scholarly journals Fact retrieval or compacted procedures in arithmetic – a neurophysiological investigation of two hypotheses

2020 ◽  
Author(s):  
Roland H. Grabner ◽  
Clemens Brunner ◽  
Valerie Lorenz ◽  
Stephan E. Vogel ◽  
Bert De Smedt
Keyword(s):  
Problem Solving ◽  
Cognitive Processes ◽  
High Sensitivity ◽  
List Type ◽  
Single Digit ◽  
Frequency Bands ◽  
Eeg Data ◽  
Neurophysiological Test ◽  
Problem Solving Strategies ◽  
Fact Retrieval

ABSTRACTThere is broad consensus that adults solve single-digit multiplication problems almost exclusively by fact retrieval (i.e., retrieval of the solution from an arithmetic fact network). In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. The fact-retrieval account postulates that these are solved through fact retrieval, just like multiplications, whereas the compacted-procedure account proposes that solving very small additions (i.e., problems with operands between 1 and 4) involves highly automatized and unconscious compacted procedures. In the present electroencephalography (EEG) study, we put these two accounts to the test by comparing neurophysiological correlates of solving very small additions and multiplications. A sample of 40 adults worked on an arithmetic production task involving all (non-tie) single-digit additions and multiplications. Afterwards, participants completed trial-by-trial strategy self-reports. In our EEG analyses, we focused on induced activity (event-related synchronization/desynchronization, ERS/ERD) in three frequency bands (theta, lower alpha, upper alpha). Across all frequency bands, we found higher evidential strength for similar rather than different neurophysiological processes accompanying the solution of very small addition and multiplication problems. This was also true when n + 1 and n × 1 problems were excluded from the analyses. In two additional analyses, we showed that ERS/ERD can differentiate between self-reported problem-solving strategies (retrieval vs. procedure) and even between n + 1 and n + m problems in very small additions, demonstrating its high sensitivity to cognitive processes in arithmetic. The present findings clearly support the fact-retrieval account, suggesting that both very small additions and multiplications are solved through fact retrieval.HIGHLIGHTSNeurophysiological test of fact retrieval and compacted procedures accountInduced EEG data are sensitive to cognitive processes in arithmetic problem solvingBoth very small additions and multiplications are solved through fact retrieval

scholarly journals PENERAPAN TEORI KONSTRUKTIVIS DALAM PEMBELAJARAN

2020 ◽  
Vol 8 (2) ◽  
pp. 19-32
Author(s):  
Fatimah Saguni
Keyword(s):  
Problem Solving ◽  
Cognitive Processes ◽  
Learning Process ◽  
Thinking Skills ◽  
Critical Thinking Skills ◽  
Contextual Approach ◽  
Learning And Teaching ◽  
Active Involvement ◽  
Problem Solving Strategies ◽  
Constructing Knowledge

Constructivism is the basis for thinking of a contextual approach, namely that knowledge is built not a set of facts, concepts, or rules that are ready to be remembered. Students must construct that knowledge and give meaning through real experience. Students need to be accustomed to solving problems, finding something useful for themselves, and struggling with ideas. The teacher will not be able to give all knowledge to students. Students must construct knowledge in their own minds. Knowledge is not static, but is constantly evolving and changing as students construct new experiences that force them to base themselves and modify previous knowledge.Learning must be packaged into the process of constructing knowledge rather than receiving knowledge. In the learning process, students build their own knowledge through active involvement in the learning and teaching process. Students become the center of activities, not teachers.Critical thinking is an attempt by someone to check the truth of information using the availability of evidence, logic, and awareness of bias. Critical thinking skills are the cognitive processes of students in analyzing systematically and specifically the problems faced, distinguishing these problems carefully and thoroughly, as well as identifying and reviewing information to plan problem solving strategies.

scholarly journals Gaze interaction enhances problem solving: Effects of dwell-time based, gaze-augmented, and mouse interaction on problem-solving strategies and user experience

2009 ◽  
Vol 3 (1) ◽  
Author(s):  
Roman Bednarik ◽  
Tersia Gowases ◽  
Markku Tukiainen
Keyword(s):  
Problem Solving ◽  
User Experience ◽  
Cognitive Processes ◽  
Dwell Time ◽  
Cognitive Strategies ◽  
Gaze Interaction ◽  
Performance Problem ◽  
Problem Solving Strategies ◽  
Subject Experiment ◽  
Augmented Interaction

It is still unknown whether the very application of gaze for interaction has effects on cognitive strategies users employ and how these effects materialize. We conducted a between-subject experiment in which thirty-six participants interacted with a computerized problem-solving game using one of three interaction modalities: dwell-time, gaze-augmented interaction, and the conventional mouse. We observed how using each of the modalities affected performance, problem solving strategies, and user experience. Users with gaze-augmented interaction outperformed the other groups on several problem-solving measures, committed fewer errors, were more immersed, and had a better user experience. The results give insights to the cognitive processes during interaction using gaze and have implications on the design of eye-tracking interfaces.

