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These proceedings are a written record of the research presented at the 42nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Mazatlán, Mexico, virtually beginning May 27, 2021 and in-person June 2-6, 2021. The conference was originally scheduled to take place October 14-18, 2020; it was postponed, due to the COVID pandemic. In accordance with the major goals of PME-NA that include promoting international contacts and stimulating interdisciplinary research, the theme was proposed as "Entre Culturas/Across Cultures". The goal of the theme was an academic exchange that would reflect the ample diversity of ways of teaching and learning of mathematics, and of the tools and communities involved in mathematics education; as well as an exploration of how the differences in cultures imply a need to consider how research results can be taken into account in varying contexts. The papers comprise 80 Research Reports, 190 Brief Reports, 147 Poster Presentations, 10 Working Groups, 2 Research Colloquia, and Plenary and special lectures. The program also includes a special tribute to Eugenio Filloy and a tribute to the PME-NA members who were affected by the COVID-19 pandemic. [These proceedings were produced with Cinvestav (Centro de Investigación y de Estudios Avanzados del IPN), México and AMIUTEM (Asociación Mexicana de Investigadores del Uso de Tecnología en Educación Matemática, A.C.), México. Individual papers are indexed in ERIC.]

We are delighted to welcome you to the International Conference on Education and New Developments 2015-END 2015, taking place in Porto, Portugal, from 27 to 29 of June. Education, in our contemporary world, is a right since we are born. Every experience has a formative effect on the constitution of the human being, in the way one thinks, feels and acts. One of the most important contributions resides in what and how we learn through the improvement of educational processes, both in formal and informal settings. Our International Conference seeks to provide some answers and explore the processes, actions, challenges and outcomes of learning, teaching and human development. Our goal is to offer a worldwide connection between teachers, students, researchers and lecturers, from a wide range of academic fields, interested in exploring and giving their contribution in educational issues. We take pride in having been able to connect and bring together academics, scholars, practitioners and others interested in a field that is fertile in new perspectives, ideas and knowledge. We counted on an extensive variety of contributors and presenters, which can supplement our view of the human essence and behavior, showing the impact of their different personal, academic and cultural experiences. This is, certainly, one of the reasons we have many nationalities and cultures represented, inspiring multi-disciplinary collaborative links, fomenting intellectual encounter and development. END 2015 received 528 submissions, from 63 different countries, reviewed by a double-blind process. Submissions were prepared to take form as Oral Presentations, Posters, Virtual Presentations and Workshops. It was accepted for presentation in the conference, 176 submissions (33% acceptance rate). The conference also includes a keynote presentation from an internationally distinguished researcher, Professor Dr. Martin Braund, Adjunct Professor at Cape Peninsula University of Technology in Cape Town, South Africa and Honorary Fellow in the Department of Education at the University of York, UK, to whom we express our most gratitude. This volume is composed by the proceedings of the International Conference on Education and New Developments (END 2015), organized by the World Institute for Advanced Research and Science (W.I.A.R.S.) and had the help of our respected media partners that we reference in the dedicated page. This conference addressed different categories inside the Education area and papers are expected to fit broadly into one of the named themes and sub-themes. To develop the conference program we have chosen four main broad-ranging categories, which also cover different interest areas: (1) In TEACHERS AND STUDENTS: Teachers and Staff training and education; Educational quality and standards; Curriculum and Pedagogy; Vocational education and Counseling; Ubiquitous and lifelong learning; Training programs and professional guidance; Teaching and learning relationship; Student affairs (learning, experiences and diversity); Extra-curricular activities; Assessment and measurements in Education. (2) In PROJECTS AND TRENDS: Pedagogic innovations; Challenges and transformations in Education; Technology in teaching and learning; Distance Education and eLearning; Global and sustainable developments for Education; New learning and teaching models; Multicultural and (inter)cultural communications; Inclusive and Special Education; Rural and indigenous Education; Educational projects. (3) In TEACHING AND LEARNING: Educational foundations; Research and development methodologies; Early childhood and Primary Education; Secondary Education; Higher Education; Science and technology Education; Literacy, languages and Linguistics (TESL/TEFL); Health Education; Religious Education; Sports Education. (4) In ORGANIZATIONAL ISSUES: Educational policy and leadership; Human Resources development; Educational environment; Business, Administration, and Management in Education; Economics in Education; Institutional accreditations and rankings; International Education and Exchange programs; Equity, social justice and social change; Ethics and values; Organizational learning and change. The proceedings contain the results of the research and developments conducted by authors who focused on what they are passionate about: to promote growth in research methods intimately related to teaching, learning and applications in Education nowadays. It includes an extensive variety of contributors and presenters, who will extend our view in exploring and giving their contribution in educational issues, by sharing with us their different personal, academic and cultural experiences. (Individual papers contain references.)