Introduction

Welcome to this digital handbook on the topic of measurement uncertainties. This is the teacher's manual giving conceptual as well as didactical background to the digital learning environment (DLE) for students that can be found here: https://lernen.physik.hu-berlin.de/measurementuncertainties. After working through this manual, you will:

Goals

After working through this manual, you will:

• know about the underlying concepts of measurement uncertainties;
• know about students' preconceptions of measurement uncertainties;
• know some strategies to address these preconceptions;
• know some didactical strategies to introduce the topic of measurement uncertainties;
• have some practical examples to address measurement uncertainties;
• have seen some concepts that go beyond the DLE.

This support manual is conceptually oriented, focusing not on numbers and definitions, but on the underlying principles, meaning, and interpretation of the concepts. The concepts are introduced based on real-world examples and data.

Orientation

The manual consists of three parts, that are divided into several steps. Each step consists of several thematical blocks. These blocks are labeled with symbols. These symbols indicate what type of content is discussed in the block:

• Textbook basics. This is the subject matter where definitions are supplemented with their meaning and interpretation.
• Didactics. This is where you will find students' views and preconceptions, ideas for teaching strategies, and ideas for didactic reduction that will help you address the topic of measurement uncertainties in your teaching.
• Further Examples. This is where you will find (links to) practical examples or further information that connect to the contents of the step.
• Advanced concepts. These are some optional concepts that go beyond the concepts of the students' DLE but might be essential for certain experiments. Advanced concepts are also labeled with a or to indicate whether it addresses the basics or the didactical part. Since these concepts are not addressed in the students' DLE, you will have to introduce these concepts yourself if you want your students to work with these concepts!

Structure

In the first part, the basic concepts regarding measurement uncertainties are introduced. In a conceptual approach, you will learn about the fundamental concepts as well as students' views and preconceptions about these concepts.

In the second part, the determination of the uncertainty is discussed. Here, you will learn about calculating the measurement uncertainty, graphing, propagation, and analyzing the uncertainty budget. This subject matter will be supplemented by a didactical analysis in which you will get to know some didactical strategies and ideas for didactical reduction.

The last part focuses on the application of measurement uncertainties in terms of data comparison. This entails the formal rules for data comparison as well as a didactical tool to identify students' views on measurement uncertainties in data comparison problems.

Download Handbook

This handbook can be downloaded here in pdf format.

Last edited: May 12th 2026
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