Advances in Mathematics Education Research

Contents
Preface
Chapter 1
Problem Solving and Mathematical Modelling as Tools in Mathematics Education
	Abstract
	Introduction
	Problem Solving in Mathematics Education
	The Circle of Modelling
	The Application - Oriented Teaching of Mathematics
	Assessing the Effect of Computers on Students’ PS  and MM Skills
	Future Research Directions
	Conclusion
	References
Chapter 2
Fuzzy Methods for Assessing Student Mathematical Skills
	Abstract
	Introduction
	Mathematical Background
		Fuzzy Sets and Fuzzy Logic
		Grey Numbers
		Neutrosophic Sets
		Soft Sets
	The Assessment Methods
		Comparison of the Rectangular Fuzzy Assessment Model with  the GPA Index
		The Hybrid Assessment Method
	Future Research Directions
	Conclusion
	References
Chapter 3
Conceptual Shortcuts and Technology  in Mathematical Problem Solving
	Abstract
	Introduction
	Using Conceptual Shortcuts in Solving Algebraic  Word Problems
	Gnomons in the Numeric Tables as Conceptual Shortcuts
		The Multiplication Table
		The Addition Table
		The Polygonal Numbers Table
	Maple-Based Mathematical Induction Proof as  a Conceptual Shortcut
	Reduction to a Simpler Problem as a Conceptual Shortcut
		Finger Rings Problem
		Connecting the Finger Rings Problem to Combinatorics
		The Case of Different Finger Rings
		From Pascal’s Triangle to Bernoulli Formula
		The Problem of Division of Stakes
	Conclusion
	References
	Biographical Sketch
Chapter 4
Proof and Proving in Mathematics:  A Didactical Perspective
	Abstract
	Introduction
	For the Format
	For the Deduction
	Examples
		Material to Produce
		The Flaw
		Material for the Student to Produce
		Material to Produce
	Epilogue
	References
	Biographical Sketch
Chapter 5
Turning Failure into Success: Digital Tutoring Activities to Overcome Difficulties in Mathematics at Lower  Secondary School
	Abstract
	Introduction
	Theoretical Framework and Related Work
	The Compiti@casa Project
	Research Methodology
	Results and Discussion
	Conclusion
	Acknowledgments
	References
Chapter 6
Education Research Focused on Geometry Teaching in the Plane and the Space
	Abstract
	Introduction
	Spatial Reasoning
	GeoGebra
	Tinkercad
	Geometry in the Plane and Connection to the Algebra: Different Ways – Different Technologies
		Importance of the Interaction between Algebra and Geometry  in Curricula
		Genetic Principles, Forms of Representation, and Types  of Illustration
	Solving Quadratic Equations
	Geometry in the Space with Tinkercad and 3D Printing
	Conclusion
	Acknowledgments
	References
	Biographical Sketches
Chapter 7
Research on the Results of Lower Secondary School Students in Mathematical Testing
	Abstract
	Introduction
	Measuring Mathematical Literacy Through PISA Tests
	PISA Assessment Levels
	Thematic Areas of School Mathematics in the Results  of Slovak Students
		Growth Phenomena
		Example: The Beauty of Powers
		Geometric Approximation
		Example: Tiling
		Conditional Decision-Making
		Example: Purchasing Decisions
	Critical and Good Areas in School Mathematics in Slovakia
	Conclusion
	Acknowledgments
	References
	Biographical Sketches
Chapter 8
Analyzing Examination Problems of Students of Mathematics Following a Didactics  of Mathematics Course
	Abstract
	Introduction
	Materials And Methods
		Examination from June, 2020
		Examination from September 2020
	Results
	Discussion
		Discussion and Interpretation on the Data  from June’s Examination Results
		Discussion and Interpretation on the Data from September’s Examination Results
	Conclusion
	References
	Biographical Sketch
Chapter 9
An Approach to Development:  Turning Education from a Service Duty to  a Productive Tool
	Abstract
	Introduction
	Main Problem: Is Education a Service Duty of the Government and the Parents, or Should It Be Considered as  a Productive Tool?
	The Relationship between Education and Economic Growth
		Literature Review
		Methodology and Results of a New Trial for Estimating  the Relationship between Education and Economic Growth
	Japan, Korea, and Singapore’s Development after Improving Their Educational Situation
	The Situation of Education in Iran
	Increasing the Quality of Education by Increasing  Teachers’ Efficiency
		Literature Review
		Methodology and Examination of a New Trial for Estimating  the Impact of a Factor on the Quality of Education
	Results and Discussion
	Conclusion
	References
Commentary
The Future of Education in the Era of  the Fourth Industrial Revolution
	Abstract
	Introduction
	The Role of Computers
	Artificial Intelligence and E-Learning in Education
	Connectivism: A New Learning Theory in the Digital Era
	Discussion and Conclusion
	References
About the Editors
Index
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