TLL MiniMa - children and adults explore mathematics

Mathematical skills acquired before starting school form the basis for successful learning at school, academic achievement, and social participation. Early mathematics education processes require competent support from educational staff.

MiniMa therefore focuses on

  • training educational staff at elementary level, teachers at primary level, and students in the field of early mathematics education (Childhood Education and Teacher Education for Primary Schools),
  • developing a Teaching and Learning Lab for early mathematics education and providing the necessary scientific and academic support,
  • developing mathematical play and learning environments for early childhood education,
  • investigating the numerous aspects of early mathematics education, such as mathematical thinking and learning processes, mathematical interactions in teaching and learning contexts, and opportunities to professionalise in mathematics education.

The MiniMa project was initiated and developed starting from 2010 by Professor Christiane Benz and Dr Johanna Zöllner.

Mathematics is not a set of knowledge. Mathematics is an activity, a way of behaving, a state of mind. [...] However, you will not acquire a mental attitude by someone just telling you how to behave. You will acquire it by doing, by solving problems, either alone or in a group - problems that involve mathematics.
Freudenthal 1982, p. 140

Professionalisation of educational staff and teachers

Once or twice a year, a training phase is organised for educational staff and teachers on mathematical content areas such as “Counting and seeing” or “Comparing and measuring”. Each training phase is divided into three modules:

1. Workshop,

2. Visit to the Join-in studio with children's groups, and

3. Follow-up meeting for retrospective and evaluation.

Each module in turn focuses on a specific facet of competence (professional, action, diagnostic, and reflective competence) that educators can acquire and further develop.

1. Workshop

Each training phase starts with a workshop that provides educators with the opportunity to acquire or deepen their specialist and didactic knowledge in the field of mathematics, thus combining theory and practice. The focus is on the basics of mathematics education (professional expertise) as well as on motivating children to discover and explore mathematics and drumming up their enthusiasm for the subject.

Educational staff and teachers as well as lecturers jointly consider which play and learning environments can be designed for a specific content area. Together with the participants, the play and learning environments are planned and designed and suggestions for expected interactions, such as actions, stimuli, and questions, are discussed. A written record of the planning and modelling process is handed over to all participants to enable them to implement the play and learning environments at their respective institutions.

The following contents have been jointly developed and tested in play and learning environments:

  • Counting and seeing,
  • Exploring patterns,
  • Comparing and measuring,
  • Building and laying,
  • Organising, sorting, and communicating,
  • Finding structures,
  • Symmetry,
  • Mathematical discoveries when mirroring,
  • Dialogue-based reading aloud and reading along with the help of mathematical picture books.

2. Visit to the Join-in studio MiniMa

After attending the workshop, educational staff and teachers have the opportunity to visit, together  with their group of children, the MiniMa Join-in studio, which is the centrepiece of the research and development project. Here, the play and learning environments that they have developed can be realised and the educators are supported in acquiring pedagogical and didactic skills.

They can observe and stimulate the children's mathematical discoveries and reflect on them together with them. They are supported by two student assistants who encourage mathematical discoveries and conversations about mathematical content and document by video recordings the children's learning processes as they discover mathematical relationships. The focus is on supporting learning processes arising while discovering and exploring mathematics (action competence).

The following guiding principles for discovering and exploring mathematics are fundamental to the work with children in the MiniMa Join-in Studio. Children discover maths...

...through play, a roundabout way,
...individually and differently,
...together with other children and the educators.

The introductory quote by Dutch mathematician and mathematics educator Hans Freudenthal describes mathematics as an activity characterised by individual and collaborative problem-solving. At the MiniMa Join-in studio, children and educators are given the opportunity to approach challenging mathematical situations in a playful and exploratory way and to engage in the investigation of mathematical ideas and contexts.

3. Follow-up meeting for retrospective and evaluation

At the end of the training phase, a joint follow-up meeting is organised for the educators to reflect on their experiences. Given some distance in terms of time, this kind of retrospective view is intended to enable an in-depth analysis. Video recordings are used to review and discuss the processes of exploring and discovering mathematics that evolve between the educators and their groups of children.

In the retrospective phases, participants reflect on communicative patterns between children and adults and their own professional actions (reflective competence). They also analyse and discuss children's solution processes against the background of theoretical models (diagnostic competence). Eventually, alternative modes of action are considered and worked out together. In addition, the design of the learning and exploration environment is evaluated and the possibilities for implementing it in the educators' everyday work are discussed.

TLL MiniMa

The MiniMa Teaching and Learning Lab combines the three-phase development and research project (workshop, visit to the MiniMa Join-in studio, follow-up meeting for retrospective and evaluation). It offers students an excellent combination of theory and practice and was awarded a fellowship for innovative university teaching by the Baden-Württemberg Stiftung and the Stifterverband in 2013.

Key research areas and publications

The MiniMa project offers multiple starting points for other research projects, which attract the interest of numerous researchers worldwide. For example, we are engaged in international dialogue with Israel, Australia, Sweden, and Norway. Selected publications on specific thematic areas are listed below.

Professionalisation processes of prospective educational staff and teachers, importance of retrospective and reflection in the acquisition of professional skills

Selected publications

  • Benz, C. (2016). Reflection – An opportunity to address different aspects of professional competencies in mathematics education. In T. Meaney, T. Lange, A. Wernberg, O. Helenius and M.A. Johansson, (Eds.), Mathematics Education in the Early Years - Results from the POEM2 Conference, 2014 (pp. 419-435). New York: Springer.
  • Benz, C., Zöllner J. (2018). Zur Bedeutung der Reflexion für Professionalisierungsprozesse. Dialog 5 (1), pp. 22-27.
  • Reuter, F. (2019). Mathematikdidaktische Reflexion im Studium der Kindheitspädagogik

Competency model: Competence in mathematics education of educational staff at elementary level

Selected publications

  • Gasteiger, H., Benz, C. (2018). Enhancing and analyzing kindergarten teachers’ professional knowledge in early mathematics education. The Journal of Mathematical Behavior, 51(9), pp. 109-117.
  • Gasteiger, H., Benz, C. (2016). Mathematikdidaktische Kompetenz von Fachkräften im Elementarbereich – ein theoriebasiertes Kompetenzmodell. Journal für Mathematik-Didaktik, 37(2), pp. 263-287.

