Analysing the Use of Worked Examples and Tutored and Untutored Problem-Solving in a Dispositional Learning Analytics Context

The identification of students’ learning strategies by using multi-modal data that combine trace data with self-report data is the prime aim of this study. Our context is an application of dispositional learning analytics in a large introductory course mathematics and statistics, based on blended learning. Building on previous studies in which we found marked differences in how students use worked examples as a learning strategy, we compare different profiles of learning strategies on learning dispositions and learning outcome. Our results cast a new light on the issue of efficiency of learning by worked examples, tutored and untutored problem-solving: in contexts where students can apply their own preferred learning strategy, we find that learning strategies depend on learning dispositions. As a result, learning dispositions will have a confounding effect when studying the efficiency of worked examples as a learning strategy in an ecologically valid context

What learning analytics based prediction models tell us about feedback preferences of students

Learning analytics (LA) seeks to enhance learning processes through systematic measurements of learning related data and to provide informative feedback to learners and educators (Siemens & Long, 2011). This study examined the use of preferred feedback modes in students by using a dispositional learning analytics framework, combining learning disposition data with data extracted from digital systems. We analyzed the use of feedback of 1062 students taking an introductory mathematics and statistics course, enhanced with digital tools. Our findings indicated that compared with hints, fully worked-out solutions demonstrated a stronger effect on academic performance and acted as a better mediator between learning dispositions and academic performance. This study demonstrated how e-learners and their data can be effectively re-deployed to provide meaningful insights to both educators and learners

Individual differences in the preference for worked examples: lessons from an application of dispositional learning analytics

Worked-examples have been established as an effective instructional format in problem-solving practices. However, less is known about variations in the use of worked examples across individuals at different stages in their learning process in student-centred learning contexts. This study investigates different profiles of students’ learning behaviours based on clustering learning dispositions, prior knowledge, and the choice of feedback strategies in a naturalistic setting. The study was conducted on 1,072 students over an eight-week long introductory mathematics course in a blended instructional format. While practising exercises in a digital learning environment, students can opt for tutored problem-solving, untutored problem-solving, or call worked examples. The results indicated six distinct profiles of learners regarding their feedback preferences in different learning phases. Finally, we investigated antecedents and consequences of these profiles and investigated the adequacy of used feedback strategies concerning ‘help-abuse’. This research indicates that the use of instructional scaffolds as worked-examples or hints and the efficiency of that use differs from student to student, making the attempt to find patterns at an overall level a hazardous endeavour

Adding dispositions to create pedagogy-based Learning Analytics

This empirical study aims to demonstrate how Dispositional Learning Analytics (DLA) can provide a strong connection between Learning Analytics (LA) and pedagogy. Where LA based models typically do well in predicting course performance or student drop-out, they lack actionable data in order to easily connect model predictions with educational interventions. Using a showcase based on learning processes of 1080 students in a blended introductory quantitative course, we analysed the use of worked-out examples by students. Our method is to combine demographic and trace data from learning-management systems with self-reports of several contemporary social-cognitive theories. Students differ not only in the intensity of using worked-out examples but also in how they positioned that usage in their learning cycle. These differences could be described both in terms of differences measured by LA trace variables and by differences in students’ learning dispositions. We conjecture that using learning dispositions with trace data has significant advantages for understanding student’s learning behaviours. Rather than focusing on low user engagement, lessons learned from LA applications should focus on potential causes of suboptimal learning, such as applying ineffective learning strategies

Evaluating the effects of adaptively presenting worked examples, erroneous examples and problem solving in a constraint-based tutor.

Learning from Problem Solving (PS), Worked Examples (WE) and Erroneous Examples (ErrEx) have all been proven to be effective learning strategies in Intelligent Tutoring Systems. A worked example consists of a problem statement, its solution, and additional explanations, and therefore provides a high level of assistance to students. Many studies have shown the benefits of learning from WEs and PS in ITSs. An erroneous example (ErrEx) presents an incorrect solution and requires students to find and correct errors, therefore helping the student to solve problems. Erroneous examples may also help students become better at evaluating problem solutions. In this project, we aim to investigate how to maximize learning by adaptively providing learning activities for students based on their performance in the domain of Structured Query Language (SQL). The project was conducted in the context of SQL-Tutor, which is a constraint-based tutor that teaches SQL. A series of studies conducted during the project produced promising results. Our first study demonstrated that a fixed sequence of WE/PS pairs and ErrEx/PS pairs (WPEP) resulted in improved problem solving and that it also benefitted students with different levels of prior SQL knowledge. We then introduced an adaptive strategy in the second study, which decided what learning activities (WE, ErrEx with one or two errors, or PS) to provide to the student based on his/her performance on problem solving. We found that students who studied with the adaptive strategy improved their post-test scores on conceptual, procedural, and debugging questions (i.e., analyzing the solution, explaining the errors, and then making appropriate corrections) with significantly fewer learning activities. The final study compared the enhanced adaptive strategy to the self-selection strategy, as well as compared the enhanced adaptive strategy to the original adaptive strategy from the second study. The results show that the enhanced adaptive strategy is superior to the self-selection strategy. However, the original adaptive strategy was the better choice compared to the enhanced adaptive strategy, for students with varying levels of prior knowledge

Example-based learning: Integrating cognitive and social-cognitive research perspectives

Example-based learning has been studied from different perspectives. Cognitive research has mainly focused on worked examples, which typically provide students with a written worked-out didactical solution to a problem to study. Social-cognitive research has mostly focused on modeling examples, which provide students the opportunity to observe an adult or a peer model performing the task. The model can behave didactically or naturally, and the observation can take place face to face, on video, as a screen recording of the model's computer screen, or as an animation. This article reviews the contributions of the research on both types of example-based learning on questions such as why example-based learning is effective, for what kinds of tasks and learners it is effective, and how examples should be designed and delivered to students to optimize learning. This will show both the commonalities and the differences in research on example-based learning conducted from both perspectives and might inspire the identification of new research questions

Understanding on Strategies of Teaching Mathematical Proof for Undergraduate Students

Many researches revealed that many students have difficulties in constructing proofs. Based on our empirical data, we develop a quadrant model to describe students\u27 classification of proof result. The quadrant model classifies a students\u27 proof construction based on the result of mathematical thinking. The aim of this article is to describe a students\u27 comprehension of proof based on the quadrant model in order to give appropriate suggested learning. The research is an explorative research and was conducted on 26 students majored in mathematics education in public university in Banten province, Indonesia. The main instrument in explorative research was researcher itself. The support instruments are proving-task and interview guides. These instruments were validated from two lecturers in order to guarantee the quality of instruments.Based on the results, some appropriate learning activities should be designed to support the students\u27 characteristics from each quadrant, i.e: a hermeneutics approach, using the two-column form method, learning using worked-example, or using structural method

Use of animation to facilitate students in acquiring problem-solving: From Theory to Practice

In this article the use of animations is explored to facilitate students acquiring of problem-solving. The goal is to spur interest in educators for further research on the use of animated videos, which combine contextualised stories, animated worked examples and practice questions on an interactive platform to teach learners mathematics concepts and problem solving skills