scholarly journals Creative Mathematical Reasoning: Does Need for Cognition Matter?

2022 ◽  
Vol 12 ◽  
Author(s):  
Bert Jonsson ◽  
Julia Mossegård ◽  
Johan Lithner ◽  
Linnea Karlsson Wirebring
Keyword(s):  
Problem Solving ◽  
Conceptual Understanding ◽  
Mathematical Reasoning ◽  
Need For Cognition ◽  
Math Performance ◽  
Equation Modeling ◽  
Positive Effects ◽  
Cognitive Motivation ◽  
Solution Methods ◽  
Creative Mathematical Reasoning

A large portion of mathematics education centers heavily around imitative reasoning and rote learning, raising concerns about students’ lack of deeper and conceptual understanding of mathematics. To address these concerns, there has been a growing focus on students learning and teachers teaching methods that aim to enhance conceptual understanding and problem-solving skills. One suggestion is allowing students to construct their own solution methods using creative mathematical reasoning (CMR), a method that in previous studies has been contrasted against algorithmic reasoning (AR) with positive effects on test tasks. Although previous studies have evaluated the effects of CMR, they have ignored if and to what extent intrinsic cognitive motivation play a role. This study investigated the effects of intrinsic cognitive motivation to engage in cognitive strenuous mathematical tasks, operationalized through Need for Cognition (NFC), and working memory capacity (WMC). Two independent groups, consisting of upper secondary students (N = 137, mean age 17.13, SD = 0.62, 63 boys and 74 girls), practiced non-routine mathematical problem solving with CMR and AR tasks and were tested 1 week later. An initial t-test confirmed that the CMR group outperformed the AR group. Structural equation modeling revealed that NFC was a significant predictor of math performance for the CMR group but not for the AR group. The results also showed that WMC was a strong predictor of math performance independent of group. These results are discussed in terms of allowing for time and opportunities for struggle with constructing own solution methods using CMR, thereby enhancing students conceptual understanding.

scholarly journals Gaining Mathematical Understanding: The Effects of Creative Mathematical Reasoning and Cognitive Proficiency

2020 ◽  
Vol 11 ◽  
Author(s):  
Bert Jonsson ◽  
Carina Granberg ◽  
Johan Lithner
Keyword(s):  
Conceptual Understanding ◽  
Fluid Intelligence ◽  
Mathematical Reasoning ◽  
Working Memory Capacity ◽  
Relevant Information ◽  
Structural Features ◽  
Learning Conditions ◽  
Routine Procedures ◽  
Basic Level ◽  
Creative Mathematical Reasoning

In the field of mathematics education, one of the main questions remaining under debate is whether students’ development of mathematical reasoning and problem-solving is aided more by solving tasks with given instructions or by solving them without instructions. It has been argued, that providing little or no instruction for a mathematical task generates a mathematical struggle, which can facilitate learning. This view in contrast, tasks in which routine procedures can be applied can lead to mechanical repetition with little or no conceptual understanding. This study contrasts Creative Mathematical Reasoning (CMR), in which students must construct the mathematical method, with Algorithmic Reasoning (AR), in which predetermined methods and procedures on how to solve the task are given. Moreover, measures of fluid intelligence and working memory capacity are included in the analyses alongside the students’ math tracks. The results show that practicing with CMR tasks was superior to practicing with AR tasks in terms of students’ performance on practiced test tasks and transfer test tasks. Cognitive proficiency was shown to have an effect on students’ learning for both CMR and AR learning conditions. However, math tracks (advanced versus a more basic level) showed no significant effect. It is argued that going beyond step-by-step textbook solutions is essential and that students need to be presented with mathematical activities involving a struggle. In the CMR approach, students must focus on the relevant information in order to solve the task, and the characteristics of CMR tasks can guide students to the structural features that are critical for aiding comprehension.

