Matematik i förskola och förskoleklass: Den mentala talraden som didaktiskt verktyg.

Based on previous research on Swedish daycare centres (förskola) and schools, the purpose of this study is to gain an understanding of how children develop their mathematical skills. The study focusses on examining how early training of children at daycare centres affects the children's mathematical skills later on in life.

The study concludes that teaching focussing on children learning to calculate the sum in arithmetical problems leads to an entirely different and less efficient learning and understanding of concepts than teaching focussing on numbers and the sequence of numbers.

The study shows that the concept of numbers (calculating the sum in arithmetical problems) is a central part of mathematics teaching in the youngest school classes in Sweden. At the same time, there are signs that early childhood educators and teachers are becoming less interested in numbers and the sequence of numbers, not least in daycare centres (förskola), but also in pre-school class (förskoleklass). Studies on the relationship between different mathematical skills show that using the concept of numbers has several disadvantages.

The studies demonstrate a negative correlation between the children's ability to work out numbers and their skills within arithmetic. However, they show that good skills in figures and sequence of numbers are an important prerequisite for improving in addition and subtraction. Furthermore, the studies concentrating on teaching trials show that children in pre-school class and in their first year of primary school make huge advances in arithmetic when they have practised numbers and sequence of numbers at daycare centres. This applies particularly to children who have previously performed poorly. Increased command and understanding of numbers and the sequence of numbers enables the pupils to use more efficient strategies when solving an exercise. One of the studies shows that the more correct answers a pupil had in a test on the sequence of numbers the more likely the pupil was to master the effective jump strategy in which the child physically jumps the arithmetical problem on the floor. When the child can form a mental sequence of numbers and calculate forwards and backwards on the basis of this, the child has a prerequisite for being able to think of numbers independently of a specifically imposed situation.

The data basis is composed of previous research, i.e. an analysis of a total of five studies.

The first study is about children's development of mathematical skills during the first year of basic school. The data material was collected in four 1st grade classes (7-year-olds) in the 2009/2010 school year. The children took different mathematical tests focusing on sequence of numbers, writing numbers and addition.

The second study examines the relationship between children's performance within a number of mathematics-related areas with particular focus on the concept of numbers. The children who took part were all aged 4-6 years, and 10-11 children took part in each age group. The children took tests on number skills, letter skills, reading skills and the concept of numbers and they solved simple arithmetical assignments.

The third study examines the effectiveness of children's problem-solving strategies in connection with answering the tests. The study included 79 children, 22 of which were in pre-school class, 22 in their 1st year of primary school, 18 in their 2nd year of primary school, and 17 in their 3rd year of primary school. The study was conducted as individual interviews, in which the children had to answer questions about sequence of numbers and arithmetic.

The fourth study conducted individual interviews with 126 pupils aged 5-8 years. The children had to answer two assignments on the sequence of numbers and two arithmetical assignments.

Finally, the fifth study presents results from three previous sub-studies about the significance of children's number skills regarding early learning of concepts in mathematics.

Johansson, B. (2013). Matematik i förskola och förskoleklass: Den mentala talraden som didaktiskt verktyg. Uppsala: Kunskapsföretaget.