Project-Based Learning: Measuring the World—Mathematics in Practice

“How tall is the linden tree in our schoolyard?” The 9th-grade students answered this question together with trainees from the Marburg Office of Land Management (AfB) during the “Measuring the World” project-based learning session at Steinmühle. This collaboration between the professional world and the school has a long tradition. It took place for the ninth time and reached more than 200 students.

To measure the height of the schoolyard linden tree, the students set up an electronic tachymeter in the courtyard and used it to take precise measurements of the tree. Trainees Ronja Gies and Joshua Fedler from AfB Marburg had brought this professional measuring device with them. It is a measuring instrument that records horizontal directions (angles), vertical angles, and slant distances. Using the measurements and formulas from “plane trigonometry” (calculating unknown sides and angles in any plane triangle), the students calculated the height of the tree. The two trainees assisted them and answered their questions.

It didn’t take long for the students to come up with the answer: “The linden tree is 13.81 meters tall—so about 14 meters! That’s hardly any different from the height we measured with our school theodolites,” the students said. In the theoretical part of the lesson, the trainees from AfB Marburg asked the students where they had already encountered geodata—that is, data related to the Earth—in their daily lives. They then explained that the Earth is by no means a perfect sphere and covered everything from the Earth as a disk to a sphere, and on to the geoid and ellipsoid. This was followed by a brief historical overview of the Kurhessian Triangulation (1821–1839) and the work of the mathematician, astronomer, and physicist Christian Ludwig Gerling (July 10, 1788 – January 15, 1864) at the University of Marburg.

 

Geodata Relevant to Public Policy

“Today, geodata plays a key role in about 80 percent of all political decisions,” said Jörg Lipphardt, a trainer at AfB Marburg. Lipphardt introduced the students to the apprenticeship program for geomatics technicians and provided information about the promising career prospects for high school graduates at the Hessian Administration for Land Management and Geoinformation (HVBG), as well as future opportunities in the field of geoinformation.

In the “Project-Based Learning” core course at Steinmühle, students explore various topics through project-based work, engaging with the material in an action-oriented and hands-on manner. Incorporating a practical component with experts into the “Measuring the World” project was the wish of math and biology teacher Malte Klimczak, who conceived the project a few years ago together with his colleague Nicole Scholtes and approached the AfB Marburg with the idea.

“What better way is there to help students understand the value of learning than by interacting with experts for whom trigonometry is a daily tool? Motivation to learn comes naturally,” said Steffen Ullwer, the class’s project teacher.

“From our perspective, it’s actually a perfect example of a win-win situation,” the trainees added. “We had to prepare for today, and in doing so, we were able to review material that will be covered in our exam later on.”