National pathway study modules in mathematics and physics in Finland

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 Finnish study modules are being developed within Omnia’s Moodle-based learning environment. Upon completion, they will be published as open educational resources (OER) and made available in Finnish and English via the national OER platform www.aoe.fi in Finland.

Module description

The purpose of preparatory studies in mathematics and physics for universities of applied sciences is to strengthen the mathematics and physics skills needed in engineering studies. The studies are targeted at vocational students in Finland’s technical fields (not just the automotive sector).

In Finland, universities of applied sciences have students who have completed either upper secondary school or vocational secondary education. The challenge for vocational students in engineering studies is their insufficient foundational skills in mathematics and physics. The goal of preparatory studies for universities of applied sciences is to reduce the skill level gap between vocational students aiming for engineering studies and students who have completed upper secondary school.

Courses description: Mathematics

The mathematics studies comprise 15 credits.

The studies begin with a review of the properties of numbers and the calculation of the values of expressions. Additionally, powers, roots, and unit conversions, along with their related calculation rules, are studied. After this, the manipulation of expressions using letters is practiced.

Following expressions, first-degree equations are solved. Special focus is given to the use of different letters and physics equations. From first-degree equations, the studies progress to second and higher-degree equations. The equation section concludes with the handling of systems of equations.

The study of functions begins with a review of linear functions, leading to polynomial functions. Finally, the topic covers exponential functions, which are important in applications.

In geometry, equations are used to calculate perimeters, areas, and volumes. In trigonometry, the trigonometry of right-angled triangles is reviewed, followed by the study of oblique triangles and more advanced trigonometry, for example, using the unit circle.

The mathematics section concludes with percentage calculations, which are important in practical work and applications. The emphasis is again on applying equations to solve problems.

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

Physics studies also comprise 15 credits. The module covers key areas of physics through theory and practical examples. In the beginning (1 credit), students practice working with physical quantities and graphical representations, and learn to understand the importance of measurement uncertainty. They are also introduced to physics as a scientific discipline (1 credit) and its relevance in engineering.

The studies include mechanics (4 credits), covering linear and rotational motion, statics, and the analysis of collisions. In addition, wave phenomena (1 credit), optics (1 credit), and thermodynamics (3 credits) are addressed, including thermal processes and the behavior of gases. In the field of electricity (3 credits), students learn the basics of electricity and electromagnetism, alternating current, and electrical engineering applications. The module concludes with the fundamentals of atomic and nuclear physics (1 credit).

The aim of the module is for students to understand physical phenomena and be able to apply physical laws in engineering studies.

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

The mathematics courses are built on the Moodle learning platform. There is one Moodle course area for each credit.

The theory is presented either as slide shows or videos, as briefly and clearly as possible. The theory sections include plenty of pre-solved model examples of varying levels. Whenever possible, concepts are illustrated with images and animations.

Picture. In this warm-up exercise, the student needs to consider the differences between the two expressions.

A central part of studying mathematics is the exercises. The exercises are self-checking, so the student immediately knows if their answer is correct. The exercises range from easy to challenging.

In addition to regular calculation exercises, the courses include various puzzles to develop general problem-solving skills.

Picture. In this puzzle, you need to connect all nine dots with four straight lines without lifting the pen from the paper.

In mathematics, the first five credits are studied mostly without calculators. In the last ten credits, students are allowed to use a scientific calculator. The tasks are intended to be solved mainly without advanced mathematical software. However, at appropriate points, tools like Wolfram Alpha and especially GeoGebra are used. Students are also trained in information retrieval and the use of artificial intelligence to aid in studying mathematics.

The courses are intended to be completed with final exams, for example, at the educational institution.

Methods of teaching and learning: Physics

The first credits of the physics module are studied through video lessons. Topics that are most essential to master before taking the first physics courses in engineering studies — such as calculations with physical quantities and understanding orders of magnitude —are taught thoroughly in videos published on YouTube (Terhi Kokkonen – YouTube). For each video, a note-taking template is provided on the Moodle platform, designed to encourage students to actively organize and process the information presented in the video lesson.

Video example of Terhi Kokkonen YouTube channel about Forces & Motion

In Moodle, the videos are also embedded as H5P activities, which means that during the video, pop-up windows occasionally appear with small tasks for the student. This allows the student to receive immediate feedback on their learning process during the lesson itself.

After the video lesson, a test is available in Moodle, containing multiple-choice, matching, and numerical questions. These are also automatically graded by Moodle. The student receives instant feedback on their performance after completing the test.

Picture. Screenshot of the structure of an online lesson. The student can print a note-taking template. The lesson video is in H5P format, which means interactive elements are embedded within the YouTube video. After the video lesson, the student tests their knowledge with a quiz.

As the preparatory physics studies progress beyond the initial courses, no more video lessons are provided. Instead, students continue learning using written material only. The idea is that once the basic skills and concepts have been taught through the video lessons, students will then be better prepared to understand theory and example problems through more independent study.

Since most students only complete one or a few of the preparatory credits, particular emphasis has been placed on developing these initial modules. The goal is that even the early parts of the module alone provide a foundation for engineering-level physics courses. If a student completes more of the preparatory physics studies, they will already be covering the same topics addressed in engineering physics — although the theory and examples are somewhat simplified, and the exercises slightly easier.

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.