Interactive Feedback for Learning Mathematics in a Digital Learning Environment

Barana, Alice; Marchisio, Marina; Sacchet, Matteo

doi:10.3390/educsci11060279

Cited by 36 publications

(36 citation statements)

References 54 publications

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“…The most used technologies for problem solving in education are: Electronic spreadsheets, graphic calculators such as Graphing Calculator 4.0 [47], online computational engines such as Wolfram Alpha [48], dynamic geometry systems such as Geogebra or Cabri Geometry [49], Computer Algebra Systems [50], Advanced Computing Environments such as Maple or Mathematica [13], but also Digital Learning Environments (DLE) [51] or Automatic Assessment Systems [52,53]. These, and many other, technologies can foster conjecturing, justifying, and generalizing by enabling fast, accurate computations, data collection and analysis, and exploration of different registers of representation [54].…”

Section: Doing and Assessing Problem Solving With Technologiesmentioning

confidence: 99%

Self-Assessment in the Development of Mathematical Problem-Solving Skills

2022

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Self-assessment, in the education framework, is a methodology that motivates students to play an active role in reviewing their performance. It is defined as “the evaluation or judgment of ‘the worth’ of one’s performance and the identification of one’s strengths and weaknesses with a view to improving one’s learning outcomes”. The goal of this research is to study the relationship between self-assessment and the development and improvement of problem-solving skills in Mathematics. In particular, the investigation focuses on how accurate the students’ self-evaluations are when compared to external ones, and if (and how) the accuracy in self-assessment changed among the various processes involved in the problem-solving activity. Participants are grade 11 students (in all 182 participants) in school year 2020/2021 who were asked to solve 8 real-world mathematical problems using an Advanced Computing Environment (ACE). Each problem was assessed by a tutor and self-assessed by students themselves, according to a shared rubric with five indicators: Comprehension of the problematic situation, identification of the solving strategy, development of the solving process, argumentation of the chosen strategy, and appropriate and effective use of the ACE. Through a quantitative analysis, students’ self-assessment and tutors’ assessment were compared; data were cross-checked with students’ answers to a questionnaire. The results show a general correlation between tutor assessment and self-assessment, with a tendency of students to underestimate their performance. Moreover, students were more precise in self-assessing in the indicators: Development of the solving process and use of the ACE, while they had major difficulties in self-assessment for the indicators: Comprehension of the problematic situation and argumentation.

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Section: Doing and Assessing Problem Solving With Technologiesmentioning

confidence: 99%

Self-Assessment in the Development of Mathematical Problem-Solving Skills

2022

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“…In this article, we described an intelligent tutoring system aimed at developing comprehension of subject-domain concepts in programming and other well-formalized domains. Some of the similar systems (e.g., [41]) even working in well-formalized domains such as mathematics and programming allow to evaluate and provide the feedback only for the errors in the answer to the final task, or some of the steps of solving it which makes the feedback more general and decreases its quality. This also limits the system's ability to determine the exact cause of the student error and so update the model of the student's knowledge as several kinds of errors can lead to the same wrong answer step.…”

Section: Discussionmentioning

confidence: 99%

Improving Comprehension: Intelligent Tutoring System Explaining the Domain Rules When Students Break Them

et al. 2021

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Intelligent tutoring systems have become increasingly common in assisting students but are often aimed at isolated subject-domain tasks without creating a scaffolding system from lower- to higher-level cognitive skills, with low-level skills often neglected. We designed and developed an intelligent tutoring system, CompPrehension, which aims to improve the comprehension level of Bloom’s taxonomy. The system features plug-in-based architecture, easily adding new subject domains and learning strategies. It uses formal models and software reasoners to solve the problems and judge the answers, and generates explanatory feedback about the broken domain rules and follow-up questions to stimulate the students’ thinking. We developed two subject domain models: an Expressions domain for teaching the expression order of evaluation, and a Control Flow Statements domain for code-tracing tasks. The chief novelty of our research is that the developed models are capable of automatic problem classification, determining the knowledge required to solve them and so the pedagogical conditions to use the problem without human participation. More than 100 undergraduate first-year Computer Science students took part in evaluating the system. The results in both subject domains show medium but statistically significant learning gains after using the system for a few days; students with worse previous knowledge gained more. In the Control Flow Statements domain, the number of completed questions correlates positively with the post-test grades and learning gains. The students’ survey showed a slightly positive perception of the system.

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“…To answer the research questions, we designed a teaching experiment involving City), from which the DELTA (Digital Education for Learning and Teaching Advances) Research Group of the University of Turin was able to obtain important results in the field of automatic formative assessment and digital education in Mathematics [32][33][34]. Here, we will analyze some of the project's activities from the point of view of the understanding of algebraic formulas.…”

Section: Methodsmentioning

confidence: 99%

From Formulas to Functions through Geometry: A Path to Understanding Algebraic Computations

Barana

2021

EJIHPE

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The teaching of algebra at the secondary school level has faced a great revolution during the last 50 years. While previously, it was focused on technicisms and pure syntactic rules, the most modern trends recommend using a functional approach to algebra and giving more prominence to conversions among different representation registers than treatments as simplifications and expansions. Nowadays, the daily practice in teaching algebra is still influenced by the traditional approach, and there is a need to offer teachers examples of activities that can give meaning to algebraic computations. This study proposes a set of interactive activities for eighth grade students, with a functional approach to formulas in a geometric context. The goal of the study is to investigate how similar activities can help students to develop multiple approaches to problems, understand algebraic formulas, and discern which main problems they face. The activities were tested with about 300 students, and qualitative and quantitative data were analyzed to answer the research questions.

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Interactive Feedback for Learning Mathematics in a Digital Learning Environment

Cited by 36 publications

References 54 publications

Self-Assessment in the Development of Mathematical Problem-Solving Skills

Self-Assessment in the Development of Mathematical Problem-Solving Skills

Improving Comprehension: Intelligent Tutoring System Explaining the Domain Rules When Students Break Them

From Formulas to Functions through Geometry: A Path to Understanding Algebraic Computations

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