# A New Model of Mathematics Education: Flat Curriculum with Self-Contained Micro Topics

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## Abstract

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## 1. Introduction

- Mathematics is a beautiful, grand structure of ideas highly connected by powerful abstractions, organised into a hierarchical structure along with the axiomatic-deductive method.
- Mathematics is a set of cognitive tools for efficient thinking. One can conceptualise mathematical thinking as a way to delegate our cognitive load in problem solving to mathematical symbolism.

## 2. Metaphors for the Process of Learning Mathematics

## 3. Philosophical Background—Deconstruction

## 4. Implementation

#### 4.1. Creating Micro Topics

- Listing dependencies;
- Substituting dependencies, i.e., removing incoming edges; and
- Installing hooks, i.e., indicators of outgoing edges.

#### 4.2. Prior Art

#### 4.3. Examples of Micro Topics

#### 4.3.1. Group Theory in Primary School

“You could think of the total symmetry of an object as all the moves that the mathematician could make to trick you into thinking that he hadn’t touched it at all”.[22]

“Numbers measure size, groups measure symmetry”.[23]

#### 4.3.2. Differential Geometry of Curves and Surfaces in Secondary School

#### 4.4. Creative Substitution

## 5. Flattening the Curriculum

## 6. Possible Criticisms

#### 6.1. Assessment

#### 6.2. Lack of the Complete Picture of the Subject

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Hoffmann, M.; Egri-Nagy, A.
A New Model of Mathematics Education: Flat Curriculum with Self-Contained Micro Topics. *Philosophies* **2021**, *6*, 76.
https://doi.org/10.3390/philosophies6030076

**AMA Style**

Hoffmann M, Egri-Nagy A.
A New Model of Mathematics Education: Flat Curriculum with Self-Contained Micro Topics. *Philosophies*. 2021; 6(3):76.
https://doi.org/10.3390/philosophies6030076

**Chicago/Turabian Style**

Hoffmann, Miklós, and Attila Egri-Nagy.
2021. "A New Model of Mathematics Education: Flat Curriculum with Self-Contained Micro Topics" *Philosophies* 6, no. 3: 76.
https://doi.org/10.3390/philosophies6030076