MARIA APARECIDA VIGGIANI BICUDO is a Full Professor at São Paulo State University (Unesp), Institute of Geosciences and Exact Sciences, Rio Claro. She received her PhD in Sciences, in the Faculty of Philosophy and Sciences, São Paulo State Institute of Higher Education. She is a tenured professor at São Paulo State University. She coordinates the PHEM - Phenomenology in Mathematics Education research group (FEM - Fenomenologia em Educação Matemática), founded in 1995. Dr. Bicudo is a scholar in the field of education, with emphasis in philosophy of education, working mainly with the topics: education, mathematics education, philosophy of mathematics, phenomenology, philosophy of mathematics education; a Research Fellow in University of California, Berkeley, Guest professor at Facoltà di Filosofia dell'Università Lateranense di Roma, Professor in the Graduation Program in Mathematics Education at UNESP, Rio Claro campus, Editor of the Qualitative Research Journal and co-editor of BOLEMA - Mathematics Education Bulletin, President of the Society of Qualitative Investigation (www.sepq.org.br), a highly qualified researcher of the National Council for Scientific and Technological Development (CNPq), a foundation linked to the Ministry of Science and Technology (MCT) to support Brazilian research. With the publication of the investigations conducted, articles in scientific journals, with the presence in national and international scientific events, the work of Dr. Bicudo impacts the community of researchers and professionals acting in Education and, more specifically, Mathematics Education.DR. BRONISLAW CZARNOCHA is a professor of mathematics at Hostos Community College of CUNY. Received his PhD in Mathematical Physics and Mathematical Foundations of Quantum Mechanics, his Dissertation: "States in Separable Algebras", Yeshiva University, New York City. His interest in investigations of learning developed through practice of teaching and ledhim to formulate the Teaching-Research NYCity methodology; he is the editor of Mathematics Teaching-Research Journal online. At present, his research interests center of the creativity of Aha!Moment and its role in learning through the development of concepts. He published around 50 papers in Mathematics Education and published 4 books in the area. DR. MAURÍCIO ROSA is Professor at the Faculty of Education, Department of Teaching and Curriculum and at the Post-Graduate Program in Teaching of Mathematics at the Federal University of Rio Grande do Sul, Brazil. He is post-doctor from Rutgers University – New Jersey – USA and from Federal University of Rio de Janeiro (UFRJ – Brazil). He is Ph.D. Mathematics Education at São Paulo State University - Unesp - Rio Claro (SP) (2008), Master in Mathematics Education (2004) from Unesp too and Graduated in Mathematics Education from Lutheran University from Brazil (ULBRA) (2002). He participated in Doctoral Program with Internship Abroad - PDEE by the Coordination for the Improvement of Higher Education Personnel – CAPES (2007), at London South Bank University - London (UK). He has experience in Mathematics, with an emphasis on Mathematics Education, working mainly on the following fronts: Digital Technologies, Distance Education, Electronic Games, Role Playing Game (RPG), Philosophy of Mathematics Education, Teacher Education, Decolonial Mathematics Education and Exclusion/inclusion in Mathematics Education (racism, homophobia, transphobia etc.). DR. MAŁGORZATA MARCINIAK is an Associate Professor at the LaGuardia Community College of CUNY and the Managing Editor of the Mathematics Teaching Research Journal. She received her PhD in Mathematics from Missouri University of Science and Technology with dissertation “Holomorphic Extensions on Toric Varieties”. She is interested in applications of theories of creativity in the classroom and already published numerous articles about this subject

• Part I: A Broad View Of The Philosophy Of Mathematics Education.- Chapter 1: The Ontological Problems of Mathematics and Mathematics Education.- Chapter 2: Scientific revolutions: from Popper to Heisenberg.- Chapter 3: Questions that are at the core of a mathematics education “project” .- Chapter 4: Networking Phenomenology and Didactics: horizons of didactical milieus with a focus on Abstract Algebra.- Chapter 5: Specifying, Defining, Generalising & Abstracting Mathematically all seen as Subtly Different Shifts of Attention.- Chapter 6: Toward a systems theory approach to mathematics education.- Chapter 7: On Mathematical Validity and its Human Origins.- part ii: philosophy of mathematics education: creativity and educational perspectives.- Chapter 8: Towards a philosophy of creativity in mathematics education.