scholarly journals Improving Calculus Learning Using a Scientific Calculator

2020 ◽  
Vol 2 (1) ◽  
pp. 220-227
Author(s):  
Miriam Dagan ◽  
Pavel Satianov ◽  
Mina Teicher
Keyword(s):  
Problem Solving ◽  
Conceptual Understanding ◽  
Computer Language ◽  
Mathematical Concepts ◽  
Problem Solving Skills ◽  
Learning Success ◽  
Cognitive Motivation ◽  
Long Term Experience ◽  
Scientific Calculator

AbstractThis article discusses the use of a scientific calculator in teaching calculus by using representations of mathematics notions in different sub-languages (analytical, graphical, symbolical, verbal, numerical and computer language). Our long-term experience shows that this may have a positive and significant effect on the enhancement of conceptual understanding of mathematical concepts and approaches. This transcends the basic computational uses, and implies a potential for real improvement in the learning success, cognitive motivation and problem solving skills of the student. We illustrate the steps we have taken towards doing this through some examples.

scholarly journals Measuring Conceptual Understanding, Procedural Fluency and Integrating Procedural and Conceptual Knowledge in Mathematical Problem Solving

2020 ◽  
Vol 8 (05) ◽  
pp. 1334-1350
Author(s):  
Thi Minh Phuong Ho
Keyword(s):  
Problem Solving ◽  
Conceptual Understanding ◽  
Structural Equation ◽  
Conceptual Knowledge ◽  
Mathematical Problem ◽  
Linear Functions ◽  
Equation Modeling ◽  
Mathematical Problem Solving ◽  
Procedural Fluency ◽  
Mathematical Proficiency

The main aim of this paper is to meassure students’ mathematical proficiency on conceptual understanding and procedural fluency, and their ability of integrating procedural and conceptual knowledge in problem solving. Based on the PCK taxonomy (Ho 2018), we design a questionnaire consisting of 12 questions with 22 tasks whose content is focus on linear functions and equations. The collected data is analysed by the statistical software IBM SPSS Statistics 22. Moreover, we use the structural equation modeling (SEM) to study the correlation between these two components of mathematical proficiency and the ability of integrating procedural and conceptual knowledge in problem solving, implemented in IBM SPSS AMOS 24. The findings show that students’ mathematical proficiency on procedural fluency on linear functions and equations is higher than that of conceptual understanding, and their ability of integrating procedural and conceptual knowledge is very low. Moreover, these categories have a bi-directional relationship, in which the affection of mathematical proficiency on conceptual understanding to the ability of integrating procedural and conceptual knowledge in problem solving is stronger than on procedural fluency.

Protecting intellectual property from insider threats

2019 ◽  
Vol 21 (2) ◽  
pp. 181-202
Author(s):  
Hyungjin Lukas Kim ◽  
Anat Hovav ◽  
Jinyoung Han
Keyword(s):  
Problem Solving ◽  
Information Security ◽  
Security Policy ◽  
Structural Equation ◽  
Equation Modeling ◽  
Problem Solving Skills ◽  
Content Type ◽  
Positive Effects ◽  
Theory Of Information ◽  
Protecting Intellectual Property

Purpose The purpose of this paper is to propose a theory of information security intelligence and examine the effects of managers’ information security intelligence (MISI) on employees’ procedural countermeasure awareness and information security policy (ISP) compliance intention. Design/methodology/approach A survey approach and structural equation modeling is utilized. Partial least squares (WarpPLS 6.0) and nonlinear algorithm are employed to analyze and examine the hypotheses. In total, 324 employees from companies in South Korea participated in the survey, which was conducted by a professional survey service company. Findings MISI positively affects employees’ awareness of information security procedural countermeasures; information security knowledge and problem-solving skills have positive effects on procedural countermeasures awareness; MISI increases employees’ compliance intention through procedural countermeasure awareness; and information security procedural countermeasures positively affect employees’ ISP compliance intention. Research limitations/implications This study proposes a theory of information security intelligence and examines its impacts on employees’ compliance intentions. The study highlights the mediating role of information security procedural countermeasures between information security intelligence and employees’ compliance intentions. Practical implications Managers should improve and explicitly demonstrate information security knowledge and problem-solving skills to increase employees’ ISP compliance intention. To protect the organization’s intellectual capital, managers should champion the development and promotion of PCM, rather than leave these functions to the information security group. Originality/value This is the first empirical study to propose and validate MISI.

