Volume 52, August 2023, 101296Author links open overlay panel

While problem-solving is the ‘main reason for mathematicians’ existence, collaboration has not been seen explicitly so central. Even though it has been an essential part for the development of mathematics, material conditions made it different and slower in the past. Today, collaborative problem-solving (CPS) is part of mathematicians’ daily experiences so that, following Polya’s idea that for mathematics learning, students shall experience mathematicians’ experiences, CPS is having his firm route to school education on the own guidance of the great master. This route meets another one, driven by the tendency for developing in all students the skills for the XXI century, giving strength to CPS as a line of research in mathematics education. We review current literature on CPS in mathematics education and attempts for the implementation of CPS in Chile. We conclude with the appearance of a new area of research, which is implementation and replication in mathematics education, where research in CPS meets the implementation taken part in Chile. This review involves research issues that, in our opinion, will continue their developing with great vitality, keeping their relative importance.

Section snippetsProblem-solving in mathematics

“The main reason for mathematicians’ existence is to solve problems, and so mathematics really consists of problems and solutions”, wrote Paul Halmos in his paper The Heart of Mathematics [12], he argues that “mathematics has many ingredients, like axioms, theorems, proofs, concepts, definitions, theories, formulas and methods, all of them certainly essential, none of them is at the heart of mathematics”. Without going further into the discussion of what is mathematics, we recognize that from

Collaborative problem-solving in mathematics education today

The advancement of technologies, their irruption in everyday life, and the challenges they pose to education have given rise to conceiving the skills for the XXI century [25] and the need for students to develop them along school years. These ideas, originated by economic concerns, have an important impact on democratization of societies by activating in all students these fundamental human skills, previously destined for an elite or the naturally talented.

One of the crucial skills for the XXI

ARPA experience in implementing collaborative problem-solving in Chile

Chilean students like to collaborate (93% of them) and they believe that collaboration is good for reaching their goals (81% of them). This statement came out of the CPS section of PISA 2015 results for Chilean students, even though they achieved 457 points, much below the Organisation for Economic Co-operation and Development (OECD) average of 500 points [24]. Inspite of having in Chile a school curriculum where PS and collaboration are important skills to be developed by all students and the

Implementation and replication

Two important initiatives took place in the mathematics community during 2021. The publication of Implementation and Replication Studies in Mathematics Education in 2021, a new journal for the dissemination and discussion of academic works related to applying and scaling up the insights of mathematics education research, and for providing a bridge between the academic community and the policy-making communities. This journal appears almost simultaneously with the special issue of

Declaration of Competing Interest

No conflict of interest.

Acknowledgements

ANID/PIA/Basal Funds for Centers of Excellence FB0003, Apoyo a Centros de Excelencia ACE210010, Proyecto Fondo Basal FB210005.

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