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10 Practices for a Problem-Solving Classroom Environment

Here are the 10 practices

Would you like to encourage reasoning, critical thinking and the discussion of strategies in the classroom? Download the 10 Practices for a Problem Solving Environment!

What are problems in mathematics?

For us, problems are fundamental to mathematical activity. They are a challenge waiting to be overcome, involving effort and perseverance. But they are also a journey, a path and the reward of spectacular views.

As we explain in this article, a problem in mathematics is any situation for which we do not have a method, an algorithm or a predefined strategy to solve. In other words, one operation could be a problem for a kindergarten student and, at the same time, a simple exercise for a middle school student.

How to encourage competency-based learning

The best way to bring competency-based learning to the classroom is to create a problem solving environment, as you can see in the following cycle:
Problem solving phases

Thinking of the math classroom in this way is the best premise to develop competencies while learning content.

What are the keys to encouraging an environment like this in the classroom? Following this you will find our 10 Practices for a Problem Solving Environment. You will find a version for each educational stage, kindergarten, elementary and middle school.

Sets of practices that inspire us

Our list of practices follows in a long tradition of sets of 10 practices to encourage better learning of mathematics. In the 50s, the Catalan professor and mathematician Pere Puig y Adam wrote ‘Ten Commandments for Mid-level Mathematics Education’ (Decálogo de la didáctica matemática media), a text with advice that even today sounds revolutionary.

A second example is the list by the Hungarian mathematician George Pólya, ‘The 10 Commandments for Teachers’, in which he places problems as the protagonists of mathematical activity.

The list is extensive, but we cannot finish without mentioning the set of practices of a great teacher from Girona, María Antònia Canals. Her ‘10 Commandments to Work with Manipulatives’ is a list of ten commandments that have influenced us greatly when thinking about many of the activities in our curriculum.

From all this inspiration, we have built our own, with examples for each educational stage, so that together, we can encourage a good learning environment in the classroom. Our list aims to review and update many of these authors’ original ideas by focusing on problem solving.

Would you like to see what we have come up with? Would you like examples to take to the classroom?

  • Albert Vilalta

    Albert Vilalta has a degree in Telecommunications Engineering and is a PhD student of Teaching of Mathematics and Experimental Sciences in the Universidad Autónoma de Barcelona (UAB). With more than 7 years of teaching experience, he is currently a professor of mathematics in the Faculty of Education at UAB and a member of the Innovamat teaching team, where he carries out research, development, training and communication tasks.

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