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# ANFOMAM Project

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## What ANFoMAM is

ANFoMAM takes its name from the Spanish version of its title, meaning Learning from children to improve primary school teachers' math specific education. It is a project supported by the Erasmus Plus programme, in the area of Strategic Partnerships for Innovation in Higher Education.

Summary of the project

## How the project was born

It has been born from different initiatives that are currently being carried out in the training of teachers in our partner universities, which seek the properly deep understanding of the basic concepts of mathematics by students, away from the transmission of mechanical and repetitive procedures.

## What is proposed

• To design and put in practice, in the subjects of the teaching degrees, mathematical activities in the form of workshops, inspired by those already being carried out in the association Sesdown in Zaragoza, with trisomy 21 children.
• To design new mathematical activities for trisomy 21 children and to observe their processes learning mathematics so that we can  understand better how all children may learn.

## Why it is developed in universities

If students of the teacher-training-grades have new learning experiences at university, the way they understand and assess mathematics will change, which would have a direct impact on their class in the near future.

## A brief description of the workshops

Understanding arithmetic algorithms

In the workshop the 4 basic operations are worked through the itinerary given by the basic algorithms. We make an analysis of the algorithms by particular examples carried out with manipulative material and with graphic representation. This allows to abstract and generalize the algorithms.

In the same way, multiple strategies are shown to approach the same concept, to integrate in a better way the learning and to train the future teacher to approach different forms of learning.

Solving arithmetic problems

The workshop has several objectives. First, it is intended to design mathematical activities that can be presented as an arithmetic problem. Secondly, ir proposes to analyse the different types of relationships between magnitudes and their possible representations with objects or materials, with drawings or gestures made with the body. Finally, we want to study how to use these representations to carry out different resolution strategies.

Relationship between arithmetic and geometry

The objective of this workshop is to design problem situations where the student can discover relationships between arithmetic and geometric concepts. For example, between the decomposition of numbers into products and areas and volumes, or between decompositions of angle values and the way of tiling a surface.

Reasoned calculation and use of the calculator

In this workshop we design and analyse calculation activities chosen ad hoc that allow the student to:

• Explain the underlying mathematica knowledge.
• Analyze not adopted strategies and foreseeable difficulties.
• Stigmatize (in order to delay) the use of algorithms.
• Improve the use of the calculator, which, combined with mental calculation, will allow to explore numerical phenomena.

History of mathematics and its teaching

The workshop aims to analyze activities and problems about ancient mathematical texts (calculation and practical problems, Greek mathematics) and other historical epochs, reflecting the variety of languages ¿¿and cultures and giving space to mathematics in Europe since the Middle Ages. In this way, the student would be able to:

• Know facets of what is mathematical knolwdge.
• Deep on some subjects of arithmetic (the decomposition of numbers to represent them symbolically, the requirement of extension of the numerical field), of measurement (the geometric base of the measure, its social character), of geometry (the figures in geometry and argumentation).

Geometry

The workshop will show us activities and problems that allow:

• To understand the place of geometric intuition in the effectiveness of arithmetic materials (Montessori etc).
• To learn to use freehand drawing with ruler and compass and construction with 3D materials in geometry.
• To approach the intuition of the continuum on horseback between the psychic and physical world of the child.
• To reflect on the relationship between the abstract geometric space and the representative visual, tactile and motor space.

Workshops for trisomy 21 children

Since 2014 the Sesdown team has organized the Mathematics Workshop for children with Down syndrome. This workshop aims to introduce children with Trisomy 21 in mathematics from their naive conceptions of number and form. The sessions are organized with a playful methodology and based on mimesis, where the mathematical contents are carefully programmed.

The work done in this workshop has been part of the doctoral thesis "Didactics of Mathematics for people with Down syndrome based on an integrated approach to elementary arithmetic and geometry" carried out by the president of the association and one of the responsible for the project, Elena Gil.