It is a common thought that for a person to be competent in mathematics, all one needs is the right knowledge about mathematical operations and the skills to solve problems. But Mogens Niss, a trained mathematician and one of the founding staff of Roskilde University, established that skills and knowledge are not the only prerequisites to attaining excellent mathematical literacy.

For a person to develop competence in math, one also requires a few exclusive cognitive skills and abilities, which he referred to as ‘competencies.’ These mathematical competencies Niss talked about are the highlight of this blog post, which we will be covering in a simple and easy-to-understand format.

**What do we mean by ‘mathematical competence’?**

Generally, being competent at something means being good at it. Because you have learned and practiced a lot in that sphere of life, you can easily handle related situations that appear in front of you.

Having mathematical competence or being competent in math is based on similar lines. However, it is a lot more than just being able to perform mathematical calculations quickly using mental math. It is a person’s ability to understand and use their knowledge of math in different situations with an element of math in it.

So, when we say that a person is mathematically competent, it means they are really good at understanding, judging, doing, and using math in multiple situations that appear in their everyday lives and where math has a role to play.

**Types of mathematical competencies as identified by Mogens Niss**

During his research^{[1]}, Niss characterized eight competencies as distinct elements of an individual’s mathematical competence. He further divided the eight competencies into two groups:

**Group 1:** Competencies related to one’s ability to “ask and answer questions in and with mathematics”

**Group 2:** Competencies related to one’s ability to “manage mathematical language and tools”

**Group 1 Competencies:**

**1. Mathematical thinking**

This competency is about having the ability to put forward questions and having an idea of the kinds of answers one can obtain mathematically. It is about understanding the scope and limitations of a mathematical concept and handling it accordingly. Furthermore, it also includes extending the scope of a mathematical concept by abstracting and generalizing results and distinguishing between various mathematical statements.

**2. Mathematical problem solving**

This competency involves two aspects of mathematics. First is the person’s ability to identify and specify mathematical problems they come across. The second is to solve varied mathematical problems that are presented by other people or by themselves.

**3. Mathematical modeling**

Modeling mathematically is a competency that allows a person to analyze existing mathematical models and interpret their different elements. It also supports them in performing active modeling, which comprises activities like building, validating, analyzing, monitoring, and communicating the results of the entire process.

**4. Mathematical reasoning**

The competency of mathematical logical reasoning helps an individual evaluate arguments suggested by others, uncover the basic idea, and devise and transform opinions into proving statements. It also supports one’s understanding of a given mathematical proof and how it differs from other kinds of reasoning.

**Group 2 Competencies:**

**1. Representing mathematical entities**

Having representation competency helps a person understand and use a wide variety of representations for mathematical purposes. It helps one understand and acknowledge the possibility of different representations of the same entity and allows the person to utilize varied representations and switch between them as needed.

**2. Handling symbols and formalisms**

Mathematical language is not the same as natural language. With this competency, an individual can understand the rules of a formal mathematical expression, decode and interpret standard mathematical language, translate natural language to formal mathematical language, and work with expressions containing mathematical formulae and symbols.

**3. Communication**

This competency helps a person understand different types of materials (written, oral, and visual) containing mathematics-related content. It also allows the person to express themselves adequately when it comes to matters about math.

**4. Using aids and tools**

The last competency Niss discussed is using tools for mathematical purposes. Having good competency in this area means a person is knowledgeable about the tools required to conduct a mathematical activity and is able to use them effectively in different circumstances.

**Relationship between mathematical competencies and math literacy**

The fact that mathematical competencies are as important as mathematical knowledge and skills, these are strongly related to the development and enhancement of math literacy. Without the activation of mathematical competencies, it would be difficult to utilize mathematical knowledge to solve problems.

Another aspect of establishing a relationship between competencies and math literacy is that both are directly related. The more a person possesses and activates mathematical competencies, the better equipped they will be to apply their knowledge to solve mathematical challenges. On the other hand, the fewer mathematical competencies they possess, the lower will be their ability to work on problems demanding strong math literacy.

Therefore, besides teaching mathematical concepts in classrooms, schools and educators must work on fostering these competencies in their students. These competencies prove helpful in comprehending mathematical information existing in the world. For example, a study^{[2]} established mathematical competencies required to interpret COVID-19 pandemic information and found five competencies that one must possess.

One way of promoting these competencies is by consciously incorporating a multitude of activities that can initiate and stimulate the eight mathematical competencies in students’ minds. This will nudge them to get on the path of developing solid mathematical proficiency.

**A quick summary of various mathematical competencies**

Competency | Associated Abilities |

Mathematical thinking | Putting forward questions. Having an idea of the kinds of answers one can obtain mathematically. Understanding the scope and limitations of a mathematical concept and handling it accordingly. Extending the scope of a mathematical concept by abstracting and generalizing results. Distinguishing between various mathematical statements. |

Mathematical problem-solving | Identifying and specifying mathematical problems that come across. Solving varied mathematical problems that are presented by other people or by self. |

Mathematical modeling | Analyzing existing mathematical models. Interpreting their different elements. Performing active modeling, comprising activities like building, validating, analyzing, monitoring, and communicating the results of the entire process. |

Mathematical reasoning | Evaluating arguments suggested by others. Uncovering basic ideas. Devising and transforming opinions into proving statements. Understanding a given mathematical proof and how it differs from other kinds of reasoning. |

Representing mathematical entities | Understanding and using a wide variety of representations for mathematical purposes. Understanding and acknowledging the possibility of different representations of the same entity. Utilizing different representations and switching between them as needed. |

Handling symbols and formalisms | Understanding the rules of formal mathematical expressions. Decoding and interpreting standard mathematical language. Translating normal language to formal mathematical language. Working with expressions containing mathematical formulae and symbols. |

Communication | Understanding varied materials containing mathematics-related content. Expressing oneself properly in matters associated with math. |

Using aids and tools | Knowledge about various math-related aids and tools. Ability to use them effectively. |

**Final thoughts**

The eight mathematical competencies characterized by Mogens Niss are fundamental to developing mathematical literacy. Our intrinsic mathematical competencies activate whenever we are in a situation requiring us to face a mathematical challenge. But which of the eight competencies is activated depends on the challenge we face. Therefore, it is said that different activities trigger different sets of competencies in an individual.

For this reason, there is no single standardized math assessment that can reliably evaluate all eight mathematical competencies together. For a comprehensive assessment, there is a need for a wide range of mathematical activities that can activate all competencies so they can be evaluated effectively for an individual.

**References**

- Niss, Mogens. (2003). Mathematical competencies and the learning of mathematics: the danish KOM project.
- Aguilar, M.S., Castaneda, A. What mathematical competencies does a citizen need to interpret Mexico’s official information about the COVID-19 pandemic?.
*Educ Stud Math***108**, 227–248 (2021). https://doi.org/10.1007/s10649-021-10082-9