Computational Math in Early Childhood Education

Description*: This course aims to reinforce the high school-level knowledge essential for pursuing higher education in the sciences (calculating with powers, working with fractions, solving simple equations and inequalities, identifying situations involving proportionality, graphing a function, and studying the variations of a function) through the solution of biomathematics problems. In an educational context, “biomathematics” refers to the set of mathematical concepts and methods (potentially aided by computer technology) used to study and model biological phenomena. This introductory course in biomathematics will focus on the concept of a mathematical function as a model for expressing relationships between quantities, within a quantitative approach to living systems. We will explore the mathematical tools used to study functions (graphical representation, concepts of limits, continuity, and derivatives), limiting ourselves to real functions of a real variable and focusing on questions regarding the evolution of biological systems. The following models will thus be introduced and studied, in order: the linear model, the exponential model, the more sophisticated Verhulst model (S-curve), and finally, the solution of optimization problems arising from biological contexts, leading to the determination of the extrema of functions.

The curriculum for this course unit will consist of:

• Two 1.5-hour scientific lectures that shed light on the concepts and methods of biomathematics
• 4 cycles, each consisting of:

• Two 1.5-hour tutoring sessions focused on a learning challenge rooted in a quantitative approach to living organisms
• 1 three-hour tutorial session focused on mastering mathematical techniques that serve as tools for problem-solving

In addition to methodological and soft skills objectives (the acquisition of common cross-disciplinary skills for the entire Bachelor’s degree in Life Sciences in the APP program), this course unit aims to provide the basic computational tools necessary for further study in the life sciences and to introduce students to the field of biomathematics. All the concepts and skills covered in this course have already been introduced in high school (prerequisites on numbers, proportionality, and power functions in middle school and 10th grade; the concept of derivatives and exponential functions in the advanced mathematics track in 11th grade; the concepts of limits, continuity, and the logarithmic function in the “Complementary Mathematics” elective in the final year of high school), with variations depending on the students’ academic tracks. The goal of this course unit is to enable students to consolidate their high school knowledge and skills by strengthening the connection between mathematical knowledge and biological knowledge, while providing students who did not continue studying mathematics through high school with rapid access to the content covered in the 11th and 12th grades (subject to a greater amount of independent study on the student’s part).

10th-grade math

100% Continuous Assessment:

• 40% Specific knowledge and expertise
• 40% Cross-functional skills
• 20% Interpersonal Skills

Syllabus: The course will proceed as follows:

• Opening Scientific Conference: Quantitative Approaches in the Life Sciences and Mathematical Language—Numbers, Functions as Models, the Discrete and the Continuous
• Cycle 1: The Linear Model
• Cycle 2: The Exponential Model
• Second Scientific Conference: Limits, Continuity, and Derivatives—Tools for Studying Functions and Understanding the Evolution of Phenomena
• Cycle 3: The Verhulst Model
• Cycle 4: Solving Optimization Problems in Biomathematics

Leaders*: Thibaut Delcroix, Thomas Hausberger

Administrative contact(s): Sophie Cazanave Pin