Do you remember math class when you went to school? What was it like for you? In many cases, math class was a place where students ‘learned’ formulas in a dull way without knowing why. In these classes, student mechanized and memorized. But Just as we put forward in the To Practice or not to Practice article, repeating until memorized isn’t a guarantee of learning.

Fortunately, there is another type of math class,** a welcoming place where mistakes are also welcome and where everyone’s participation is celebrated**, where we don’t only work on content (numbers, geometry, etc.) but we also work on competency (reasoning, solving problems, etc.). Classes where students **see the world through math glasses**.

Although there is now a written rule (**the LOMLOE**) to incorporate competencies in class, in a class rich in math, it has **always **been worked on together with content. So, it is not surprising that more and more teacher find value in more competency-based teaching. They have understood that the foundation of knowledge is the student **learning from understanding, not repeating**.

## Competency-based activities and problems in math

A competency-based activity is one in which has **mathematic competencies** as its manifesto. That is, how math is learned. Generally, the activity starts with **a problem, a question, a challenge to which we don’t have a predetermined strategy ready to solve it**.

Traditionally, **a contextualized situation** (for example ‘17 people are travelling on a bus, 4 more get on at the next stop. How many people are there now?’) doesn’t have to be a problem because normally it has a defined path to get to the answer and doesn’t imply a challenge. However, this doesn’t mean that we shouldn’t propose contextualized situations in the classroom. They are fundamental in working on basic arithmetic operations, reading comprehension and connections to daily life.

## In class...

Let’s imagine a class in which a teacher sets an activity with some number cards going from 1-9 and asks the students to take two and add the digits. After practicing for a short while the teacher asks, “If I take two cards randomly, what results can I get?” At this moment, **the students should realize that there is more than one solution and they should think of strategies to find all of them** without missing or repeating any.

These kind of activities implicitly contain basic ideas from **the Problem Solving process** (**understanding **formulations, **designing **strategies of systematic and exhaustive thought, **checking **a solution, etc.) and, differently to contextualized situations, we can’t automatize them. Math is creating, imagining, looking for strategies… and having a good time discovering the world!

In this way we can see **how a teacher’s management of a class is very important for a child to learn how to question**. So we must encourage a good problem solving environment in class. We must create **open situations** in which the student can analyze what is happened and go further. If a task allows students to ask questions, this is a good sign.

We as teachers and role models should generate these situations and **place questions at the center of learning**. And, above all, we should celebrate and value a student asking a really good question. In the article The Question in the Math Class we explain what is the role of the teacher in this new educational paradigm.