Beliefs about early mathematics education

Selected publications

  • Benz, C. (2012). “Maths is not dangerous” - Attitudes of people working in German kindergarten about mathematics in kindergarten". European Early Childhood Education Journal. 20(2), pp. 249-261.
  • Benz, C. (2012). Attitudes of kindergarten educators about math. Journal für Mathematik-Didaktik, 33(2), pp. 203-232.

Research into the effectiveness of learning environments in the area of children's arithmetic development with a focus on the perception of quantities and the determination of numbers

Selected publications

  • Sprenger, P., Benz, C. (2020). Children’s perception of structures when determining cardinality of sets—results of an eye-tracking study with 5-year-old children. ZDM, 51 (1), p. 187.
  • Sprenger, P., Benz, C. (2019). Perceiving and using structures in sets - the contribution of eye-tracking in a three-level evaluation process. In U. T. Jankvist, M. van den Heuvel-Panhuizen and M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019) (pp. 2355–2362). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
  • Schöner, P., Benz, C. (2018). Visual Structuring Processes of Children When Determining the Cardinality of Sets – The Contribution of Eye-Tracking. In C. Benz, H. Gasteiger, A. S. Steinweg, P. Schöner, H. Vollmuth and J. Zöllner (Eds.), Early Mathematics Learning – Selected Papers of the POEM Conference 2016. New York: Springer.

Understanding of geometric concepts

Selected publications

  • Maier, A. S., Benz, C. (2020). ‘A triangle is like a tent’. Children’s Conception of Geometric Shapes. In: Mathematics Education in the Early Years. Results from the POEM4 Conference 2018. Springer.
  • Maier, A. S. (2019). Geometrisches Begriffsverständnis von 4- bis 6-jährigen Kindern. In England und Deutschland (Empirische Studien zur Didaktik der Mathematik). Münster: Waxmann.
  • Maier, A.S., Benz, C. (2014). Children’s conceptual knowledge of  triangels manifested in their drawings. In P. Liljedahl,  S. Oesterle,  C. Nicol,  & D. Allan, (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 4) (pp. 153-160). Vancouver, Canada: PME.
  • Maier, A.S., Benz, C. (2013). Selecting Shapes: How Children Identify Familiar Shapes in Two Different Educational Settings. In V. Ubuz (Ed.), Proceedings of the 8th Congress of the European Society for Research in Mathematics Education (pp. 2186-2177). Antalya, Turkey: ERME

Learning environments for early mathematics education

Selected publications

  • Zöllner, J., Reuter, F. (2018). Wie messen Kinder? Überlegungen zu Einheiten beim Messen. Fördermagazin Grundschule (4), pp. 19–24.
  • Schöner, P. (2017). Mentales Rotieren. Materialkartei zu Würfelgebäuden. Fördermagazin Grundschule (4), pp. 35–38.
  • Reuter, F. (2016). Eselsschwanz und Ringelschwänzchen. Direkter und indirekter Vergleich im Größenbereich Längen. Fördermagazin Grundschule (3), pp. 10–14.
  • Zöllner, J. (2016). Längen indirekt vergleichen. Fördermagazin Grundschule (3), pp. 5–9.
  • Schöner, P., Benz, C. (2014). Muster und Strukturen finden. In der MachmitWerkstatt MiniMa. Fördermagazin (4), pp. 27-30
  • Benz, C. (2012). Es fährt ein Boot nach Schangrila – Förderung arithmetischer Kompetenzen im Elementar- und Primarbereich. Mathematik differenziert (1), pp. 40–46.
  • Zöllner, J., Benz, C. (2011). Das kleine Krokodil und die ganz große Liebe – Lernanlässe zum Messen und Vergleichen. Mathematik differenziert (4), pp. 18–25.

Selected publications

  • Zöllner, J. (2020). Längenkonzepte von Kindern im Elementarbereich. Wiesbaden: Springer Fachmedien Wiesbaden.
  • Zöllner, J., Benz, C. (2015). The role of units in the concept of length for four- to six-year-old children. Asia-Pacific Journal of Research in Early Childhood Education, 9(3), pp. 67–83.
  • Zöllner, J., Benz, C. (2014). I spy with my little eye: Children comparing length indirectly. In T. Meaney, O. Helenius, M. L. Johansson, T. Lange and A. Wernberg (Eds.), Mathematics Education in the Early Years (pp. 359–370). Cham: Springer and Springer International Publishing.
  • Zöllner, J., Benz, C. (2013). How four to six year old children compare length indirectly. Antalya, Turkey: Cerme8.

Team MiniMa

Prof. Dr. Christiane Benz
Institut für Mathematik
Room 2.B200
Dr. Johanna Zöllner
Institut für Mathematik
Room 2.A244
Sprechstunde im SoSe 2024: Mittwoch 10-11 Uhr

Friederike Reuter, M.A.
Institut für Mathematik
Room 2.A143
Bitte vereinbaren Sie Sprechstundentermine per E-Mail.
8500Day-care and primary school children
1700Educators working in day-care centres and at primary schools
221Students of programmes in Childhood Education and Teacher Education for Primary Schools
Last updated: 04.01.2024
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