MA+3

Background 

This research project focuses on how children gradually learn simple addition (e.g., 4+3), a central question for early mathematics education. Two main theories are currently debated:

• The memory retrieval theory (Logan, 1988): children start by counting explicitly, then gradually learn to retrieve results directly from memory.

• The automated counting theory (Barrouillet & Thevenot, 2013; Thevenot & Barrouillet, 2020): counting persists, becoming faster and unconscious, which creates the illusion of memory retrieval.

The objective is to determine whether teaching should promote rapid counting practice or the direct memorization of results.

To bypass the ethical and practical limitations of studying learning processes in children, an experimental alphabet arithmetic task is used with adults. This approach simulates initial learning by replacing the number line with an alphabet line (e.g., C+3=F). This paradigm provides precise control over learning parameters.

The UMA (Unified Model of Arithmetic) model by Braithwaite & Siegler (2024) was chosen as a baseline. It is a robust computational model capable of simulating various arithmetic learning processes in children. The project consists of adapting UMA to the alphabet task.

Previous experimental data (particularly from Stéphanie Chouteau's 2024 thesis) and new collaborations (notably with Catherine Thevenot's team in Lausanne) will be used to validate the model.

Student contributions

The student will participate in the project's development through the following stages:

1. Literature review: familiarize themselves with addition learning theories and existing models (both in children and in the adult alphabet task).

2. Getting started with the UMA model: understand the architecture and the provided Python code.

3. Implementation: develop an initial version of alphabet learning within UMA based on Chouteau's model (2024).

4. Estimation and validation: adjust the model's parameters using experimental datasets (cross-validation).

5. Testing and generalization: test the resulting model on other available datasets.

6. Skills development for the team: contribute to building internal expertise on UMA for future applications involving broader arithmetic data (particularly in children).