Joint Learning in Mixed-Age Primary Mathematics Teaching

Applicant

Prof. Dr. Marcus Schütte
Faculty of Education, Institute of Educational Science, Chair of Primary School Pedagogy/Mathematics, Technische Universität Dresden

Institution

TU Dresden

Duration

01.01.2016 – 30.06.2019

Funding volume

302,000 € (Quality Initiative Teacher Education, BMBF)

Initial situation

In order to maintain school locations in Saxony's peripheral districts despite declining pupil numbers, school-organisational and curricular changes are being discussed. These include considerations of mixed-age teaching, e.g. in mathematics. In age-heterogeneous learning groups, learning at the same pace in the traditional sense is impossible. To address this dilemma, forms of teaching that, in the spirit of internal differentiation, offer different tasks at different levels of demand are an obvious choice. In reality, however, in a strongly course-oriented subject like mathematics this often results in extremely individualised and separated learning, in which the joint exploration and discovery of mathematical relationships is impeded and teachers reach the limits of what is organisationally feasible. The focus of the planned project is therefore on the development and trial of mathematics-education concepts that offer opportunities for "natural differentiation" (Hirt & Wälti, 2008). Such "mathematical learning environments" have so far been tested only sporadically in mixed-age teaching and have, moreover, related almost exclusively to introductory mathematics teaching (e.g. Rathgeb-Schnierer & Rechtsteiner-Merz, 2010). At present, these concepts are meeting with increasing interest in open-minded teaching staff, which the planned project seeks to address productively.

Aims

By analysing the feasibility of mixed-age teaching using the example of the subject of mathematics for years 1–6, the project seeks to address the future challenges that arise in Saxony in particular for rural schools as a result of demographic and generational change.

Approach

To implement this project successfully, it is first necessary to capture the starting situation of teachers in Saxony. This refers in particular to surveys on didactic traditions and patterns of perception of mathematical teaching-learning processes in heterogeneous learning groups among teachers, as well as on teachers' attitudes towards forms of mixed-age teaching. Building on the results, learning environments are then developed in a second step that are specifically geared towards mixed-age learning in mathematics and that make this possible for years 1–6. The aim is to enable individualised learning in cooperation with others for children in highly heterogeneous learning groups, so that mixed-age grouping does not lead to a "lonely" learning of pupils who merely happen to be in the same place. The concepts to be tested are to be developed, among other things, in workshops with the participation of (subject) teachers. The planned measures are evaluated in parallel in order to embed them at a structural level permanently in the module structure of teacher education at TU Dresden.

Work programme

Phase 1: Interview study on the conceptions that teachers in mathematics, but also lecturers in teacher education, associate with the term mixed-age teaching (contrasting experienced and very young teachers); identification of starting points for initial and further teacher education.

Phase 2: Conception of learning environments for mixed-age learning in mathematics (among other things in further-training workshops and courses). Phase 3: Evaluation of the courses.

Dissemination plan

The basis of the project is the idea, on the one hand, of preparing the Saxony location in the area of mixed-age mathematics learning for the current challenges of the coming years. On the other hand, however, structural results are also to be achieved that can be used beyond the subject of mathematics. In this respect, there is potential for synergy effects in all subject didactics in the Free State of Saxony, especially in light of the inclusive teaching-learning settings to be implemented in the future, which have strong points of connection with the research focus chosen here. For example, mathematics-education concepts that are tested and scientifically supported in partnerships between Saxon university locations for teacher education and associated schools, in cooperations between university and school, can later also be used as a model for other subject didactics and for mixed-age learning in higher year levels.

The aim is to provide the topic of "learning in mixed-age groups" with a broad foundation of scientific principles. The results of the planned analysis will feed both into university didactics and into the content of teaching (educational sciences and subject didactics) and will thus benefit future generations of teachers. They will also benefit teachers already working through further training and thereby strengthen the theory–practice exchange between university and school.

Outlook

Following the successful trial of course formats on mixed-age teaching in mathematics for years 1–6, the formats are to be permanently established in teacher education programmes and as further training. Transfer to other subjects and higher year levels is being aimed for.