# The 10 best teaching practices to become good at Maths

It all started with the **industrial revolution of the 18th ^{century} with** the golden age of the steam engine used as an engine to run the powerful machines of the textile and metallurgical sector.

In this new society, industry demanded a workforce able to read and calculate to allow the economic success of its enterprises. In the republican schools, the pupil, future employee, thus followed a schooling which answered these needs: to learn to listen, to memorize and to carry out the instructions.

Alternative education experts have denounced these **rigid teachings** and thus developed alternative learning methods aimed at **unleashing students’ potential**.

And it is among all these learning techniques that we are going to identify the **10 most effective practices**.

**What is my pedagogical mother tongue?**

First of all, to become good at math, the first question to ask is: **how do I learn best? **Listening, doing, watching? The pedagogue **Antoine de la Garanderie** has worked all his life to answer these questions. He thus identified the different learning profiles of individuals.

There are therefore **3 mental languages**: **visual**, **auditory** and **kinesthetic; **3 forms of learning thanks to which we have the most facility to learn.

By identifying our predominant language or mental language, we give ourselves the means to **learn in the best conditions**.

**How do I learn?**

Is there a **better way** to teach, to assimilate knowledge? Who would be universal? Which would be specific to each?

- Attention,
- Memorization,
- Comprehension,
- The reflection,
- And creative imagination.

The **mental gesture** is, just like the physical gesture, an action that one does but to implement the **act of knowledge** .

First, the learner concentrates on the notion to be learned. In his **mental language** , he (she) will evoke in his mind the information he (she) receives.

Then, he (she) will **memorize** these same evocations because the goal is to use this new notion to solve problems

After that, to understand it and so that this notion has its place in his memory, the student **brings meaning** to it by confronting it with existing notions in his memory.

It is only then that he (she) **confronts** the new evocation memorized and understood with other rules that he (she) has in memory.

Finally, because he (she) can rely on his (her) acquired knowledge, he (she) will be able to **invent** and discover when faced with an unusual situation.

**How do I learn math? Playing.**

__Montessori pedagogy begins with manipulation and repetition. For the child psychiatrist “Children cannot think without their hands”. She then develops the notion of fine motor skills__, where intelligence and the hand go hand in hand.

The child, therefore, needs to touch, to look, to move, in short the child needs something **concrete** in order to assimilate an **abstract concept. **The pedagogue has therefore invented many educational games, the most popular and effective of which are:

- blue and red number bars for
**numeration** - pearls for operations
**,**and - the snake game for
**memorization**

**How do I learn math? Starting with… an apple**

The __Singapore method__ has demonstrated its effectiveness since its introduction in 1995 in Singapore schools by allowing the country to appear in the top 5 nations for the teaching of mathematics.

It is strongly inspired by the pedagogical observations of the educational psychologist **Jerome Bruner**: the teaching of mathematics begins with the **concrete** in order to understand **the abstract. **From these theories, the Singapore system built the **image and abstract concrete approach** there.

4 **Apples** will be represented by 4 circles then by 4 dots. We start from the manipulation of objects dear to Maria Montessori (4 apples), then we continue with an image representation of the objects (4 circles) and we end with the abstract shape of these apples by points (4 points).

**How do I learn math? By evoking in several ways. **

With the **multiple representations** of addition below, we allow very early, from the first classes, to give meaning to numbers and the meaning of operations between them.

How?

We will also try to **manipulate abstract objects** by **multiple representations** of common operations such as addition or subtraction or even geometry.

For example, you have always been shown an isosceles triangle, the two sides of equal length on the right and on the left. And when asked if the 2nd is isosceles (Just the same, but turned around), the majority of college students questioned do not recognize it and answer no. However, by accustoming children very early to the different representations of a geometric object or an operation, we bring meaning **and** a **better understanding**.

**How do I learn math? By being wrong.**

Error is synonymous with repeated efforts to arrive at a solution, which is why in mathematics error is encouraged. Isn’t it the sweat of success?

Moreover, in their problem-solving practice, the **Singapore method** values **effort** and **mistakes**, one does not go without the other.

*“The error is quite normal because it is an episode in the restructuring and expansion of knowledge. –* Regine Douady*.*

**How do I learn math? By repeating in several ways. **

It is not enough to know, it is not enough to understand, it is not enough to do. It is necessary to **repeat** to learn so that the new notion becomes knowledge.

This is the observation that **Jerome Bruner** (him again!) has made and he has therefore developed a method to remedy this: the **spiral approach**. In this one, a concept is approached at different times of the school program.

The students will then deepen the new concept, in different ways, several times during their schooling. This will stimulate them cognitively and motivate them.

**How do I learn math? By explaining out loud. **

What is most important? The result or the journey that leads us there?

Psychopedagogy expert ** Barak Rosenshine** has clearly answered it: the journey!

According to his observations, **the most successful teachers** encourage their students to **put “a loudspeaker on their voice”** . That is, teachers lead by example by explaining out loud the mental process they use to solve a problem.

Before that, they announce the result or the objective at the beginning of the course; The children then only focus their attention on the process of solving the problem.

What would be the schedule of the **ideal class session **according to Rosenshine? Sequentially:

**The scenario**: He announces the precise objective of the lesson (example: “we are going to learn to count to 100 with cubes”**Modeling**: The teacher performs in front of the students the action to be taught by unfolding aloud the path of his thought.**Guided****practice**: The children do the operation in turn, guided by the teacher.**Autonomous****practice**: The children repeat the action alone.**Objectification**: The student at the end of the lesson is able to formulate what he has learned.

**How do I learn math? By concretely proving.**

By definition, Mathematics is a *“science which studies by means of deductive reasoning the properties of abstract beings (numbers, geometric figures, functions, spaces, etc.) as well as the relations which are established between them”*

Therefore, learning mathematics is first about **making sense of the abstract**.

Effective alternative methodologies begin with making a concept concrete. In mathematics, one might think that conscientiously applying the methodologies and techniques learned is the proof of successful learning.

**Beware of this resolution mechanism,** exclaimed experts in mathematical education such as those in Singapore!

Do these students really understand **the meaning**? Well, it turns out most of the time not. Even good students get caught up in this mechanic.

To avoid this, one must **always find that the theory is concretely correct**.

This is why, in the **Singapore method**, even if a child is good at abstraction, he will always be asked to prove it physically, concretely (find a synonym for concretely)

DETENTION

**How do I learn math? By speaking the “mathematical language”.**

The “ **mathematical language** ”. is a separate language. She is also old. Understanding it is already a big step towards a peaceful and motivating learning of maths.

We immediately think of the many symbols and their meanings, but it is above all a language that has evolved over time.

Let us take the example of the term “ **développer** ” which appeared in the 12th century in the French language and in the mathematical language a little later. We will therefore “ **expand** ” this equation 2(3y+1) for the following result: 6y+2. But what about the reverse, that is to say starting from 6y+2 to obtain 2(6y+1)? For congruent beings, we would see the term ” **envelop** “? Well no. It is the term **factorize** that is used, a clever word that was born in the… 20th century! What disrupts the learning of mathematics…

I suggest you go even further in the study of mathematical language in a future article, what do you say?

## Influence and Legacy

In France, national education offers great freedom to teachers to pass on their knowledge, within the strict framework of the school curriculum. A freedom that implies a heavy responsibility.

What do these 10 practices that we have collected among **the best alternative pedagogies** for mathematics teach us? First, the **crucial role of the educator** in guiding the child in his learning. And his mission will therefore be to adapt these concepts to his teaching.