What is the math of it all

Talking about math is part of learning - especially when the learner is talking

We know from research that students learn most when they are active themselves (e.g. Freeman et al., 2014). Students should do as much as possible themselves in order to think through the matter and develop problem-solving skills. It is therefore important as a teacher to take into account the “principle of minimal help” according to Zech from mathematics didactics. The point is to provide as much help as necessary and as little as possible. Dr. Thomas Trebing from the Technical University of Darmstadt has already published on this topic (Trebing, 2015; Trebing, 2016) and further developed the model. That is why we invited him on June 29th, 2017 for a short training course for the ZLL team and for tutors at the TUHH. Both offers met with great interest.

He identifies three forms of interaction or learning guides:


  1. Speaking maker
    This includes open (return) questions such as "What have you been thinking about so far?" or "How did you figure this out?"
  2. Impulse generator
    These are work instructions, how "Please first write down what is sought and given." Or "Please make a sketch first. If it is still unclear to you, contact me again. "
  3. active listener
    This includes questions of understanding, mirroring z. B. "You shrug your shoulders." or "You frown." and paraphrases, like "So you mean ...".

The first and third forms of interaction stimulate an exchange between the teacher and the student. Here it is important to let the students speak for themselves as much as possible and thus allow them to think (see title).

If, however, many students have questions at the same time in the course, impulses such as the instruction to draw a sketch or to exchange ideas with the person sitting next to you stimulate independent (further) work and enable the teacher to devote himself to other questions .

If you are interested in further tips on minimal help, please feel free to contact me (Jenny Alice Rohde).


  • Quote in the title based on Karl Duncker
  • Freeman, S., Eddy, SL., McDonough, M., Smith, MK., Okoroafor, N., Jordt, H. & Wenderoth, MP. (2014). Active learning increases student performance in science, engineering, and mathematics. Proc Natl Acad Sci USA 111, Pp. 8410-8415.
  • Trebing, T. (2016): Principle of minimal help in tutor teaching films - training use and first results. In: Eßer, A .; Kröpke, H; Wittau, H. (Hg.) (2016): Tutorial work in Discourse III. Qualification for the future. Muenster. Pp. 73-84.
  • Trebing, T. (2015). Tutorials: The principle of minimal help in university arithmetic exercises. In: New ways in tutorial teaching in the introductory phase. Zitzelsberger, Olga (Ed.): New ways in tutorial teaching in the introductory phase: Documentation of the conference of the same name in March 2014 at the TU Darmstadt. Münster: WTM, 2015. (Writings on general university didactics; 1), ISBN 978-3-942197-41-0. Pp. 101-115.