National pathway study modules of mathematics and physics in Estonia

Foreword

The Auto CoVE 2.0 consortium is developing innovative study modules and training courses across three European Qualifications Framework (EQF) levels. All modules developed within the project are funded by the European Union and are completely free for users.

The Estonian pathway study modules are being developed within Eesti Maaülikool’s Moodle-based learning environment. Upon completion, they will be published as open educational resources (OER) and shared through the corresponding Estonian national open educational resources library platform.

Module description

In Estonia, students graduating from vocational schools often encounter difficulties when aiming to continue their studies in engineering at the university level. A key barrier is the limited number of mathematics and physics lessons included in vocational curricula, which leaves many students without the necessary foundation to succeed in national exams or handle the demands of first-year university studies.

To address this challenge, specially developed preparatory mathematics and physics modules offer focused support for vocational graduates. These modules are designed to strengthen core mathematical competencies, build problem-solving confidence, and prepare students for the academic rigors of engineering education.

The purpose is not just to fill in missing knowledge, but also to provide a more welcoming and accessible path to university.By aligning the content with the expectations of universities of applied sciences and integrating practical, engineering-relevant examples, the modules empower students to transition more smoothly into their chosen fields and thrive in their future studies.

Courses description: Mathematics

1. Simplifying Algebraic Expressions
   – Roots, powers, and logarithms.

These are fundamental for manipulating and understanding formulas, scaling systems, and solving exponential and logarithmic equations, which appear in everything from circuit analysis to population modeling.

2. Vectors and Vector Operations
   – Basic calculations and applications involving vectors.

Vectors are essential in fields like mechanics, electrical engineering, and computer graphics. Understanding vector operations allows engineers to describe forces, directions, and physical quantities in multidimensional space.

3. Equations and Systems of Equations
   – Linear and nonlinear equations, solving techniques.

Engineers often deal with systems that involve multiple variables and constraints. Mastering linear and nonlinear equations enables them to model systems accurately and find optimal solutions.

4. Functions of One Variable
   – Derivatives and their applications.

Derivatives help in understanding rates of change, such as velocity, acceleration, or stress-strain relationships in materials. This is vital in design and analysis tasks.

5. Integrals and Basic Applications
   – Introduction to integration and practical use cases.

Integration is used to calculate quantities like area, volume, work, and heat transfer. It plays a central role in fields such as fluid dynamics and thermodynamics.

All courses developed within the project are funded by the European Union and are completely free for users. Upon completion, they will be published and stored in the Electude study module platform. In the picture below you can see an example of the course contents in Electude system.

Within the AutoCoVE 2.0 framework, Electude plays a pivotal role by providing its state-of-the-art e-learning platform to all partner VET institutions. The platform offers access to nearly 2,000 technical modules, facilitating the development of innovative study materials and training courses focused on modern vehicle technologies, including electric and hydrogen-powered systems.

Courses description: Physics

1. Mechanics: Kinematics of Translational and Rotational Motion: Understanding how objects move—both in straight lines and rotations—is crucial for designing machines, vehicles, and structures.
2. Mechanics: Forces in Mechanics: Engineers must analyze forces to ensure stability, safety, and performance in everything from bridges to robots. This forms the basis of structural and mechanical engineering.
3. Mechanics: Work, Energy, and Conservation Laws: These laws help engineers understand how energy is transferred and conserved in systems, essential for optimizing performance and efficiency.
4. Fundamentals of Thermodynamics: Isoprocesses: Thermodynamics is key in fields like mechanical, chemical, and energy engineering. Understanding isoprocesses helps in analyzing engines, refrigeration, and energy systems.
5. Electrostatics: Electric Charge and Field, Capacitors: These concepts are vital in electronics and electrical engineering, where controlling and storing electric energy is central to circuit design.
6. Direct Current: Ohm’s Laws: Ohm’s laws are fundamental in understanding how electrical circuits operate. They are essential for designing and troubleshooting electronic and electrical systems.

All courses developed within the project are funded by the European Union and are completely free for users. Upon completion, they will be published and stored in the Electude study module platform. In the picture below you can see an example of the course contents in Electude system.

Within the AutoCoVE 2.0 framework, Electude plays a pivotal role by providing its state-of-the-art e-learning platform to all partner VET institutions. The platform offers access to nearly 2,000 technical modules, facilitating the development of innovative study materials and training courses focused on modern vehicle technologies, including electric and hydrogen-powered systems.

Methods of teaching and learning: Mathematics & Physics

Supporting Independent Learning: H5P and STACK Tools

A key goal of the courses is to support independent, flexible learning. Moodle’s H5P videos enhance focus and interactivity, while STACK-based mathematics exercises allow students to enter symbolic expressions. STACK (System for Teaching and Assessment using a Computer algebra Kernel) is an advanced tool used in Moodle to support mathematical problem-solving. It allows students to input full mathematical expressions — not just select from multiple-choice answers — making it ideal for practicing real problem-solving in mathematics and engineering. STACK is a powerful support tool for learning by doing. It checks student responses in real time and provides immediate, detailed feedback, helping learners understand not just whether an answer is right or wrong, but why. Mastering this tool early in the course makes the learning experience smoother and much more effective. To help students get comfortable with STACK, a dedicated practice section is provided at the beginning of the course. This section includes introductory questions that are not about mathematical content, but are specifically designed to:

• Teach the layout of STACK questions
• Practice using the correct syntax (e.g., how to enter powers, fractions, square roots, etc.)
• Understand how feedback is presented after submitting an answer

These tools make the platform highly effective for self-study, especially for learners who may need to balance their studies with work or other commitments. Students can repeat lessons, retake tests, and progress at their own pace—developing both knowledge and the confidence to succeed in further engineering studies.

Picture. Example of one of the tasks.

Innovative Study Modules and Training courses

The Auto-Cove 2.0 consortium is developing innovative study modules and training courses focused on alternative fuel vehicle service and sales across three European Qualifications Framework (EQF) levels:​

• EQF Level 4: Study modules tailored for technical and business students.​

• EQF Level 5: Training courses designed for vehicle engineering students at the tertiary level.​

• EQF Levels 4, 5, and 6: Training courses aimed at vehicle field teachers in vocational colleges and universities of applied sciences. These courses will also serve to upskill current workshop leaders, car mechanics, and professionals in vehicle sales and spare parts across all seven partner countries.

These educational initiatives aim to address the urgent need for expertise in servicing electrified and hydrogen vehicles, ensuring that both new graduates and existing professionals are equipped to navigate the evolving landscape of the automotive industry.

All courses developed within the project are funded by the European Union and are completely free for users. Upon completion, they will be published and stored in the Electude e-learning platform.

Within the AutoCoVE 2.0 framework, Electude plays a pivotal role by providing its state-of-the-art e-learning platform to all partner VET institutions. The platform offers access to nearly 2,000 technical modules, facilitating the development of innovative study materials and training courses focused on modern vehicle technologies, including electric and hydrogen-powered systems.