Math curricula are increasingly focusing on mathematical competencies, whereas instructions on how to develop these competencies are largely missing. In her recently presented doctoral thesis, Anna Ida Säfström has developed a tool for analysing mathematical competencies in children and adolescents.
Previous research has dealt with development of competencies through assignments and tests. Säfström has in turn studied how a group of 5-year-olds approach mathematical problems and relate to whole numbers, for example when working with Lego bricks. Through her studies she has developed a tool that describes how students use and develop different competencies in practice.
THE TOOL COMPRISES five different competencies: ability to handle representations, procedures, connections, reasoning and communication.
‘Let’s think of the number four. It can be represented by the digit 4 or a Lego brick with four knobs. To find out whether a brick has four knobs, you can count and point to them. This is a procedure. You can see a connection between four and two, that four is twice as much as two. And you can reason and communicate about all of this,’ says Säfström at the Department of Mathematical Sciences.
EACH COMPETENCE has two aspects: a productive aspect, which concerns use, application and construction, and an analytical aspect, which implies reflection and an outside perspective. The questions that Säfström asked the 5-year-olds were developed specifically to enable them to express different competencies.
‘The interaction between the five different competencies was obvious in the children’s activities. The way they spontaneously used connections and reasoning shows that these competencies are not something that has to be put off until they get older.’
THE TOOL CAN be developed further so that teachers can use it to evaluate their teaching. In one study, Olle, 5, builds with Legos at the same time as he reasons about what he is building. By studying Olle and using the tool, Säfström is able to analyse the competencies Olle uses.
‘Olle demonstrates the connection between length and shape through a measurement procedure, which he also communicates. Piece by piece, Olle builds a symmetrical ship but has no words for it. In such a situation, a teacher can introduce new concepts in the learning process. The competencies are developed when they are practised, suggesting the need for students to participate in appropriate activities,’ says Säfström.
Briefly about the doctoral thesis
Anna Ida Säfström obtained her PhD in Mathematics/Natural Science, specialising in Education, on 26 April 2013.
Thesis title: Exercising mathematical competence: Practising Representation Theory and Representing Mathematical Practice.
Link to the thesis: http://hdl.handle.net/2077/32484