How do working memory, general anxiety and math anxiety affect female students’ math performance?

2020 ◽  
Author(s):  
Nachshon Korem ◽  
Orly Rubinsten
Keyword(s):  
Working Memory ◽  
Latent Variables ◽  
Math Anxiety ◽  
Verbal Working Memory ◽  
Math Performance ◽  
Equation Modeling ◽  
Current Evidence ◽  
Unique Contribution ◽  
Shared Variance ◽  
Numeric Information

Current evidence suggests that math anxiety and working memory govern math performance. However, these conclusions are largely based on simple correlations, without considering these variables as a network or examining correlations at the latent variables level. Thus, questions remain regarding the role of the unique and shared variance between math anxiety, working memory and math performance. The purpose of the current study was to (i) uncover the underlying relationships between the variables to understand the unique contribution of each element to the network; (ii) measure the shared variance and identify the interactions between affect and cognition that control math performance. Our analytical approach involved both network analysis approach and structural equation modeling, with a sample of 116 female students.Results show that math anxiety and working memory affect math performance by different mechanisms. Only working memory tests that included numeric information were correlated to math anxiety. Each of the various working memory tasks correlated differently to math performance: working memory as a single latent variable was a better predictor of math performance than visuospatial and verbal working memory as two separate latent variables. Overall, both working memory and math anxiety affect math performance. Working memory tasks that include numeric information can affect performance in math anxious individuals.

Algorithmic Puzzles

2011 ◽  
Author(s):  
Anany Levitin ◽  
Maria Levitin
Keyword(s):  
Problem Solving ◽  
Computer Science ◽  
Algorithm Design ◽  
Divide And Conquer ◽  
Algorithmic Problem ◽  
Design Strategies ◽  
Job Interviews ◽  
Skill Levels ◽  
Problem Solving Skills ◽  
Solution Methods

While many think of algorithms as specific to computer science, at its core algorithmic thinking is defined by the use of analytical logic to solve problems. This logic extends far beyond the realm of computer science and into the wide and entertaining world of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many classic brainteasers as well as newer examples from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures. The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving. Mastery of these strategies--exhaustive search, backtracking, and divide-and-conquer, among others--will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the 150 puzzles contains hints and solutions, along with commentary on the puzzle's origins and solution methods. The only book of its kind, Algorithmic Puzzles houses puzzles for all skill levels. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking through more difficult puzzles.

scholarly journals Students’ agency, creative reasoning, and collaboration in mathematical problem solving

2021 ◽  
Author(s):  
Ellen Kristine Solbrekke Hansen
Keyword(s):  
Problem Solving ◽  
Driving Forces ◽  
Mathematical Reasoning ◽  
Mathematical Problem ◽  
Linear Functions ◽  
Shared Understanding ◽  
Interaction Patterns ◽  
Collaborative Processes ◽  
Mathematical Properties ◽  
Shared Agency

AbstractThis paper aims to give detailed insights of interactional aspects of students’ agency, reasoning, and collaboration, in their attempt to solve a linear function problem together. Four student pairs from a Norwegian upper secondary school suggested and explained ideas, tested it out, and evaluated their solution methods. The student–student interactions were studied by characterizing students’ individual mathematical reasoning, collaborative processes, and exercised agency. In the analysis, two interaction patterns emerged from the roles in how a student engaged or refrained from engaging in the collaborative work. Students’ engagement reveals aspects of how collaborative processes and mathematical reasoning co-exist with their agencies, through two ways of interacting: bi-directional interaction and one-directional interaction. Four student pairs illuminate how different roles in their collaboration are connected to shared agency or individual agency for merging knowledge together in shared understanding. In one-directional interactions, students engaged with different agencies as a primary agent, leading the conversation, making suggestions and explanations sometimes anchored in mathematical properties, or, as a secondary agent, listening and attempting to understand ideas are expressed by a peer. A secondary agent rarely reasoned mathematically. Both students attempted to collaborate, but rarely or never disagreed. The interactional pattern in bi-directional interactions highlights a mutual attempt to collaborate where both students were the driving forces of the problem-solving process. Students acted with similar roles where both were exercising a shared agency, building the final argument together by suggesting, accepting, listening, and negotiating mathematical properties. A critical variable for such a successful interaction was the collaborative process of repairing their shared understanding and reasoning anchored in mathematical properties of linear functions.

