present study investigates whether teachers' diagnosis of misconceptions with decimal fractions is subject to judgment biases. For this purpose, we propose a cognitive model for diagnosing misconceptions based on the process of hypothesis testing. The study results show that the formulation of alternative hypothesis and the processing of relevant information are predictors of high judgment accuracy when diagnosing misconceptions. Furthermore, normative and confirmatory biased judgment processes could be distinguished. Implications for teacher education are discussed

Literaturliste zum Artikel "Strategien der Binnendifferenzierung" von Katharina Loibl und Timo Leuders

Literaturliste zum Artikel "Strategien der Binnendifferenzierung" von Katharina Loibl und Timo Leuders. Der dazugehörige Artikel erscheint in: "Pädagogik" Weinheim 2021 H.

Toward an overarching framework for systematizing research perspectives on diagnostic thinking and practice

Assessing students’ learning processes and products is considered a core requirement of effective teaching. As such, it is an object of research in several disciplines and research areas. To structure the various corresponding research perspectives and provide a broader, yet still systematic view of the field, we propose an overarching framework that allows for systematizing foci of interest, goals, methodologies, and theoretical premises as four integral aspects of conducting research in this area. We demonstrate the benefits of the overarching framework by using it as a tool to analyze and systematize previous research from four different research perspectives. Based on this framework, we discuss the strengths and limitations of existing studies and, in particular, highlight theoretical premises that are rarely explicitly addressed but become more obvious by using the overarching framework. In addition, we provide directions for future research by drawing connections within and between research perspectives. Our analyses illustrate how the overarching framework can provide a foundation for research synthesis and inform future studies