- Chapter 9: A Framework for Creative Insights within Internalization of Mathematics.- Chapter 10: A Reconsideration of Appropriation from a Sociocultural Perspective.- Chapter 11: Towards a Philosophy of Algorithms as an Element of Mathematics Education.- Chapter 12: The times of transitions in the modern education.- Chapter 13: Some Examples of Mathematical Paradoxes with Implications for the Professional Development of Teachers.- Part Iii: Philosophy Of Critical Mathematics Education, Modelling And Education For Sustainable.- Chapter 14: A Performative Interpretation of Mathematics.- Chapter 15: Reflective Knowing in the Mathematics Classroom: The Potential of Philosophical Inquiry for Critical Mathematics Education.- Chapter 16: Mathematical Modelling: A Philosophy of Science Perspective.- Chapter 17: Education for Sustainable Development (ESD) in mathematics education: reconfiguring and rethinking the philosophy of mathematics for the 21st century.- Part Iv: Philosophy Of Mathematics Education In Diverse Perspectives, Cultures, And Environments.- Chapter 18: Asé o’u toryba ‘ara îabi’õnduara!.- Chapter 19: Mathematics Education andUbuntu Philosophy: the analysis of antiracist- mathematics-activity-with-Digital-Technologies.- Chapter 20: Philosophy, Rigor, and Axiomatics in Mathematics: Imposed or Intimately Related?.- Chapter 21: Idealism and Materialism in mathematics teaching, an analysis from the Socioepistemological Theory.- Chapter 22: Cognitive and Neurological Evidence of Non-Human Animal Mathematics, and Implications for Mathematics Education

MARIA APARECIDA VIGGIANI BICUDO is a Full Professor at São Paulo State University (Unesp), Institute of Geosciences and Exact Sciences, Rio Claro. She received her PhD in Sciences, in the Faculty of Philosophy and Sciences, São Paulo State Institute of Higher Education. She is a tenured professor at São Paulo State University. She coordinates the PHEM - Phenomenology in Mathematics Education research group (FEM - Fenomenologia em Educação Matemática), founded in 1995. Dr. Bicudo is a scholar in the field of education, with emphasis in philosophy of education, working mainly with the topics: education, mathematics education, philosophy of mathematics, phenomenology, philosophy of mathematics education; a Research Fellow in University of California, Berkeley, Guest professor at Facoltà di Filosofia dell'Università Lateranense di Roma, Professor in the Graduation Program in Mathematics Education at UNESP, Rio Claro campus, Editor of the Qualitative Research Journal and co-editor of BOLEMA - Mathematics Education Bulletin, President of the Society of Qualitative Investigation (www.sepq.org.br), a highly qualified researcher of the National Council for Scientific and Technological Development (CNPq), a foundation linked to the Ministry of Science and Technology (MCT) to support Brazilian research. With the publication of the investigations conducted, articles in scientific journals, with the presence in national and international scientific events, the work of Dr. Bicudo impacts the community of researchers and professionals acting in Education and, more specifically, Mathematics Education.DR. BRONISLAW CZARNOCHA is a professor of mathematics at Hostos Community College of CUNY. Received his PhD in Mathematical Physics and Mathematical Foundations of Quantum Mechanics, his Dissertation: "States in Separable Algebras", Yeshiva University, New York City. His interest in investigations of learning developed through practice of teaching and ledhim to formulate the Teaching-Research NYCity methodology; he is the editor of Mathematics Teaching-Research Journal online. At present, his research interests center of the creativity of Aha!Moment and its role in learning through the development of concepts. He published around 50 papers in Mathematics Education and published 4 books in the area. DR. MAURÍCIO ROSA is Professor at the Faculty of Education, Department of Teaching and Curriculum and at the Post-Graduate Program in Teaching of Mathematics at the Federal University of Rio Grande do Sul, Brazil. He is post-doctor from Rutgers University – New Jersey – USA and from Federal University of Rio de Janeiro (UFRJ – Brazil). He is Ph.D. Mathematics Education at São Paulo State University - Unesp - Rio Claro (SP) (2008), Master in Mathematics Education (2004) from Unesp too and Graduated in Mathematics Education from Lutheran University from Brazil (ULBRA) (2002). He participated in Doctoral Program with Internship Abroad - PDEE by the Coordination for the Improvement of Higher Education Personnel – CAPES (2007), at London South Bank University - London (UK). He has experience in Mathematics, with an emphasis on Mathematics