scholarly journals The effect of risk communication on preventive and protective Behaviours during the COVID-19 outbreak: mediating role of risk perception

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Seyed Taghi Heydari ◽  
Leila Zarei ◽  
Ahmad Kalateh Sadati ◽  
Najmeh Moradi ◽  
Maryam Akbari ◽  
...  
Keyword(s):  
Risk Perception ◽  
Risk Communication ◽  
Structural Equation ◽  
Online Survey ◽  
Equation Modeling ◽  
Mediating Role ◽  
Positive Effects ◽  
Global Pandemic ◽  
And Control ◽  
New Evidence

Abstract Background The COVID-19 outbreak is a global pandemic, during which the community preventive and protective behaviors play a crucial role in the containment and control of infection. This study was designed to contribute to the existing knowledge on how risk communication (RC) and risk perception (RP) affect protective and preventive behaviors (PPB) during the COVID-19 outbreak. Methods The required data were extracted from a national online survey of Iranian adults aged 15 and older during March 15–19, 2020 (n=3213). Data analysis was performed using structural equation modeling. Results The study findings reveal that RC has direct and indirect positive effects on PB. Furthermore, this study also provides new evidence indicating that RP mediates the relationship between RC and PB and there is a two-way relationship between RC and RP. These interactions may have impact on risk communication strategies which should be adopted during this pandemic. Conclusion The study findings have remarkable implications for informing future communications as well as interventions during this ongoing outbreak and subsequent national risk events.

scholarly journals The Diffusion Mechanism of Megaproject Citizenship Behavior: The Role of Institutional Isomorphism

2021 ◽  
Vol 13 (15) ◽  
pp. 8123
Author(s):  
Delei Yang ◽  
Jun Zhu ◽  
Qingbin Cui ◽  
Qinghua He ◽  
Xian Zheng
Keyword(s):  
Structural Equation ◽  
Diffusion Mechanism ◽  
Vital Role ◽  
Citizenship Behavior ◽  
Equation Modeling ◽  
Positive Effects ◽  
Diffusion Limited ◽  
The Relationship ◽  
Mimetic Isomorphism

Megaproject citizenship behavior (MCB) has been confirmed to a play vital role on megaproject performance. Although current research has argued that institution elements have had an impact on MCB diffusion, limited studies have empirically investigated the distinct effectiveness of various institution elements on driving MCB’s widespread diffusion in construction megaprojects. Based on institution theory, this study proposes a theoretical model comprising institutional elements (i.e., normative and mimetic isomorphism), owner’s support, relationship-based trust, and their effect or impact on MCB’s diffusion. Based on 171 industrial questionnaires collected from managers of contractors and designers in megaprojects. Partial least squares structural equation modeling (PLS-SEM) was used to validate the established model. The results indicated that both normative and mimetic isomorphism have positive effects on facilitating MCB diffusion, and owner’s support has shown partial mediation in promoting MCB diffusion through normative isomorphism, as well as full mediation in the promoting of MCB diffusion through mimetic isomorphism. Meanwhile, relationship-based trust exerts a positive moderating effect on the relationship between mimetic isomorphism and MCB. This study extends current literature on driving MCB diffusion from the perspective of institutional theory, contributing by providing four implications for megaprojects managers to “buy in” more extensive MCB.

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