Aim of the Short-Term Curriculum

Please note: The provided information can be accessed in all partners’ languages here:

General Information:

Target Group: Mathematics Teachers (Primary and Secondary Level)


  • Set of measurement tools for participants (folding ruler, measuring tape etc.)
  • Prepared math trail close to the training’s location
  • Adapted slides that are available on Material for the Short-Term Curriculum in all partner languages

Aims of the training:

Teachers get in touch with an innovative theory-based approach of teaching outdoor mathematics supported by technology. Hereby the teachers achieve the following skills and competences:

  • Knowledge about outdoor education and math trails
  • Use of digital tools and creation of learning environments
  • Analysis and development of (outdoor) mathematics tasks with regards to relevant characteristics and the curriculum
  • Planning, conduct and reflection of an outdoor lesson with students
  • Peer- and expert review of math trails tasks

The aim of the first module is to present the theoretical background and the benefits of outdoor education. After a short introduction to the MathCityMap system in general and presenting the idea behind the two-component system, the teachers run a beforehand prepared math trail in groups in close vicinity to the location of the advanced teacher training. By doing so, they get to know the app from the student’s perspective.

The second and third module focus on the teacher’s perspective, introducing the web portal and its basic functions. A live demonstration of the web portal shows how to create tasks using different answering formats and putting tasks together in a trail. Afterwards, the teachers are supposed to create a task on their own, using a given picture and sample measures in order to get familiar with the web portal. At the end of the second module, working groups and the digital classroom. In a working group it is possible to share tasks and trails with other users.

The third module starts with an explanation of criteria for meaningful tasks, e.g. attendance and activity, meaning that the students should have to be in front of the object or situation the task is about and that they have to engage in a mathematical way by taking the measurement or count some properties. Afterwards, the teachers are asked to go outside, identify an object or a situation fulfilling the described criteria (Jablonski, Ludwig & Zender, 2018) and to collect the necessary data and take a picture. By putting this information in the web portal, the teachers create their own task. Upon completion of the first three modules of the Short-Term Curriculum the teachers are familiar with the MathCityMap system, both from student’s and teacher’s perspective and can therefore use it during their own classes.

During the aforementioned break of around two weeks the teachers should create a whole trail consisting of at least five tasks as a homework before attending the last two modules. After the organization in groups in the fourth module and the assignment of the as a homework prepared trails to each other the teachers run the math trails outside and test the tasks. By assessing and reviewing the tasks of each other, the teachers gain more experience in the creation and evaluation of a task for MathCityMap, improving the overall quality of their own tasks and trails. Based on the feedback from the other participants, the teachers can adapt their tasks and create a final trail.

The fifth and last module introduces the teachers to the MathCityMap review system. To ascertain an according quality, each tasks is being reviewed by a certified reviewer or member of the MathCityMap team.  The teachers are presented with the technical process of reviewing tasks and are asked to assess several sample tasks. Afterwards, the participants receive a feedback based on their review.


  • Blane D. C., & Clarke, D. (1984). A mathematics trail around the city of Melbourne. Monash: Monash Mathematics Education Centre, Monash University.
  • Blum & Leiss (2005) Blum, W. & Leiß, D. (2005). Modellieren im Unterricht mit der “Tanken”-Aufgabe. In: Mathematik lehren, (128), S. 18-21.
  • Department for Education and Skills (DfES) (2006). Departmental Report 2006. Online: (letzte Prüfung: 10.08.2020).
  • Dillon, J., Rickinson, M., Teamey, K., Morris, M., Choi, M., Sanders, D., & Benefield, P. (2006). The value of outdoor learning: evidence from research in the UK and elsewhere. School Science Review, 87 (320), S. 107-111.
  • Greefrath, G. (2018): Anwendungen und Modellieren im Mathematikunterricht. Didaktische Perspektiven zum Sachrechnen in der Sekundarstufe, 2. Auflage. Berlin: Springer Spektrum.
  • Kleine, M., Ludwig, M., & Schelldorfer, R. (2012). Mathematik draußen machen – Outdoor Mathematics. Praxis der Mathematik, 54 (47), S. 2-8.
  • Ludwig, M., Jesberg, J., & Weiß, D. (2013). MathCityMap – faszinierende Belebung der Idee mathematischer Wanderpfade. In: Praxis der Mathematik, 55 (53), S. 14-19. 
  • Muller, E. (1993). Niagara Falls Math Trail. Ontario, Canada.
  • Sauerborn, P., & Brühne, T. (2014). Didaktik des außerschulischen Lernens. Baltmannsweiler: Schneider-Verlag Hohengehren.
  • Schukajlow, S., (2006). Schüler-Schwierigkeiten beim Lösen von Modellierungsaufgaben – Ergebnisse aus dem DISUM-Projekt. In: Beiträge zum Mathematikunterricht 2006. Hildesheim: Franzbecker, S. 493-496.
  • Shoaf, M. M., Pollak, H., & Schneider, J. (2004). Math Trails. The Consortium for Mathematics and Its Applications (COMAP).

Adaptation to MathCityMap@home

In the context of the Covid-19 pandemic, we developed a use case of MathCityMap for distance learning: MathCityMap@home.

MathCityMap@home still uses the original concept and the two components of MCM. As in the out-of-school context, teachers create tasks and math trails in the sense of mathematical learning paths for their students in the web portal. The students download this path to their smartphone and solve the tasks using the hints and automatic solution checking. In contrast to the original concept, however, the tasks of MathCityMap@home are set to be solved not only on site but also at home.

In order to educate teachers in using MathCityMap@home, we adapted the MathCityMap Short-Term Curriculum to the adapted version of MathCityMap@home and online teacher trainings. Despite a change in the usage of the system, the aims and structure remain similar. As for the MathCityMap Short-Term Curriculum, the corresponding slides can be downloaded from