IDENTIFICATION OF PROBLEM SOLVING STRATEGIES IN MATHEATICS AMONG HIGH SCHOOL STUDENTS

2017 ◽  
Vol 4 (36) ◽  
Author(s):  
J. Navaneetha Krishnan ◽  
P. Paul Devanesan
Keyword(s):  
High School ◽  
High School Students ◽  
Problem Solving ◽  
Sample Survey ◽  
Survey Method ◽  
Teaching Mathematics ◽  
School Students ◽  
Problem Solving Strategies ◽  
Achievement In Mathematics

The major aim of teaching Mathematics is to develop problem solving skill among the students. This article aims to find out the problem solving strategies and to test the students’ ability in using these strategies to solve problems. Using sample survey method, four hundred students were taken for this investigation. Students’ achievement in solving problems was tested for their Identification and Application of Problem Solving Strategies as a major finding, thirty one percent of the students’ achievement in mathematics is contributed by Identification and Application of Problem Solving Strategies.

scholarly journals Using process data to understand problem-solving strategies and processes for drag-and-drop items in a large-scale mathematics assessment

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Yang Jiang ◽  
Tao Gong ◽  
Luis E. Saldivia ◽  
Gabrielle Cayton-Hodges ◽  
Christopher Agard
Keyword(s):  
Problem Solving ◽  
Time Allocation ◽  
Large Scale ◽  
Solution Process ◽  
Process Data ◽  
Mathematics Assessments ◽  
Assessment Design ◽  
Eighth Grade Students ◽  
Problem Solving Strategies ◽  
Drag And Drop

AbstractIn 2017, the mathematics assessments that are part of the National Assessment of Educational Progress (NAEP) program underwent a transformation shifting the administration from paper-and-pencil formats to digitally-based assessments (DBA). This shift introduced new interactive item types that bring rich process data and tremendous opportunities to study the cognitive and behavioral processes that underlie test-takers’ performances in ways that are not otherwise possible with the response data alone. In this exploratory study, we investigated the problem-solving processes and strategies applied by the nation’s fourth and eighth graders by analyzing the process data collected during their interactions with two technology-enhanced drag-and-drop items (one item for each grade) included in the first digital operational administration of the NAEP’s mathematics assessments. Results from this research revealed how test-takers who achieved different levels of accuracy on the items engaged in various cognitive and metacognitive processes (e.g., in terms of their time allocation, answer change behaviors, and problem-solving strategies), providing insights into the common mathematical misconceptions that fourth- and eighth-grade students held and the steps where they may have struggled during their solution process. Implications of the findings for educational assessment design and limitations of this research are also discussed.

scholarly journals Teachers’ Use of Technology Affordances to Contextualize and Dynamically Enrich and Extend Mathematical Problem-Solving Strategies

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 793
Author(s):  
Manuel Santos-Trigo ◽  
Fernando Barrera-Mora ◽  
Matías Camacho-Machín
Keyword(s):  
Problem Solving ◽  
High School Teachers ◽  
Digital Technology ◽  
Dynamic Models ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
School Teachers ◽  
Use Of Technology ◽  
Technology Affordances ◽  
Problem Solving Strategies

This study aims to document the extent to which the use of digital technology enhances and extends high school teachers’ problem-solving strategies when framing their teaching scenarios. The participants systematically relied on online developments such as Wikipedia to contextualize problem statements or to review involved concepts. Likewise, they activated GeoGebra’s affordances to construct and explore dynamic models of tasks. The Apollonius problem is used to illustrate and discuss how the participants contextualized the task and relied on technology affordances to construct and explore problems’ dynamic models. As a result, they exhibited and extended the domain of several problem-solving strategies including the use of simpler cases, dragging orderly objects, measuring objects attributes, and finding loci of some objects that shaped their approached to reasoning and solve problems.

scholarly journals Remote Virtual Simulation for Incident Commanders—Cognitive Aspects

2021 ◽  
Vol 11 (14) ◽  
pp. 6434
Author(s):  
Cecilia Hammar Wijkmark ◽  
Maria Monika Metallinou ◽  
Ilona Heldal
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Cognitive Processes ◽  
Research Methodology ◽  
Current Knowledge ◽  
Learning Objectives ◽  
Virtual Simulation ◽  
Practical Training ◽  
Case Research ◽  
Action Case

Due to the COVID-19 restrictions, on-site Incident Commander (IC) practical training and examinations in Sweden were canceled as of March 2020. The graduation of one IC class was, however, conducted through Remote Virtual Simulation (RVS), the first such examination to our current knowledge. This paper presents the necessary enablers for setting up RVS and its influence on cognitive aspects of assessing practical competences. Data were gathered through observations, questionnaires, and interviews from students and instructors, using action-case research methodology. The results show the potential of RVS for supporting higher cognitive processes, such as recognition, comprehension, problem solving, decision making, and allowed students to demonstrate whether they had achieved the required learning objectives. Other reported benefits were the value of not gathering people (imposed by the pandemic), experiencing new, challenging incident scenarios, increased motivation for applying RVS based training both for students and instructors, and reduced traveling (corresponding to 15,400 km for a class). While further research is needed for defining how to integrate RVS in practical training and assessment for IC education and for increased generalizability, this research pinpoints current benefits and limitations, in relation to the cognitive aspects and in comparison, to previous examination formats.

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