Dataset Information

Supporting Mathematical Argumentation and Proof Skills: Comparing the Effectiveness of a Sequential and a Concurrent Instructional Approach to Support Resource-Based Cognitive Skills.

ABSTRACT: An increasing number of learning goals refer to the acquisition of cognitive skills that can be described as 'resource-based,' as they require the availability, coordination, and integration of multiple underlying resources such as skills and knowledge facets. However, research on the support of cognitive skills rarely takes this resource-based nature explicitly into account. This is mirrored in prior research on mathematical argumentation and proof skills: Although repeatedly highlighted as resource-based, for example relying on mathematical topic knowledge, methodological knowledge, mathematical strategic knowledge, and problem-solving skills, little evidence exists on how to support mathematical argumentation and proof skills based on its resources. To address this gap, a quasi-experimental intervention study with undergraduate mathematics students examined the effectiveness of different approaches to support both mathematical argumentation and proof skills and four of its resources. Based on the part-/whole-task debate from instructional design, two approaches were implemented during students' work on proof construction tasks: (i) a sequential approach focusing and supporting each resource of mathematical argumentation and proof skills sequentially after each other and (ii) a concurrent approach focusing and supporting multiple resources concurrently. Empirical analyses show pronounced effects of both approaches regarding the resources underlying mathematical argumentation and proof skills. However, the effects of both approaches are mostly comparable, and only mathematical strategic knowledge benefits significantly more from the concurrent approach. Regarding mathematical argumentation and proof skills, short-term effects of both approaches are at best mixed and show differing effects based on prior attainment, possibly indicating an expertise reversal effect of the relatively short intervention. Data suggests that students with low prior attainment benefited most from the intervention, specifically from the concurrent approach. A supplementary qualitative analysis showcases how supporting multiple resources concurrently alongside mathematical argumentation and proof skills can lead to a synergistic integration of these during proof construction and can be beneficial yet demanding for students. Although results require further empirical underpinning, both approaches appear promising to support the resources underlying mathematical argumentation and proof skills and likely also show positive long-term effects on mathematical argumentation and proof skills, especially for initially weaker students.

SUBMITTER: Sommerhoff D

PROVIDER: S-EPMC7858258 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Supporting Mathematical Argumentation and Proof Skills: Comparing the Effectiveness of a Sequential and a Concurrent Instructional Approach to Support Resource-Based Cognitive Skills.

Sommerhoff Daniel D Kollar Ingo I Ufer Stefan S

Frontiers in psychology 20210121

An increasing number of learning goals refer to the acquisition of cognitive skills that can be described as 'resource-based,' as they require the availability, coordination, and integration of multiple underlying resources such as skills and knowledge facets. However, research on the support of cognitive skills rarely takes this resource-based nature explicitly into account. This is mirrored in prior research on mathematical argumentation and proof skills: Although repeatedly highlighted as res ...[more]

PMID: 33551899

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Project description:Developing a position on a socio-scientific issue and defending it using a well-reasoned justification involves complex cognitive skills that are challenging to both teach and assess. Our work centers on instructional strategies for fostering critical thinking skills in high school students using bioethical case studies, decision-making frameworks, and structured analysis tools to scaffold student argumentation. In this study, we examined the effects of our teacher professional development and curricular materials on the ability of high school students to analyze a bioethical case study and develop a strong position. We focused on student ability to identify an ethical question, consider stakeholders and their values, incorporate relevant scientific facts and content, address ethical principles, and consider the strengths and weaknesses of alternate solutions. 431 students and 12 teachers participated in a research study using teacher cohorts for comparison purposes. The first cohort received professional development and used the curriculum with their students; the second did not receive professional development until after their participation in the study and did not use the curriculum. In order to assess the acquisition of higher-order justification skills, students were asked to analyze a case study and develop a well-reasoned written position. We evaluated statements using a scoring rubric and found highly significant differences (p<0.001) between students exposed to the curriculum strategies and those who were not. Students also showed highly significant gains (p<0.001) in self-reported interest in science content, ability to analyze socio-scientific issues, awareness of ethical issues, ability to listen to and discuss viewpoints different from their own, and understanding of the relationship between science and society. Our results demonstrate that incorporating ethical dilemmas into the classroom is one strategy for increasing student motivation and engagement with science content, while promoting reasoning and justification skills that help prepare an informed citizenry.

Project description:BackgroundMany people want to build good habits to become healthier, live longer, or become happier but struggle to change their behavior. Gamification can make behavior change easier by awarding points for the desired behavior and deducting points for its omission.ObjectiveIn this study, we introduced a principled mathematical method for determining how many points should be awarded or deducted for the enactment or omission of the desired behavior, depending on when and how often the person has succeeded versus failed to enact it in the past. We called this approach optimized gamification of behavior change.MethodsAs a proof of concept, we designed a chatbot that applies our optimized gamification method to help people build healthy water-drinking habits. We evaluated the effectiveness of this gamified intervention in a 40-day field experiment with 1 experimental group (n=43) that used the chatbot with optimized gamification and 2 active control groups for which the chatbot's optimized gamification feature was disabled. For the first control group (n=48), all other features were available, including verbal feedback. The second control group (n=51) received no feedback or reminders. We measured the strength of all participants' water-drinking habits before, during, and after the intervention using the Self-Report Habit Index and by asking participants on how many days of the previous week they enacted the desired habit. In addition, all participants provided daily reports on whether they enacted their water-drinking intention that day.ResultsA Poisson regression analysis revealed that, during the intervention, users who received feedback based on optimized gamification enacted the desired behavior more often (mean 14.71, SD 6.57 times) than the active (mean 11.64, SD 6.38 times; P<.001; incidence rate ratio=0.80, 95% CI 0.71-0.91) or passive (mean 11.64, SD 5.43 times; P=.001; incidence rate ratio=0.78, 95% CI 0.69-0.89) control groups. The Self-Report Habit Index score significantly increased in all conditions (P<.001 in all cases) but did not differ between the experimental and control conditions (P>.11 in all cases). After the intervention, the experimental group performed the desired behavior as often as the 2 control groups (P≥.17 in all cases).ConclusionsOur findings suggest that optimized gamification can be used to make digital behavior change interventions more effective.Trial registrationOpen Science Framework (OSF) H7JN8; https://osf.io/h7jn8.

Dataset Information

Supporting Mathematical Argumentation and Proof Skills: Comparing the Effectiveness of a Sequential and a Concurrent Instructional Approach to Support Resource-Based Cognitive Skills.

Publications

Supporting Mathematical Argumentation and Proof Skills: Comparing the Effectiveness of a Sequential and a Concurrent Instructional Approach to Support Resource-Based Cognitive Skills.

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