Kindergarten and First Grades

Since I worked at ISEC (almost 10 years), I am a big fan of the successful Singapore Math. There, I had the opportunity to create, coordinate and teach more than 10 curricular units dedicated to this subject.

Recently, I had the excellent opportunity to collaborate with APECEF (5 years), and that allowed me to experience the application of the method.

At the same time, I was co-author of a series of school books adapted to the Portuguese syllabus, following this same method. Regarding this, I have already organized more than 100 training courses for teachers, some in Portuguese, others in English.

I have also had the opportunity to collaborate consistently on the Azorean project «Prof. DA» (qualified teachers in solving learning difficulties), coordinated by Professor Ricardo Cunha Teixeira. It is an excellent initiative (with good results) that aims to bring the fundamental ideas of Singapore Math to the ground.

What is Singapore Math.?

In Singapore Math, three edifying theories stand out: 1) Concrete-Pictorial-Abstract approach (CPA), inspired by the work of the American psychologist Jerome Bruner, which defends a step-by-step transition from concrete situations to abstract thinking; 2) principle of variability developed by the Hungarian mathematical educator Zoltán Dienes, pointing the use of different examples and contexts in learning, as well as multiple representations; 3) the ideas defended by the English psychologist Richard Skemp, underlining the importance of establishing connections and mathematical structural relationships, in order to achieve a deep understanding of the subjects. This happens in an integrated way. Great importance is given to structure (order), orality and concretizations/schemes.

Regarding books, there are 3 series with the Singapore seal: Primary Mathematics, Math in Focus e Maths - No Problem! To organize the curricular units at ISEC, I was inspired by the first collection; to conceive Viva a Matemática! series, the inspiration came from the last two. In summary, the pages are clean and clear, there are good and varied problems, focusing on well-defined purposes and obeying careful categorizations. The use of problem solving is a constant (bar model is a classic). The strategy is to allow children understand mathematics, both at the procedural level and (simultaneously) at the conceptual level.

Singapore's results are extremely good, as shown in the following graphs (TIMSS):

What are the subjects of teacher training that I organize?

Generalist, kindergarten, numbers and operations, geometry, fractions, problem solving (bar model), use of school books, etc.

I have organized teacher training courses on this method in many institutions such as Colégio de São Tomás, Colégio do Ramalhão, Colégios Fomento (Planalto, Mira Rio, Horizonte, Cedros), Colégio O Castanheiro, Colégio Militar, Seixal International School, Escola Internacional de Vilamoura, Escola EB da Malveira, Externato O Parque, Colégio Crescer no Campo, Escola do Largo, CED Jacob Rodrigues Pereira, Colégio das Descobertas, Mundos de Vida, Salesianos de Lisboa, Colégio O Beiral, Escola EB Paredes, Colégio Cesário Verde, Colégio Valsassina, Cooperativa de Ensino A Colmeia, Escola Básica Vasco da Gama, Externato Marcelino Champagnat.

To answer frequently asked questions, discuss issues, schedule possible teacher training sessions, just contact me through my contacts.

Top left, a class I observed in Singapore (2020). Top right, I'm participating in MNP conference | Maths – No Problem! (London, 2018). Below, a teacher training session in S. Miguel island (2019).