Mathematical Reasoning of Children and Adults

lt;p> Alina Galvão Spinillo is a Full Professor in the Post-Graduate Program in Cognitive Psychology at the Federal University of Pernambuco, Brazil. She is also one of the leaders of the Group for Research in Psychology of Mathematics Education at the same university. She served as Coordinator of the Working Group Sociocognitive and Language Development of the National Association for Research and Post-Graduate Programs in Psychology (ANPEPP), Brazil. She is a level 1 researcher with the National Council for Scientific and Technological Development (CNPq). She holds a bachelor's degree in Psychology and a master's degree in Cognitive Psychology both from the Federal University of Pernambuco. She holds a Ph.D. in Developmental Psychology from the University of Oxford (England), and completed a post-doctorate at the University of Sussex (England). Her investigations deal with the following topics: psychology of mathematics education with emphasis on the development of complex mathematical concepts (such as proportion, chance, fractions, combinatorial reasoning), number sense in children, children's knowledge about texts of different genres, development of textual awareness, textual production and comprehension of narrative, expository and argumentative texts in children. Some of her research studies examine the relations between learning and cognitive development, extracting educational implications for the elementary school years.

Sintria Labres Lautert is an Associate Professor in the Department of Psychology and in the Post-Graduate Program in Cognitive Psychology at the Federal University of Pernambuco, Brazil. Coordinator of the Working Group in Psychology of Mathematics Education of the National Association for Research and Post-Graduate Programs in Psychology (ANPEPP, 2010-2020), Brazil and one of the leaders of the Group for Research in Psychology of Mathematical Education (NUPPEM), Brazil. She received a master's degree and a Ph.D. in Cognitive Psychology from the Federal University of Pernambuco, (Brazil). Post-doctorate at the Poincaré Institute for Mathematics Education, Tufts University (USA). Her research interests focus on conceptual development (multiplicative structures, particularly division and the role of meanings, properties, relations, and symbolic representations in the learning of mathematics). Her most recent interest involves decision-making and concept formation in the field of financial education, and professional development of mathematics teachers and teaching of statistic in elementary school.

Rute Elizabete de Souza Rosa Borba is an Associate Professor in the Post-Graduate Program in Mathematical and Technological Education at the Federal University of Pernambuco, Brazil. She is also leader of the Study Group on Combinatorial and Probabilistic Reasoning (Geração) at the same university. She served as Vice-President of the Brazilian Society of Mathematical Education and Coordinator of the Working Group 01 (Mathematics in Early Childhood Education and Early Years of Elementary School). She holds a mathematics degree from the Federal Rural University of Pernambuco and a master's degree in Cognitive Psychology from the Federal University of Pernambuco. She holds a Ph.D. from Oxford Brookes University (England), and completed a post-doctorate at the Federal University of Mato Grosso do Sul (Brazil). Her investigations deal with the following topics: conceptual development (combinatorial and probabilistic reasoning, and the role of meanings, properties, relationships, and symbolic representations in mathematical learning), analysis of textbooks and training of teachers who teach mathematics.

1. Mathematical reasoning: the learner, the teacher, the teaching and learning.- 2. Number sense and flexibility of calculation: a common focus on number relations.- 3. Number sense in a developmental perspective: comparing the mastery of its different components in children.- 4. Mental and neural foundations of numerical magnitude.- 5. Strategies and accuracy in the number line task in Colombian and Brazilian deaf children.- 6. 1, 2, 3... Let's count: The development of counting at the beginning of compulsory schooling.- 7. How do Kindergarten children deal with possibilities in combinatorial problems?.- 8. A Kindergarten student's uses and understandings of tables while working with function problems.- 9. Performance and strategies used by Elementary School 5th graders when solving problems involving functional reasoning.- 10. Contributions of digital technologies to the development of algebra-ic thinking at school.- 11. How teachers deal with students' mathematical reasoning when promoting whole-class discussion during the teaching of algebra.- 12. The posing of mathematical problems by university students of mathematics.- 13. What do low-educated adults and children think about the uses of mathematics?.