MA+3

Background 

This research project focuses on how children gradually learn simple addition (e.g., 4+3), a central issue in early elementary mathematics education. Two major theories are at odds with each other:

• The theory of retrieval from memory (Logan, 1988): Children begin by counting explicitly, then gradually learn to retrieve the results from memory.

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

The goal is to determine whether to focus on training in rapid counting or on directly memorizing the results.

To circumvent the ethical and practical limitations associated with studying learning in children, an experimentalalphabetic arithmetic task is used with adults. It simulates early learning by replacing the numerical sequence with an alphabetic one (e.g., C+3=F). This paradigm provides precise control over learning parameters.

The UMA (Unified Model of Arithmetic) model by Braithwaite & Siegler (2024) is chosen as the basis. It is a robust computational model capable of simulating a variety of arithmetic learning processes in children. The project involves adapting UMA to the alphabetic task.

Previous experimental data (notably from Stéphanie Chouteau’s dissertation, 2024) 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 steps:

1. Literature review: to familiarize oneself with theories of addition learning and existing models (in children and in adult literacy tasks).

2. Getting Started with the UMA Model: Understanding the Architecture and the Provided Python Code.

3. Implementation: Develop an initial version of the literacy program in UMA based on Chouteau’s model (2024).

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

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

6. Team skill development: contribute to building internal expertise in UMA with a view to future applications involving larger sets of arithmetic data (particularly among children).