How can we re-conceptualise learning with understanding in a complex world?

How can we promote learning with understanding in an increasingly complex
world?

What features should a task have in order to promote learning with understanding? How to research the complex dynamic of learning with understanding promoted by
such tasks? What can we learn from this research to use within the classroom and in designing lessons/tasks?

How can we establish connections in mathematics learning: Between different areas of mathematics? Between mathematics and other subjects? Between mathematics and everyday life?

What implications does the increasingly complex world have in terms of numeracy or mathematics literacy? How does this inform our practices within the classroom and in designing lessons/tasks?

What kind of mathematics training should teachers have in order to be able to promote learning with understanding?

How can teacher training contribute to establishing connections between the various areas of Mathematics?

How can teacher training contribute to establishing connections between Mathematics and other subjects?

How to promote connections between school mathematics and academic mathematics, in teacher training?

What type of competences do we need to include in professional training programs for mathematics teachers to cope with the increasingly complex world challenges?

In relation to connections and understanding, what kind of teaching methods are more appropriate?

How do we evaluate and/or research the resources from the perspective of the connections and the understanding they try to promote?

How can we promote mathematics education as a means to explore environmental issues?

How can we promote mathematics as a means to reflect on the sustainability of the world?

How can mathematics promote "living together"?

How can ICTs contribute to learning rich in connections, in an increasingly complex world?

How can ICT be used in teacher training to promote understanding in mathematics?

How can we use ICT as teaching-learning tools, rather than instruments that replace students’ cognitive efforts?

Is it possible to understand peoples’ lives from an ethnomathematics perspective?

How can school mathematics take into account the culture developed by young people in their everyday lives?

How to take advantage of cultural aspects to enrich the teaching and learning of mathematics?

How can we create hybrid spaces linking school-mathematics to mathematics situated in cultural, everyday contexts?

What dos it mean to develop a critical approach to mathematics and culture in an increasingly complex world?

Phrases like “mathematics is the language in which God has written the universe” (Galileo Galilei) or “all things in nature occur mathematically” (René Descartes) express the idea that if we want to understand
the world, then we need to use mathematics. But can we use mathematics without understanding? John von Neumann once said “Young man, in mathematics you don't understand things. You just get used to
them.” One way to interpret this statement would be to say you could use mathematics (with success) without understanding it. Or, perhaps we can speak of a kind of understanding that is merely instrumental
instead of relational (Skemp, 1976) or intuitive, or formal (Byers & Herscovics, 1977). Another different way to read von Neumann’s statement is to take it as a clarification that understanding is not a black and
white issue. There may be degrees of understanding. And there may also be a form of understanding that impedes better understanding. In the words of Richard Skemp, “to understand something means to
assimilate it into an appropriate schema. This explains the subjective nature of understanding, and also makes clear that this is not usually an all-or-nothing state” (Skemp, 1971, p. 46). Pragmatically, the power
of adaptability of a schema results from its connection to a greater number of concepts, but it may happen that what is an appropriate schema at one particular time may be obsolete and turn into an obstacle later on (Brousseau, 1997).

Let’s get back to René Descartes: “All things in nature occur mathematically”. A different idea implied by this saying would be that to understand mathematics we need to connect our mathematical
understandings with our understandings of the world we live in (natural, psychological and socio-cultural; see also Skemp, 1979). This idea is at the base of the concept of mathematization, or, more precisely,
horizontal mathematization (Freudenthal, 1991). Concurring with this idea is the belief many have that Mathematics is a cultural product based on human experiences, such as counting, measuring, locating,
designing, explaining, and playing (Bishop, 1988). Nevertheless, mathematical understanding has to do with both the learning of invariants and the acquisition of cultural tools in which children can represent
mathematical ideas, in a dynamic and interconnected process (Nunes & Bryant, 1997). This idea is in line with a recent formulation of understanding in epistemology, in which understanding of a given
phenomenon has to be maximally well-connected and it may have degrees of approximation (Kelp, 2015).

