## Current research in problem solving

**Presentation**

The Atlantic webinars on research in mathematics education are an initiative of the three research societies in Mathematics Education from Portugal, Spain and Brazil:

These webinars aim to create an opportunity for socialisation and debate of the research currently carried out in the three countries on a specific theme, which will be chosen annually, creating an Atlantic bridge for dialogue and sharing.

Each year, a cycle of three webinars on the same topic is held, each hosted by a researcher nominated by each of the societies. The first edition of the webinars will be held in 2022 and has problem solving as its general theme.

The webinars take place online, always on Wednesdays, and last 90 minutes, divided between a presentation by the researcher and a discussion with the participants.

Registration to the webinars is free and should be done **here**

Live streaming on **SBEM’s youtube channel**

**Organising Committee**

Ana Paula Canavarro, António Domingues, Agostinho Homa, Clara Jiménez, Claudia Lisete Groenwald, Edelmira Badillo, Gilberto Januário, Lurdes Serrazina, Neusa Branco, Nuria Climent, Pere Ivars, Rosa Tomás Ferreira.

## Programme

#### Webinar 1

#### Mathematical Problem Solving with Technology: from student activity to teacher didactic knowledge

Researcher: **Hélia Jacinto**, *Institute of Education of the University of Lisbon*

**Wednesday, September 28th, 2022**

**Time:** 13:30 Brazilian time (Brasilia); 17:30 continental Portugal time; 18:30 Spain time.

Digital technologies currently offer a wide range of possibilities for the teaching and learning of mathematics because, in addition to driving innovative ways of accessing knowledge, they support the development of mathematical thinking through activities such as manipulation and exploration that can lead to the identification of variants or invariants, as well as to the formulation of conjectures and generalisations.

This webinar will discuss the role of digital technologies in a very concrete mathematical activity – non-routine problem solving – revisiting a study whose participants were young people proficient in this activity and presenting results from a new research that seeks to understand aspects of mathematics teachers’ didactic knowledge needed to teach problem solving with technologies.

Thus, in a first step, we will present the theoretical framework that enabled the development of an explanatory model of Mathematical Problem Solving with Technologies (MATR) processes, based on the observation of primary school students solving problems and expressing their mathematical thinking.

In the following, and based on another study in which we interviewed and observed experienced mathematics teachers solving non-routine problems using digital technologies, we will discuss some aspects of Knowledge to Teach Mathematical Problem Solving with special focus on one of the components of this framework: the mathematics teacher’s proficiency in solving problems with technologies.

Problem-solutions developed with different technological tools, either by primary school students or mathematics teachers, will be discussed in order to highlight essential elements of their activity and that illustrate the transformative role of technology.

Both studies suggest that the efficient integration of digital technologies into mathematics problem-solving activity involves a particular type of ability – techno-mathematical fluency.

The webinar will close with a synthesis of the results achieved and a reflection on the possible implications for both the teaching and learning of mathematics and for professional development initiatives and teacher training.

#### Webinar 2

#### Problem solving and traits of high mathematical ability

Researcher: **Ángel Gutiérrez**, *University of Valencia, Spain*

**Wednesday, October 26th, 2022**

**Time:** 13:30 Brazilian time (Brasilia); 17:30 continental Portugal time; 18:30 Spain time.

Problem solving is the most typically mathematical activity and, in the school context, the activity that most clearly identifies the mathematical ability and mathematical reasoning skills of each student.

In this session, I will present results from several current lines of research on the use of problem solving for the identification and care of students with high mathematical ability in Primary and Compulsory Secondary Education (ESO). I will show examples in which it can be observed how students, when solving problems, bring into play different skills recognised as typical of high mathematical ability, such as generalisation, transfer, creativity, visualisation, etc.

I will also briefly present, with examples, the theoretical framework of levels of cognitive demand, which we use in our research to describe and differentiate different styles of reasoning during problem solving.

This framework provides a complementary approach to the previous one, as it focuses on analysing the cognitive effort made by students during the different stages of problem solving.

#### Webinar 3

#### Problem Solving and Proposition: in association with ICT's, research and practice in Mathematics Education

Researcher: **Norma Suely Gomes Allevato**, *Universidade Cruzeiro do Sul, Brazil*

**Wednesday, November 30th, 2022**

**Time:** 12:30 Brazilian time (Brasilia); 17:30 continental Portugal time; 18:30 Spain time.

More than in previous times, in current research and curriculum prescriptions Problem Solving and Proposition has taken a prominent position.

Consequently, they have triggered reflections on their *modus operandi* and driven the development of research focused on teaching, learning, assessment, curricula and teacher training.

Moreover, when associated with Information and Communication Technologies, Problem Solving and Proposition of Problems highlight new aspects to be considered and raise new questions to be investigated, whose answers provide subsidies to guide teaching practice and mathematical learning at all levels of education, especially in Basic Education.