Education, working mainly on the following fronts: Digital Technologies, Distance Education, Electronic Games, Role Playing Game (RPG), Philosophy of Mathematics Education, Teacher Education, Decolonial Mathematics Education and Exclusion/inclusion in Mathematics Education (racism, homophobia, transphobia etc.). DR. MAŁGORZATA MARCINIAK is an Associate Professor at the LaGuardia Community College of CUNY and the Managing Editor of the Mathematics Teaching Research Journal. She received her PhD in Mathematics from Missouri University of Science and Technology with dissertation “Holomorphic Extensions on Toric Varieties”. She is interested in applications of theories of creativity in the classroom and already published numerous articles about this subject

• Part I: A Broad View Of The Philosophy Of Mathematics Education.- Chapter 1: The Ontological Problems of Mathematics and Mathematics Education.- Chapter 2: Scientific revolutions: from Popper to Heisenberg.- Chapter 3: Questions that are at the core of a mathematics education “project” .- Chapter 4: Networking Phenomenology and Didactics: horizons of didactical milieus with a focus on Abstract Algebra.- Chapter 5: Specifying, Defining, Generalising & Abstracting Mathematically all seen as Subtly Different Shifts of Attention.- Chapter 6: Toward a systems theory approach to mathematics education.- Chapter 7: On Mathematical Validity and its Human Origins.- part ii: philosophy of mathematics education: creativity and educational perspectives.- Chapter 8: Towards a philosophy of creativity in mathematics education.- Chapter 9: A Framework for Creative Insights within Internalization of Mathematics.- Chapter 10: A Reconsideration of Appropriation from a Sociocultural Perspective.- Chapter 11: Towards a Philosophy of Algorithms as an Element of Mathematics Education.- Chapter 12: The times of transitions in the modern education.- Chapter 13: Some Examples of Mathematical Paradoxes with Implications for the Professional Development of Teachers.- Part Iii: Philosophy Of Critical Mathematics Education, Modelling And Education For Sustainable.- Chapter 14: A Performative Interpretation of Mathematics.- Chapter 15: Reflective Knowing in the Mathematics Classroom: The Potential of Philosophical Inquiry for Critical Mathematics Education.- Chapter 16: Mathematical Modelling: A Philosophy of Science Perspective.- Chapter 17: Education for Sustainable Development (ESD) in mathematics education: reconfiguring and rethinking the philosophy of mathematics for the 21st century.- Part Iv: Philosophy Of Mathematics Education In Diverse Perspectives, Cultures, And Environments.- Chapter 18: Asé o’u toryba ‘ara îabi’õnduara!.- Chapter 19: Mathematics Education andUbuntu Philosophy: the analysis of antiracist- mathematics-activity-with-Digital-Technologies.- Chapter 20: Philosophy, Rigor, and Axiomatics in Mathematics: Imposed or Intimately Related?.- Chapter 21: Idealism and Materialism in mathematics teaching, an analysis from the Socioepistemological Theory.- Chapter 22: Cognitive and Neurological Evidence of Non-Human Animal Mathematics, and Implications for Mathematics Education

MARIA APARECIDA VIGGIANI BICUDO is a Full Professor at São Paulo State University (Unesp), Institute of Geosciences and Exact Sciences, Rio Claro. She received her PhD in Sciences, in the Faculty of Philosophy and Sciences, São Paulo State Institute of Higher Education. She is a tenured professor at São Paulo State University. She coordinates the PHEM - Phenomenology in Mathematics Education research group (FEM - Fenomenologia em Educação Matemática), founded in 1995. Dr. Bicudo is a scholar in the field of education, with emphasis in philosophy of education, working mainly with the topics: education, mathematics education, philosophy of mathematics, phenomenology, philosophy of mathematics education; a Research Fellow in University of California, Berkeley, Guest professor at Facoltà di Filosofia dell'Università Lateranense di Roma, Professor in the Graduation Program in Mathematics Education at UNESP, Rio Claro campus, Editor of the Qualitative Research Journal and co-editor of BOLEMA - Mathematics Education Bulletin, President of the Society of Qualitative Investigation (www.sepq.org.br), a highly qualified researcher of the National Council for Scientific and Technological Development (CNPq), a foundation linked to the Ministry of Science and Technology (MCT) to support Brazilian research. With the publication of the investigations conducted, articles in scientific journals, with the presence in national and international scientific events, the work of Dr. Bicudo impacts the community of researchers and professionals acting in Education and, more