Concerning the learning and teaching of mathematics in the complexity of our world, we can revalue the ideas of Galileo, Descartes and Von Neumann on the central role of mathematics in the context of the
genetic approach of epistemology proposed by Piaget to the logical-mathematical dimension of the construction of scientific knowledge. Piaget proposed replacing the positivist hierarchization of science
with an interdisciplinary cyclic epistemology. This approach to epistemological interrelationships in the context of learning, conceived in the digital environment of education, calls into question not only the
connections of mathematics as a scientific discipline, but also the connections of mathematics as an academic subject. How is it possible to make the presence of mathematics visible in the understanding of
other school subjects? How to collaborate with other teachers of mathematics and of other courses? This question of interdisciplinarity is in close interaction with the learning and teaching of the complexity and
variety of the natural and social phenomena of our era.

The official languages of the conference are French and English. Everyone is asked to speak slowly and clearly so that all participants can understand and contribute to discussions. All speakers must prepare their slides or diorama in both languages. We rely on and appreciate the help of those who can translate, to assist their colleagues within each working group. Animators in most cases are able to help in both languages.

Dept. of Educational Studies

University of Oxford

Dept. de Didáctica de la Matemática

Universidad de Granada

Dept. d'Educació Lingüística i Literària, i Didàctica de les Ciències Experimentals i la Matemàtica

Universitat de Barcelona

Instituto de Educação da Universidade de Lisboa

School of Teacher Education, Charles Sturt University

Alexandra Gomes

Ema Mamede

Filipa Balinha

Joana Tinoco

Letícia Martins

Maria Helena Martinho

Paula Cardoso

Pedro Palhares

Sara Ribeiro

Alexandra Gomes - Portugal

Ana Serradó – Spain

Andreas Moutsios-Rentzos - Greece

Ema Mamede - Portugal

Fragkiskos Kalavasis - Greece

Gail FitzSimons - Australia

Gilles Aldon - France

Javier Díez-Palomar - Spain

Lisa Boistrup - Sweden

Marcelo Bairral - Brasil

Monica Panero - Switzerland

Pedro Palhares - Portugal

René Screve - Belgium

**MARCH, 3, 2019**

Proposals for ORAL PRESENTATIONS and WORKSHOPS

**MARCH, 31, 2019**

Contributions to the FORUM OF IDEAS

**APRIL, 15, 2019**

Reply from the International Program Committee

**APRIL, 30, 2019**

Conference Fee

**MAY, 15, 2019**

Submission of the final paper

**MAY, 31, 2019**

Third Announcement (Final Program)

__Before April 30, 2019:__

• Participant, 300€

• Accompanying person, Student, Pre-school Educator, Elementary or Secondary Teacher, 160€

__After April 30, 2019__

• Participant 360€

• Accompanying person, Student, Pre school Educator, Elementary or Secondary Teacher 220€

Quality Class WITH lodgment (10 nights) 300€

Quality Class WITHOUT lodgment 160€

Click HERE to see full payment instructions.

We hope that all participants will contribute “actively” to the conference by sharing with others their experiences and views in the various sessions, particularly in the working groups. Moreover, you are encouraged to send a proposal for an oral presentation or a workshop, or to bring a contribution to the Forum of Ideas.

Proposals for ORAL PRESENTATIONS and WORKSHOPS can be made by sending a FOUR PAGE text
(about 1800 words or 12000 characters with spaces), BEFORE MARCH, 3, 2019.

Proposals for the FORUM OF IDEAS, can be made by sending a ONE PAGE text (about 450 words or 3000
characters with spaces), BEFORE MARCH, 31, 2019

Click HERE to **read full instructions on how to submit** your work.

**You also MUST register yourself** on line on the conference webiste by clicking HERE

Participants must book hotel or other accommodation by themselves. Please book your hotel in advance if
you wish to have a nice place! You will be able to travel by bus from the center of Braga to the conference
venue, so the city center will be a good place to stay.

Click HERE to find further information for visitors and how to reach Braga.

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- University of Minho

Institute of Education, Gualtar Campus

Braga, Portugal - +351 253 60 12 12
- cieaem71@gmail.com

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