specifically, Mathematics Education.DR. BRONISLAW CZARNOCHA is a professor of mathematics at Hostos Community College of CUNY. Received his PhD in Mathematical Physics and Mathematical Foundations of Quantum Mechanics, his Dissertation: "States in Separable Algebras", Yeshiva University, New York City. His interest in investigations of learning developed through practice of teaching and ledhim to formulate the Teaching-Research NYCity methodology; he is the editor of Mathematics Teaching-Research Journal online. At present, his research interests center of the creativity of Aha!Moment and its role in learning through the development of concepts. He published around 50 papers in Mathematics Education and published 4 books in the area. DR. MAURÍCIO ROSA is Professor at the Faculty of Education, Department of Teaching and Curriculum and at the Post-Graduate Program in Teaching of Mathematics at the Federal University of Rio Grande do Sul, Brazil. He is post-doctor from Rutgers University – New Jersey – USA and from Federal University of Rio de Janeiro (UFRJ – Brazil). He is Ph.D. Mathematics Education at São Paulo State University - Unesp - Rio Claro (SP) (2008), Master in Mathematics Education (2004) from Unesp too and Graduated in Mathematics Education from Lutheran University from Brazil (ULBRA) (2002). He participated in Doctoral Program with Internship Abroad - PDEE by the Coordination for the Improvement of Higher Education Personnel – CAPES (2007), at London South Bank University - London (UK). He has experience in Mathematics, with an emphasis on Mathematics Education, working mainly on the following fronts: Digital Technologies, Distance Education, Electronic Games, Role Playing Game (RPG), Philosophy of Mathematics Education, Teacher Education, Decolonial Mathematics Education and Exclusion/inclusion in Mathematics Education (racism, homophobia, transphobia etc.). DR. MAŁGORZATA MARCINIAK is an Associate Professor at the LaGuardia Community College of CUNY and the Managing Editor of the Mathematics Teaching Research Journal. She received her PhD in Mathematics from Missouri University of Science and Technology with dissertation “Holomorphic Extensions on Toric Varieties”. She is interested in applications of theories of creativity in the classroom and already published numerous articles about this subject

• Part I: A Broad View Of The Philosophy Of Mathematics Education.- Chapter 1: The Ontological Problems of Mathematics and Mathematics Education.- Chapter 2: Scientific revolutions: from Popper to Heisenberg.- Chapter 3: Questions that are at the core of a mathematics education “project” .- Chapter 4: Networking Phenomenology and Didactics: horizons of didactical milieus with a focus on Abstract Algebra.- Chapter 5: Specifying, Defining, Generalising & Abstracting Mathematically all seen as Subtly Different Shifts of Attention.- Chapter 6: Toward a systems theory approach to mathematics education.- Chapter 7: On Mathematical Validity and its Human Origins.- part ii: philosophy of mathematics education: creativity and educational perspectives.- Chapter 8: Towards a philosophy of creativity in mathematics education.- Chapter 9: A Framework for Creative Insights within Internalization of Mathematics.- Chapter 10: A Reconsideration of Appropriation from a Sociocultural Perspective.- Chapter 11: Towards a Philosophy of Algorithms as an Element of Mathematics Education.- Chapter 12: The times of transitions in the modern education.- Chapter 13: Some Examples of Mathematical Paradoxes with Implications for the Professional Development of Teachers.- Part Iii: Philosophy Of Critical Mathematics Education, Modelling And Education For Sustainable.- Chapter 14: A Performative Interpretation of Mathematics.- Chapter 15: Reflective Knowing in the Mathematics Classroom: The Potential of Philosophical Inquiry for Critical Mathematics Education.- Chapter 16: Mathematical Modelling: A Philosophy of Science Perspective.- Chapter 17: Education for Sustainable Development (ESD) in mathematics education: reconfiguring and rethinking the philosophy of mathematics for the 21st century.- Part Iv: Philosophy Of Mathematics Education In Diverse Perspectives, Cultures, And Environments.- Chapter 18: Asé o’u toryba ‘ara îabi’õnduara!.- Chapter 19: Mathematics Education andUbuntu Philosophy: the analysis of antiracist- mathematics-activity-with-Digital-Technologies.- Chapter 20: Philosophy, Rigor, and Axiomatics in Mathematics: Imposed or Intimately Related?.- Chapter 21: Idealism and Materialism in mathematics teaching, an analysis from the Socioepistemological Theory.- Chapter 22: Cognitive and Neurological Evidence of Non-Human Animal Mathematics, and Implications for Mathematics Education